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Full text of "The notation of polyphonic music, 900-1600"

LIBRARY OF 
WELLES LEY COLLEGE 




PURCHASED FROM 
LIBRARY FUNDS 



THE MEDIAEVAL ACADEMY OF AMERICA 
PUBLICATION NO. 38 



THE NOTATION 
OF POLYPHONIC MUSIC 

900-1600 



THE NOTATION 
OF POLYPHONIC MUSIC 

900-1600 



By 
WILLI APEL 

Fifth edition 
Revised and with Commentary 




THE MEDIAEVAL ACADEMY OF AMERICA 
CAMBRIDGE, MASSACHUSETTS 
1953 



The publication of this book was made possible by grants of funds to the 
Academy from the Carnegie Corporation of New York, the American Council 
of Learned Societies, the Committee on Musicology of the American Council 
of Learned Societies, and the Weyman Foundation of the Department of 
Music of Harvard University. 



L.f 



© Copyright by 

THE MEDIAEVAL ACADEMY OF AMERICA 

1942 

1949 

1961 



Library of Congress Catalog Card 
No. -61-12067 



MUSIC LIBRARY 






Printed in U. S. A. 



TO 

ARCHIBALD T. DAVISON 



Quid valet subtilitas 
ubi perit utilitas. 

Speculum Musicae. 



Digitized by the Internet Archive 

in 2012 with funding from 

Boston Library Consortium Member Libraries 



http://archive.org/details/notationofpolyphOOapel 



PREFACE 

A BOOK on musical notation, especially the first one to appear in 
the United States of America, can hardly have a more appropri- 
ate introduction than the following passage from Waldo S. Pratt's article 
'On Behalf of Musicology,' which appeared in the first volume of The 
Musical Quarterly, in 191 5: 

It is true that only those with exceptional training, peculiar access to 
materials, and leisure for long and hard labor can hope to discover, and 
publish that which is new to the scientific world. But a humbler type of 
'original research' is possible for all, that which discovers to the student 
what he knew only from the authorities. Every such effort toughens the 
muscles of the reasoning faculties, and helps to set us free from the bond- 
age to mere tradition and the idolatry of mere authority, which debilitates 
the mind like insidious poison. 

These words serve as an eloquent expression of the raison d'etre of a 
book whose aim is 'to set us free from the bondage to mere tradition,' 
which hopes to enable the student to 'discover what he knew only from 
the authorities,' and which is designed to prepare him for 'original re- 
search' in the field of early music. 

Twenty years have elapsed since Johannes Wolf published the first and, 
to the present day, the only complete study on musical notation. The 
extraordinary merits of this book do not need to be emphasized here, 
since they are known to every student of musicology. It suffices to say 
that a score of years has by no means outdated it or rendered it useless. 
Today it is still an excellent example of what it was meant to be, namely, 
a 'Handbuch der Notationskunde' or, in other words, a work in which the 
entire field of musical notation from the earliest periods to the present 
day is treated. So broad a scope necessarily involves the inclusion of 
much material of infrequent occurrence and of subordinate importance; 
and on the other hand, a rather cursory treatment of material which, 
from the student's point of view, is certainly deserving of more thorough 
discussion. The unavoidable shortcomings of so comprehensive a plan 
as is carried out in the Handbuch, together with the natural progress in 
musicological research made during the last twenty years, constitute the 
point of departure of the present book, and indicate its position in the 
literature on the subject: it deals exclusively and thoroughly with those 



viii Preface 

forms of musical notation whose problems the student is most frequently- 
called upon to solve in his studies, namely, the notation of polyphonic 
music prior to 1600. 

The book sets forth the familiar systems of notation, such as the white 
mensural notation, in a new way which, it is hoped, will be found more 
adequate and informative than former presentations. It also deals with 
many problems hitherto neglected or insufficiently clarified, for instance, 
the various notational systems of the thirteenth century. It is hoped, 
therefore, that it will prove to be of interest not only to the novice, but 
also to the scholar well versed in the subject. 

Great care has been taken to arrange and to expound the material in 
such a manner as to make the book useful for both the students and 
teachers in universities and colleges, as well as for self-instruction. In- 
deed, it follows rather closely courses given by the author at Harvard 
University from 1937 to 1941. The arrangement and methods employed 
in these courses have proved so satisfactory that the writer feels justified 
in applying them here. The fundamental idea has been to renounce the 
principle of historical development and to treat the matter in nearly 
reverse order, i.e., by beginning with the latest stage of evolution and, 
by means of a methodical explanation of the problems encountered there, 
to prepare the student for the study of the earlier systems. This pro- 
cedure is justified by the fact that the development of notation from 1100 
to 1600 is characterized by a gradual simplification and rationalization, 
by steps leading from extremely vague notions to the laws and principles 
prevailing in our days. Thus, an arrangement of the material in the 
reverse order is in harmony with one of the most elementary principles 
of pedagogy, i.e., to proceed from the known to the unknown. 

/Another principle observed in this book is to avoid as much as possible 
everything of purely theoretical importance. Since the explanations of 
the theorists of the thirteenth to the sixteenth century have been of great 
value in solving many problems of early notation, a great deal of atten- 
tion has been given them in the publications by Bellermann, Riemann, 
Wolf, and others. But from the present state of our knowledge it seems 
desirable to eliminate as much of this material as possible, and to make 
the sources of actual music the basis for investigation and explanation. 

The discussions are based entirely on photostatic reproductions of 
original sources, not on printed versions such as frequently appeared in 
previous publications on our subject. This seems to be desirable since 
often the intrinsic problems are artificially changed or partly eliminated 
by the transliteration of the old style of writing into modern print. 

In order to provide practice for the student, transcriptions of the 



Preface ix 

facsimiles have not, as a rule, been given in full, but only as much of 
them as has been deemed necessary in order to illustrate the principle. 
For the same reason, these transcriptions are assembled in a separate 
appendix, to which the student may prefer not to resort until he has tried 
to find a solution of his own. 

There remains the pleasant duty of expressing my sincere gratitude to 
all those who, in one way or the other, have helped to make possible the 
publication of this book. First of all, I wish to refer the reader to its 
first page, on which the name of my revered and dear friend, Professor 
Archibald T. Davison, appears; and I wish to add that this dedication 
is not only the expression of personal friendship, but an acknowledgment 
of active participation. Indeed, it was his kind interest that enabled me 
to give the courses which form the basis of the present book; it was at 
his suggestion that the book was begun; and it was his unflagging enthu- 
siasm which has encouraged me time and again to devote my best energies 
to making it what he wanted it to be. 

With the foregoing reference to the inaugurator of this book as a point 
of departure, I may be allowed to proceed in chronological order. The 
preparatory studies and the completion of the manuscript have been 
made possible chiefly through a grant from the Milton Fund of Har- 
vard University. The considerable expense involved in the enlargement 
of microfilms has been borne largely by the Isham Memorial Library of 
Harvard University whose remarkable collection of photographic repro- 
ductions of early music sources, started by the present writer, includes 
practically all the material he has been working with. The difficult task 
of securing photographic reproduction from European libraries has been 
greatly facilitated by the kind cooperation of Mme Odile de Van, Paris, 
and of the authorities at the British Museum and at the libraries of 
Florence, Modena, Turin, and Naples. For the revision of the text and 
similar matters I am deeply indebted to Dr Everett B. Helm and Dr 
Lloyd Hibberd, both of Cambridge, who have spent many hours of 
tedious and patient work upon the manuscript. Dr Hibberd, who has 
been working with me in this field for several years, has also given many 
useful hints which have greatly contributed towards the clarification of 
difficult explanations. For the reading and translation of the mediaeval 
French, Italian, and Latin texts I have had the very good fortune to 
have the advice of Professor George B. Weston and Dr John P. Elder, 
both of Harvard University. 

As regards the publication of the book, I am most deeply indebted to 
the Mediaeval Academy of America, Cambridge, for having considered 
this book to be worthy of inclusion in their series of scholarly publications, 



x Preface 

and, in particular, to their secretary, G. W. Cottrell Jr, for his active 
interest and his most efficient handling of the many problems involved 
in the preparation of the publication. J also wish to express my grati- 
tude to the Academy's secretaries of publication, Dr Paul L. Ward and 
his successor, Dr Henry M. Willard, for their great patience and meticu- 
lous care in reading the manuscript and the proofs. Last, not least, due 
acknowledgment must be made to the American Council of Learned 
Societies, to its Committee on Musicology, to the Weyman Foundation 
of the Music Department of Harvard University, and to the Mediaeval 
Academy of America for their financial aid without which all the other 
efforts would have failed to reach their ultimate goal. 

Willi Apel 

Cambridge, Massachusetts 
December 1941 

PREFACE TO THE FOURTH EDITION 

The practical test to which this book has been put within the past eight years 
has shown its general usefulness and, at the same time, has brought to light 
its deficiencies. Most of these are in the nature of minor errors, misprints, or 
linguistic slips. Serious objections, however, have been raised to parts of the 
chapter on Square Notation. 

I am very glad to have the opportunity of correcting these deficiencies, not, 
as in previous printings, in a make-shift manner, but on the basis of a revised 
edition. The chapter on Square Notation has been to a large extent rewritten, 
after careful examination of the suggestions received from other scholars. 

In many instances the text, although essentially correct, appeared to be in 
need of amplification, qualification, or additional information. This material 
has been gathered in a Commentary (pp. 437-451), to which reference is made 
by means of asterisks added on the margin of the main text. 

Grateful acknowledgment is made of the valuable assistance received from 
Dom Anselm Hughes, O.S.B., Mr Gustave Reese (New York University) and 
Mr Oliver Strunk (Princeton University). My particular gratitude goes to 
Dr Manfred F. Bukofzer (University of California) for his active collaboration 
on the chapter on Square Notation, and to Dr A. T. Davison (Harvard Uni- 
versity) who, on the basis of his teaching experience, has made many valuable 
suggestions for improvement and correction. 

The book has been kindly received by many scholars and by a great number 
of students. While mentioning this fact it is only fair to state that, in the 
opinion of one esteemed colleague, *M. Apel {The Notation 0} polyphonic music, 
85) a totalement fausse le probleme de la notation mensuraliste,' and that, in 
the same writer's view, 'La fausse perspective de l'ouvrage de M. Apel est encore 
mise en evidence par l'ordre antichronologique de ses demonstrations.' The 
reader is warned. 

W. A. 
February 1949 

PREFACE TO THE FIFTH EDITION 

A number of errors have been corrected. Several items have been added to 
the Commentary. 

W. A. 

January 1961 



CONTENTS 

Page 

LIST OF FACSIMILES xv 

ABBREVIATIONS xviii 

INTRODUCTION xix 

PART I: THE NOTATION OF SOLOIST MUSIC 

I. Keyboard Scores 3 

II. Keyboard Partituras 16 

III. Keyboard Tablatures 21 

A. German Keyboard Tablatures 21 

B. Spanish Keyboard Tablatures 47 

IV. Lute Tablatures 54 

A. Italian and Spanish Lute Tablatures 56 

B. French Lute Tablatures 64 

C. German Lute Tablatures 72 

PART II: THE NOTATION OF ENSEMBLE MUSIC: 
WHITE MENSURAL NOTATION 

I. NOTATIONAL SlGNS 87 

Notes 87 

Ligatures 87 

Rules for Ligatures 91 

Subsidiary Symbols 94 

II. Mensuration 96 

A. Tempus y pro/atio, and modus 96 

B. Tempus imperfectum cum prolatione imperfecta . . 100 

C. Tempus perjectum cum prolatione imperfecta . . . 107 

Imperfection 107 

Alteration 112 

Punctus divisionis 115 

D. Prolatio perfecta .120 

E. Modus and maximodus 124 

xi 



xii Contents 

Page 

III. Coloration 126 

A. Coloration in tempus imperfectum cum prolatione im- 

perfecta 127 

B. Coloration in tempus perfectum cum prolatione im- 

perfecta 130 

C. Coloration in prolatio perfecta 136 

D. Half-Coloration 142 

IV. Proportions 145 

A. History and Terminology 145 

B. Proportio d 'up/a and tripla in General . . . . 148 

C. Proportio dupla 151 

D. Proportio tripla 155 

E. Other Proportions 157 

Proportio quadrupla 157 

Proportio sesquialter a 158 

Proportio quint upla y sesquitertia 160 

Successive Proportions 161 

F. Augmentation 163 

G. Examples 168 

H. Canons 179 

I. Proportional Time Signatures and Tempo . . . 188 

PART III: THE NOTATION OF ENSEMBLE MUSIC: 
BLACK NOTATION 

I. Introduction 199 

II. Primitive Notation 204 

III. Square 4 Notation 215 

A. General Characterization 215 

B. Modal Notation 220 

The Rhythmic Modes 220 

The Ligatures 223 

Repeated Notes 225 

Plica 226 

Examples 230 

Ext ens io modi 234 

Fractio modi 235 

Conjuncturae 240 

Consonance and Dissonance 244 



Contents xiii 

Page 

Notation of the Tenors 245 

Notation of the Upper Parts 252 

Examples 254 

C. Syllabic Notation 258 

D. Duplum Notation 267 

E. Motet Notation 271 

JV. Pre-Franconian Notation 282 

A. The Codex Montpellier, fasc. II-VI 284 

Notation of the Tenors 286 

Examples 289 

Duple Meter 290 

Notation of the Upper Voices 294 

Ligatures 296 

Plica 298 

Examples 298 

B. The Codex Bamberg 302 

Notation of the Tenors 303 

Notation of the Upper Voices 304 

C. The Codices Torino and Huelgas 306 

V. Franconian Notation 310 

A. The Franconian System 310 

Single Notes 310 

Ligatures 312 

Examples 315 

B. The Innovations of Petrus de Cruce 318 

C. The Roman de Fauvel 325 

The Tenors; modus and maximodus . . . .327 

Red Notes 328 

Notation of the Upper Parts 330 

Semibreves signatae 332 

Conjunctura and plica 333 

Examples 334 

VI. French Notation 338 

A. The Innovations of the Ars Nova 338 

B. The Notation in the Works of Machaut .... 343 

Imperfection and Alteration ■ . 344 

Determination of the Mensuration .... 346 



xiv Contents 

Page 

Ouvert and clos 049 

Examples 3™ 

C. The Notation of the Later Sources 360 

VII. Italian Notation 368 

A. The Origin of Italian Notation 368 

B. The Principles of Italian Notation 369 

Divisiones oyo 

Note Forms yii 

C. Examples of Italian Notation xi± 

D. The Early Stage of Italian Notation 382 

VIII. Mixed Notation 385 

A. General Characterization 385 

B. Examples of Mixed Notation 386 

C. Syncopation 305 

IX. Mannered Notation 403 

A. General Characterization 403 

B. Principal Features 404 

Signs of Mensuration 404 

Special Notes 405 

Coloration 405 

C. Examples 407 

D. Discussion of Examples from Other Publications . 426 

COMMENTARY 437 

INDEX 453 

APPENDIX: TRANSCRIPTIONS 



LIST OF FACSIMILES 

Page 

i. Marcantonio da Bologna, Recerchari, motetti> canzoni ... 5 

2. Attaingnant, ^uatorze gaillardes 7 

3. MS London, Br. Mus. Add. 29996 11 

4. Mulliner Book, MS London, Br. Mus. Add. 30513 ... 13 

5. MS London, Br. Mus. Add. 29996 13 

6. Ascanio Mayone, Primo libro di . . . capricci 17 

7. Buxheimer Orgelbuch, MS Munich, Stb. Mus. Ms. 3725 . 25 

8. Arnolt Schlick, Tabulaturen etlicher Lobgesang 27 

9. MS Basle, Univ. B\b\. F IX 22 (Kotter) 29 

10. MS St. Gall, Stiftsbibliothek 530 (Sicher) 31 

11. Bernhard Schmid, Tabulator Buck 35 

12. Vienna, Stb. Ms. 184.91 (Regina Clara Im Hoff) .... 36 

13. Bach, Orgelbuchlein, MS Berlin, Stb. P 283 39 

14. Ueborgh tablature, Philadelphia, Curtis Institute .... 41 

15. Conrad Paumann, Fundamentum, MS Wenigerode Zb 14 . 45 

16. Antonio Valente, Intavolatura de cimbalo 5 1 

17. Antonio de Cabezon, Obras de musica S3 

18. Luys de Milan, Libro de musica 57 

19. Petrucci, Intabolatura de lauto 63 

20. Denis Gaultier, La Rhetorique des dieux, Berlin, Kupferstich- 

kabinett Ms. 142 73 

21. Hans Judenkunig, Ain schone . . . Underweisung ... 79 

22. Hans Newsidler, Ein newgeordnet . . . Lautenbuch ... 81 

23. Dufay, Quelfronte signorille (MS Oxford, Canon. 213) . . 103 

24. Benet, Sanctus (Trent Codex 92) 105 

25. Dangier tu mas tollu (Chansonnier Laborde) 109 

26. Dufay, Ave regina (MS Oxford, Canon. 213) i J 9 

27. Pierre de la Rue, Kyrie (Misse Petri de la Rue) .... 121 

28. Leonel Power, Anima mea (MS Florence, Magi. XIX. 112 bis) 135 

29. Monsieur (Munich, Stb. Cim. 351a) l 37 

30. Ockeghem, Et resurrexit (MS Rome, Chigi cod. C. VIII, 234) 139 

31. Lantins, Ce ieusse fait (MS Oxford, Canon. 213) . . . . 141 

32. Bartholomeus de Bononia, Vince con lena; dolce conpagno 

(MS Oxford, Canon. 2/3) • H3 

xv 



xvi List of Facsimiles 

Page 

33. Tinctoris, Proportionate musices (MS Brussels) . . . . 153 

34. Ockeghem, Kyrie (MS Rome, Chigi cod. C. VIII, 234) . . 165 

35. Isaac, Ideoque {Choralis Constantinus) 169 

36. Isaac, Piae vocis laudes {Choralis Constantinus) . . . . 171 

37. Isaac, Dico ego (Choralis Constantinus) 174 

38. Isaac, De radice (Choralis Constantinus) 173 

39. Lantins, Je suy exent (MS Oxford, Canon. 213) . . . . 177 

40. Obrecht, Kyrie (Missa Si dedero, tenor) 183 

41. Obrecht, Kyrie (Missa Si dedero, other parts) 185 

42. Tu patris (Musica Enchiriadis) 205 

43. Ut tuo propitiatus (MS Oxford, Bodl. Libr. 572) .... 205 

44. Viderunt hemanuel (MS Paris, Bibl. Nat. lat. 3549) . . . 211 

45. Alleluia vocavit Jhesus (Codex Calixtinus) 213 

46. Go; Flos filius est (MS Florence, plut. 29.1) 229 

47. Descendit de celis (MS Wolfenbiittel 1206) 233 

48. Instrumental dances (MS Brit. Mus. Harl. 978) .... 239 

49. Benedicamus Domino (MS Florence, plut. 29.1) .... 247 

50. (a) Scio cui credidi; (b) Alleluya (MS Paris, Bibl. Nat. lat. 

15/39) 249 

51. Varicus clausulae (MS Florence, plut. 29.1) 255 

52. (a) Mulierum; (b) Domino (MS Florence, plut. 29.1) . . . 257 

53. Hac in annijanua (MS Wolfenbiittel 677) 259 

54. Hut main-Hec dies; V autre jor-Flos filius (Chansonnier Roy, 

Paris, Bibl. Nat.//?. 844) 273 

55. 56. Laus Domino — Eius; Homo quo vigeas — Et gaudebit (MS 

Wolfenbiittel 1206) 275,281 

57. Candida virginitas — Flos filius (MS Brit. Mus. Add. 30091) 285 

58. Ave beatissima — Ave Maria — Johanne; Salve virgo — Ave lux — 

Neuma (Codex Montpellier) 291 

59. Diexje — Amors qui ma — Et super (Codex Montpellier) . . 293 

60. Mout mefu — Robins — Portare (Codex Bamberg) . . . - 3°5 

61. Hei diex—Mal latus—t (MS Torino, Bibl. Reale 42) . . 307 

62. Et in terra pax (Codex Huelgas) 3°9 

63. Huic ut—Huic ut—\ (Codex Montpellier) 3 l6 

64. Diex qui — En grant — Aptatur (Codex Montpellier) . . . 317 

65. Aucun ont — Lone tans — Annuntiantes (Codex Montpellier) . 321 

66. Firmissime — Adesto — Alleluia (Roman de Fauvel) . . . 3 2 9 

67. Garrit gallus — In nova fert — ? (Roman de Fauvel) . • • 33 l 

68. Machaut, Ne pens ez pas (MS Paris, B. N./rf. 1584) ... 353 

69. Machaut, Dous amis (MS Paris, B. N.frc. 1384) .... 357 



List of Facsimiles xvii 

Page 

70. Machaut, Biaute qui toutes (MS Paris, B. N.frf. 9221) . . 359 

71. Kyrie (MS Cambrai, Bibl. Comm. Ms. 6) 363 

72. J. Tyes, Et in terra pax (Old Hall MS) 365 

73. Jacopo da Bologna, AquiV altera; Fortune (MS Paris, B. N. 

ital.568) . . . 375 

74. Bartolinus de Padua, Perche cancato (Codex Reina) . . . 377 

75. Benedicamus Domino (MS Paris, B. N. ital. 568) .... 379 

76. Or qua conpagni (MS Rome, Rossi 215) 383 

77. Giov. de Florentia, Naschoso el viso Landini, Choi gli occhi; 

(MS Florence, Bibl. Naz. Pane. 26) 387 

78. Landini, Se pronto (Codex Squarcialupi) 391 

79. Landini, Nessun ponga (Codex Squarcialupi) 393 

80. Paolo (tenorista), Benche partito (MS Paris, B. N. ital. 568) . 399 

81. Paolo (tenorista), Amor tu solo (MS Paris, B. N. ital. 568) . 409 

82. Je la remire; Machaut, Se vous nestes (Modena, Bibl. Est. 

L.568) . . . 411 

83. Je ne puis (Codex Chantilly) 413 

84. Anthonellus, Dame gentil (MS Modena, Bibl. Est. L. 568) . 41 5 

85. Tout houme veut (MS Torino, Bibl. Naz. J II 9) .... 419 

86. Biaute parfaite (Codex Reina) 421 

87. Jacopinus Selesses, En attendant (MS Modena, Bibl. Est. L. 

568) 4^3 

88. Baude Cordier, Belle bonne (Codex Chantilly) 427 



ABBREVIATIONS 



AfMW 
AHdM 
AM 
CS 

DTOe 
GdM 

Gr. Rom. 
GS 

HdN 

JfMPV 

Km. Jb. 

MfM 

M% 

MuT 

OH 

RHdM 

SchT 
SIMG 

VfMW 
ZfMW 
ZIMG 



a p. a, 

ap.p 

B 

c.o.p. 

D 

F 

L 

M 



I. Books and Periodicals 
Archiv fur Musikwissenschaft, Leipzig, 191 8-1927. 
G. Adler, Handbuch der Musikwissenschaft, 2 vols., Berlin, 1929. 
Acta Musico/ogica, Copenhagen, 1928-. 
E. Coussemaker, Scriptorum de musica medii avi nova series, 

4 vols., Paris, 1 864-1 876. 
Denkma/er der Tonkunst in Oeslerreich, Leipzig, 1894-. 
J. Wolf, Geschichte der Mensuralnotation, 3 vols., Leipzig, 

1904. 
Graduate Romanae Ecc/esiae, Paris, 1924. 
M. Gerbert, Scriptores ecclesiastici de musica, 3 vols., St 

Blasien, 1784. Facsimile edition, Milan, 1931. 
J. Wolf, Handbuch der Notationskunde, 2 vols., Leipzig, 1919. 
Jahrbiicher fur musikalische Wissenschaft, Berlin, 1863, 1867. 
Kirchenmusikalisches Jahrbuch, Leipzig, 1885-1911. 
Monatshefte fiir Musikgeschichle, Berlin, 1 869-1 904. 
The Musical Quarterly, New York, 1915— . 
H. Bellermann, Die Mensuralnoten und Taktzeichen des XV. 

und XVI. Jahrhunderls, Berlin, 1858, 1930. 
H. E. Wooldridge, The Oxford History of Music, vol. 1, Oxford, 

1 901. 
H. Riemann, Handbuch der Musikgeschichte, 5 vols., Leipzig, 

1904. 
J. Wolf, Musikalische Schrifttafeln, Buckeburg, 1930. 
Sammelbande der Internationalen Musikgesellschaft, Leipzig, 

1 899-1914. 
Vierteljahrsschrift fur Musikwissenschaft, Leipzig, 1 884-1 894. 
Zeitschrift fiir Musikwissenschaft, Leipzig, 191 8-1935. 
Zeitschrift der Internationalen Musikgesellschaft, Leipzig, 

1899-1914. 

II. Technical Terms 

Mx maxima 

p.a. punctus additionis 

p.d. punctus divisionis 

S semibrevis 

Sf semifusa 

Sm semiminima 

t tactus 



a parte ante 
a parte post 
brevis 

cum opposita proprietate 
duplex longa 
fusa 
longa 
minima 



INTRODUCTION 

THE DISCIPLINE of musical notation comprises a knowledge of 
the methods of writing down music. In general, it is concerned 
with music of all periods, but the term 'notation' is usually employed 
with special reference to those cases in which the forms of the signs and 
the principles governing their use are essentially different from those to 
be found in modern practice. Thus, the field of notation proper covers 
European music from the beginning to the seventeenth century, and the 
music of all other nations outside of the European development in so far 
as it is preserved in writing. 

Within this field one meets with a large variety of types of notation. 
Therefore, it will be our first task to attempt a survey of them. This 
task is rendered more difficult by the fact that in the previous publica- 
tions on the subject classifications and terms have been used which upon 
closer examination do not always prove unambiguous or appropriate. It 
has been deemed necessary, therefore, to make a new survey of the whole 
field and, accordingly, to introduce certain changes in the traditional 
terminology. 

Our classification is based upon two considerations, the first of which 
deals with the number of parts of a given composition, and the second 
with the number of participants performing the composition. The for- 
mer point of view leads to a division of music into two chief categories, 
namely, music consisting of only one part, and music including more than 
one part or, in other words, monophonic and polyphonic music. 1 To 
the former field belong the music of the ancient Greeks, the entire tradi- 
tion of the Gregorian chant, of the Latin sequences and hymns, of the 
Italian laudi and Spanish cantigas, also the music of the French trou- 
badours and trouveres, of the German Minnesingers and Meistersingers, 
that of the Byzantine and Russian liturgies, and finally the vast rep- 
ertory of Oriental music and similar bodies. 2 The second category, that 
of polyphonic music needs no further description. 

1 The term 'polyphonic' is used throughout the present study to include all music comprising more 
than a single line of melody (monophonic music) whether the number of parts is strict or free, and 
whether the texture is contrapuntal or harmonic. 

2 A monograph on Notation of Monophonic Music, planned as a continuation of the present book, 
is under preparation. 



xx Introduction 

Although there are certain ties of relationship v/hich exist between 
monophonic and polyphonic music, the two fields are clearly marked off 
from each other. This is also true of their notation. Without consider- 
ing details it will suffice to mention a basic feature which clearly dis- 
tinguishes the notation of monophonic music from that of polyphonic 
music, namely, the arrangement. Monophonic music has always been 
written in a purely linear arrangement of the signs, i.e., in a single line 
following the course of the melody and, obviously, it can only be set 
down thus. Polyphonic music, however, includes both horizontal and 
vertical relationships; here, various methods of arrangement are possi- 
ble. Two principles must be distinguished which may be called, for our 
convenience, score-arrangement and part-arrangement. 

By the term score-arrangement we refer to a scheme in which the 
voices of a composition are written one underneath the other, arranged 
in such a way that simultaneous tones appear in a vertical or nearly 
vertical alignment. In modern practice, this principle is shown in the 
piano score or in the orchestral score. 

The term part-arrangement applies to music which is written without 
regard to the vertical coincidence of the tones, each part being treated 
as a notational entity distinct from the others and appearing on a dif- 
ferent section of the page or two opposite pages (choir book notation), 
or in different books (part books, Slimmbiicher). A modern example of 
the latter method is the different parts of a string quartet. 

Historically, score-arrangement is the earliest method of writing used 
for polyphonic music. All the earliest documents of part music illus- 
trate the practice of the vertical arrangement of the voices, a principle 
which was applied to text-syllables {Musica enchiriadis, ninth century; 
see Facsimile 42), to letters (Guido of Arezzo, Micrologus, ca. 1000; see 
Facsimile 43), to neumes (School of St. Martial; see Facsimiles 44, 45), 
and to notes (School of Notre Dame, ca. 1200; see Facsimiles 46 ff.). 

Score-arrangement gave way to part-arrangement in the second quarter 
of the thirteenth century (see Facsimiles 57ft*). This change is one of 
the various innovations which accompanied the rise of the motet (see 
p. 271). In the documents of the period from about 1250 till 1450, the 
parts of a composition are almost always written on different sections of 
a page or of two opposite pages, in certain standard allocations (see 
p. 283). Manuscripts of the late fifteenth century, such as the Glogauer 
Liederbuch {ca. 1470), furnish the earliest examples of a more recent 
practice, namely, that of writing in part-books {Stimmbiicher), one book 
for the discantus, one for the altus, etc. This method was generally 
adopted for the printed publications of choral music in the sixteenth 



Introduction xxi 

century. With the establishment of regular barring (about 1600) and 
the rise of orchestral music, score-arrangement reappears, displacing part- 
arrangement which has survived only in the separate parts used in 
orchestral and in chamber music. 

We now come to the second principle of classification mentioned above, 
namely that based upon the number of performers. This point of view 
leads again to a division of music into two categories, namely music 
performed by a group of participants and music performed by a single 
musician. In the field of monophonic music this distinction is of rela- 
tively little value, at least from the standpoint of notation. However, 
it has a very real significance if applied to the field of polyphonic music. 
Here it leads to a distinction between two species of polyphonic music, 
namely, polyphonic music for a group of performers (one at least to 
each part), and polyphonic music for a single performer (executed on a 
keyboard instrument or a lute). For these two types of part music the 
terms 'polyphonic ensemble music' (or simply ensemble music) and 'poly- 
phonic soloist music' (or simply soloist music) will be used in this book. 
The term ensemble music almost covers the field which is traditionally 
designated as vocal or choral music, but also includes instrumental pieces 
for a group of players. Polyphonic soloist music is, of course, necessarily 
instrumental music. 

By mentioning the terms vocal and instrumental we touch upon a 
much discussed problem, namely that of the use of these two mediums 
in music prior to 1600. Whereas, according to the view of nineteenth 
century historians, nearly all the music written before 1600 was vocal 
music {a cappella), more recent investigations have made it clear beyond 
any doubt that instruments played an important part in the performance 
of the so-called vocal music, at least prior to 1550. Owing to this dis- 
covery the terms vocal and instrumental music lose much of their sig- 
nificance and can no longer be considered as an appropriate basis for 
classification, as they have been over and over again. Indeed, such a 
classification not only is ambiguous but also results in a rather arbitrary 
separation of what are closely connected styles (for instance, a textless 
instrumental piece by Obrecht and a vocal motet by the same composer), 
as well as in an amalgamation of widely different ones (for instance, a 
so-called organ ricercare by Willaert — actually chamber music for, e.g., 
three viols — and a genuine organ ricercare by Cavazzoni). 

A much more solid and useful basis of classification is furnished by 
our above distinction between ensemble and soloist music. 1 The former 

1 This dichotomy has been emphasized by the present writer in a paper on 'The Importance of 
Notation in Solving Problems of Early Music' (published in: Papers Read by Members of the Ameri- 



xxii Introduction 

category naturally includes what is commonly called vocal or choral 
music, but does not rule out instrumental participation in the perform- 
ance of such music, and also includes purely instrumental pieces written 
'in vocal style,' such as the ricercares of Willaert, and other examples of 
sixteenth century chamber music. On the other hand, the category of 
soloist music includes instrumental music of an entirely different charac- 
ter, that is, organ and lute music which comprises such totally contrast- 
ing forms as the prelude and the toccata alongside others which, al- 
though borrowed from ensemble music, underwent typical changes when 
adopted into the soloist repertory (coloraturas, cadential passages, 
'Freistimmigkeit,' etc.). 

These brief hints must suffice here in order to indicate how our classi- 
fication can be supported by considerations of style and form. More 
important, from the point of view of this book, is the fact that it is most 
clearly indicated in the notational systems used for the two classes 
under consideration. If, for the moment, we restrict ourselves to the 
period in which the question 'vocal-instrumental' and, consequently, our 
substituted dichotomy of soloist and ensemble, attain acute importance 
(ca. 1 250-1 600), a very simple and categorical statement can be made, 
: namely, that music written in part-arrangement is ensemble music, and 
music written in score-arrangement is soloist music. 1 From the scores 
of early ensemble music (prior to 1250), the scores for soloist music, 
usually known as tablatures, are distinguished by special features such 
as the use of figures and letters, or the writing of several parts on one 
staff, etc. 

The notation for ensemble music includes mensural notation, a term 
which refers to the use of strictly measurable and unambiguously deter- 
mined notational characters, which were introduced about 1250 by 
Franco of Cologne (see p. 310). It is customarily divided into two large 
categories, that of black (mensural) notation (1250-1450) and that of 
white (mensural) notation (1 450-1 600). The former falls again into a 
number of systems which represent distinctly different phases of a con- 
tinuous development (see p. 199). The notational systems antecedent 
to mensural notation are treated in this book under the headings of 
'Primitive Notation' (ca. 900-1150), and of 'Square Notation' (ca. 

can Musicologkal Society, Washington, 1938), and has been elaborated in L. Hibberd, The Early 
Keyboard Prelude, a Study in Musical Style (Harvard dissertation, unpublished, 1941). 

1 For the discussion of certain objections which might be raised with regard to the first part of 
this statement, see p. 61 of the paper mentioned in the previous footnote. A startling example of 
the failure to distinguish between ensemble and soloist music is embodied in the recent publication 
of the Ricercares of Annibale Padovano (Edition de l'Oiseau de Lyre, Paris, 1934), in which these 
compositions are offered as organ music with pedals(!) and all manner of modern registration. 



Introduction xxiii 

1 175-1225), with Tre-Franconian Notation' forming the transition to 
'Franconian,' i.e., the first true mensural notation. 

As has been remarked above, the notational systems for soloist music 
are usually called tablatures. According to the instrument to which 
they belong, they are customarily distinguished as organ tablatures, lute 
tablatures, guitar tablatures, etc. Further distinctions are made ac- 
cording to nations. Thus, one speaks of German and Italian organ 
tablatures, of Spanish and French lute tablatures, and so forth. 

Unfortunately, these customary classifications are not entirely satis- 
factory. Their chief disadvantage — to mention only one point— lies in 
the fact that the notation used in the sixteenth century sources of 
English, Italian, and French organ music is essentially the same as that 
employed in the piano score of the present. This means, first, that the 
customary distinction between 'English organ tablatures,' 'Italian organ 
tablatures,' and 'French organ tablatures' is a national, not a notational, 
classification. It means, second, that from a methodical point of view, 
the name 'Italian organ tablature' (or English or French, but not Ger- 
man) could and should be applied to nineteenth century piano compo- 
sitions. Yet, one would, doubtless, hesitate to refer to a Beethoven 
pianoforte sonata as an example of Italian organ tablature. 

To avoid these and similar ambiguities yet another classification and 
terminology within the field of soloist music have been adopted in this 
book. We shall distinguish between sources written exclusively with 
notes and others in which letters or figures are used. It is only to the 
second class that the name tablatures will be applied. To this class 
belong the Spanish organ (or, more accurately, keyboard) tablatures 
(written in figures), all the lute tablatures (written in figures or letters), 
the late German keyboard tablatures (written in letters), and the early 
German keyboard tablatures (written partly in letters and partly in 
notes). 

In the other group, in which music is written exclusively with notes, 
we may further distinguish between the following species: notation of 
the whole composition on two staves (or, occasionally, on a single staff 
of double extension), and notation with an individual staff for each part 
(mostly four staves). The first type is that of the present piano score. 
Therefore, we shall refer to this notation as keyboard score. 1 It embraces 
the Italian, French, and English 'organ tablatures.' The other species 
(single staff for each voice) is the so-called partitura, which was employed 

1 In view of the fact that in the sixteenth century organ, harpsichord, and clavichord employed 
the same repertory to a large extent, the terms 'keyboard score,' 'keyboard tablature,' etc., are 
preferable to terms such as 'organ score,' or 'organ tablature.' 



xxiv Introduction 

especially by the Italian composers of the seventeenth century. When 
used for writing keyboard music we may call it conveniently keyboard 
parti tura. 

The understanding of the above explanations will be facilitated by the 
accompanying chart which shows the varieties of notation in a methodical 
and approximately chronological order. 



Introduction 



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H o 'C 



PART I 

THE NOTATION OF SOLOIST MUSIC 



I. KEYBOARD SCORES 

THE METHOD of writing keyboard music in a manner similar to 
that of the piano score of our day occurs first in an Italian publica- 
tion of 1523, namely: Marcantonio da Bologna, Recerchari, Motetti, 
Canzoni (Venice), a page of which is shown on Facsimile 1. Two staves* 
of six lines each are used, the upper staff for the right hand, and the 
lower staff for the left. From the standpoint of contemporary mensural 
notation (see p. 85 ff) two features are particularly interesting since they 
indicate an advance which was not reached in the writing down of 
ensemble music until several decades later. These features are the bar- 
line and the tie. As they are both employed in a very consistent and 
logical manner, one might well conclude that various prior attempts in 
this direction had been made (regarding bar-lines see p. 9). 

The clef sign at the beginning of each staff indicates middle c (c 1 ). 
The mordent-like sign at the end of the staff is the custos (guardian, also 
called 'direct') which refers the player to the first note of the same part 
in the next staff. The note- values are: brevis (B), semibrevis (S), minima 
(M), semiminima (Sm), fusa (F), semifusa (Sf). 1 Their forms, together 
with those of the corresponding rests, are indicated in the following 
chart which also includes the modern signs derived from them. 



Old form of notes: 2 
Modern form of notes : 
Old form of rests: 
Modern form of rests: 



B S 

(B) © 

i m x z 

1 - - * 



M 


Sm 


F 


Sf 


I 


1 


I 


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d 


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Each note (or rest) is equal to two, and only two, notes (or rests) of 
the next smaller value. This is another progressive feature of keyboard 
and lute notation in contrast to contemporary mensural notation, in 
which a note was equal to two or to three notes of the lower grade, ac- 
cording to the 'mensuration' (perfect or imperfect, see p. 96). The 

1 The abbreviations: B {brevis), S {semibrevis), M {minima), Sm {semiminima), F {fusa), and Sf 
{semifusa) will be used throughout the book. 

2 These notes are called 'white notes' ('white notation') although only the larger values are actu- 
tually white. 



4 The Notation of Soloist Music 

ledger lines for notes above or below the staff are not drawn separately 
for each note, but continuously for a group (cf. measures 1-2 and 9-10). 
In the chord-like formations of the left hand (measures 8-10) the single 
M placed between the two triads belongs to the middle voice and is 
preceded by another M in the same voice (middle tone of the first triad). 

The dots which appear rather frequently below or above single notes 
(upper staff, measure 3, 4, 6, 8; lower staff, measure 3, 5, 6, 7) indicate 
chromatic alterations, either flatting or sharping. Since at that time 
the use of chromatic tones was still limited, no confusion arose from this 
summary method. It was understood that a B, an E, or an A could 
only be flatted, whereas an F, a C, or a G could only be sharped. Thus, 
in this notation, a B with a dot is a B-flat, and an F with a dot is an 
F-sharp. 

Although, from the evolutionary point of view, the S corresponds to 
the modern whole note, it appears advisable to reduce the note values in 
the transcription, i.e., to transcribe the S as a half note, and the other 
values correspondingly. Reductions of this type may be applied to all 
early music through the end of the sixteenth century. The preserva- 
tion, customary in scholarly publications, of the original note values 
brings about an appearance of sluggishness which is highly detrimental 
to an understanding of early music. It also has led to a great uncer- 
tainty concerning the question of tempo in early music. There will be a 
fuller discussion later of the principles of reduction of note values to be 
applied to compositions in mensural notation (cf. the chapter on Propor- 
tional Time Signatures and Tempo). In the case of keyboard and lute 
music the practice of the sixteenth century is too varied and involved to 
allow for the establishment of general principles. As a rule, the tran- 
scription of the S as a half-note will lead to a satisfactory result, i.e., to the 
representation of the beat in moderate tempo by a quarter-note. What- 
ever scale one chooses, should, of course, be indicated at the beginning of 
the transcription. 

The transcription of the first four measures is given in the appendix, No. 1. An inter- 
esting feature of the piece is the 'Freistimmigkeit' (cf. rour voices in meas. 4, 5; three in 
meas. 1, 2, 6-7; full chords in the last measures). In a case like this, attempts to bring 
about correct part-writing (by the introduction of rests) are of no avail. 

Seven years after Marcantonio's publication, we encounter the same 
method of notation in France in seven books of keyboard music published 
by Attaingnant in 1529-30. Facsimile 2 is taken from one of these 
books, Quatorze gaillardes, neuj pavanes, sept branles et deux basses danses, 
le tout reduit de musique en la tabulature de jeu d'orgues . . . (Paris, 
i53o). 



Keyboard Scores 
Facsimile i 



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6 The Notation of Soloist Music 

In Attaingnant's publications we already find the modern staff of five 
lines. However, it was not until about ioo years later that this method 
became generally accepted. The notes of smaller value are slightly 
different from those of Marcantonio's book. The Sm does not appear 
here as a blackened M, but as a white M with a flag, I . Accordingly, 
the F appears as a white note with two flags, £ , whereas the Sf is a 
blackened F, f identical with that of the Italian book. This ambiguity 
in the forms of the Sm and F occurs also in the sources of mensural nota- 
tion from 1450 to 1550, with preference given to the black shapes (see 
♦ p. 87). 

Three signs for chromatic alteration are used in Attaignant's books: 
the flat, the sharp, and the dot. The former two (the sharp very rarely) 
are used preferably for chords, whereas in melodic formations the dot is 
employed almost exclusively. As in the book of Marcantonio da 
Bologna, the dot has the function of raising or lowering a note by half- 
step, according to which is the more natural direction. However, in 
Attaingnant it has a third meaning, that is, cancellation of a B flat in 
the signature, as is illustrated by the following two examples (in example 
b, the dot belongs to the higher, not the lower note) 1 : 




It may be noted that in Attaingnant's books, as well as in many other 
examples of early keyboard music, the arrangement of the notes within 
the measure differs somewhat from the modern practice. If, for ex- 
ample, a long note occurs in the lower staff against a group of smaller 
notes in the higher, the long note is not placed at the beginning, but in 
the middle of this group (see measure 6). Furthermore, in order to save 
space, the notes in any one part are written as closely together as pos- 
sible, with the result that notes which are to be played simultaneously 
often do not appear in a strictly vertical alignment (see measure 1). 

Attaingnant uses smaller note values than does Marcantonio. They 
may, therefore, be transcribed without reduction, that is, with the M 
represented by a half-note. The one- and two-flagged white notes, then, 
correspond to the quarter- and eighth-notes. 

1 Cf. W. Apel, Accidentien und Tonalitat, Strassburg, 1937, p. 49 (examples 146, 148). 



Keyboard Scores 
Facsimile i 







^^z |~ni~p s^^g^g 



Nf#fi lr^ 



3-S-& 




3=m : 



Attaingnant, Quatorze gaillardes . . . Paris, 1530 
From pages 14 , 15 



8 The Notation of Soloist Music 

The beginning of the branle commun is transcribed in the appendix, No. i. In the 
third measure, the change "from the cadential F-sharp to the truly melodic F is worth 
noticing — and, of course, preserving. So is the change from E to E-flat in the first 
measure of the last brace. 

Other interesting examples of sixteenth century keyboard scores occur 
in England. The English keyboard literature of this period embraces 
two schools, that of early Tudor music (ca. 1 520-1 560) and that of the 
virginalists (ca. 1 570-1 620). It is especially in the first group that we 
find many notational features of interest. The sources of this period 
are listed here in a tentative chronological order (the dates are estimates): 

London, Brit. Mus. Roy. App. 58 (circa 1520) 

London, Brit. Mus. Roy. App. 56 (circa 1520) 

London, Brit. Mus. Add. 15233 (circa 1530) 

London, Brit. Mus. Add. 29996 (circa 1550) 

Oxford, Christ Church College, MS 371 (circa 1550) 

London, Brit. Mus. Add. 305/3, Mulliner Book (circa 1560) 

Among the composers are: Hugh Aston (1480?-! 522), John Redford 
(1491 P-I543?), William Blitheman (?-i5ai), Thomas Allwoode and 
Master Shepard (probably contemporaries of Blitheman), as well as 
many others. 

The compositions in these sources are written on two staves, of six, 
seven or eight lines each. A Tut sunt celi (at the end of Add. 15233) 
and a few other compositions are notated on a single staff of twelve or 
thirteen lines, a manner of writing which occurs also in the sources of 
the virginalistic period (Fitzwilliam Virginal Book). 1 

These manuscripts display various features indicating that the English, 
in their notation of keyboard music as well as in many other respects, 
clung to older traditions to a degree unknown in other countries. These 
conservative features make English keyboard notation individual and 
offer new and interesting problems to the student. 

1 The practice of notating all the parts of a piece on one single staff should not be confused with 
a method widely used in early music (prior to 1250; see Facsimile 53 and Coussemaker. Histoirr it 
l' harmonic au moyen-age, Paris, 1852, pi. 24, 25), in which two (or more) different staves are put to- 
gether as close as possible, probably to save space. A single staff proper would entail the validity of 
one and the same clef for the entire staff; but in these early examples we find the same clef (C) indi- 
cated twice on different lines, so that actually each part has its own clef and, consequently, its own 
staff. In fact, in music of this period a single staff for two or more parts is impracticable since all 
the parts have approximately the same range. 

Apart from insignificant instances of a purely demonstrative character, such as occur in certain 
theoretical writings (e.g., Martin Agricola. Musica instrumentalis, 1529, p. 50), the use of a single 
extended staff for the notation of several parts is exhibited only in keyboard music. The oldest 
examples are found in the Ileborgh tablature (see p. 40 ff. Facsimile 14), and in the tablature of Wolf- 
gang Neuhaus (see p. 40). See alsc HdN a, 259. 



Keyboard Scores 9 

Among these features is first the absence, or at least the inconsistent 
use, of bar-lines. The modern principle of barring is carried out with 
remarkable regularity in all the Italian and French sources of keyboard 
music and, as will later be seen, in almost all the tablatures for both 
keyboard and lute. Indubitably, its introduction marks one of the 
greatest advancements of the notation of solo music (keyboard and lute) 
over mensural notation (ensemble music). The English organists, how- 
ever, did not accept this innovation until the middle of the sixteenth 
century. Even in the sources after this time (Mulliner Book, Fitzwilliam 
Virginal Book) bar-lines are used rather sparingly and inconsistently, so 
that frequently long measures of uneven length result. All the earliest 
MSS would seem to have lacked bar-lines in the original writing; however, 
such lines have been added frequently by a later hand. In some cases, 
they are strangely crooked or bent, due to the fact that the scribes of 
the original paid little attention to the vertical alignment of the notes. 

The composition beginning in the second brace of Facsimile 3 (77. 
versus) serves as an example. Here, as in many cases of manuscript 
music, the chief difficulty lies in the obscurity of the handwriting rather 
than in the intrinsic problems of notation. The clefs are those of 
modern practice, namely the G-clef in the upper staff, the F-clef in the 
lower one. The G-clef is a G with a loop added whereas the F-clef is 
a sort of C followed by a sign which looks like two minims turned head 
to head. This shape is explained as a gradual transformation of the 
letter F. Here follow certain of the main forms of the F-clef, in chrono- 
logical order 1 : 



It should be noted that, in all these shapes, the note f is on the middle line of the staff 
although with the first three characters the dots or strokes appear a semitone higher 
than with the other, more recent ones. 

The signs above and beneath the clefs are flats (B-flat). For the 
transcription, a reduction 1 :i (M = quarter-note) appears to be appro- 
priate. The system of barring depends upon whether \- or 4-meter 
is chosen for the rendition in modern notes. The latter method (two S 
to the measure) makes more familiar reading and is, perhaps, preferable. 
However, in music of the period under consideration, a musical phrase 
may well consist of an uneven number of S, thus leading to a cadential 

1 See the Facsimiles nos. 44 (twelfth century); 49, 50, 64 (thirteenth century); 73, 74 (fourteenth 
century); 31, 33 (fifteenth century); 27, 35 (sixteenth century). Examples of the C-clef occur on 
nearly all the facsimiles, while the much rarer G-clef is shown on nos. 44, 33 B and C, 35, 3, 4, 5, 6, 
8, 9, 10. 



io The Notation of Soloist Music 

close in the middle of a measure. Hence it will occasionally be found 
necessary to introduce a single measure of \ or 4. At any rate, in 
music of this rather archaic type, modern barring should not be under- 
stood to entail regular accent, but only to serve as a guide for the eye. 

The beginning of the transcription is given in the appendix, No. 3. The 'original' bar- 
lines do not always conform with the duple meter chosen for the modern writing. Of 
stylistic interest is the repeated occurrence of the diminished triad in root position 
(E G B-flat). In the next-to-last "measure" of the original the tenor part is one M short. 
An M-rest seems to be missing between the S on a and the M on b, or else the missing 
' value is supplied by the Mon g in the bass. 

A second conservative feature of the English keyboard scores is the 
use of ligatures. Ligatures are a typical device of the notation for en- 
semble music from 1200 to 1600, but were not used for the writing down 
of soloist music, except in England. A full explanation of the ligatures 
will be given later (p. 87 ff). For the present purpose it will suffice to 
mention one special type, namely the so-called ligatura cum opposita 
proprietate, which is characterized by an upward dash to the left side of 
the first note. Such a ligature embraces two notes which appear either 
in form of two adjoining squares or that of a diagonal body {ligatura 
obliqua) the beginning and end of which determines the two notes it 
represents. The value of these two notes is always an S each: 

A third peculiarity of English keyboard notation is the use of blackened 
notes. For certain purposes, which will be explained later, the white 
B y S and M were replaced by others which show black heads, a change 
which was referred to as coloration or blackening. Special forms were 
used for the 'blackened' Sm: 





B 


s 


M 


Sm 


normal: 


a 


« 


I 


i 


blackened: 


M 


♦ 


1 


W) 



It should be noticed that the blackened M is identical in shape with the 
normal Sm and that the blackened Sm looks like the normal F (or in its 
second form, like the M). Which note is represented by one of these 
ambiguous forms appears from the context, i.e., chiefly from the form of 
the S used in the passage under consideration. 

In the English manuscripts, the only sources of keyboard notation 
employing blackened notes, coloration serves two different purposes 
which must not be confused. Coloration is frequently used only to 



Keyboard Scores 
Facsimile 3 



11 



m "N'^w 



t 



i j!i^iili|iiW« 



ii 



i*3 



S 



^S 



^~y 



3ZJ5I 




MS London, British Museum Add. 2ggg6 (ca. 1540) 
Page 160' 



12 



The Notation of Soloist Music 



mark off a middle voice from the neighboring ones. An example of this 
practice is to be found in the Sahator withe a meane from the Mulliner 
Book (Facsimile 4). Here the middle voice is written in blackened notes 
which have the same value as the corresponding white notes. More- 
over, the middle voice is parcelled out between the upper and lower 
staves, indicating whether it is to be played with the right or with the 
left hand. Why this blackening of the middle part was used in some 
pieces, and not in others, is a difficult question to answer. In the present 
instance, one might suppose that it has some connection with the expres- 
sion 'meane' of the caption, a term which, in all probability indicates a 
middle part of special importance, perhaps a cantus firmus. 1 Still, such 
coincidence is not present in every case. 

More interesting, but more difficult also, is the use of coloration for 
another purpose, that is, the introduction of ternary rhythm. In this 
function, coloration represents an important feature of mensural nota- 
tion and will be explained later in detail (see p. 126 ff). Here it will 
suffice to say that a blackened S equals two-thirds of a white S and that 
a blackened M is half of a blackened S, thus equalling one third of a 
white S: !-£«;» -£ . Therefore, a blackened S and M together equal 
a white S, and so do three blackened M:*l.*;lll.+ - A blackened 
ligature (cf. the first measure of the second brace) equals, of course, 
two blackened S. 

As far as the transcription into modern notation is concerned, two 
methods are possible which may be indicated as follows: 

Beginning of the '2. verse" (Facsimile 5) : 



(bU = J 




*A9 J . — nP 



The first method is to be recommended when the ternary rhythm 
occurs only occasionally, while the second is to be used when it obtains 
throughout a piece. In the English sources, the latter type is by far the 
more frequent — perhaps, indeed, the only one. If, then, the second 
method (b) is adopted, the blackened M becomes the ordinary quarter- 
note, the blackened S the half-note, and the white S the dotted half-note 
of 4-meter. However, the latter value is also indicated by a dotted 
black S (beginning of the 6th staff). The sign .32. at the beginning 

1 Cf. C. Pfatteicher, John Redford, Kassel, 1934, pp. 63-65 



Keyboard Scores 
Facsimile 4 



13 




k&Stfti 



11 § I 



-}»lo*tv* VOtHj* f wean 



i ' ■ 



M Ml ' 1 






r7tr^'>h'^ 



Mulliner Book 

MS London, British Museum Add. 30513 {ca. 1560) 

From page 42' 



Facsimile 5 







MS London, British Museum Add. 2ggg6 {ca. 1540) 
From page 9' 



14 The Notation of Soloist Music 

means 'three against two' {proportio sesquia/tera), and merely serves to 
explain and confirm the meaning of the blackened notes. 

The second brace of the piece shows some interesting rhythms in the bass part. The 
blackened notes M M S S at the beginning indicate a rhythm which can be rendered 
more properly, if two 4-measures are replaced by one ij-measure, a change of rhythm 
which is frequent in the courantes of Bach (see the explanations on 'courante-coloration,' 
p. 127). The fourth measure of the bass is an example of syncopation, which, according 
to early theory, consists of the breaking up of a normal group by the intercalation of 
longer values. Indeed, a metrical group (one 4-measure) is formed by the initial black 
M and the final black S; however, these two notes are separated by five white S in the 
value of a dotted half-note each. See the transcription in the appendix, No. 4. 

Let the foregoing suffice to show the beginnings of that musical nota- 
tion which today has the most extended usage, and which is now the 
only one employed for keyboard music. To be sure, its further develop- 
ment and eventual universal acceptance were not achieved immediately. 
The keyboard score found least objection in England, where it became, 
in the hands of the virginajists, a convenient means of notating music 
composed in an idiomatic keyboard style. It was retained in France 
and Italy, though a rival appeared in the form of the keyboard partitura, 
which, because of ease of polyphonic reading, was frequently preferred 
around 1600, especially for works in a contrapuntal style, such as can- 
zonas, ricercares, etc. Germany, on the other hand, was the last country 
to adopt the keyboard score. Joh. Ulrich Steigleder's Ricercar Tabu- 
latura 1 of 1624 appears to be the earliest German example of this nota- 
tion. In southern Germany, because of the Italian and French influence 
which prevailed there, this manner of writing quickly became established 
in general usage. In northern and central Germany, however, even to 
the end of the seventeenth century, the organ composers remained true 
to the national method of notation, the German organ tablature (see 
p. 21 ff). Not until the beginning of the eighteenth century, after the 
decline of the great north-German tradition in organ music, and the rise 
of the musical rococo (Mattheson, Telemann) was the keyboard score 
universally accepted in northern Germany. 



The notation on two staves was called in Italy 'intavolatura,' a name 
which occurs already in the second-oldest source of Italian organ music, 
that is, the Intavolatura cioe recercari canzoni himni magnificati (Venice, 
1542) of Hieronimo di Marcantonio da Bologna (i.e., Girolamo Cavaz- 
zoni, the son of Marcantonio da Bologna). For this reason the notation 

1 The only extant copy of this publication, for which Steigleder himself engraved the copper 
plates, is in the Landesbibliothek, Stuttgart. 



Keyboard Scores 1 5 

under discussion is frequently referred to in modern writings as the 
Italian organ tablature, for instance in Joh. Wolf's Handbuch der Nota- 
lionskunde {HdN), 11, 272 ('Italienische Klavier- und Orgeltabulaturen'). 
Similar names are used for the keyboard scores of French or English 
origin ('Franzosische . . . Tabulaturen, Tabulaturen der Virginalisten'). 
A practically complete list of French, Italian, and German keyboard 
scores is given in HdN 11, 270-279. This list deserves a few comments 
to enable the student to make best use thereof. The heading 'Franzos- 
ische Orgel- und Klaviertabulaturen' denotes keyboard scores which have 
five lines in each staff. The title 'Italienische Orgel- und Klaviertabu- 
laturen' includes sources in which other numbers of lines occur, e.g., 
HI, etc. In this class there is a special group 'Handschriften' (p. 275) 
which includes a number of English documents, namely, the manuscripts 
from London, British Museum. It would be more logical to list these 
with the group: 'Tabulaturen der Virginalisten.' In fact, Add. 29996 
appears in both groups. Finally, since a special grouping called 'Deutsche 
Klaviertabulaturen' is made, it should include German publications 
(Pachelbel, Froberger) which appear elsewhere in Wolf's list. The name 
'Deutsche Klaviertabulaturen' should not be confused with the name 
'Deutsche Orgeltabulaturen,' which indicates an entirely different sys- 
tem of notation (HdN 11, 19). In the terminology of the present book 
the former term means keyboard scores of German origin; the latter 
signifies German keyboard tablatures. 



II. KEYBOARD PARTITURAS 

WE NOW turn to a consideration of those documents of keyboard 
music in which a separate staff is used for each voice-part of 
the composition. The earliest books written in this manner are certain 
Italian publications of the late sixteenth century (see p. 19). Fre- 
quently, this kind of notation is indicated in the titles by terms such as 
Partitura {di canzone) or (Canzone) spartiti; while titles like Intavolatura 
{di cembalo) or (Toccate) intavolate point to a notation on two staves 
(keyboard score). 

Facsimile 6 serves as an example of the keyboard partitura, a notation 
which scarcely offers any problems. The four clefs indicate g, c, c, and 
F. The forms of the F and Sf are: 1 I . The sharps appear in a 
diagonal position (see tenor, second measure, second note). 

As in Attaingnant's publication (p. 6), the notes within a measure are written here 
without regard of their vertical coincidence, in order to save space. The bar-lines 
(which are omitted at the beginning and at the end of the staff) mark off groups of two, 
three or four S. Since a transcription without reduction appears to be musically cor- 
rect, each bar of the original divides into several measures in the modern writing. In 
the last bar, the altus seems to be too short, since there are only three S as against four 
in the other voices. However, from the standpoint of early notation the writing is cor- 
rect, since the missing S is supplied by a part of the final L which, therefore, sounds 
* ahead of the L of the other voices. See appendix, No. 5. 

Of particular interest is the absence of sharps in various passages — 
such as the third bar of the original — which, from the point of view of 
nineteenth century tonality, would seem to call for a sharped F. Cases 
of this sort which, as is well-known, abound in early music, raise the 
question as to the necessity or justification of the 'editorial accidentals' 
which appear no less abundantly in many modern editions of early 
music. A thorough discussion of the problem of accidentals or, as it is 
frequently called, of musica ficta, would far exceed the limitations of 
this book. Instead, another approach to this important matter has been 
adopted, that is, short discussions of the special cases arising with the 
various musical illustrations to be considered. Only this much need be 
said in general: the generosity with which editorial accidentals have been 
inserted in most modern editions of early music far exceeds what can be 
supported and justified by scholarly evidence. Preferences created by 

16 



Keyboard Partituras 
Facsimile 6 



17 



IIITfi 




1 \ 

tiiii 
i*nei 



ill) 

mi 

ill? 

1 1 1 1 

ill! 



rrra 



JM) 



I I ITT 

Mill 
■ 1 ■ 1 1 



\\ 

(i !! 

5 5 11 

t i i 1 1 > j 



ii 



I I &a Mill 

' *1 I4»l I I 

1 ! ! I ! ' 

?4+*i 1 j j j ( j 

I 



tt8 I Bit 



^♦! 1 i' 



»i 1 1 1 



111! 

mi 

riii 

! I I I 

MM 
Mil 
I I4>l 
MM 
MM 
III I 
I I K4 
I I M 



fe-S I I 

XI It 



l*H©i 



II 



I I I] 



1 ■ *»i 1 r 
1 1 *^» 1 1 - 

! «-!♦ 



I I l<5>l 

i : w \ 



IIS* 



W 

sm 



MM ch 1 41 



TO 

urns 



I I l<*l 

Mill 
Mill 



II 



ill! 
1111 

! LI 



iffll 



|fflf 



^ O 



1 8 The Notation of Soloist Music 

the harmonic idiom of nineteenth century classical music have been 
allowed to play much too great a role in this matter, and a few generalities 
taken from theoretical writings have been adopted as the answer to a 
question which actually calls for separate and detailed investigations in 
every period, perhaps in every single document. It is gratifying to see, 
however, that, within the last decade, things have taken a turn for the 
better, and that a number of recent editors have been more judicious 
and reserved in the question of editorial accidentals. 1 As far as the 
sources of keyboard and of lute music are concerned, this writer has 
called attention to the fact that the original accidentals are, as a rule, 
perfectly reliable and do not need correction or completion, save in some 
special cases. 2 

As regards the piece under consideration, no editorial sharps are needed. 
It is a typical example of a sixteenth century phenomenon (especially 
frequent in keyboard music) which combines a major tonality for har- 
monic formations (dominant triad with the leading tone) with a strictly 
diatonic, i.e., modal, scale for melodic progressions, particularly in rapid 
passages. Very informative in this respect is the passage at the end of 
the second staff (alto), which starts with a (harmonically conditioned) 
F-sharp, but continues with a (melodically justified) F of the descending 
scale. The corresponding passage of the discant shows that in this source 
sharps have no prolonged validity (as throughout the modern measure), 
since both the first and the second C are provided with an accidental. 

As mentioned above, the partitura, because of its clearer display of 
polyphony, was frequently preferred around and after 1600 to the nota- 
tion on two staves. As a matter of fact, it turns out to be especially 
suitable for the presentation of pieces in strict counterpoint such as 
ricercares, canzonas, fantasias and capriccios. It is unsuited for pieces 
in an idiomatic keyboard style such as variations, preludes or toccatas 
in which full chords with more than four notes may frequently occur. 
However, in the early seventeenth century, strict counterpoint was so 
commonly regarded as the foundation of organ style that sometimes 
even toccatas were set for four parts and notated in partitura. The 
works of the Neapolitan masters Giov. Maria Trabaci and Ascanio 
Mayone contain interesting examples of this practice which was, to be 
sure, of only transitory importance. 3 

1 See, for instance, D. Plamenac, Johannes Ockeghem, Samtliche Werke, Messen I-VIII, p. xv; 
L. Ellinwood, The Works of Francesco Landini, Cambridge, 1939, p. xlii. 

2 See W. Apel, Accidentien und Tonalitat, pp. 29, 43. 

3 For a discussion of these works, see W. Apel, 'Neapolitan Links between Cabezon and Fresco- 
baldi' (Af£, 1938). 



Keyboard Partituras 19 

The earliest documents of keyboard partitura 1 are certain Italian 
publications of the late sixteenth century, for instance: 2 

1577 : Cipriano de Rore, Tutti i madrigali . . . a quattro voci spartiti et 
accomodati per sonar d'ogni sorte d'istromento perfetto . . . (Venice) 

1577: Musica de diversi autori; la bataglia francese et canzon d'uccelli. 
Partite in caselle per sonar d'istrumento perfetto ( VeniceJ 

1580: Antonio Valente, Versi spiritual • . . spartiti per suonar negli 
organi . . . (Naples) 

In the early seventeenth century, the partitura spread from Italy to 
other countries, and appeared at practically the same time in Portuguese 
and German publications: 

1620: Manoel Rodriguez Coelho, Flores de Musica pera instrumento de 
tecla et harpa (Lisbon) (. . . for keyboard instruments and the harp) 

1627: Hans Steigleder, Tabulaturbuch darinnen dass Vater Unser . . 
(Strassburg) 

1624: Samuel Scheldt, Tabulatura nova (Hamburg) 

The title of the last publication is of special interest since it refers 
expressly to a 'new tablature,' i.e., to a new kind of notation not employed 
theretofore in Germany. The reader will realize that the word 'tabula- 
tura' for this notation is, to say the least, not in harmony with the ter- 
minology observed in this book in which the term tablature is reserved 
for notations with letters or figures. Even from the point of view of 
that time, the denomination of a partitura as 'tablature' was not or- 
dinary. It would seem that it was the word 'nova' rather than 'tabu- 
latura' which was emphasized by the title of Scheidt's book. In the 
preface, the author refers to his notation in a few sentences which are 
cited here, as they throw an interesting light on the whole situation of 
notation as it was in Germany in the early seventeenth century: 

Quod . . . singulae voces quinis et non senis lineis Anglico-Belgico more 
descriptae, in gratiam organistorum Germanorum facta m, cum plerisque 
tabulatura ilia Anglico-Belgica omnino ignota . . . , in qua sex lineae dex- 
tram, sex itidem sinistram manum concernunt, vocibus ita confuse inter se 
positis ut saepius etiam mediocriter in Musicis versatus haereat, et quae 

1 A practically complete list of partituras is given in HdN n, 276 and 307. 

2 The first two of these books contain arrangements of ensemble music (madrigals, chansons) for 
a keyboard instrument {instrumento perfetto means the 'harmonic' instruments — organ, harpsichord, 
etc. — in contradistinction to the 'melodic' instruments, viol, flute, etc.). 

It is interesting to note that the partitura was used first for soloist music (either arranged from 
ensemble music — see above — , or original — as in the case of the publications of Valente and others — ) 
before it was used for the writing down of orchestral music (earliest instance the Ballet comique de 
la Royne, 1582; see Grove's Dictionary 0/ Music and Musicians, 1938, article 'Score'). 



20 The Notation of Soloist Music 

notula Cantum, Altum, Tenorem vel Basin repraesentet, addubitet. Ea 
de causa quamlibet vocem vides hie seorsim positam . . . 

The single voices are written here on five lines and not on six, as is the 
Anglo-Flemish usage. This has been done for the convenience of the 
German organists, most of whom are completely ignorant of the Anglo- 
Flemish tablature. In this tablature we find six lines for the right hand 
and six for the left, and the voices are put together in so confusing a man- 
ner that even a fairly well-experienced musician will hesitate and wonder 
which notes to attribute to the discantus, altus, tenor, or bass. For this 
reason, one finds here each voice placed on a separate staff . . . 

Scheidt's reference to an 'Anglo-Flemish' tablature is easily understood 
from the fact that the English tradition of keyboard music was adopted 
by the Netherland composer Sweelinck, of whom Scheidt was a pupil. 
This musical lineage explains also why Scheidt was familiar with the 
English keyboard score on two staves of six (or more!) lines each, in 
contrast to his countrymen who, according to himself, were ignorant of 
it. In order not to trouble the German organists with the 'vocibus ita 
confuse inter se positis' of the keyboard score, he prefers the principle 
of the keyboard partitura, in which one finds 'quamlibet vocem . . . 
seorsim positam.' 

Apparently, when Scheidt published this book, both notations, the 
keyboard score and the keyboard partitura, were unknown in Germany. 
From the fact, however, that he rejects the score notation as unsuitable 
for the German musicians, it would appear that the notation used in 
Germany before this time was related more closely to the principle of 
the partitura than to that of the score. We shall find this supposition 
confirmed in the following consideration of the national German key- 
board notation before Scheidt, the German keyboard tablature. 



III. KEYBOARD TABLATURES 

A. German Keyboard Tablatures 

THE GERMAN keyboard tablature is characterized by the use of 
letters instead of notes for some or all of the parts. 
The method of denoting pitch by the letters a, b, c, etc. of our alphabet 
originated in the ninth century. 1 In that period, various systems were 
in use, some of which applied the letters A-P to the tones of two octaves 
(this system is commonly, but not quite accurately, called Boethian 
notation; cf. HdN i, 38 and G. Reese, Music in the Middle Ages [New 
York, 1940], pp. 134, 135), whereas others repeated the letters A-G for 
the various octaves. The treatises of the ninth and tenth centuries 
also vary with regard to the initial tone of the series, as appears from the 
following tabulation: 



modern : 


G A 


B 


c 


d 


e 


f g 


a 


b 


c' 


d' 


e' P g' 


a' b' c" 


I. 






A 


B 


C 


D E 


F 


G 


H 


I 


K L M 


NOP 


II. 


A 


B 


C 


D 


E 


F G 


H 


I 


K 


L 


M N O 


P 


III. 


(E) F 


G 


A 


B 


C 


D E 


F 


G 


A 


B 


C D E 


F(G) 


IV. 


r a 


B 


C 


D 


E 


F G 


a 


b 


c 


d 


e f g 

-1 


a 

a b c 

a b c 



I: Scholia Enchiriadis (GS 1, 209). 

II: Anon. II (GS 1, 342); this system has been used also in various musical sources, for 
instance, in the 11th-century MS Montpellier H. 159 where it is used in combina- 
tion with neumes (see HdN 1, 44), and in the famous two-part piece Ut tuo pro- 
pitiatus from MS Oxford, Bodley 572 (see p. 207; Facsimile 43). 

Ill: Notker Labeo (GS 1, 96); Hucbald (GS 1, 118); Bernelinus, (GS 1, 326). 

IV: Oddo of Cluny (GS 1, 253, 265), hence the name Oddonic letters; the double letters 
were also used by Guido of Arezzo. 

Since the mediaeval scale included the tone B-flat in addition to the 
B-natural, separate indication of these degrees was necessary. They 
were both designated by the letter b, this being written in two shapes, 
round: b (b molle) for the B-flat, and square: b (b quadratum) for 
the B-natural. In later usage, the square b assumed the following 
shape: h , and was, especially in Germany, falsely identified with the 

1 Letters were also used in Greek notation; see HdN i, 16 ff. 

21 



22 The Notation of Soloist Music 

letter h, the round form being called simply: b. This nomenclature and 
manner of writing, i.e., h for B-natural and b for B-flat, is found in all 
German tabiatures and persists to the present day in Germany. It may 
be noticed that another variant of the square b lead to the sign fc) for 
the natural, and still another to the sign # for the sharp. Thus, all 
the material for our notation of accidentals, the flat, the sharp and the 
natural, developed from one original sign, the letter b. 

Although in the Middle Ages the letters remained restricted chiefly 
to the theoretical and pedagogical fields, they attained practical impor- 
tance in the German keyboard tabiatures of the fifteenth and sixteenth 
centuries. The origin of this peculiar method of notation can be traced 
back to an English manuscript of the early fourteenth century {ca. 1325). 
Two leaves from the MS Brit. Mus. Add. 28550, the so-called Roberts- 
bridge Codex, contain the earliest preserved example of what is usually 
called German organ tablature. The justification of the name 'German' 
lies in the fact that the same notation, slightly more developed, appears 
one hundred years later in Germany alone of all countries (Ludolf Wilkin 
tablature, 1432), 1 where it was adopted exclusively for the writing down 
of keyboard music until Scheidt's Tabulatura Nova (keyboard partitura) 
and Steigleder's Ricercar Tabulaturen (keyboard score), both from 1624. 
Even after this date, many important sources of keyboard music, par- 
ticularly those from North-Germany, were written in this notation. 

It is customary to distinguish between two types of German keyboard 
tabiatures. The first was in use from the early fifteenth century to the 
middle of the sixteenth century and is usually referred to as 'old German 
organ tablature.' In this type, letters are employed for all the voices 
except the highest which is written in notes. The second period opens 
with the books of the colorists (Ammerbach, 1573), and is known as 
'new German organ tablature.' Here, all the parts are written in letters. 

1. Old German Keyboard Tablatures 

We shall start our explanations of this notation by a discussion of an 
example taken from the so-called Buxheimer Orgelbuch, ca. 1460. The 
reason for our choice lies in the fact that in this source for the first time 
the principles of this notation appear firmly established, whereas the 
earlier manuscripts show certain peculiarities which demand special 
consideration and which, therefore, will be discussed later. 

The piece in question, a composition by Boumgartner (Facsimile 7), 

1 Cf. L. Schrade, Die handschrijtliche Ueberlieferung der dltesten Instrumentalmusik, Bonn, 1931; 
W. Apel, 'Early German Keyboard Music' (Af«£, 1937). 



German Keyboard Tablatures 23 

is in three parts. The upper part is written in notes; the two lower ones 
are written underneath in two rows of letters. The notes appear on a 
staff of six or seven lines, with a C-clef. The forms are those of the 
so-called black notation such as had been used in mensural notation 
prior to 1450: 

S M Sm F 

• 1 J * 

The rests are those of the table, p. 3. 

A comparison of these notes with those of white notation used in the 
former specimens shows that the smaller values have here one more 
flag. For instance, the F is here a double-flagged note, as against the 
one-flagged shape of white notation. In order to escape confusion in 
this matter it is imperative to avoid flat identification of any of these 
signs with those, similar in appearance, of modern notation (e.g., eighth- 
or sixteenth-note). They should always be referred to by their ancient 
names and determined in relation to the semibrevis, the identity of 
which is always clear. The corresponding modern notes will have to 
be determined on the basis of the reduction chosen. It will be seen 
that, if the reduction is 1:2, the double-flagged F becomes the double- 
flagged sixteenth-note of the modern system. 

The flags of successive Sm and F in descending line are frequently 
drawn as one coherent line, somewhat similar to the cross-strokes 
of modern notation. Still, there is a difference which should not be 
overlooked, if possible errors are to be avoided. A group of four Sm, 
for example, is always written thus: H£j" , i.e., with the flag of the last 
note extending a little to the right side of the last stem. On the other 
hand, in a group like this: Ijl (cf. the first measure), the last note is 
not a Sm, but a M, the whole group being equal to: Sm, Sm, M. Simi- 
larly, the group of five connected notes at the end of measure 3 consists 
of four F and a Sm as the last note. 

The stems of the M, Sm and F invariably proceed upwards. Down- 
ward stems, such as appear occasionally (measures 2, 7 and 8) indicate 
chromatic alteration. This alteration may be sharping or flatting, de- 
pending on the note in question (cf. the remarks about the chromatic 
dot in French and Italian keyboard scores, pp. 4, 6). Thus the double- 
stemmed note in measure 2 is an F-sharp M while the second to the 
last note in the first brace is a B-flat S. This manner of indicating 
accidentals by a sign directly connected with the note excludes the 
presumption of prolonged validity, at least as a principle. 



24 The Notation of Soloist Music 

In the third and fourth staves of our example, there are notes with a 
downward stem to which a little triangular loop is attached: ♦ This 

sign, which should not be confused with the plain downward stem, in- 
dicates an ornament which in later sources (e.g., Joh. Buchner, Funda- 
mentum she ratio vera, 1 ca. 1520) is called a mordent. It may be 
transcribed by our modern sign of the simple shake :-w, although its 
execution was probably somewhat different. According to Buchner, 
the main note was not to be played twice or three times, but held, and 
only the auxiliary note was quickly repeated, a technique similar to 
that used for a trill on the violin. If both the mordent and chromatic 
alteration are desired for one tone, the alteration is indicated by a 
diagonal dash: * 

The letters a, b, c, etc. used in the German tablatures have their 
present-day meaning (with h denoting B-natural, b denoting B-flat). 
Special attention is needed in order to avoid confusion of the letters c 
and e. For instance, in the second brace, the third and fifth letters of 
the upper row are both e, whereas the corresponding letters of the lower 
row are both c. Two octaves are distinguished in a way similar to that 
of modern practice, the lower being indicated by plain letters and the 
higher by a dash above the letter: c (one-line c). Where these octaves 
begin and end has to be determined separately for each manuscript, 
since the scribes differ in this regard. In the present case, it appears 
from the immediate succession of b and c (cf. measures 3, 5) that the 
new octave starts with c. 

The capital letters, which usually appear at the beginning of a piece, 
are merely decorative; in later sources, however, they signify the lowest 
octave (see p. 30). 

The indication of chromatic tones in the letter-notation is a feature 
of special interest and of considerable importance for the study of acci- 
dentals in the period under consideration. Whereas the B-natural and 
the B-flat are distinguished by different letters (h and b), all the other 
chromatic tones are indicated by a little loop or scroll attached to the 
letter, as follows: 

# % f & 

c# d# f# g# 

1 Buchner's Fundamentum, which includes an extensive treatise on composition' as well as a 
large collection of organ pieces, exists in two MSS: Zurich, Stadtbibliothek, cod. 284, and Basle, 
Universitats-bibliothek, F I 8. A large portion of the Fundamentum has been published by C. 
Paesler in VjMW v; see also E. V. Werra, in Km. Jb. 1895, and w - Nagel in MJM xxm. 



German Keyboard Tablatures 
Facsimile 7 



25 







Buxheimer Orgelbuch 

MS Munich, Staatsbibliothek Mus. Ms. 3725 (ca. 1460) 

Page 61 



26 The Notation of Soloist Music 

This scroll is an abbreviation of the Latin syllable -is which was taken 
over by German terminology to indicate sharping (cis = C-sharp). In- 
deed, except for the B-flat, all chromatic tones are invariably designated 
as sharps, for instance, E-flat as D-sharp, A-flat as G-sharp. The ob- 
servation of this principle brings about what would seem to be, at first 
glance, a rather strange use of enharmonic equivalents. For instance, 
in the third measure of the present example, the sixth letter of the 
lowest row is b, and the corresponding letter of the higher row is d-sharp. 
The actual meaning is the fifth E-flat to B-flat. 

Above each letter there is a sign indicating its time value. These 
signs are similar in appearance to the note values to which they are 
equal, and are obviously derived from them : 

B (tern.) B (bin.) S M Sm F 

i r> h 

For the transcription (see appendix, No. 6), a reduction 1:4 of the note values seems 
appropriate. The piece is an interesting example of fifteenth century Lydian, charac- 
terized by the prevalence of B-natural in the melody, and by a change from B-natural 
to B-flat in the lower parts, the former being preferred for ascending, the latter for 
descending lines. No editorial accidentals are needed. The tendency to avoid chro- 
matic tones in quick passages and ornamenting figures — already observed in a previous 
example— here leads to interesting formations (cf. the succession F#-F in meas. 
2, and B-Bb in meas. 6 of the third brace). Occasionally, the distinction of octaves 
appears to be inaccurate, in the letter-notation. The frequent crossing of the lower 
parts is a characteristic of the style of the Burgundian School (Dufay, Binchois, fl. ca. 
1440) to which all the pieces of the Buxheimer Orgelbuch belong, most of them being 
* intabulations of Burgundian chansons. 

The next source of German keyboard tablature to be considered is 
Arnolt Schlick's Tabulaluren etlicher Lobgesang und Lidlein uff die Orgeln 
und Lauten (Mainz, 15 12). Except for a single musical illustration 
contained in Sebastian Virdung's Musica geiutscht of 1511, it is the 
earliest instance of keyboard music published in print. Facsimile 8 
shows the first page of the book. 

In contrast to the Buxheimer Orgelbuch Schlick uses white notes, as 
follows: 

S M Sm F Sf 

i £ { I 

Chromatic alterations are indicated by a small loop attached to the 
note (cf. the sixth note of the example). 

In the letter-notation, tones of the great octave (below c) are desig- 
nated by a horizontal dasn beneath the letter. It is probably from 



German Keyboard Tablatures 
Facsimile 8 



27 



tw* 



H 40 

t- 40 

-» 025 

h cp5 

-4 JO 

H 40 

-4 tJ) 

H 40 

H 40 
-4 iu 

H JO 

J- -IO 




-0 



•40 



- « 



to 



tT> 



W5 



-4 


<3 * U-+- 


^3 




< t*3 




* «l 


^3 




« ' °l 


§5 


H 


« t «-» 


-4 _ 


*^' *> 






i u— 


^> 




< t^> 


■<i hH 


H 


l c 









t?5 





« 




-S> 




e5 


u 


^T 




u 


<SI 


1^3 


tnj 






y^ 




4-1 













s 



JO 



28 The Notation of Soloist Music 

this method of indicating the lower tones in a manner 'contrary' to that 
used for the one-line octave, that the name contra-octave (also contra- 
bassoon, etc.) originated. 1 The metrical values are indicated by the 
same signs as in the Buxheimer Orgelbuch, except that the dot indicating 
an S is lacking, a letter without a rhythmic sign being understood as 
having the value of an S. The T-like symbols in the first and third row 
are ^-rests affixed to a fragment of a stafT line, which alternate with 
M-rests having the form of an inverted T. 

There are no bar-lines in this tablature; instead, groups of notes 
representing a measure are marked off into blocks separated by small 
spaces. In the present composition, Salve Regina, each block contains 
three M (six Sm). The fifth group contains one Sm too many; but, as 
a compensation, the seventh group is one short. Apparently, the last 
note of the fifth and the sixth group has to be tied over, so that synco- 
pation results. 

It is interesting to note that the parts of this composition, in contrast 
to those of the Buxheimer Orgelbuch, move in separate ranges, and that 
the arrangement of the parts in the tablature corresponds to their 
respective ranges, the lowest voice being written in the lowest row, etc. 
This arrangement, natural as it is, is not always observed in the German 
keyboard tablatures. In the sources after Schlick, one usually finds the 
lowest part written immediately underneath the melody, i.e., as the 
highest row of letters, so that the following order results: discant, bass, 
alto, tenor. Some scholars have considered this curious method as an 
anticipation of the thorough-bass practice, with its characteristic em- 
phasis on the discant and the bass. Another explanation, and a more 
plausible one, has been given by O. Kinkeldey, 2 who calls attention to 
the fact that in some books of mensural notation the four parts are 
arranged in a similar manner, with the bass underneath the discant on 
the left-hand page, and the other voices on the right-hand page. 

Facsimile 9 from Kotter's tablature of 15 13 (Basle, Universitats- 
bibliothek, F IX 22) illustrates this arrangement (cf. the first chord, 
with f written on top of F and c). 3 Other features of this tablature are: 

1. The notes are the black characters of the Buxheimer Orgelbuch; 
however, instead of the lozenges we have the round heads still in use in 
modern notation. 

2. In a series of F or Sf> only the first note of the group bears the 

' In modern usage, the term contra-octave signifies the octave below the great octave. 

2 Orgel und Klavier im 16. Jahrhundert, Leipzig, 1910, p. 190. 

8 The inscription reads: Anabole (Greek, prelude) in fa, 7o(hannes) Kot(ter). 



German Keyboard Tablatures 
Facsimile 9 



29 




3<d The Notation of Soloist Music 

stem and flag indicating time-value, whereas the following notes are 
written only as heads. Naturally, these are meant to be notes of the 
same value: A*«- J7J2 • 

3. The sign of the mordent is a small loop, similar to that used in 
Schlick (cf. the first note). Chromatic alteration is indicated by a 
downward stem carrying a diagonal dash (cf. the first note of the second 
staff), 

4. In the letter-notation, tones of the two-line octave are indicated 
by a double letter with a horizontal dash: cc (cf. second brace, end of 
the middle row of letters). 

5. In the letter-notation, consecutive F or Sf are indicated, not by 
single rhythmic signs but in a manner similar to that of the cross-stroke 

in modern notation: ti£p • These fence-like marks form a striking 

feature of all the later German keyboard tablatures. 

A transcription without reduction is recommended (l«d ). This means that the 
double-flagged F becomes a one-flagged eighth-note, thus leading to what looks like a 
doubling of the smaller values. There are several instances of incorrect writing in this 
piece. The rest after the first note of the top voice should be an F-rest, instead of an 
Sf-vtst. The /aw-rest in the second staff should be dotted. In the next measure, the 
first note of the highest row of letters is indicated as a dotted M, that is, equal to M + Sm, 
whereas its actual value is only M + F. The whole piece is reproduced in W. Apel, 
Musik ausfriiher Zeity vol. 1 (Mayence, 1932). 

The notation just described is typical of all the examples of German 
keyboard tablature in the first half of the sixteenth century. They 
offer few difficulties, except those presented by their graphological pecu- 
liarities. With many of the handwritten documents a preliminary study 
is necessary to determine the meaning of the different signs indicating 
letters. This task is best accomplished by a consideration of letters in 
vertical arrangement (chords) or in simple melodic formations such as 
scales and schematic coloraturas. The following table shows the forms 
of Kleber's manuscript tablature of 1520-24 (Berlin, Staatsbibliothek, 
Mus. Ms. Z 26) : 

FGABHcc#dd#e f f# g g# a b h 

The letters c and e are particularly apt to be confused. 

Facsimile reproductions from Kleber's tablature are given in HdN 11, 
26 and in SckT> p. 16. 



German Keyboard Tablatures 
Facsimile io 



3i 



^3 



-£. ■©■ Ui L ft y$f « t r r<?r */» **7^ 

S ^ 2X ^ r/f pr r/v' r//- „ 

** 'Y -fr W *f fy" A ^ cc r 



J3l 



^ p/r /?f pv p/ pv *T 



— <VT 

rT— ^ T 

- — rf_* L. 



Zi- 



W 



zz: 






Pf p; vrr f/r fly' /> ^ ^/-^ 



T/r 



ag ,# a; # 



*&» $" -csr #■ g: «f « «2 .a? 



? 



r? ty> ?r tt{ Wf flf w tf 



1 



MS St. Gall,.Stiftsbibliothek jjo (ca. 1525) 
Page 10 



32 The Notation of Soloist Music 

A page from Fridolin Sicher's tablature of about 1525 (Library of the 
Monastery St. Gall, 5J0 1 ), written in more hasty characters, may serve 
as a final illustration of the old German keyboard tablature (Facsimile 
10). It contains an In dulci jubilo, and the beginning of a Resonet. A 
peculiarity of this tablature is the writing of the rhythm J J 1 in this 
manner YI , which is applied to notes as well as to letters. For the 
benefit of those whose several hours labouring has not been wholly suc- 
cessful, it may be said that both pieces are transcribed in H. J. Moser's 
* Fruhmeister der deutschen Orgelkunst (Leipzig, 1930). 

2. New German Keyboard Tablatures 

In the second half of the sixteenth century the writers of keyboard 
tablatures began to use letters not only for the lower parts, but for the 
melody also. It is this exclusive use of letters for all the voices that dis- 
tinguishes the so-called new German keyboard tablature from the earlier 
type. To the modern mind, this change appears bizarre. One would 
expect to find a gradual decline in the use of letters and an increased use 
of notes, yet actually the development proceeds in the opposite direction. 
Nevertheless, the new method is perhaps not so illogical as it seems to be 
at first sight. As a matter of fact, letters are rather convenient symbols 
for tones, particularly since they obviate the use of the staff" which always 
has been a source of trouble, especially in printing music. The high 
cost of publishing music written on a staff" may have been a decisive fac- 
tor in the adoption of the new system. The use of letters also saves 
space, as can be seen on Facsimile 9, in which the three rows of letters 
occupy no more space than one row of notes. Even J. S. Bach still re- 
sorted to the letter-tablature in some of his autographs when the paper 
did not offer sufficient space for a staff. 2 

The books of new German organ tablature include the printed publi- 
cations of the so-called 'colorists,' Nikolaus Ammerbach (1571, 1583), 
Bernhard Schmid (1576, 1577), Jacob Paix (1583), Bernhard Schmid, 
the younger (1607), and others. They also include numerous seven- 
teenth century manuscripts, many of which are listed in HdN 11, 32ff. 

These tablatures do not call for general explanations beyond those pre- 
viously given, except for a consideration of the metrical signs. While 
the German keyboard tablatures of the first half of the century show 

1 Cf. W. R. Nef, 'Der St. Gailer Organist Fridolin Sicher und seine Orgeltabulatur' (Schweizerisches 
Jahrbuchfiir Musikwissenschaft, vn, 1938). 

2 Orgelbiichlein (Berlin, Staatsbibliothek, Mus. Ms. P 283), pp. 9, 17, 22, 26, 30; see Facsimile 
13- 



German Keyboard Tablatures ^ 

a rather confusing variety of rhythmical signs (see the explanations in 
HdN ii, pp. 20, 23, 27), a new and uniform practice, originating in the 
Italian lute books (see p. 62), appears in the sources now under con- 
sideration. The £ is always represented by a plain vertical stroke 
which formerly denoted the M. Accordingly, the signs for the smaller 
values show two more flags than the corresponding signs of mensural 
notation, as appears from the following chart: 

S M Sm F Sf 
mensural notation {figure de musica) : * i j \ | 

tablature {figure de sonatori) : ' ' ^ ^ & 

The Italian names are those of Don Bartolomeo Lieto's Dialogo quarto di musica, 1559; 
see HdN n, 64. 

The correctness of this concordance is attested not only by various 
theoretical writers, but also by a comparison of pieces preserved in 
both systems of notation (e.g., the innumerable intabulations of motets, 
chansons, etc.). 

Modern editors have frequently overlooked or dismissed these facts, 
and have transcribed pieces from German tablatures on the basis of a 
merely external similarity of metrical signs, i.e., of the number of flags, 
so that, e.g., the Sm of the tablature became a sixteenth-note of modern 
writing. 1 This actually means a reduction 1 4 of the note values, which 
is definitely too great for the period under consideration and which 
considerably obscures matters of tempo and of style. The proper re- 
duction for the sources under consideration is 1 :2 which means that the 
metrical signs of the tablature lose one flag. In external aspect, such 
a change has, of course, the appearance of the reverse procedure, that 
is, enlargement 1 :2. Once the situation is clearly understood, there 
would seem to be little danger of referring to it as what it seems to be 
(enlargement) rather than what it really is (reduction). It is interest- 
ing to note that the above-explained principles still hold good in the 
case of J. S. Bach, who, whenever he uses letter-notation for the closing 
measures of an organ-chorale, replaces the whole note (i.e., the old S) 
by the plain vertical stroke. Naturally, no actual reduction of time- 
values is permissible in music so late as Bach's, which means that the 
metrical signs of his tablature lose two flags. 

The printed examples of this notation offer scarcely any problems. 
Facsimile 11, from the Tabulatur Buck of B. Schmid, the younger, of 
1607 serves as an example. The simple stroke representing the S 
appears in the form of the letter J. The rhythmical signs for the smaller 

1 For instance, W. Merian in: Der Tanz in den deutschen Tabulaturbuchern, Leipzig, 1927. 



34 



The Notation of Soloist Music 



values are combined in fence-like drawings similar to those of the tabla- 
ture of Kotter (Facsimile 9). Likewise, the lines indicating higher oc- 
taves are drawn as uninterrupted horizontal strokes for an entire group of 
notes: a g f e (end of the first line). If, in such a group, some notes 
belong to the two-line octave, separate dashes are added on top of the 
long dash: c b a g. Note that the letter c has the shape of the modern 
letter r (see the explanations on seventeenth century French lute tabla- 
tures, pp. 71, 72). Apparently, the one-line octave begins here with 
the letter h, not c, as appears from a consideration of the bass line at 
the top of the page. 

The pieces on this pages are transcriptions into German tablature of the 'toni' (preludes 
in the different modes) which originally appeared — in keyboard score — in the Intonazioni 
d'organo di Andrea Gabrieli, et di Gio: suo nepote, of 1593. The two first columns of the 
page are occupied by the conclusion of the Secundus tonus which is a fifth lower than the 
Secundus tonus transpositus per quintam superiorem (the first C-sharp on the page cor- 
responding to the G-sharp at the beginning of the third column). Of particular interest 
is the clash between the harmonically conditioned C-sharp in the initial measure of the 
page and the melodic C in the bass-line: 




The reader is advised to compare his transcriptions with the very inaccurate reprints 
of the Intonazioni contained in L. Torchi's L Arte musicale in Italia, vol. in, p. 131 flf. 
Torchi and many other writers ascribe these pieces to Giovanni Gabrieli, whereas B. 
Schmidt names Andrea Gabrieli as the composer. Stilistic considerations doubtless 
support the latter's view (see A. Gabrieli's toccatas in the same volume). 

In the numerous manuscript specimens of the new German keyboard 
tablature, the chief obscurity lies in their graphological peculiarities. 
Facsimile 12, taken from the Klavierbuch der Jungfrau Regina Clara Im 
Hqff (Vienna, Staatsbibliothek Ms. 18491) of 1629, serves as an example: 1 

G A B h c c# d d# e f f# g g# a b 



A 3*IMr>v^_£^<vf*/C*3V* 



6 



In both pieces of our facsimile (Fit/is sass in einen Botgen, and Falscher Schaffer ist das 
recht) the number of voices alternates between three and four, in a manner characteristic 



Compare these characters with those of Kleber's tablature, p. 30. 



German Keyboard Tablatures 
Facsimile ii 



35 






? r t 

^5 WPd » gTg *0*h tHi 




ff pppp p^ wm <* 
ws *zrfc #W #rne g 

? I 



/ 



Num. 4- 

Secundp To ¥ <-> V? 

nm tranfio- $ *. u JT 

fituiperqutn J tt 

tamjuperw- j JL 



rem. 



? v W 



WFfJ 

J 

J 

r 
j 
v 



ttft 



?T?# 



i 

/ 
J 



9 



-r$-r? 



ff^ f?w w ^ppp ^^ / 

T^JT **r$- T?tfT TTT? T^rf * 



*?#? #F? Vr$** 

/ 



J 

/ 



Bernhard Schmid, Tabulatur Buck von allerhand . . . Prae/udiis, Toccaten, 

Motteten, Canzonetten, Madrigalien und Fugen. Strassburg, 1607 

From folio A I v 



36 



The Notation of Soloist Music 
Facsimile 12 



* r * • 









4#fc 



f # # 



» * 5 T 1 



> •» »• 



lr " 3 i jg — f 






"■■■I •* 

'Mr 






4W^ 



^r-M 



r 4fc 



•5- « y » A J-* 3 VlL'vjr 






3' AAA 



5 5 










W 



T-y 



-v J ** 9" y r y f 9 



c Si 






T" 



; : :i; 



zl 



c c $ A 



Klavierbuch der Jungfrau Regina Clara Im Hoff 
Vienna, Staatsbibliothek Ms. 18491 (1629) 



German Keyboard Tablatures 37 

of the keyboard style of the mid-seventeenth century (Froberger). The tiny hooks 
appearing underneath certain letters (e.g., the first and third at the beginning) are signs 
of ornamentation the exact meaning of which is doubtful (mordent?). Occasionally, the 
metrical signs appear within the row of letters, indicating rests. The third brace is 
transcribed in the appendix, No. 7. 

In the seventeenth century, the new German organ tablature spread 
particularly in North Germany. Not only are all the important collec- 
tions of organ music in that period thus written down, — for instance, the 
famous Liineburger Tabulaturen (containing compositions of Tunder, 
Reinken, Hanff, Buxtehude and others), — but also contemporary instru- 
mental and even vocal scores. Interesting examples are to be found 
in the edition by G. Harms of the complete works of Buxtehude (Ham- 
burg, 1925-37; see vols. 5, 6). 1 

Facsimile 13 is a page from J. S. Bach's Orgelbuchlein in which tabla- 
ture is used whenever the page reserved for an organ chorale did not 
provide enough space. We leave it to the student to decipher — of 
course, without the aid of the Peters edition. Let it suffice to point 
out that the rhythmic signs of the tablature are the traditional ones 
(with two flags more than those of the ordinary notation), and that the 
four-flagged sign (corresponding to the sixteenth-note) is replaced by 
the figure 4. 

3. The Earliest Specimens of German Keyboard Tablature 

We began our consideration of the German keyboard tablatures 
with the Buxheimer Orgelbuch, since it is the earliest document showing 
the principles of this notation fully developed. The few sources pre- 
ceding it display certain primitive features which make them interesting 
subjects for individual studies rather than examples for general explana- 
tions. In fact, most of them have been dealt with in monographs to 
which the interested student is referred. Here we must restrict our- 
selves to a few brief remarks. 

The reproduction on p. 38 shows part of a page from the oldest extant 
document of keyboard tablature, contained in the early fourteenth cen- 
tury MS Brit. Mus. Add. 28550 (Robertsbridge Codex). The upper voice 
of the two-voiced composition (an instrumental estampie, not a prelude; 
of. the erroneous designation in Frotscher, Geschichte des Orgelspiels 
[Berlin, 1935], 1, 62), is written on a staff with notes, while the lower one 
appears underneath written in letters. In order to clarify the grapho- 

1 See also p. 17 of SchT and G. Harms, Samuel Scheidts Werke, 1937, vol. 5. 



38 



The Notation of Soloist Musi 



w ^^^m-fm m 



n^m^^r'^^^ i 



Ofeatftcwu fitnp.jj 



3 



ffi?. r \l m dft^ 



EXE 



S g«jjgS*g §S^ 



__riiPiiBJH/*»iirn 



3| zjffigg 







4+ 



aC 



VC«r- 



PS==C 



isp* 5 ^ 



logical obscurities of the original, there follows a transliteration of the 
first line. 



I 5 asasaagafgt agf^fga^ac # a# cd# c dc # c 
Retrove. pr/me/s pundus. \ 



a ad dsde -Fedc # c dc# cdc#c 

A thorough understanding of the staff-notation requires a knowledge 
of the Italian mensural notation of the fourteenth century (see p. 384). 
Suffice it to say that the brevis is the unit of time-measurement, equiva- 
lent to our beat and, therefore, best transcribed as a quarter-note. 
Three such breves form a measure of 4 (modus perfectus). The smaller 
values are combined in groups equalling a brevis and marked off from 
one another by dots (punclus division is). Rhythmical differentiations 
within such a group are obtained by the use of stemmed semibreves. 
The £ with a downward stem is half of a B; the plain S is half of a B 
or a quarter of a B depending upon whether there are two or four such 
notes in a group; the S with an upward stem {minima) is one-eighth of 
a B. The small circles on top of the first two S are probably orna- 



German Keyboard Tablatures 
Facsimile 13 



39 




.2 

cS 






o 



4 o 



The Notation of Soloist Music 



ments (mordent?). The white B would seem to indicate prolongation 
of the preceding black B. 

In the letter-notation, the letter s (abbreviation of Lat. sine, 'without') 
indicates a rest. The sharp-like sign stands for the B-natural (see 
p. 21 f). Following is the transcription of the beginning: 1 




rrrai mA nn 




It is not until one hundred years later that we again meet examples 
of this same notation, all of which are of German origin. They are 
listed here in an approximate chronological order: 2 

i. Tablature of Ludolf Wilkin, 1432 (Berlin, Staatsbibliothek, theol. lat. 

quart. 290) 
1. Tablature of Adam Ileborgh, 1448 (Philadelphia, The Curtis Institute 

of Music) 

3. Tablature of Wolfgang de Novo Domo (Neuhaus), ca. 1450 (Hamburg, 

Stadt-und Universitatsbibliothek, ND VI No. 3225) 

4. Fragments of a tablature, ca. 1450 (Breslau, Dominikanerkloster) 

5. Fundamentum organisandi magistri Conradi Paumanni, 1452 (Werniger - 

ode, Library of Fiirst Stolbergk, MS Zb 14) 

6. Tablature, anonymous, ca. 1450 (Erlangen, Universitatsbibliothek, 729) 

The most important of these sources, namely, the tablatures of 
Ileborgh and Paumann, may be briefly considered here. 

Facsimile 14 shows the first page of the Ileborgh tablature. It begins 
with the following lines of Latin text, incorporating many abbreviations 
(not preserved below), as was customary at the time: 

Incipiunt praeludia diversarum notarum secundum modernum modum 

1 For further studies of this MS see the facsimiles in H. E. Wooldridge, Early English Harmony, 
London, 1897, 1, pi. 42-45, as well as the transcriptions and explanations by J. Wolf (Kirchen- 
musikalisches Jahrbuch, 1899; AjMW \; GdM 1, 357; GdM m, no. 78; HdN 11, 5) and J. Handschin 
{ZjMW xii, xin). The primus functus of the above piece is also contained in W. Apel, Musik aus 
friiher Zeit, 11. The transcription in Early English Harmony, 11, 1913 (H. V. Hughes) contains 
numerous errors. 

2 Literature (a) general: L. Schrade, Die altesten Denkmaler der Orgelmusik, Miinster, 1928; W. 
Apel, 'Early German Keyboard Music' (MQ xxm). (b) Special: W. Apel, 'Die Tabulatur des 
Adam Ileborgh' {ZjMW xvi); F. Feldmann, 'Ein Tabulaturfragment des Breslauer Dominikaner- 
klosters' (ZfMW xv); F. W. Arnold and L. Bellermann, 'Das Lochamer Liederbuch . .' {J/MfV 11); 
K. Ameln, Locheimer Liederbuch und Fundamentum organisandi, Berlin, 1925 (facsimile edition). 



German Keyboard Tablatures, 
Facsimile 14 



41 




( *t7^? H A%8r?fr < 



m 



£ «M<t*MM«t«Pt<V«MS 



swate* 



te«feH^=,— 




Tablature of Adam Ileborgh (1448) 

Philadelphia, The Curtis Institute of Music 

Page 1 



42 The Notation of Soloist Music 

subtiliter et diligenter collecta cum mensuris diversis hie inferius annexis per 
fratrem Adam Ileborgh Anno Domini 1448 tempore sui rectoriatus in 
stendall. 

Here begin preludes in various keys according to the modern manner (in 
modern style?), cleverly and diligently collected, with diverse mensurae 
appended hereinbelow, by brother Adam Ileborgh, in the year of our Lord 
1448, during the time of his rectorate in Stendall. 

Above the first staff one reads: 

Sequitur preambulum in C et potest variari in d, f, g, a. 

There follows a preamble in C which may be transposed into the keys of 
d, f, g, a. 

This preamble is written on a staff of eight lines, with six letters, 
namely, C, G, D, F-sharp, C, g underneath. The rhythmic interpreta- 
tion of the melody presents difficulties, owing to the absence of bar-lines, 
and to the employment of a special note not encountered in our previous 

studies, i.e., \ . This shape of note, with a one-flag stem both upward 

and downward, occurs in the Italian sources of the late fourteenth 
century with various meanings. 1 In all cases, it signifies a small note- 
value, a meaning which is in harmony with the practice of Paumann's 
Fundamentum, as will be seen subsequently. In the Ileborgh tablature, 
however, this interpretation fails to lead to a satisfactory result. A 
closer study of the codex shows that the sign in question has here an 
opposite meaning, namely, that of a long note. 2 

In his monograph on the Ileborgh tablature this writer has called 
attention to the strikingly free, rhapsodic character of the preambles, 
suggesting that it was this rambling style to which the words 'secundum 
modernum modum' referred. A similar lack of definiteness is to be found 
in the various notational signs, none of which seems to have an accurate 
and invariable meaning. The double-stemmed note, for example, may 
have the character of a /o?iga, a brevis or a semibrevis, according to the 
context. Likewise, the notes of familiar form can hardly be identified 
with any definite quantity of duration. Under these circumstances it 
appears that no accurate transcription into modern notation is possible. 
The version given below will, at least, afford an insight into the notational 
problems of this specimen. 

The letters written underneath the staff present another peculiar 

1 Cf. GdM 1, pp. 298, 306, 327, 352, 354; HdN 1, 313. See p. 405 of the present book. 

2 See W. Apel, 'Die Tabulatur des Adam Ileborgh' {ZfMlV xvi), p. 193. 



German Keyboard Tablatures 



43 



difficulty. If one tries to play them together with the corresponding 
tones of the upper voice, he will easily see that the resulting two-part 
composition does not make sense. Especially strange is the fact that 
the last note of the lower voice should be g — which fits very poorly with 
the C-tonality of the whole piece. The solution of the puzzle lies in 
the fact that two successive letters always are to be played simultane- 
ously in pairs, as if they were arranged vertically, instead of horizontally. 

Thus, the single row of letters actually represents two voices: 



This curious manner of writing loses its apparent oddity and becomes 
logical and plausible if perceived as an expression of a special technique, 
i.e., of the double pedal. The letters, then, indicate tones to be played 
on the pedal 1 in such a way that, with each pair, the first one is to be 
played with the left foot and the second with the right foot. A tran- 
scription of this preamble follows: 2 




jjJjjJ^jJiJJ^JJiJJJi'^ffr/rTTrrr^ ^ 



Our facsimile shows two other preambles, each written in two parts on 
a single staff, without letters. From the historical point of view, this 
manner of writing is interesting as the earliest indication of that prin- 
ciple which is utilized in the keyboard-score, that is, the writing of 
several parts on one staff. The reason for the use of this notation 

1 Cf. the inscription at the bottom of Facsimile 14: Preambulum bonum pedale she manuale. 
This is the earliest known indication of pedal in musical sources. Regarding the use of pedal in the 
Buxheimer Orgelbuch see A. Schering, Studien zur Geschkhte der Friihrenaissance, Leipzig, 1914, p. 
144 ff. 

2 See the article in M^xxiii, p. 213, from which the above illustration has been reproduced by 
permission of the publishers. 

Similar notational features occur in the Wilkin-tablature (1432), a page of which is reproduced 
in SchT, p. 32/33. The pairs of letters to be found in the measures of the first staff denote simul- 
taneous tones, as in Ileborgh. The double-stemmed note also has the same meaning as in the 
Ileborgh tablature, that is, of a fermata. The various shapes used for these held tones are worth 
noticing. At the bottom of p. 32, a two-voice Kyrie is notated in letters exclusively. Its primitive 
style reminds one of the organum of the tenth century. 



44 The Notation of Soloist Music 

instead of that employed in the first preamble, is probably to be found 
in the word manualiter which excludes pedal performance. 

A peculiarity of this MS is the indication, in the letter notation, of 
the tone G-sharp, not as an altered (raised) G, but as an altered (lowered) 
A, e.g., (p. 7): 



D A E A£ D A = 



It will be remembered that just the reverse practice is found in the 
Buxheimer Orgelbuch and in the later sources, in which flat tones (E- 
flat) are written as sharps (D-sharp). 

The last document of German organ tablature to be considered here 
is the Fundamentum organisandi Magisiri Conradi Paumanni Ceci de 
Nuerenberga Anno 1452 (Foundations of Composition by the Blind 
Master Conrad Paumann from Nuremberg), which is preserved jointly 
with the Lochamer Liederbuch. The student who has read the explana- 
tions concerning the slightly later Buxheimer Orgelbuch will be familiar 
with the general notational principles of the Fundamentum} The 
following remarks deal with the peculiarities of this manuscript. 

1. Chromatic alteration is indicated by a downward stem which 
usually carries a small diagonal dash. The following three forms are 
used indiscriminately: •••, with the second being the most frequent 
one. 

2. The chromatic sign, in any of its three shapes, signifies either 
sharping or flatting, depending upon the tone with which it is asso- 
ciated. See the explanations on the 'chromatic dot' in the early Italian 
and French keyboard scores (pp. 4, 6). 2 

3. The note form J , known to us from the Ileborgh tablature, 

occurs frequently in the Fundamentum^ though with a different meaning. 
It nearly always follows a M, together with which it expresses a dotted 

1 The Buxheimer Orgelbuch also contains a Fundamentum organisandi C.P.C. (Conradi Paumanni 
Caeci) which is a more complete version of that in the MS from 1452. The first page of this Funda- 
mentum is shown in SchT, p. 97. 

2 J. Wolf's remarks about the chromatic alterations in the Fundamentum (HdN u, 15) are some- 
what obscure, particularly the statement: 'Merkwiirdigerweise gewinnt er den Ton b ebenfalls ais 
Kreuzton von der Stufe h aus.' The inherent contradiction of this remark results from Wolf's 
assumption previously made that all the altered tones of the top voice are sharps ('er sieht in der 
Oberstimme alle alterierten Tone als Kreuztone an'). The incorrectness of this statement becomes 
especially evident from a study of the facsimile-page reproduced in Wolf's book (p. 14, Des Klaffers 
neyden). The third measure shows the chromatic stem used in connection with the tone a; doubt- 
less, what is here meant is an a-flat, not an a-sharp. The false relation between this a-flat and the 
a-natural of the lower voice is a typical and frequent stylistic feature of this period and of 16th cen- 
tury music. 



German Keyboard Tablatures 



45 



Facsimile 15 







?^o. 








SI 4 



v» 




3*^. 



iJ 



-1 Ril; V* *) ,F 






\ 







H ^^o 



N 



So-. 



46 The Notation of Soloist Music 

rhythm: iX = i-i = J.J . Occasionally, (for instance, on p. 79, st. 5, meas. 

2 of the facsimile edition) it follows upon a S: ♦ J*l = $y«3eJJ . 

It should be noticed that this interpretation, though commonly ac- 
cepted, 1 is not entirely satisfactory. The most obvious objection is 
that the same dotted rhythm is frequently expressed in the ordinary 
manner, by a dotted M followed by a Sm. In fact, both manners of 
writing repeatedly occur in close proximity (cf. Facsimile 15, last two 
meas. of syst. 3 and second meas. of syst. 4). Moreover, the theory of 
a note exercising a 'dotting' influence upon the preceding note is some- 
what odd and cannot be accepted without question. However, an 
explanation is offered by an analogous feature of contemporary mensural 
notation, that is, the so-called minor color which consists of a blackened 
S followed by a blackened M: ♦ 1 . As is explained on p. 128, the dotted 
rhythm, A-l-J.J, which this combination represents, is a modification of 
what originally was a triplet rhythm: ♦ !- <^J . A similar explanation 
could be applied to the above notational signs of the Fundamentum. In 
fact, it would be possible to assume that these signs here still retain 
their supposedly original triplet meaning, an interpretation which would 
obviate the first of our two objections, as they would then express a 
rhythm different from that indicated by the dotted M. We submit 
this theory as a possible explanation of this notational peculiarity, and 
illustrate it by the following transcription of the above-mentioned 
measures: 




* 

4. In the last pages of the Fundamentum proper (p. 81, 86, 87; the 
pages 82-85 and 88-92 are insertions of a later hand) the forms J 
and t occur repeatedly, probably with the meaning of an ornament 
(mordent). 2 

x See the explanations and transcriptions in JfMWu and in HdNn, 13. 

2 The ornamentations in the Fundamentum are explained by J. Wolf as follows {HdN II, 16): 

'Nur als Verzierungen sind die Formen i und 4 zu deuten. Vielleicht verbirgt sich hinter ihnen 

dzr flos harmonicus oder der Mordent. Jedenfalls verbietet sich angesichts der folgenden Stellen 
die Auffassung als alterierter Ton.' As far as the first form is concerned, these remarks are obscure 
since, on p. 15 of HdN, its meaning as a sign of chromatic alteration is clearly set forth. As regards 
Wolf's example in support (p. 17, first example), a study of the original (p. 75, last measure) shows 
that the dash is drawn through the stem horizontally, not diagonally. It serves merely to strike 
out the downward stem, i.e., to cancel an error of writing. 



Spanish Keyboard Tablatures 47 

5. As to the letters, the main octave ends with b (i.e., B-flat) and 
the one-line octave begins with h (i.e., B-natural). The horizontal dash 
indicating the higher octave appears frequently in the form of a scroll 
reminiscent of the modern sign for the mordent. The metrical values 
of the letters are indicated by small red notes wherever deemed advisable 
for clarity's sake. 

Facsimile 15 shows a two-part composition Ellend du hast (Misery, 
thou hast), a section of which, beginning with measure 6 of the third 
brace, is transcribed in the appendix, No. 8. 

The piece contains various clerical errors, particularly in the upper part, some of 
which are obvious whereas others require conjecture. In measure four of the fourth 
brace we suggest changing the second note to an M y and the last note to an S, half of 
which would go to the following measure. No editorial accidentals are necessary. 
Particularly interesting is the cadential ornamentation in the last measure of the first 
brace of p. 77, with its wavering between F-sharp and F-natural. 1 

In conclusion we wish to call attention to an interesting notational 
hybrid showing mixed features of German and of French origin, namely, 
the MS Munich, Staatsbibliothek, Mus. Ms. 2987. , 2 

B. Spanish Keyboard Tablatures 

The scarcity of documents on Spanish keyboard music of the 
sixteenth century 3 makes it difficult to investigate the early history 
of notation in that country. It is not unlikely that Spanish composers 
of organ music prior to 1550 employed a notation similar to that of the 
Italian keyboard score. At any rate, shortly after 1550 various attempts 
were made to introduce a national notation based entirely on figures. 
The Spanish theorist Bermudo, in his Declaration de instrumentos musi- 
cales (Ossuna, 1555), deals at length with this question. 4 He advocates 
a new system of keyboard notation, according to which the white and 
the black keys from C to a" are numbered by figures from 1 to 42. His 
lowest octave is a short octave, containing only eight tones instead of 
twelve, in the following arrangement: 

D E Bb (black keys) 

C F G A B (white keys) 

1 See the explanations on the 'Schwankungsmordent' in Accidentien und Tonalitdt, p. 23. 

8 See W. Apel, 'Du Nouveau sur la musique Francaise pour orgue au xvie siecle' {La Revue 
Musicale xvin, 97). 

s For a survey of sixteenth century Spanish organ and lute music see W. Apel, 'Early Spanish 
Keyboard and Lute Music' (MQ xx). 

4 Cf. O. Kinkeldey, Orgel und Klavier im 16. Jahrhundert, 191 2, p. 20. 



48 The Notation of Soloist Music 

His figures then represent these tones: 



2 3 4 
D E F 



5 6 7 
G A Bb 



11 12 13 14 15 16 17 
d eb e f f# g g# 



B 



9 
c 

30 
a' 



10 



42 



In applying this material to actual compositions, Bermudo uses a 
starT which, in spite of its apparent similarity, has nothing in common 
with the staves either of the piano score or of mensural notation. Its 
lines do not indicate pitch, but represent the separate voices of the com- 
position, and, accordingly, may vary in number from two to four, five 
and even six. The figures written on a given line indicate the tones of 
the corresponding voice. Here follows the beginning of Bermudo's 
example: 




«- 



kAuh 



2-f~H~ 



-3*~ 



B-&toHfi 25-21 



IS- 



B-H~±6 



H- 



•H444 



llaen 



■tS— -Mr 






(57— 5^ 

23 



?5-/-|J/-J5 
B*-2*H»3o 



T37-5-W 
2^-2^-te 



20 — HnB-aj-H 

riattgo rs wa 



Bermudo also mentions another, more practical method of notation 
by figures, i.e., the employment of figures for the white keys only, the 
black keys being indicated by sharps and flats. Here, the number of 
figures employed undergoes a substantial reduction, thus making the 
system considerably simpler. Indeed, this notation has been used re- 
peatedly in musical practice. Joh. Wolf {HdN 11, 266) mentions a 
manuscript tablature in the possession of O. Chilesotti, written in this 
notation. Another example, of greater importance, is represented by 
an Italian publication of 1576, the Inlavolatura de Cimbalo by Antonio 
Valente, who is notable as the earliest known representative of the 
Neapolitan school of cembalists, later members of which are Giovanni 
Maria Trabaci and Ascanio Mayone. 



Spanish Keyboard Tablatures 



49 



Facsimile 16 shows a page of this book, 
the white keys, as follows: 

1234567 



The figures 1 to 23 represent 



CFG 



B, 



short octave 
3 14 15 16 



d' 



P 



20 
c" 



21 
d" 



22 
e" 



A cross (sharp) above the figure denotes the neighbouring black key: 



xxxxxxxx 
3 4 6 7 9 10 11 13 

E Bb, c# eb f# g# bb c# 



etc. 



short octave 
The parts for the right and left hand are separated by a long horizontal 
line. Above the part for the right hand, metrical signs are given accord- 
ing to a system derived from the Spanish and Italian lute tablatures. 
The principle of this method is, first, not to indicate different time- 
values of simultaneous tones, but only the shortest one and, second, to 
indicate these shortest values only for the first note of a series of equal 
values, with the understanding that the same metrical sign applies to 
the following notes until it is cancelled by a different one. This ingeni- 
ous method, which actually satisfies the requirements of polyphonic 
music to a remarkable degree, may be illustrated by the following 
example showing the gradual reduction in the metrical signs: 

A. Time value indi- B. Time values indi- C. Time values indi- 
cated in both voices cated in a single line cated in a single line 
with each tone: with each tone: with each first tone: 




The metrical signs used by Valente are those known to us from 
the tablature of Schmid. The plain vertical stroke is explained, in the 
preface, as the balluta over semibreve (beat or semibrevis; see p. 23)- 
In addition to these metrical signs there are, occasionally, special in- 
dications given with single notes the duration of which would not be 
clear without them. These are: ;=i£M : = 2M : = 3M 
? = 4 M (placed behind the figure). The letter t, placed above a 
figure, indicates a trill or mordent. The first brace is transcribed in the * 
appendix, No. 9. 

There is a third species of Spanish keyboard tablature, which, because 
of a further reduction in the number of figures employed, meets the 



5<d The Notation of Soloist Music 

needs of practical music still better, and merits attention for its sim- 
plicity and clarity. In this notation, the white keys of one octave, i.e., 
from f to e', are designated by the figures i to 7, and the lower and 
higher octaves are distinguished by small dashes or dots attached to the 
same figures, as is shown in the following chart: 



$H312,3 4j5&7 12 34 5 67 V 2' 3' 4' 5' 6' V V 2' 3> 

As in the first species of Spanish tablature described by Bermudo, 
each voice is represented by a horizontal line on which the figures are 
written. The chromatic alterations are indicated by sharps and flats, 
and rhythmical signs are added wherever deemed necessary. There are 
three Spanish publications extant which are notated in this manner, 
namely: 

Venegas de Henestrosa, Libro de cifra nueva para tecla harpa y vihuela (Alcala, 
1557)- 

(new book of ciphers for keyboard instruments, harp, and lute) 
Antonio de Cabezon, Qbras de musica para tecla harpa y vihuela . . . reco- 
piladas y puestas en cifra por Hernando de Cabezon su hijo (Madrid, 1578) 
(musical works . . . compiled and notated in ciphers by Hernando 
de Cabezon, his son) 
Francisco Correa de Araujo, Libro de tientos y discursos de musica pratica 
(Alcala, 1626) 
(book of tientos and explanations of practical music). 

Of these books, only the second has been available for examination. 1 
From its subtitle puestas in cifras . . . one may conclude that the compo- 
sitions of this book were written first in another notation, but transcribed 

* by Cabezon's son into 'cifras,' i.e., notation with figures. 2 

To supplement details already given on this notation we might men- 
tion that a fc| (b durum, i.e., B-natural) or B {b molle, i.e., B-flat) printed 
at the beginning of each composition indicates whether the scale to be 
used is the Lydian or the F major scale, i.e., whether the tone repre- 
sented by the figure 4 is a B-natural or a B-flat. The accidentals X 
(sharp) and b (flat) are printed, not before the affected notes, but 
either below or following them. The metrical signs are added sparingly 
according to the system employed in Valente's book. There are two 

1 New edition of the works of Cabezon in: F. Pedrell, Hispaniae schola musica sacra, Barcelona, 

* 1894-98, vols. Ill, IV, VII, VIII. 

2 The Obras are a posthumous edition; Antonio de Cabezon died in 1566. 



Spanish Keyboard Tablatures 51 

Facsimile 16 



r f 


r 


r 




r r 




f 1 


!>. 17 
17; 15 I*** 


•4 


it 

I* 


& 


* 

17 !» 171*15 |< 




1, 13 #11W? 


t 


7 «■ 

* 4 

4 


7 8 p 11 u ij; 8 
J. * Pi 


7*7: 


13k 13 It I31213lfc 


r r 








r 




r 




■ r i< 


X x 

17 18 13 18 18 


X t 
*o 18 18 17 ltf If 18 


t 
17 


t X 
1(5 Tf 14 IJ 14 IJ 


m. ■; 


»3 




14 

X 

II 
10 


11 


14 13 
X II 

II 


X j>: 11 10 
II| 8; 
IO 


rr 


r 


r 


r 


r 


r 


r r ' 


1615 14 


»4 

St 
1 1 


14 
11 


14: X t t t 

II II IJ 14 13 


t 

X 
II 


11 10 11 tt 



131 p 10: X*i 3: i« 7» » 8 9 7 10 11: 7: ion p 10 10: X p 8 p 7 p: 1? 
7 * 8 8 a 8 7* a? 

4*4 ■«: +' 3' 



r 




r 


r 


r 


r 


r 


f 


r 






r 


r 


■ 


t>. " 




















X 






X 








t 


* 






t 






«3 X 14 


18 


j6 


18 


10 s 


1 10 


11 10 


p; 1 1:3, 


16 


it iop8 f 


14 






n 14 11 11 


14 


»4-- 


17 


4 »7 


8 < 


; 9: u 


X 7 6T- 4 


« 


6 


7 




a p 




8 p 10:7s 


9 a 


11 


10 


At 






7 X X 


4 


4 


X 




4-- 




7 3 




P 


7 








*•• 4 
3= 




X 


*•• 

3-' 








X 

4 




7 


i 




r 




r 










r 






r 


r 




l>. 


18 




»4 


X 


X Xi 


















10- 


t 


t t » »i 


18 


ai i8j 


x x 








t' x 


18 








14. 17 1* j 


5 » 4 ij 11 '18 


17: 


20 17: i 4 


11 14 14! 


is 




16 18 


16 


16 






7 


11 


jt 10: 71 it 


10 


X 10 


IOJ Ij 


11 




10 


13 14. X 1 


J »4 


>4 


>3 


M 


4 


9 


U X X 


7 


7 7 


X • 


P 




8 


11. II. 


11 


X 






X 


7 


P 7 9 


i 


« $ 


7 


7 






9. 10. 


7 


11; 






a> 




X 

4 




1 














r 








r 


f 


r 


h 














I 8 



t x X 11 so) sot 301 20: 

17 1 8 18 18 18 10 18 18 17; 19* *6 »5 14 »f «»" '7 18 17 

M 14 *I Ifc X Xj Itf If 14 I) 14 ! *1 "X M u ij: 9 I? 1 

Mi »l »* y- 1* 11 11 p. 8 8 

11 loe so 



Antonio Valente, Intavolatura de cimbalo. Naples, 1576 
Page 4 



5- 



The Notation of Soloist Music 



other signs which frequently occur in this tablature, a comma: , and a 
diagonal dash: /. The former indicates tying of the preceding note, 
the latter signifies a rest. 

Facsimile 17 serves as an illustration. The page contains two 
short pieces, both in four parts and with a B-flat in the 'signature.' In 
measures 7 and 8 of the first piece, the figure 3 above the staff indicates 
triplets; apparently, the eleven notes of the measure fall into three 
groups of triplets and two plain eighth-notes. The second piece is in 
ternary rhythm, with three semibreves to the measure, as is indicated 
also by the time-signature Q3 . In the second measure of the last 
staff, there is a change to even meter, as is indicated by the semicircle. 
Following is a transcription of the last five measures of the page: 




Actually the sign (£3 has a more definite meaning than merely to indi- 
cate triple meter. It is a proportional sign which signifies threefold 
diminution (see under Proportions, p. 157). In other words, in the 
section thus denoted, three notes (three S) consume the same amount 
of time as one note (one S) in the section without proportion, marked 
by the sign C {tempus imperfection, see p. 96). It appears that in the 
piece under consideration (as well as in many others presenting this 
problem) a measure of the section in triple meter has the same duration 
as one of the section in duple meter. In view of this fact a transcription 
such as given above is misleading, since here the J-measures seem to be 
three times as long as they actually are. Below are two renditions 
which correctly indicate the temporal relationship between the two 
meters (see also p. io^-f)- 



Spanish Keyboard Tablatures 
Facsimile 17 



53 



DE JNTOWIO DE QATtECom 



4 



B 








iHW i-i r l - r - rsiUI 



m 



iff 



jji 



43B 



Jo 



* L 7 6SUS- 



Jc/o J 



+ 



'H JiUi '-HHH^H- 



c/o c/ 



"4 1 * 




** 



r-7-f- 



■H-* 



J 

.£ 



f 7*4 7 



-4^-*-,^. 



J. JJ 



-7-rf- 



■H-t-f 



■* 1 J 4 s - 



-s— * 



-4-i-M— * 



3 4 t 6 1- 



1 4— $- 



3 — H 






-J—! 



Antonio de Cabezon, Obras de musica. Madrid, 1578 
Page 37 



IV. LUTE TABLATURES 

LUTE TABLATURES play a unique role in the field of notation, 
because they are based on principles fundamentally different from 
those of all other varieties of notation. If we conceive notation as a 
link connecting the writer of a composition with its performer, i.e., as 
an expedient showing the player or singer the tones which the com- 
poser wants him to produce, then we must realize that, generally speak- 
ing, there is a direct and an indirect way to achieve this goal. In a 
notation representing the latter method, the player is referred to his 
instrument through the medium of numerous elements of a distinctly 
intellectual character, such as pitch, intervals, tonality, accidentals, 
scales and many other such points. In a notation representing the direct 
method, however, his fingers are referred immediately to the technical 
devices of his instrument, the keys, frets, strings, holes, etc. In German 
terminology, these two species are distinguished as 'Tonschrift' and 
'Griffschrift,' terms which may be conveniently translated 'pitch nota- 
tion' and 'finger notation.' 1 

Although the method of 'pitch notation' is much longer and more 
complicated, it proves in the end to be by far the more successful one; 
in fact, nearly all kinds of musical notation belong to this indirect type. 
There are, however, several notational systems of the opposite type, 
springing from the very natural desire to avoid burdening the player 
with intellectual technicalities and to cut short the road leading to 
practical performance. It is this desire which again and again leads to 
inventions in the field of piano-teaching, and to popular advertise- 
ments such as 'Piano playing learned in ten easy lessons.' Precautions 
about such short cuts, as far as the piano and other highly developed 
instruments are concerned, are, we hope, unnecessary. But in dealing 
with instruments of simpler type and of a more popular character the 
situation is different. Here, a pure finger notation is occasionally useful 
and desirable, as for instance with the zither and ukulele. 

In the history of notation, the lute is probably the earliest instrument 
for which a finger notation was invented and developed. Because of 

1 In Grove's Dictionary, article 'Notation,' the above two types are characterized as 'symbolical' 
and 'practical,' and as being directed to the 'conceptive' and 'executive* faculty. 

54 



Lute Tablatures $$ 

the tremendous vogue which lute playing enjoyed in the sixteenth and 
early seventeenth centuries and the vast literature of lute music created 
during the period, lute tablature is certainly the most important nota- 
tion of this kind. 1 We may well assume that the striking popularity of 
the lute was greatly favoured by the invention of a notation which 
exempted the player from studying the theoretical foundations of music, 
and furnished him with the shortest guide to the music itself. 

Without considering in detail the history of the instrument (for which 
the reader is referred to HdN n, 35 and various monographs 2 ), suffice 
it to say that the lute was of oriental origin, and that in its earliest 
preserved description by Al Farabi, the great Arabian writer of the 
tenth century, it is said to have had four strings tuned in fourths. As 
early as the twelfth century, the lute had five strings or, more accurately, 
nine strings in five courses, the highest string being single, while the 
eight lower strings were arranged in four pairs of equal pitch. 3 

There is no document of music extant for the four or five-stringed 
lute. The earliest lute tablatures known are designed for a lute with 
six strings (the five lower ones doubled in unison or octave), an instru- 
ment typical of the sixteenth century. Certain features of the German 
lute tablature (cf. p. 74 ff), however, show clearly that this notation was 
originally invented for the five-stringed lute, and later on augmented to 
suit a lute with six strings. 

During the sixteenth century, three types of lute tablature were in 
use, and, according to their native countries, these are called: Italian, 
French, and German lute tablatures. The Italian type was employed 
also by the Spanish lutenists. Of all the varieties, only the French 
survived in the seventeenth and eighteenth centuries. 

The basic and common principle of all these tablatures is derived from 
the fact that there are six strings along the fingerboard of a lute, with 
a number of frets (nine or more) crossing it, each indicating a chromatic 

1 Similar notations were introduced, during the seventeenth century, for other lute-like instruments 
(guitarre, chitarrone, mandora, angelica, Hamburger Citrinchen, etc.). The notations for these 
instruments and others, such as viol, violine, flute, have been studied by J. Wolf in HdN II, 115-248. 
Since the literature contained in these tablatures is of a rather subordinate importance — both his- 
torically and artistically — it has not been deemed necessary to enter here into a study of this field. 
The interested reader is referred to the above publication, in which the subject has been treated 
exhaustively. 

2 0. Koerte, 'Laute und Lautenmusik bis zur Mitte des 16. Jahrhunderts' (Beihefte der IMG III, 
1901); A. Koczirz, Oesterreichische Lautenmusik im 16. Jahrhundert (DTOe xvm, ii, and xxv, ii); 
G. Morphy, Les Luthistes espagnoh du XVIe Steele, Leipzig, 1902; L. de la Laurencie, Les Luthistes, 
Paris, 1928; J. Zuth, Handbuch der Laute und Guitarre, Leipzig, 1926-28; M. Brenet, 'Notes sur 
l'histoire du luth en France' (Rivista Musicale Italiana, v, vi). 

3 In the subsequent explanations, we shall not distinguish between string and course, using the 
former term for either a single string or for two strings tuned in unison or in octave. 



$6 The Notation of Soloist Music 

step. For example, should an open string give the tone of C, the same 
string, if pressed down on the first, second, and third fret, would pro- 
duce a C-sharp, D, and D-sharp respectively, etc. Thus, there are 54 
(or more) intersections available to the player who must know which 
ones to touch in a given moment. This information is exactly what he 
finds in his tablature. It is only with respect to the manner of signify- 
ing these intersections that the tablatures of the various countries differ. 

A. Italian and Spanish Lute Tablatures 

The earliest extant document of this notation are the lute books 
published by Petrucci in the early sixteenth century, namely: Intabula- 
tura de laulo, libro primo-quarto (Venice, 1507, 1508). The earliest 
preserved book of Spanish lute 1 music is: Luis de Milan, El Maestro 
(Valencia, 1535). For a special reason it seems advisable to begin our 
explanations with an example from the Spanish book and to consider 
the notation of the Italian sources later. 

In Facsimile 18 six horizontal lines represent the six strings of the 
lute. These strings are tuned in fourths and thirds, according to the 
scheme: 4, 4, 3, 4, 4. As to the actual pitch of the tuning, there is 
some difference of opinion, not only among modern writers, but among 
lutenists of the sixteenth century as well, some of them giving the pitch 
of the lowest string as A, others as G. In still other sources, the pitch 
is left to the will of the player. Hans Neusiedler, for instance, says 
{Ein newgeordnet kuenstlich Lautenbuch, Niirnberg, 1536): 'zeuch die 
oberste Sait so hoch als du magst' i.e., tune the upper string as high as 
you like. From a study of those examples in which a voice-part in 
staff-notation is added to an accompaniment of the lute in tablature, it 
appears that the customary tuning was in G. 2 This statement does not 
touch, of course, upon the question of whether the G of the sixteenth 
century was the same as the G of the modern concert pitch. Probably 
it was considerably lower. But, to take into consideration this circum- 
stance would lead to a transposition not only of the lute music but of 
all the music of the sixteenth century — a problem which can not concern 

1 The Spanish lute, vihuela, actually is a guitar. However, the tuning as well as the musical 
repertory of this instrument connect it much more closely with the sixteenth century lute than with 
the seventeenth or eighteenth century guitar. See the article 'vihuela' in Grove's Dictionary. 

2 Attaingnant, Tres breve etj 'ami Here introduction, 1529 (seep. 66); Diego Pisador, Libro de musica 
de vihuela, 1552 (cf. HdN 11, 77 and 108; also SchT, 61). In the compositions for voice and lute in 
Schlick's Tabulaturen (cf. p. 26) the tuning is in A (see the facsimiles in HdN n, 42 and in G. Harm's 
new edition, p. 14). 



Spanish Lute Tablatures 
Facsimile 18 



57 



muumaiuunu 



<>0 



>_ Cflapananatc a^> 
1-— ■*Kttfl6oerrce fcrrn 



-o-2-i— o- jf 7f -3F- 



5^Fto-^ 



jZZ 



■e-o- 



J j3 ^O 



W- 



5-* 



-o-* 



0-2- 



— Jicuct cop.fua pvj 
-i-^Jloe f mloe (51a paua 
lapsfladaf tod 00 
06 tunics q thilla* 
rcrsfoloo valgan 
tgojavncomp*0. 






tl 



♦ o ♦ 



* * o ^ 



nmunm " M 



♦ ♦ ♦ ♦ Q 



~* zj r *J 



J - J J - , L J J H F — 3- 232 



J J f J f J 1 J 



^H?- 



■3H8-0-5- 



-o~2-?-+ 



o <* o 



h nniiiniu»^iuiii 



1 -'* 


|iJN.j — .-2-5--f-*~5 — 


-**> — 


J *■ 1 J 




'J' -J" -i 


3 -, i 














- ° , -, * 


1 







inmunu^ « uauui 



■f-f- 



-5-^70 — 2 j 



■*-*■ 



■j-* 



-3-^-0—0-2- 



-D-2-4-0-* 



---0- 



■j-a- 



m i 1 ' 4 ' 111 ? n 

^ O v< 6 <y $ $ $ ^^$^4 

— 5— 2— 1 : 


ioiiii 


iillll 


♦ ♦♦ 


fc= 










— ■ — 3— 245-a-o— 0-2- 

1 * -» 






■J -2 


■J- 


"3 J 




O J ■ 


s 
























6tequc agoiafcfTgueeadotaue quadcrno t»c raufica para canfar v 

ranerqucmlatabUodpicfcmcltbiooetifjccq baUariadcs.€nd qtj» 

ballareps pillancicoap fonadas en caftdlano p en poitugnca:? m ftjm 

Iflfanojaactfraacoloiadases la bo? one fcba&c cantor poaicre pjime^ 

rod villanco.-aflTcomo cfraenla trfbuda:? faWdobtfoctaftcrJegBftwaWclto 

coIo2adaBmiramloqcucrdao€lap(t>uelatocanpaqtjellacanearefa. 



Luys de Milan, 
L/^ro ^ musica de vihuela de mano y intitulado El Maestro. Valencia, 1535 

Folio G VI V 



58 The Notation of Soloist Music 

us here. In the subsequent transcriptions of lute music the G-tuning 
will be consistently used- In other words, the open strings of the lute 
give the tones G, c, f, a, d', and g'. 1 

As mentioned above, each of these strings is represented in our tabla- 
ture by a horizontal line, with the lowest line standing for the lowest 
string. 2 On each line, figures from o to 9 appear which indicate the 
frets, with o signifying the open string, 1 the first fret etc. According 
to the tuning of the string, the figure o on the lowest line reads G, and 
the same figure on the fourth line means a. Each subsequent figure 
stands for a tone which is as many chromatic steps higher as the figure 
indicates. Thus, figure 3 on the second line means a note which is 
three half-tones higher than C, that is, D-sharp or E-flat. 

In the light of these explanations, to transcribe a composition from 
such a tablature into modern notation will offer scarcely any problems, 
although the perpetual counting may prove rather fatiguing. The task 
of the transcriber may, however, be facilitated by the employment of 
certain expedients or schemes which show immediately the tone in 
question. Two schemes of this kind are given here: 

A. 

12 3 4 5 6 7 8 

I g gt a b\> b 4 <* & 

-/ — ft *"ff "et a W Z 



/// "a tfc b""\ — c$ d eV- 



IV — / ft g """gf a" bl b""\ — c#- 

V — 4 d e\> f ft — ""g 'M' 

VI — IcPIl'gf^ZlAl^Ji i; j fl — c 4 d ek- 



This drawing represents the fingerboard of the lute, with the neck 
turned to the left side. At each intersection, the corresponding tone is 
indicated in letters. For greater simplicity, the various octaves have 
not been identified in the case of each letter, but are merely indicated 
by three dotted lines marking off the regions of the two- and one-line 
octaves, the middle octave, and the great octave. The Roman numerals 
indicate the strings and the Arabic figures signify the frets. 

1 Occasionally, the A-tuning deserves preference, in order to avoid unusual keys; see p. 77. 
1 It is this arrangement of the lines, as will be seen later, which distinguishes Milan's notation 
from that of other Spanish and Italian lute books (cf. p. 61). 



Spanish Lute Tablatures 



59 



B. 




/ 
// 
in 

IV 
V 
VI 



-3—4- 



-8— 9- 



■7 — 8 9- 



-8 9- 




This scheme proves especially convenient, since it refers the tran- 
scriber immediately from the signs of the tablature to the notes of modern 
staff notation. 

Diligent practice in transcribing will develop in the student numerous 
time-saving devices. As a rule it is advisable not to proceed by tran- 
scribing complete measures, but to follow each single line of the tabla- 
ture for the whole piece or a section of it, i.e., transcribing first all the 
figures on one line, and then proceeding to those of another line. By 
this method one avoids the confusion caused by continually darting 
from one line to another. The chart on page 6o illustrates the gradual 
completion in the transcription of the first staff of Facsimile 18, according 
to the method outlined. 

As with all the lute tablatures, the notation here provides no possibility 
of indicating different time-values or different rhythms occurring simul- 
taneously in various parts. Only the smallest of simultaneous values is 
indicated, as in the Spanish keyboard tablatures (Valente, Cabezon; 
see pp. 49, 50). However, although in these systems the duration of 
each individual note in the various parts becomes perfectly clear from 
the polyphonic context, the situation is different in the lute tablatures. 
Here, the notation as such contains no reference to polyphonic texture, 
since the lines of the staff do not represent voices — as they do in the 
Spanish keyboard tablatures — but strings. Moreover, the true lute 
style is not strictly polyphonic, because of the limitations of lute tech- 



60 The Notation of Soloist Music 




nique; rather is it a style which, although frequently including polyph- 
onic elements, treats them freely, and combines them with other 
manners of writing, such as the homophonic, the figured, and the 'frei- 
stimmig.' Therefore, the question arises as to whether a transcription 
should faithfully retain the time-values of the tablature, or whether it 
should embody an interpretation of the original as a free polyphonic 
fabric. Both possible methods may be illustrated by the following 
example: 



Facsimile 18, second staff, measures $-6. 
Strict transcription: 

♦ =J 



Polyphonic interpretation: 
« = J 




J. W. Wasielewski, one of the first to investigate the lute music of 
the Renaissance, has followed the strict method, in his Geschichte der 
Instrumentalmusik im 16. Jahrhundert, (Bonn, 1878), whereas O. Korte, 



Italian Lute Tablatures 61 

in his Laute und Lautenmusik bis zur Mitte des 16. Jahrhunderts (Beiheft j 
der Internationalen Musikgesellschaft, Leipzig, 1901), has strongly advo- 
cated the polyphonic interpretation. His method was adopted by prac- 
tically all the editors of lute music, 1 until L. Schrade, in his reprint of 
Milan's El Maestro {Publikationen Aelterer Musik 11, Leipzig, 1927) once 
more urged strict adherence to the original signs, by declaring the 
polyphonic interpretation to be tantamount to a falsification of the 
original. 2 

An objective weighing of the arguments for and against both methods 
leads to the conclusion that neither can be exclusively preferred. Each 
has its advantages and its disadvantages. The literal transcription 
may be recommended especially for the early pieces in free style, such 
as the preludes (called 'ricercare') of Dalza, Spinaccino, and some of 
the fantasias by Milan. However, in the case of compositions which are 
obviously under contrapuntal influence (such as the numerous intabula- 
tions of vocal pieces) one could hardly go wrong in allowing such influ- 
ence to find expression in the transcription. A transcription in a style 
reminiscent of the free keyboard polyphony of Froberger, Frescobaldi or 
Bach (in his toccatas, preludes etc.) would seem to be preferable in 
these cases. 

We now turn to a Facsimile (no. 19) from the Italian lute books 
mentioned above. The principal difference between this tablature and 
the notation of Milan's book lies in the reversed order of the lines repre- 
senting the lute strings. The lowest line here stands for the highest 
string, and the highest line for the lowest string. At first sight, this 
arrangement appears to be alien and unnatural. As a matter of fact, 
however, it is more in accord with the practical needs of the player than 
is the other. The lutenist holds the fingerboard of his instrument in 
his left hand, and plucks the strings with his right. In doing so, the 
back of the lute is pressed against the player's body, so that the front, 
as well as the plane of the fingerboard and the strings, comes to an 
almost vertical position. This causes the lowest string to lie on top, 
i.e., in the same position in which it appears in the tablature. The 
lutenist playing from such a book consequently connects the signs 
written on the top line directly with the highest string of his instrument 
which, in sound, is the lowest. Thus, still another intellectual detour 
is eliminated, and technique and writing are that much more in agree- 

1 E.g., J. Wolf in Isaac's Weltliche Werke (DTOe xiv, i); A. Koczirz in DTOe xvm, 2. 
1 In a reply to arguments brought forward by O. Gombosi, Schrade has taken a considerably less 
definite stand. Both articles appeared in ZJMfV, xiv, p. 185 and p. 357. 



6i The Notation of Soloist Music 

ment. This order is used in all the Italian and Spanish lute tablatures 
with the single exception of Milan's. 

Barring this reversed order of the strings, the explanations previously 
given hold good. A deviation of minor importance is that of the metrical 
signs. Instead of the complete notes used in Milan's book, we find the 
same flagged stems as in the new German keyboard tablatures (see 
p. 23)- 1° the preface to Petrucci's Intabulatura de laulo, libro secondo, 
they are explained as follows: 1 

Questo sonno li segni: | Tf^ • El primo significa la mesura a che devi 
tegnir: la qual bisogna pigliarla si larga che in qual tempo tu possi dare le 
botte del numero diminuto: per che lo secondo segno vale per la mita del 
primo, el terzo per la mita del secondo, . . . 

These are the (metrical) signs: ITf*^ • The first signifies the measure 
(beat) to be observed, which has to be taken slowly enough so as to allow 
for the beats of the smaller values; because the second sign is the half of the 
first, the third the half of the second, . . . 

Additional signs are the 'signs of proportion' (i.e., proportio tripla, 

see p. 148): f p . The first of these equals one third of an S, the second 

is the half of the first. Furthermore the signs: 11 occur. The second 

equals £ of an S, the first f : 2 I PPFP -I J JTXJUmiH -I Jl -[7T?I 

The figures 10, 11, 12 for the higher frets are replaced by the Roman 
* numerals x, x, x. 

It goes without saying that, for transcriptions from this type of lute 
tablature, the translation scheme (B) of p. 59 must be altered, so that 
the figures shown there on the lines VI, V, IV, etc. will appear on the 
lines I, II, III and so forth. 

Extensive lists of Italian and Spanish lute tablatures are given in 
HdN 11, 66 and 112. Additional examples for study are available in 
SchT, r8, 70, and 62. 3 

1 Ci. HdN 11, S3- 

1 See Korte, Laute und Lautenmusik, p. 101. 

a In the lute-books of Fuenllana, Pisador, and others, red figures are used to indicate a vocal 
part, as against black figures for the lute accompaniment. See the illustrations in HdN n, pp. 109/ 
no and 1 13. Regarding the question whether the red figures were also included in the lute accom- 
paniment, see J. Bal, 'Fuenllana and the Transcription of Spanish Lute Music' {AM xi). 



Italian Lute Tablatures 
Facsimile 19 



63 



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U± 



v; 



!£..<> 



<)<T 




i 

I 
I 
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L. 
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64 The Notation of Soloist Music 

B. French Lute Tablatures 

The earliest known documents of French lute tablature are two books 
published by Attaingnant in 1529: Dixhuit basse dances garnies de Re- 
coupes ei Tordions . . . , le tout reduyt en la labulature du Lutz (Paris, 
1529), and Tres breue et jamiliere introduction pour entendre et appren- 
dre par soy mesme a iouer toutes chansons reduictes en la tabulature du Lutz 
avec la maniere daccorder le diet Lutz . . . (Paris, 1529). 

From its title and contents, the second book appears to be designed 
for the self-instruction of the lute student. It is, indeed, of particular 
interest for us, since it begins with a very detailed explanation of all fea- 
tures of French lute notation. The 'Troys breues rigles pour estre tost 
et facilement introduict en la tabulature du lutz' which open the book 
have been reprinted in full by Wolf, HdN 11, 72. A short abstract will 
suffice for the present purpose. 

1. The fingerboard has eight frets (touches) which are marked by the 
letters: b, c, d, e, f, g, h, i. Occasionally, a ninth fret is marked k. The 
letter a is used for the open string. 

2. The lute has eleven strings arranged in six courses (ordres), the 
lowest three of which are doubled in octaves, the fourth and fifth in 
unison. The highest string, the so-called 'chanterelle,' is a single one. 

3. The strings are tuned as usual. As regards pitch, the indications 
of the book are not definite. We learn that the lowest string may be 
tuned 'en si bas ton que vouldres.' From the pieces for lute and voice 
it appears that the lowest string was a G, whatever its actual pitch may 
have been. 

4. The metrical signs are the usual ones, the plain vertical stroke 
for the 'semibreve,' and those with one to four flags for 'minime, semi- 
minime, crochue, and fredon.' The author says that breves, longae and 
maximae never occur in lute tablature, since the resonance of a string 
does not endure beyond a semibreve. Metrical signs, when written on 
the staff, indicate a rest. 

5. The staff (espasse) consists of five lines (rigles). The tones to 
be produced on the sixth (lowest) string are written underneath the staff. 

From the last statement it is obvious that in French tablatures the 
lines representing the strings are arranged in the same order as in Milan's 
book, i.e., with the highest string on top. The main difference is the 
use of letters (the Introduction uses capital letters, the later sources use 
small letters) instead of figures, and of a staff with five instead of six 
lines. 

The reproduction on page 65 shows a Fortune a bien couru sur mot from 



French Lute Tablatures 



65 



mm mm ^^^^l*I* m mm mm m mm 

■ €CC CM C AC P €AC - AC^A - ■■ — rrr;: 



£-OCH>— D 



AAA A 



-D— IHO 

■ A i CA — h 



©€-»< 



•A-e-D- 



■ AC A A A 



4~€- 



e-A-c- 



f> MP MP MM M MM !> MM. MI> MMMM 



1 



*e- 



**€- 



•A-e 



f^-r 



*HH>- 



-Afh 



-e*«H 



■A*D— t"^t>»€> A«-I>A«-A- 



A€rt 



C C - 



• ACA— " A A 



€-A- 



■fr— €- 



4— €- 



M MM O 



■PC- P C A C P-; 



-M 



the Introduction. The small dashes which sometimes occur between two 
letters merely facilitate orientation. The dots appearing under certain 
notes are fingerings for the right hand, i.e., for the plucking of the strings. 
The dot refers to the index finger, whereas the neighbouring letters with- 
out a dot are to be played with the thumb. If the third or fourth finger 
is desired, two or three dots are used. 

The chief difficulty presented by this piece and, in fact, by a great 
number of those contained in Attaingnanfr's two books, is that of meter, 
or correct barring. As a rule, no bar-lines are given in the original 
source. Our piece shows grouping in blocks which, however, have no 
significance since they merely comprise notes of equal metrical value. 
J. Wolf, in HdN 11, 76, transcribes the composition in triple meter (2, 
reduced, in the following example, to 4) : 



a f(M) = 


J 


















•- I 


m- 


1*" 1*" 




r n — ■ 


-r r 


i % 


ns] 



















It cannot be said that this result is altogether satisfactory. Another 
rhythmic interpretation is suggested by a version of the same piece for 
lute and voice, which exists in the same book and in which the voice- 
part is written in alia breve with bar-lines separating measures of 
four M (see the following reproduction; the complete piece in SchT, 
61): 



66 



The Notation of Soloist Music 



, rhrt 



Routine a bitconru for mop. if 



Att tflHt l flllfll^ 



However, the even meter thus suggested proves even less acceptable 
than Wolf's interpretation, from the point of view of harmony as well as 
of phrasing. Particularly in the second section, the barring is musically 
wrong. 1 

An examination of the whole piece from a musical standpoint reveals 
that the real meter is neither 4 with two up-beats, nor \ with three 
upbeats, but I with three upbeats. Certain typographical errors, indi- 
cated below, obscure this fact: 



UJJ 




The notes above the staff indicate certain variants of the lute version. Errors: (a) dot 
is missing; (b) S instead of M. 

It appears that our piece belongs to the class of 'pavanes' in slow 
triple meter, of which the piece by Milan (Facsimile 18) is another ex- 
ample. A reduction 1 :2 of the above transcription would make the 
similarity of rhythm still more striking: 



Pieces of this type are very frequent in the dance literature of the 
sixteenth century, but their true rhythm is usually obscured in the 
original notation. For instance, in the books of the Spanish lute com- 
posers Narvaez (1538), Mudarra (1546), and Pisador (1552), all the 

1 See also A. de la Laurencie, Chansons au luth, Paris, 1934, p. 39. 



French Lute Tablatures 



67 



pieces are barred, but in measures equalling only one S each. In mod- 
ern terms, this means that the bar-lines mark off single beats, not meas- 
ures. The modern reader, desirous of decreasing the abundance of 
bar-lines, is naturally inclined to combine two such beats into a measure. 
It is only after some puzzling over the queer result of his procedure that 
he discovers that the measure actually includes three beats. The fol- 
lowing example, showing (a) the original and (b) the correct modern 
barring of Luys de Narvaez' Guardame las vacas (from the Libro del 
Delphin de musica, Valladolid, 1538) serves as an illustration: 1 




The practice of using even meter (or, at least, bar-lines suggestive 
thereof) for pieces which, from the musical point of view are indubita- 
bly in ternary rhythm, persisted long into the seventeenth century. 
Numerous examples have been given by Riemann, in his Handbuch der 
Musikgeschichle (cf. 11, ii, 195, 196, 296). A particularly striking exam- 
ple is Frescobaldi's Partite sopra Varia la Romanesca, the original barring 
of which is as follows (see G. Tagliapietra, Anthologie alter und neuer 
Musik, [Milano, 1934], iv, 20): 



4*J 




The small strokes underneath the staff indicate the true rhythm, in \- 
time without upbeat. 

Returning to the lute books of Attaingnant we refer the reader to p. 
68 of the Schrijttajeln, where he will find a Basse danse beure frais, the 
rhythm of which has been the obiect of considerable speculation and 
controversy. 2 We trust that the interpretation in x-meter, given below, 

1 Complete transcription in W. Apel, Musik ausfriiher Zeil II, 14. 

* In his Studien zur Vorgeschichte der Orchestersuite im 15. und 16. Jahrhundert (Berlin, 1925) 
F. Blume has maintained that there were two types of the basse danse, one in duple and one in triple 
meter. This statement has been strongly criticized by C. Sachs in an article 'Der Rhythmus der 
Basse Danse' {AM in, 107), in which he sums up his opinion as follows: 'Die Basse danse ist zu alien 
Zeiten und in alien Landern geradtaktig' (p. no). In order to support his view, Sachs reproduces 



68 



The Notation of Soloist Music 



will speak for itself. It should, however, be borne in mind that in 
dances of this type it is not possible to draw a clear distinction be- 
tween I- and 8-meter. The triple rhythm may take the form of three 
quarter-notes or of three eighth-notes. The rhythm of the last meas- 
ures of the basse dance is obscured by typographical errors. The last 

f as well as the following f are printed too far to the right side. 

The former belongs over the letter c, the latter over % The next two 

signs appear a bit too far to the left side; moreover, the second of these, 

with two flags, must be changed into one with one flag. A correct 

transcription was given by O. Gombosi in AM vn (1934), p. 25. 




The notation just explained is maintained in the later French lute- 
books of the sixteenth century, for instance: 
Adrian Le Roy, Premier livre de tabulaiure de luth (Pans, 1551) 
Guillaume Morleye, Premier^ second et troisieme livres de tabulature de leut 
(Pa ris, 1552-1558) 

the Basse danse Beurefrais in two rhythmic versions, one by Blume in 4-meter, and one by himself 
in |-meter. Unfortunately, the latter is almost as unsatisfactory as the former. The reader is 
advised to compare these two versions with the transcription given above. It would appear, there- 
fore, that Sachs's categorical statement cannot be accepted. 

In this connection, attention may be called to the transcriptions of lute dances contained in H. 
Bruger's publication, Pierre Attaingnant (Wolfenbiittel, 1927). The rhythmic interpretations given 
here are frequently suspect and some of them indubitably wrong. For instance, the two tourdion 
which, in p. 7 and 14, are rendered in 4-meter with upbeat, actually are in 4-meter (without upbeat), 
as a dance bearing the name tourdion (see the article in Grove's Dictionary) may well be expected to 
be. Both dances show, towards the end of the first section, that change from 4 (4) to 2 which is a 
typical feature of the seventeenth century courante and which in mensural notation was expressed 
by coloration (see p. 130 0- On the other hand, the branle gay which Bruger (p. 9) transcribes in 
4-meter with upbeat, evidently is in 4-meter with upbeat, as appears clearly from the fact that an 
initial phrase of nine (one plus eight) quarter-notes is repeated. Only in the second section of this 
dance would Bruger's rendition seem to be correct. 



French Lute Tablatures 69 

Albert de Rippe de Mantoue, Premier . . . {sixiesme) livre de tabulature 

de leut (Paris, 1 554-1 558) 
Valentin Bacfarc, Premier livre de tabelature de luth (Paris, 1564). 

A new feature appears in the Pratum Musicum of Emanuel Hadrianus 
(Antwerp, 1584) in which the Italian staff of six lines is used, an innova- 
tion which asserted itself throughout the ensuing periods of French 
tablature. During the seventeenth century, further development of 
the notational system was necessitated by the increase of the number of 
strings. In addition to the six strings running over the fingerboard, 
so-called bass-courses (Bordun-Saiten) were introduced, which ran 
alongside the others without crossing the fingerboard and the frets. 
These were, of course, unchangeable in pitch, so that a single sign was 
sufficient to signify them. The signs for the bass-courses were written 
underneath the staff" representing the six fingerboard-strings. The most 
common designation was the letter 'a' with an increasing number of 
dashes: a, a, a, a. in the following scheme, the tuning of the main 
strings is indicated as a chord, that of the four bass-courses, as succes- 
sive notes: 



The earliest tablatures utilizing this system of tuning and notation 
are: Leopold Fuhrmann, Testudo Gallo-Germanica (Nurnberg, 161 5); 
Elias Mertel, Horius musicalis novus (Strassburg, 161 5); and Jean- 
Baptiste Besardus, Novus partus (Augsburg, 1617). 

Numerous lute tablatures of the seventeenth century show long diago- 
nal lines drawn underneath or above a group of letters. The meaning 
of these signs is explained in A Brief e and easye instruction to learn the 
tablature . . . englished by J. Alfred Londenor (1568); 

It is also necessarie to give thee to understande, to what purpose the barres 
that be drawen bias, under the letters or passages doe serve for, and for thy 
better understandyng, I have here drawen thee an example at large, and 
very familier, in the whiche thou shalt not finde one example, trimmed or 
measured, that thou shake neede to remove any of thy fingers, from the 
said measure: the knowledge of the said barre is so necessarie, that hauying 
founde out, and exercised the same, thou shake not neede to remove, but 
those fingers whiche thou shalt be forced, whiche we call close or couert 
plaie. 



7° 



The Notation of Soloist Music 





* 










* 




a Ab^alba-k^ 




• |*a AbSa 


a 




bib^i •» b • 




IbAb-B • 


^ c-» • 




v 7 . ^ 






a. • 




^ Ui 




!fv^ 




a* o-b flu 




c 


.1** *B 


b • »*D b CL 1 




a a- 


c a cb c*o • 




*D • *T> 


C A.C*B 


c*» • 


** . . . 




^^ • 


c : 


• 




c ^ 




^ 


c_. 


-^ 




■ ft 



Evidently, these bars indicate sustaining of tones or chords, a technique 
which was called: close or covered play. Approximate transcription: 




(Note that in the above example, as in many tablatures, the letters are 
printed above the line, instead of on the line). 

For an explanation of the signs of ornamentation used in seventeenth 
century lute tablatures, the reader is referred to the detailed studies in 
HdNii, 147-157, in the preface to A. Koczirz, Osterreichische Lautenmusik 
zwischen 1650 und 1720 (DTOe xxv, ii) and, particularly, to Janet 
Dodge's article: 'Ornamentation as Indicated by Signs in Lute Tabla- 
tures' (SIMG ix). 

In the period between 1620 and 1650, the extraordinarily rapid ad- 
vance in lute technique made in France led to much experimentation 
regarding the tuning as well as the indication of the bass-courses. In- 
stead of the signs: a, a, a, a we find the figures 7, 8, 9, 10 (tablature of 
Friderici, formerly library of Dr. W. Wolffheim), or the signs: a, 8, 9, x 
(Michelangelo Galilei, Primo libro d ' intavolatura di liuto, Munich, 1620), 
which are augmented to: a, 8, 9, x, xi, xn, xm (7 bass-courses) in the 
tablature of Dusiacki (Padua, 1620), while still another designation: 
a, a, a, a, 11, 12 is used in the lute book of Virginia Renata von Gehema 
(Berlin, Staatsbibliothek, Mus. Ms. 40264). 

Around 1640, a new system, called nouveau ton was introduced by the 
famous lute composer Denis Gaultier (ca. 1 600-1 672). It quickly super- 



French Lute Tablatures 71 

seded all the others. Here the main strings are tuned A-d-f-a-d'-f : 




[4 5 g] 

(The symbols in brackets indicate later additions and modifications.) 

Facsimile 20 is taken from the famous Hamilton Codex of the Berlin 
Staatsbibliothek in which the compositions of Gaultier are collected 
under the title: La Rhetorique des dieux} The graphological details of 
this manuscript are explained below: 

Letters Rhythmic signs 

a£^ r dj) <P sf 3 J|1 ^^ 

abcdefg J J* J» «h 

The first measures are transcribed in the appendix, No. 10. * 

Gaultier's system remained in use without essential alterations 
throughout the last period of lute music, that is, till the end of the 
eighteenth century. More detailed examination of this field is beyond 
the scope of the present book. Suffice it to say that later lutenists, such 
as Esaias Reusner (1636-1679), Silvius Leopold Weiss (1686-1750) and 
others, made frequent use of the scordatura, i.e., of alterations of the 
normal tuning of'the strings for certain pieces or series of pieces (suites). 
These alterations are indicated at the beginning of the piece in the so- 



called accord. For instance, the following accord: 2 \ indicates 

e — 

a 4 

that the second bass-course (a) is the lower octave of the tone indicated 
by the letter b on the third line, that is, of F#; and that the fifth bass- 
course (4) is the lower octave of the tone indicated by e on the first line, 
that is, of C#. Hence, the tuning of the bass-courses is: G, F#, E, D, 



C#. Similarly, the accord: f b - leads to the tuning G, F, El?, 



l O. Fleischer, 'Denis Gaultier' (Vierteljahrsschrift fiir Musikwissenschaft ii, 1886); A. Tessier, 
La Rhetorique des dieux, Paris, 1932. 

2 Cf. H. Neemann, Lautenmusik des i/./fS. Jahrhunderts, Berlin, 1939, pp. 10, 12, 88. 



-jl The Notation of Soloist Music 

D, C. The reader is advised to study the accords reproduced on the 
table opposite p. 128 in HdN 11, in which the complete tunings of various 
plucked instruments is given. For instance, the following scheme: 



given for the Angelique (Angelica), 



an instrument with 16 strings tuned diatonically, shows that, starting 
with d' as the pitch of the fifth string from below, the pitch of the sixth 
string (represented by the letter a) is the same as that of the third fret 
(letter c) of the fifth string, hence, e'. Similarly, the open fourth string 
is c', because its third fret (letter c) gives the same pitch as the open fifth 
string (letter a), etc. 

Material for further studies in the field of the late French lute tabla- 
ture 1 is contained in the above-mentioned edition of Neemann, which 
includes a reproduction of the original together with the transcription 
into notes. Following are a few brief remarks regarding the examples 
contained in J. Wolf's Schrifttafeln, which may also serve as additional 
exercise: 

Nos. 24, 35, and 73 use the 'old tuning' (vieil ton) G-c-f-a-d'-g'. In 
no. 73, the bass-courses a, a, a are tuned F, E, D. 

Nos. 27, 36, 51, and 76 are in the 'new tuning' (nouveau ton) A-d-f-a- 
d'-P. In no. 27, seven bass-courses, tuned diatonically from G to A, 
are indicated by the signs: a, a, a, a, 4, 5, 6. In no. 51, five bass-courses 
are denoted as follows: a, a, a, I, 11 ( II ). The strongly curved symbol 
of this manuscript (and of no. 36) is the letter d, whereas the angular 
sign is the letter c. The letter c frequently adopts a shape reminiscent 
of the letter r (cf. no. 76). 

The notational system of the French lute tablature was also applied 
to numerous other stringed instruments, such as the mandora (cf. 
SchT y no. 98), the 'Hamburger Cithrinchen,' a small cittern (cf. SchT, no. 
26), the viols (cf. HdN 11, 225 ff.), etc. Whereas Wolf's example for the 
mandora is in the old tuning (for five strings only: A-d-g-b-e'), the 
tuning of the Cithrinchen is: c-e-g-b-e'. 

C. German Lute Tablatures 

During the sixteenth century the German lutenists utilized a notation 
which, according to Agricola (Musica instrumentalis deudsch, Wittenberg, 
1529) was invented by Conrad Paumann (1410-1473). Although this 

1 See the extensive list of French lute tablatures, printed and manuscript, in HdN n, 95 ff. 



French Lute Tablatures 
Facsimile 20 



73 



LADEDICASSE. 



O cw 






s:^: 



Oi a . _ r~ — 



z 



^ ^^CW - 



13ZSZL 



E 



^=jg 









^12 






/ ^ 



I 



a r 



£3=^=^ 



^4*= 



4 * ^ 



4*^ 



^Sf 






n 



r r 



n 



<*t^\ 






r t tfjtf 



^ r~ fa 



# 



-*£- 



< & <f \Y> 



^ 



^1 



j r> 1 tMg ^\ ac^ CL llj2 



U-CL 



(*+> 




tt^± 



W& 



-t*-e- 



Jk — c- 



jr A f & 



-¥*- 



O o*~ 



&- 



tt^t 



^<*al 



M2 



r~ 



*4r 



W<%^ 



& — *a r r , r 



-if-" 



t fi r 



-&- 



o 



/O 



42 (£ 1^ 



^1 <*- 



^* — F- 



r r -p 



■#=- 



«j> g r~ 



O 



<V, 



n 



1 



42 u- 



*&£ 



=45=^: 



^ < * 



^ 



Denis Gaultier, La Rhetorique des dieux 

Berlin, Kupferstichkabinett Ms. 142 (ca. 1650) 

From pages 25', 26 



74 The Notation of Soloist Music 

statement is probably incorrect — an obvious objection being that a blind 
man is not very likely to have invented a notational system — it illustrates 
the ancient and somewhat legendary origin of the German lute notation, 
the principles of which revert to a period antedating considerably the 
first preserved documents (15 12). Indeed, the relatively ancient origin 
of this system is revealed by its many primitive and awkward features 
which form a strong contrast to the rationalized methods of the French 
and Italian tablatures. Most striking among these is the fact that the 
German notation was obviously designed for a lute with only five strings 
(such as was used in the fourteenth and fifteenth centuries), and was 
augmented later to suit an instrument with six strings. 

In contrast to the French, Italian, and Spanish tablatures, in which 
the fingers of the player are easily directed by a clear representation of 
the fingerboard with its strings and frets, the Germans used a notation in 
which each one of the fifty four or more places on the fingerboard was 
marked by a special sign — a method reminiscent of Bermudo's forty 
two figures for the keys of the organ. Unfortunately, the scheme of the 
German symbols for the lute is much more confused than Bermudo's 
plain series of figures. In order to explain the German tablature we 
must begin by considering the lute as lacking the sixth (lowest) string 
{Grossbrummer). The remaining five strings, called Mittelbrummer, 
Kleinbrummer, Mittelsaite, Sangsaite, Quintsaite (or Kleinsaite) are num- 
bered 1, 2, 3, 4, 5, and are indicated by these figures if used as open 
strings. The places on the first fret are marked by the first five letters 
of the alphabet, a, b, c, d, e, running across the fingerboard. The sec- 
ond fret bears the five letters f, g, h, i, k, and the same procedure is con- 
tinued with the following frets. Since the letters of the German alphabet 
were then only twenty-three in number, two new signs had to be added 

for the fifth fret, namely, £ and <? , called 'et' and 'con.' 1 For the 

sixth, seventh, and other frets the alphabet was repeated, either in dou- 
bled letters: aa, bb, etc., or in letters with a horizontal dash: a, B, etc. 

Obviously, this method of placing the letters across the fingerboard, 
following the frets, is less satisfactory than the French method of plac- 
ing them length-wise, following the single strings. In the French sys- 
tem, successive letters of the alphabet indicate neighbouring tones of the 
chromatic scale. In the German system, they indicate tones which are 
a fourth or a third apart, while, on the other hand, successive tones of 
the chromatic scale are denoted by every sixth letter of the alphabet, for 

1 These characters are abbreviations of the Latin syllables et and con; see A. Cappelli, Lexicon 
Abbreviaturarum, Leipzig, 1928, pp. 78, 408. 



German Lute Tablatures 



75 



instance: a, f, 1, etc. The C-major scale c, d, e, f . . . therefore is 
indicated as follows: i, f, q, 2 (or x) . . . 

Although the above scheme of signs for the five upper strings is com- 
mon to all the German lute tablatures, there is considerable variance 
regarding the signs used for the sixth string, the Grossbrummer, which 
was added after the notation for the upper strings had already been 
established. The various notational methods used for this string appear 
in a picture of the 'Lautenkragen' (fingerboard) contained in Hans 
Newsidler's Ein Newgeordnel kunstlich Lautenbuch (Niirnberg, 1536), 
a reproduction of which is given here: 




•t T — . /a a »» Ti «-b — 
« 2 .2 o ~- . . a 2 ■? ,Z 



'" ** « " 2 c r* «3 
w ■=■ • • 5 a ■ ST. 5 § - SL v 



cr « -j. £ 2. " a' = -a 

** «** *»" ** «* r> ~ "* ,' 

^ rr »» <* 3 ■ — S -iSt 



The larger drawing shows the signs for the five upper strings as well as 
Newsidler's own preference for designating the Grossbrummer, namely, 
the letters A, B, C, D, E, F, G, H for the frets, and the sign ^ (at the 
bottom) for the open string. Other systems are indicated on a small 
drawing to which the text on the right side pertains. Following is a 
translation of this text: 



y6 The Notation of Soloist Music 

Here is shown that the first Grossbrummer is designated in three of four dif- 
ferent methods. Three of these are shown underneath the Lautenkragen on 
three lines, and the fourth manner is shown on the Kragen. The three 
lines have been added for the benefit of those who may understand one 
method but not the others. But the method on the Lautenkragen is the 
best and clearest one, and is based on the foundation of music. 

The following drawing is a copy of Newsidler's Lautenkragen in mod- 
ern characters and in horizontal position. To the four methods ex- 
plained by Newsidler yet another method (III) has been added; this 
one is used in Arnold Schlick's Tabulaturen (Mainz, 1512), the earliest 
source of German lute music. 







ft 


i> 









ft 


b 





4— 


—4— 


— i — 


— — 


— i— 


—7- 


—2— 


i — 





t 


3— 


— — 


— h— 


M 


— s — 


— * — 


— c 


hr- 


— n — 


— s 




// 


A 


B 


/// 


■h 


A 


JV 


f 


a 


V 


i 


2 



-B- 

C D E 

F L Q 

f 1 q x aa ff 11 

3 4 5 6 7 8 9 



The Roman numerals added at the left side of this chart refer to the 
following lute books which utilize one or another of the five systems for 
the Grossbrummer: 

I. Hans Newsidler, Ein Newgeordnet kunstlich Lautenbuch (Nurnberg, 
1536) 
Sixt Kargel, Lautenbuch . . . (Strassburg, 1586) 
Melchior Newsidler, Teutsch Lautenbuch (Strassburg, 1574) 
II. Hans Judenkunig, A in schone kunstliche underweisung (Vienna, 1523) 
Hans Jacob Wecker, Lautenbuc h . . . (Basel, 1552) 

III. Arnolt Schlick, Tabulaturen etlicher lobgesang und Udlein (Mayence, 

1512) 

IV. Wolff Heckel, Discant Lauttenbuch, Strassburg, 1552; Tenor Lautten- 

buch (Strassburg, 1556) 
Bernhard Jobin, Das Erste {Das Ander) Buch Newerlessner . . . Lau- 

tenstiuk (Strassburg, 1572, 1573) 
V. Hans Gerle, Ein Newes sehr KiXnstlichs Lautenbuch (Nurnberg, 1552) 
Sebastian Ochsenkuhn, Tabulaturbuch auff die Lautten (Heidelberg, 1558) 

The transcription of pieces written in the German lute tablature is, of 



German Lute Tablatures 



11 



course, very fatiguing and slow work. The following scheme will facili- 
tate the task: 



News idler: 

+ 12 3 4 5 



Judenktmig - : 
A 1 2 3 4 5 



ABC D E F G 



BCD E F G H I 





Facsimile 21 from Judenkunig's book of 1523 serves as a first illustra- 
tion. The transcription presents no difficulties except, possibly, that of 
identifying the Gothic letters of the German alphabet, some of which * 
are written in a rather quaint fashion. The following transliteration of 
the second brace will prove helpful to the reader: 



s s 
D y n r 


s e 9 p 

yocs 


P 

7 
nkl 


7 
z c 
D il 






(7 = et; 


9 = con) 



o c 7 

Dzizco IC07 



The beginning is transcribed in the appendix, No. 11. If instead of the G-tuning the 
tuning in A is used, the tonality of the preamble changes from B-flat to C. It goes 
without saying that the latter key is intended. 



7» 



The Notation of Soloist Music 



Facsimile 11 shows a piece by Newsidler which is remarkable for vari- 
ous reasons. It is called Der Judentantz (The Dance of the Jews) and 
represents one of the earliest examples, if not the earliest, of satire in 
music. As in almost all pieces of this genre, the satirical character is 
expressed by cacophonous dissonances. In fact, our dance is written 
in a strikingly modern idiom of bitonality such as rarely occurs before 
the advent of the twentieth century. At the beginning of the music, 
Newsidler gives the pertinent remark: 



The Jew's dance, 
sound well. 



It must be played very quickly, otherwise it will not 



Preceding this, there is a lengthy explanation dealing with the tuning 
of the lute. As a matter of fact, our piece is the earliest example of the 
so-called scordalura y that is, a deliberate deviation from the normal tun- 
ing. Following is a translation of the passage: 

Here follows the Jew's dance, and whoever wants to play it, must tune the 
lute differently. Now follows the tuning: First, tune the Mittelbrummer and 
the Kleinsaite which is next to the Mittelbrummer, at the pitch of the figure 
four (4), and also the Kleinbrummer. . . . And the Obere (Ebrer) Quintsaite 
must be tuned equal to the t, then the tuning will be right. Many other 
dances may also be played with this tuning. 1 

Since the symbols 4 and t denote the tones d and f'#, the tuning is 
as follows: G d d a d' f#. 

Below is a transcription of the first measure of the dance, and of its last 
measure, immediately before 'Der Hupfauf (jumping dance, after dance 
in triple meter) : 




A complete transcription is contained in W. Apel, Musik aus friiher Zeit, 1, 10. The 
transcription given by A. Koczirz in DTOe xvm is based on a different interpretation of 
Newsidler's remarks, leading to the following scordatura: G d d' d' d' f'#. However, 
Koczirz's interpretation is erroneous. The third string {Kleinbrummer), which is nor- 
mally f, cannot be raised to the pitch of d', but can only be lowered to d. His error 
regarding the fourth string is obviously caused by the words: 'die klein saitten die newen 
dem mitl Brumer stet' which, indeed, give rise to doubt as to which string is meant by 

1 The sentence: 'Muss gleich lautten. . . . als da 4 gleich lautten' has been omitted in the 
translation since it merely duplicates the preceding sentence. 



German Lute Tablatures 
Facsimile 21 



79 



FFFFFFF 



JDMbhtViifitne 



rrrr 

hynt 



PFFFPFF 



FFFFFFFF 

togf2fe » 



rrrr 

voir 



m 

nt e 



ir r 



rrFFFF 

e 



FFFF 

I 2o* 



FFFFIFFFFrr 

2?gp tSppyro 



rrrr 
« ?p 

y?8? 



rrrr 

ittm 



mm 

Z ry 



rr*r 



rrrr 

«P 



p? 

C2 



ey 



irrr 

yp*j> 



rrrr 



?rrr 

nmfy 



rrrr 

i*Si 



FFFFFFFFFF 



FFFFrr 

2 n 
Hnytj 



FFFFrrpFFrr 

c p \1 1 



rFFrr 

2 8im« 



FFFFrr 

c * 



rr rr 

eny£> 



rr 
n 1 



If 



#'»&» 



Hans Judenkunig, ^wi schone kunstliche Underweisung. Vienna, 1523 



8o The Notation of Soloist Music 

the term klein saitte. Koczirz interprets it as denoting the fourth string {Mittelsaite), 
whereas it actually refers to the fifth string (Sangsaite). That the latter interpretation 
is correct appears particularly from the last measure of the dance (see above) in which, 
according to the other version, the letter s would indicate an f# , instead of the c'# of 
our transcription. 

Additional examples for the study of the German lute tablature are 
available in SchT, pp. 9, 45, and 59. 



German Lute Tablatures 81 

Facsimile 11 



fWWMT^i **«* 

$$-014 Unitf^ it £5d>Ua>t 

1 It ' » * I * „ 

ff 6tc**>!0ab«* 3tobot TCang/tmb wee fit fd>l*gttt wa/bct mttf$ bte Emm 
anbarajte&em tttmrolgrtb 5U0/5t«^iSr(iUd)bmWTitl«rit35w$mcr vttbfete 
Kan frtttt«t/bte Hcwcn t>t m rmtl Bntnta: fict/bcr jteffar ffcn/glad) ate b« 4* 
»ttb &m Hcsit25ttimer* HTufj glad? touttat /wte txemul Brnma: wtcttoege* 
tmlt bar mitl 25twroar vfi bie fatten bar Xltxomf vftbtc Oa'tt Banner muflat 
all toe? ait glacfoc ffcm b^bm/vnb bar jteffa: via* ale b« 4 gletd> laatttat/ »fi 
bit gbttr quint: fmttat miifj man bent t glad) $10)01/ fb iff ba $ttg wc&k 
Q Tgttmgg and) vi\ anba: tatg ana) auff ban $ng fcfrlagot* 
fraPlubot Cant* tm |i 1 1 1 rr 
ccnutfjgarfa-be* tEttitFf ffrf 

tywb/ gefd)lagai I C cUvlJ c f»s£ <T"Ta*ff efplTtpif cT7? 
nwbat/fttttflUnt J 4 4 a I4 4 n 

tztutwoU v* \ 3 % I (3 3 I 

% % % % 

II J ! 



mmmnmmmn mm 



f*M fffvfftvtf^ttf / 114*4141 844 Atlffll 

* \* t a 1 :"$}/ 

* 4 * 4 4 3 * U 4 * 4 

1 .|i ./. |, T J, ,|, ,/ 
' LJ - e J L 



Hans Newsidler, £/» w^w kunstlich Lautenbuch. Niirnberg, 1544 



PART II 

THE NOTATION OF ENSEMBLE MUSIC: 
WHITE MENSURAL NOTATION 



WHITE MENSURAL NOTATION 

HAVING TREATED in the preceding part of our book the nota- 
tion of music for a soloist instrument (organ, clavier, lute), we 
turn now to the notation of polyphonic ensemble music. It is under- 
standable that this field is considerably broader and more difficult than 
that which we have hitherto considered. We are presented here with 
a seven-hundred-year-long development embracing the period from 
about 900 to 1600, during which the principles of notation underwent 
such radical changes that a series of different systems arise, each of 
which demands a separate study. 1 The student who has made himself 
familiar with the notation of the works of Okeghem, Isaac and Josquin 
is confronted with entirely different problems when he turns back to the 
sources of the French or Italian Ars Nova, and again with a new situa- 
tion in studying the organa of the Notre Dame School or the motets of 
the thirteenth century. 

During its entire evolution the main, and only real, problem of men- 
sural notation was one of time values and time relationships. Indeed, 
the other fundamental problem of notation, i.e., the indication of pitch, 
had already been solved satisfactorily before polyphonic music began to 
develop. There is only one isolated document of polyphonic music, the 
Winchester Troper of the eleventh century, in which the problem of 
pitch-determination exists, since it is written in cheironomic or staffless 
neumes. In all the later sources, however, the use of the staff, that 
ingenious invention of Guido of Arezzo, eliminates this problem; there- 
fore only the other one — that of time values and rhythm — remains. 

Considering the history of this problem from its beginnings to the late 
sixteenth century, the amount of time, labour and ingenuity spent to 
bring about what seems to us but a few paltry results is incredible. 
Parturiunt monies et nascitur ridiculus mus, one is tempted to exclaim, 
upon discovering that an intellectual struggle of many centuries was 
needed in order to find two devices of such utter simplicity, namely, the 
bar-line and the tie — devices which were unknown in earlier music but 
which, in connection with the principle of binary mensuration, free the 
modern musician from the intricacies of mensural notation and provide 

1 See the survey of notational systems on p. xxv, and the additional classification on p. 199- 

85 



86 White Mensural Notation 

a simple and clear expression of almost every conceivable time value 
and rhythm. 

Such a statement, however, should not lead to a wrong conclusion 
regarding the value and the importance of early notation. Nothing is 
more dangerous and misleading in the study of the arts than to regard 
achievements of the past from the standpoint of technical progress. A 
superficial observer sees only what has been gained in a fight and not 
what has been lost. The true historical mind, however, sees that in the 
history of humanity there is no possibility of perfection, and that there 
is only a very faint hope of approaching it. Instead, there is something 
far more important, namely, constant change and ceaseless renewal. It 
is in this frame of mind that the student should approach the problems of 
early musical notation. In wrestling with its intricacies he will dis- 
cover that notation, far from being merely an intellectual puzzle, is in 
all its various stages the perfect expression of the music it represents. 
Indeed, apart from the fascination of deciphering obscure systems of 
writing, his studies will reward him with an insight into the style and 
structure of early music such as cannot possibly be gained in another 
way. 

As has already been pointed out in the introduction, the development 
of notation proceeds from extremely vague and ambiguous relationships 
to ever clearer and more exact indications. At the same time, it pro- 
gresses gradually from very unfamiliar concepts to those with which we 
are acquainted in our present-day system. For this reason, as in the 
section on soloist music, we shall not in the following study pursue the 
order of the historical development, but begin with that system of nota- 
tion of ensemble music which is closest to our own, in time as well as in 
character — the so-called white mensural notation. 



I. NOTATIONAL SIGNS 

THE WHITE mensural notation 1 embraces the period from the 
middle of the fifteenth to the late sixteenth century. The name 
'white' refers to the use of white notes for the longer values, instead of 
the black forms of the preceding period. This change is, of course, the 
result of purely external considerations. Filling in the heads of the 
notes with black ink involved considerable unnecessary trouble and loss 
of time. It also may have proved more difficult on thin paper than on 
the parchment of the earlier manuscripts. Therefore around 1450, the 
scribes began to leave the notes unfilled. The term 'mensural' comes 
from musica mensurata — a designation used by early theorists to differ- 
entiate the regularly measured polyphonic music (motet, etc.) from 
musica plana, i.e., the unmeasured Gregorian plainsong. 

Notes. The notes used in white mensural notation are: maxima (Mx) y 
longa (L), brevis (B), semibrevis (S), minima (M), semiminima {Sm) y 
fusa (F), and semifusa (Sf). Their shapes and those of the correspond- 
ing rests are as follows: 

Mx L B S M Sm F Sf 

Notes: ^ ^ B i U U) I 



Rests: 



Of the two forms given for the Sm and F the black ones are by far the 
more frequent. Occasionally, both varieties are found in one and the 
same MS, or even in the same composition with no apparent difference 
in meaning (see, e.g., Facsimile 30, contra, third staff). The two-flagged 
.F-rest is very rare. The L- and Mv-rests consist of strokes covering 
two or three spaces depending upon whether the L equals two or three 
B (imperfect or perfect modus, see under Mensuration, p. 99). 

Ligatures. In addition to the single notes, mensural notation employs 
certain symbols which represent combinations of two or more tones and 

1 The earliest modern explanation of white notation, and one which is still very useful today is 
A. Bellermann's Die Mensuralnoten und Taktzeichen des 15. und 16. Jahrhunderts, published first in 
1858 (MuT). J. Wolf deals with this subject in HdN 1, 381-465. 

87 



88 White Mensural Notation 

which are called ligatures. These forms developed from certain neumes 
(i.e., mnemonic signs indicating upward or downward progress of the 
melody without showing the exact pitches or the rhythm), such as were 
in use during the ninth, tenth, and eleventh centuries for the writing 
down of plainsong. In the earliest stages of polyphonic music the liga- 
tures are used abundantly, as a glance at our facsimiles nos. 44-53 
(around 1200) readily shows. In later times they lose more and more of 
their original importance; however, they are still comparatively frequent 
in the sources of the fifteenth century. In the sixteenth century they 
gradually disappear and only a few of the simplest forms survive until 
the middle of the seventeenth century. 

Although we are concerned here with the latest stage in the develop- 
ment of the ligatures, a few words about their history will be helpful in 
clarifying certain peculiarities of their form and meaning. 

The four simplest neumes were: punctum, virga, clivis, and podatus: 
•//"*!/ . The first two each indicate a single tone, the punclum 
normally a shorter one than the virga. Each of the latter two signs 
represents a pair of tones which descend in the c/ivis and ascend in the 
podatus. When (around n 50) the neumes changed to the more definite 
forms of the so-called Roman chorale notation, these four signs took on 

the following shapes: ■ ■ ■ ■ • These forms are still used today 

as neume-like symbols in the liturgical books of the Catholic Church. 
However, about 1200 (School of Notre Dame) the same signs were 
adopted for the writing down of polyphonic music and, in this function, 
acquired definite metrical values. The two signs for single tones 
became brevis (B) and longa (L) respectively, whereas, in each of the two 
group-signs, or ligatures, the first note became a B, the second a L. 
Thus, the third of the above symbols meant two tones in descending 
motion, the first a B, the second an L } and the fourth signified the same 

values in ascending motion, e.g.: fr = ■ J a - a ll • 

In order to express other combinations of B and L, these two basic 
forms were then subjected to certain modifications, for the indication of 
which the terms proprielas and perfectio were evolved. These terms 
refer to what was then viewed as the 'proper' and 'perfect' rhythmic 
sequence, i.e., brevis followed by longa. Therefore, a ligature having 
this evaluation was said to be cum proprietate et cum perjectione^ the 
former term referring specifically to the first note (initialis), the latter 



Ligatures 89 

to the last note (finalis) of the ligature. The other combinations of B 
and L, namely, L L, B B, and L B, were considered as lacking in one or 
both of the two basic requirements, a condition which was expressed by 
replacing the word cum (with) by the word sine (without). Therefore, 
if a ligature is sine proprietate its initial note is not B, but L; and if a 
ligature is sine perjeclione its final note is not L, but B. There result 
the four following combinations: 

cum proprietate et cum perfectione (cum-cum) : B L 

sine proprietate et cum perfectione (sine-cum) : L L 

cum proprietate et sine perfectione (cum-sine) : B B 

sine proprietate et sine perfectione (sine-sine) : L B 

To make these changes in value apparent in the notation the forms 
of the original ligatures were modified in certain ways, as the following 
table shows: 

Designation Value Shape 

desc. asc. 

cum proprietate et cum perfectione B L y (l) 3 ^ ^ (9) 

sine proprietate et cum perfectione L L % (3) ] ] w J^ ao) 

cum proprietate et sine perfectione B B ^ (5) ^ t6) 

sine proprietate et sine perfectione LB S <- 7) J (6 > 

As may be seen from this table the proprietas, i.e., the value of the 
initial note, is determined by the presence or absence of a vertical 
descending stroke at the left. This principle, simple in itself, is compli- 
cated by the fact that in the two original forms cum-cum, the descending 
ligature (1) has a stroke while the ascending one (2) has none. Cor- 
respondingly, in the derivative forms sine proprietate, the descending 
ligature is written without a stroke [(3), (7)] and the ascending ligature 
\yith a stroke, either on the left or, more frequently, on the right side of 
the lower note [(4), (8)]. 

Change in the perjectio — that is, the value of the finalis — from L to B 
is indicated by modifying the shape of the body of the ligature. Two 
kinds of change are employed, dependent upon whether the ligature 
ascends or descends. If it ascends, the second note instead of being 
written vertically above the first as in (2) and (4), is written with the 
head turned to the right, as in (6) and (8). If the ligature descends, 
however, the change of perjectio is indicated by replacing the square 



9 o 



White Mensural Notation 



shape of the body by a diagonal one, the so-called ligatura obliqua, so 
that the two forms sine perfectione, (5) and (7), result. 

Two remarks must be made in regard to the oblique forms. First, 
such a ligature represents only those tones which are indicated by its 
beginning and end, not the intermediate tones as the novice might 
at first think. Therefore: ^jf is c'-g; gj^ E is c'-f. Secondly, the 
oblique form affects only the value of the second note without in any 
way changing the value of the first note, which is determined solely by 
the presence or absence of the stroke. 

The above-mentioned forms of ligatures constitute the basis of the 
teaching of Franco (around 1260) and of the mensural notation of the 
ensuing periods. While, in the succeeding development, the descend- 
ing forms remained unchanged, the ascending forms underwent further 
alterations. The most important change resulted from the awkward- 
ness of writing the ascending ligature cum-cum [see the form (2) of the 
table] because of the close proximity of two notes, particularly if the 
interval was a second. In seeking a more satisfactory . form, scribes 
took their cue from the related form sine perfectione [(6), (8)], and em- 
ployed the same means which, with the first note, were used to indicate 
the opposite value of the initialise namely, the stroke. There resulted 
the forms (9), (10), in place of (2) and (4). 

To these forms must be added another modification of the two basic 
signs which is termed ligatura cum opposita proprietate {c.o.p.). It is 
indicated by an upward stroke on the left side of the initialis. These 
ligatures are the only ones in which smaller values than a B are expressed. 
In them, each of the two notes has the value of a S (see p. 10 ). 

There follows a tabulation of the ligatures as they appear in white 
notation: 1 



Symbol 


Form 




Valu< 




desc. 


asc. 




cum-cum 
sine-cum 
cum-sine 




cP if) 


B L 
LL 
B B 


sine-sine 
c.o.p. 


U 




LB 

S S 



1 The bracketed shapes of the ascending ligatures cum-sine and sine-sine are exceedingly rare, and 
their evaluation has been the subject of a heated controversy among fifteenth century theorists. 
The above interpretation is supported by Tinctoris (CS iv, 43) and by Adam von Fulda (GS in, 
365), but is vigorously denounced by Tinctoris' adversary Gafurius {Practica Musicae, 1496, lib. n, 



Rules for Ligatures 91 

Up to this point we have considered only those ligatures which con- 
sist of two notes and which therefore are called ligatura binaria. How- 
ever, the scope of ligatures is considerably enlarged by the numerous 
forms in which more than two notes can be expressed by a ligature: 

ligatura ternaria, quaternaria etc., as for example: Ffc^ p^ 3 L^ftf c y = fk . 

In these ligatures all the notes between the first and the last are called 
mediae (middle notes). Each media generally has the value of a B, 
except where it is the second note of a ligature c.o.p., as in the third of 
the above examples, or where it is marked as a L or Mx, as in the third 
or fourth example. The reader may try to verify that the four ligatures 
have the following values: BBL;BBBB;SSBBBL B; L B Mx B L. 

Rules for Ligatures. Whereas, in the preceding explanations, we have 
considered the ligatures from the standpoint of historical development, 
we shall now study them systematically by means of a set of rules from 
which the value of any ligature can be determined. In theoretical 
treatises of the fifteenth and sixteenth centuries such rules are given in 
a rather cumbersome and obscure presentation, or else in the form of 
Latin or German poems which lack in clarity whatever they gain in 
shortness. 1 Following is a presentation of these rules in what is in- 
tended to be a concise, clear and useful form. 

A. Rules about the meaning of the tails. 

1. A note with a downward tail to the right is L. 
1. An ascending tail to the left of the initial note makes that note 
and the following one a S each. 

3. An initial with a downward tail to its left side is B. 

B. Rules for notes not covered under A. 

4. All middle notes are B. 

5. An initial note in descending position (i.e., followed by a lower 

cap. v; cf. E. Praetorius, Die Mensurakheorie des Franchinus Gafurius, Leipzig, 1905, p. 18), who 
holds that exactly the opposite values are correct, namely B-B for the form without a tail, and L-B 
for that with a tail. Obviously, his interpretation is based upon a comparison of these shapes with 
their equivalents in square shape, whereas that of the Tinctoris and Adam von Fulda is based upon 
their similarity with the corresponding oblique forms in descending motion. The two or three 
examples of the ascending form with a tail which the present writer has encountered in his studies 
support the latter view, since in each case this form has the value B-B. One example (from the 
Codex Chantilly, ca. 1400) occurs on Facsimile 83, fifth staff, last ligature; three others are found on 
a facsimile from the Old Hall MS (ca. 1450) reproduced in vol. in of A. Ramsbotham, The Old Hall 
Manuscript, Westminster, 1938 (frontispiece, staves 8, 10, and 11). See pp. 364, 412. 
1 See, e.g., MuT, 10. 



92 White Mensural Notation 

note) and a final note in descending position (i.e., preceded by 
a higher note) are L. 

6. An initial in ascending position and a final in ascending position 
are B. 

7. A final note in oblique form is B. 

There follow schematic illustrations of these rules, for the sake of 
greater clearness. Diagonal dashes refer to ascending or descending 
position; horizontal dashes indicate that the direction has no influence: 1 

A. 1. cj-.-cj-.-c] = L 
2. l^-.tb-.tfi-.b- = S S 

B. 4. _ D _ . _^_, - C v J _ = B; BB 

5. D X ,(^,X D = L 

6. D /./D = B 
7- ^ =B 

As experience shows, the rules 1, 2, and 4 are more or less obvious and 
are easily remembered. For the others, the present writer has found the 
following working rule helpful: cf is B B and % is L L; a descend- 
ing tail at the beginning alters the first note, oblique form alters the last. 

Since in the determination of a ligature the tails are of prime impor- 
tance, the student must be warned not to confuse these tails with certain 
strokes which merely serve to connect notes of different pitch. Such a 
stroke occurs in the example (a) (see below) between the second and the 
third note. It has absolutely no influence on the value of the notes; if 
the second note were to be a L, the stroke would have to extend below 
the following note, as that before the last note which actually is a 'tail.' 
There might also be some doubt in the student's mind as to whether such 
a tail, found in the middle of a ligature, belongs to the preceding or to 
the following note, i.e., whether it is a tail attached to the left or to the 
right side of a note. However, it may be generally observed that no 
note of a ligature may have a tail to the left side except the initial. 
Hence, the tail belongs to the preceding note, making it a L. 

In studying the following examples, the beginner is advised to apply 
the rules in their above order. 



Example (a) flu^l . The fifth note is L (rule 1); the initial is B (rule 



3); the three following notes are B (rule 4); the last note is L (rule 5). 
Thus the ligature means: B B B B L L or, in notes: " ' 'q^ln • It 

1 A similar method of schematic designation has been used by O. Ursprung in an article on 'Die 
Ligaturen, ihr System und ihre methodische und didaktische Darstellung' {AM xi). 



may 



Rules for Ligatures 93 

be noted that the third and fourth notes could just as well be written 



in square shapes, instead of in oblique form: f^pL . From the view- 
point of logic and simplicity this manner of writing would even be pref- 
erable, since the oblique form has real significance only at the end of a 
ligature in descending position. However, oblique writing is frequently 
employed elsewhere, probably for its greater ease of writing. 

Example {b) ^ffi . The fourth and fifth notes are L (rule 1); the 

first two notes are S (rule 2); the third and the sixth notes are B (rule 

4) ; the last note is B (rule j):S S BLLB B: gggg . 

Any note of a ligature may be dotted. If an initial or middle note is 
to be dotted, the dot is written above that note, e.g.: 



In ligatures two successive notes of the same pitch are impossible. 
If, e.g., this passage: rf\f were to be changed so that the third note is d, 
it must be written thus: 



In acquainting oneself with ligatures, it is useful not only to resolve 
given forms into single notes but also to follow the opposite procedure 
i.e., to write a series of single notes in ligature. The following exercise is 
recommended: Write in ligature each of the three melodic phrases (1), 
( 2 )y (3)} combined with each of the three rhythmic patterns (a), (b), 
(c): 



(a) BLB BLB (b) S S B BBB (c) LB B LB L 

By combination there result nine melodic-rhythmic formulae each of 
which is to be written in ligature. The combination (3) (a), for exam- 
ple, is as follows: 



Finally, a few peculiarities of rare occurrence must be mentioned. A 
rectangular body of double length, with or without a tail, indicates a 
Mx: d=b yzFh = B Mx L; °a = L Mx (see Facsimile 28). In some 

earlier sources (MS Canonici misc. 213 of the Bodleian Library) one 



finds occasionally forms such 



as: U,yJ . Here, the downward dash 



94 White Mensural Notation 

makes the second note of the ligature a L, whereas the upward dash calls 
for a B, thus giving these two forms the values S L or S B respectively. 

As a final example we reproduce the tenor of the Laudamus te of an early 
fifteenth century mass by Arnaldi, 1 contained in MS Bologna, Bibl. Univ. 
2216. The notation is in the black notes of the earlier period which, 
however have the same significance as the white shapes explained above. 

The student may determine the value of each note and, after the study 
of the following chapter, transcribe it in tempus imperjeclum. 

Subsidiary Symbols. Our study of the graphical signs of white notation 
will be completed by a brief elucidation of certain subsidiary symbols of 
reference, repetition, and correction, which are conventionally used in 
the sources under consideration. 

(a) The signum congruentiae: $ S z serves to indicate points of coin- 
cidence in the various parts. An example of this practice is found in the 
two texted parts of Dona i ardenti of Facsimile 23 (staves 6 and 8). The 
sign is regularly used in canonic pieces to indicate either the fugal en- 
trance of the imitating part or, in mensuration canons, the places where 
the various singers have to stop. For an example of the latter practice, 
see Facsimile 27 and the explanations thereof. Another sign of refer- 
ence is the custos which indicates the pitch of the first note of the next- 
following staff (see p. 3). 

(b) Repetition of sections is indicated in the fourteenth century 
sources by a simple vertical dash similar in appearance to a B- or a L- 
rest (Facsimiles 68 and 70; see the explanations on ouvert and clos y p. 349). 
In the fifteenth and sixteenth centuries the sign of repetition occurs in 
the following shapes: ty :|f # . Another sign of frequent occurrence is 
the pause, known under names such as mora generalise corona^ diadema, 
signum tacilurnitatis or quielantiae. The following shapes are used: 

(c) If, by mistake, a white note had been written as a full black note, 
the letter v (vacua, empty) was used to correct the error. Some other 
signs which serve the same purpose and which are probably deteriora- 
tions of the letter v are shown here: Z n 1'° • 

1 In MS Bologna, Lie. Mus. J/, p. 3, the same composition is attributed to Z. Micinella. 



Subsidiary Symbols 95 

A dash erroneously attached to a B or a S was cancelled either by a 
diagonal stroke through the dash, or by another dash leading in the oppo- 
site direction: 3,| = « . 

If notes were written too high or too low, the correction was indicated 
in the following manner: : SE=E±z-, ^=^ • For more details see HdN 1, 
43°- 



II. MENSURATION 

A. Tempus, Prolatio, and Modus 

IN THE PRECEDING explanations we have purposely avoided 
expressing the characters of mensural notation in modern note values, 
for the simple reason that such transcription depends upon an additional 
factor, mensuration. By this term is meant the metrical relation 
between the value of one note and that of the next smaller degree. In 
modern notation this relation is always duple — i.e., a given note, unless 
dotted, is always equal to two of the next smaller species. In mensural 
notation, however, an undotted note may be either duple or triple — i.e., 
equal to two or three smaller notes, depending upon the mensuration of 
the piece and the value of the neighbouring notes. A ternary note is 
called perfect; a binary, imperfect. These terms go back to the rhyth- 
mic concepts of the thirteenth century, when the ternary division was 
considered perfect because it consists of 'beginning, middle, and end.' 
The dogma of the Holy Trinity also played some part in this concept and 
terminology. 

In the system of white mensural notation the choice of perfect or im- 
perfect mensuration exists chiefly in the case of two notes, the B and the 
S. The larger values are usually imperfect, while the smaller notes are 
always so: 

Mx = iL;L .- = 2 B; B = 2 or 3 S; S = 2 or 3 M; M = 2 Sm; Sm = 2 F; 

F = 2 Sf 

The mensuration of the B is called tempus, and exists in the two 
varieties: tempus perfeclum, indicated by a whole circle O ; and tempus 
imperfectum, indicated by a semicircle, open to the right C . The 
mensuration of the S is called prolatio. Prolatio perfecta is indicated by 
a dot placed in the middle of these signs, whereas the absence of the dot 
* calls for prolatio imperfecta. Thus four combinations result: 

tempus imperfectum cum prolatione imperfecta: C &=*♦ *-*♦ 

tempus per fee turn cum prolatione imperfecta: O «=*♦♦ o=ii 

tempus imperfectum cum prolatione perfecta: C «=<►♦ o=ii^ 

tempus perfectum cum prolatione perfecta: H=«*« o = i^i 

96 



Mensuratii 



97 



To supplement the signs indicating these mensurations, we intend to 
use occasionally another system of designation which is more easily 
grasped; namely, to indicate the tempus by Arabic figures 2 or 3, and the 
prolatio by the same figures thereafter in italics: 2 or j. Thus the four 
mensurations are also represented by the following symbols: C=[2, <?]; 
= [3,2}; G=[2,j]; ©=[3>jl- 

An understanding of the meaning of these mensurations is considerably 
facilitated by an appropriate choice of modern note-values for their tran- 
scription. As was the case with the tablatures, a 'literal' rendition of 
the mensural notes by their modern equivalents in shape, i.e., of an S 
by a whole-note, or an M by a half-note (see the table on p. 3) is not 
to be recommended. This method which was the customary one with 
editors of the nineteenth century (Bellermann, Proske, Ambros, Commer, 
and others) has been abandoned in more recent times because of its 
clumsiness and lack of comprehensiveness, chiefly as a result of Riemann's 
precedent. Unfortunately the newer publications exhibit no uniformity 
in the choice of scale of reduction. Many editors transcribe the semi- 
brevis as a half-note (1 : 2); others as a quarter-note (1 : 4); others continue 
to transcribe without reduction. Moreover, in many publications dif- 
ferent scales of reduction are chosen for different pieces and, sometimes, 
for different sections of one and the same composition. 

In our discussions of white mensural notation we shall invariably em- 
ploy a reduction of 1 :4, transcribing the S as a quarter-note. 1 In doing 

1 The proper choice of modern equivalents for the mensural notes is, of course, closely bound up 
with the consideration of the tempo for the piece in question. Our basic principle in this matter is, to 
choose the scale of reduction in such a way that the modern quarter-note becomes the beat in moder- 
ately slow tempo, somewhere in the vicinity of M.M. 60. As will be seen later (p. 188 ff), the men- 
sural notes signified not only relative values but had, in a given period, fairly constant absolute 
durations as well, a fact which makes it possible to choose a uniform scale of reduction for practically 
all the pieces of any one period, or, at least, of any one type. It must be noticed, however, that, in 
turning from one period to another, the 'absolute' value of any given note changed considerably, 
namely from short to much longer durations. This appears particularly in the case of the B which, 
around 1:225, designated the shortest value of music (brevis, short), while, in the sixteenth century, 
it was the longest value in practical use. As a matter of fact, the 'moderate beat' was represented 
successively by the L (1200-1250), the B (1250-1300), the 6" (1300-1450), the M (1450-1600) and 
finally the Sm, i.e., the quarter-note (1600-present), so that reductions in the ratios of 1:16, 1:8, 
1:4, 1:2, and 1:1 appear appropriate for the periods just named. 

It will readily be noticed that, as far as the period of white notation (1450-1600) is concerned, the 
scale of reduction used in our study is not in agreement with the above general explanations which 
actually would call for a reduction 1:2 (M = quarter-note) instead of 1:4 (S = quarter-note). 
Much as the present writer regrets to be inconsistent in a fundamental matter, he has, after much 
hesitation and deliberation, decided in favor of the reduction 1:4. because this method offers con- 
siderable advantage from the notational point of view. It seemed to him that in the present study 
the clarification of the notation should take preference over other considerations. It may be noticed, 
however, that even from the point of view of the tempo the transcription 6" = quarter-note is not 



98 White Mensural Notation 

so, the four above mensurations become the expression of metrical rela- 
tionships which, in modern notation, are signified by certain simple 
meters, namely, 4-, \-> %-, and g-meter respectively. As a matter of fact, 
in [2, 3], e.g., the B, S, and M are in the same numerical relationships as 
are the (dotted) half-note, the (dotted) quarter-note, and the eighth- 
note in g-meter. The following table shows the four mensurations and 
their modern equivalents: 

Transcription Example 

of notes 

1=1 ♦ 1 i 

J J )) 1 J iJ JEiJ. J>. 

4 

J. J. J> Ji 1 J.J.J7LJ JJJ.i 
J. J J> J) « J. J -T3 1 J -TJ3 J 1 

.U.J. J> Ji • JJ.iJ.JJ]J.iJ.JJ>i 

In theoretical writings, this scheme of four mensurations is broadened 
considerably by the inclusion of the L and the Mx as additional elements 
of rhythm. The mensuration of the L was called modus longarum {modus 
minor, 'lesser mood') and that of the Mx modus maximarum {modus 
major, 'greater mood'). Since each mensuration could be either per- 
fect or imperfect,. a system resulted which included 16 combinations of 
modus maximarum, modus longarum, tempus and prolatio. A confusing 
variety of signs for these combinations were invented by the theorists 
but almost never used in practice. For a survey of them, the reader is 
referred to the detailed explanations in HdN 1, 410-415. 1 

entirely wrong, owing to the fact that the normal tempo of the Flemish music was such as to be ca- 
pable of being interpreted in two different beats, either M.M. 45, or M.M. 90 (approximately). Thus, 
one has a choice between two transcriptions, one with S = quarter-note in 'adagio,' or one with 
M = quarter-note in 'moderate' The latter is more natural to the modern interpreter; the former 
is chosen here for the reasons set forth above. 

1 We hope to save the student of this subject unnecessary pains by reminding him that the nomen- 
clature used by the early theorists is far from being consistent and unambiguous. For instance, the 
terms major and minor were used not only with reference to modus, but also to prolatio. However, 
although in the former connection they designated two different mensurations {modus maximarum 
and modus longarum), they signified, in the latter connection, the perfect and imperfect varieties of 
one and the same mensuration, prolatio major and minor being identical respectively with prolatio 
perfecta and imperfecta. Unfortunately, the latter meaning of the term occurs also occasionally in con- 
nection with modus. In HdN 1, 412, two signs (circles within circles) are reproduced which, accord- 



Mensu- 


Mete 


ration 




C [*,*] 


k 


G fe 3] 


% 


O & 2\ 


% 


O I3,J] 


% 



Mensuration 99 

Indeed, from the standpoint of the musical practice the situation is a 
good deal simpler. The modus maximarum (or, as we shall call it, 
maximodus) is of very slight practical importance in the period under 
consideration (see, however, p. 124). The modus longarum (or as we 
shall call it simply, modus) must occasionally be considered in certain 
types of composition, namely, in the motets and masses which are based 
upon a cantus firmus-\\ke tenor. In these pieces, the upper voices are 
written chiefly in B> S and M or, in other words, in lempus and prolatio, 
whereas the tenor is written chiefly in L and B or, in other words, in 
modus. Since tempus and prolatio indicate the rhythmic organization 
corresponding to the contents of the modern measure, the introduction 
of modus obviously results in the appearance of regular groups ot 
measures, namely, either two {modus imperfeclus) or three {modus per- 
fectus). In a manner analogous to the abbreviations for lempus and 
prolalio given above, we shall indicate the modus by Roman numerals 
II or III; thus [III, 3, 2] means: modus perfeclus cum tempore perjecto 
cum prolatione imperfecta. Here follows a schematic example of this 
mensuration: 

Discant: 

II J Jl J1J> J J J3IJ3J JJJT3/3J I J J3IJ J I 

Tenor: 

21 J. iJ. U. U^ U- i J J l 

In the musical documents of the period in question the modus is not, 
as a rule, indicated by a special sign, but by the L-rests which usually 
appear either at the beginning or in the course of the tenor. According 
to whether these rests cover two or three spaces of the staff, the L is 
understood to be imperfect or perfect (see p. 87). 

From these explanations it appears that the introduction of maximodus 
would mean the formation of regular phrases each of which includes a 
regular number of measures. There is only one period in the history of 
music when such a principle of extremely uniform construction appeared 
in composition, i.e., the period of Machaut, Dunstable, and Dufay, 



ing to Adam von Fulda and other theorists have the meaning of: modus major cum tempore perfecto 
cum prolatione majori (minori). Obviously, in this case modus major does not mean modus maxi- 
marum, but the perfect variety of modus in the usual sense, i.e., modus longarum. Wolf's explana- 
tions on Taktzeichen suffer much from his failure to clarify the exact meaning of the various terms, 
or else, from the inclusion of designations and signs to which no clear meaning can be attached. 



IOO 



White Mensural dotation 



who, in some of their'isorhythmic motets' arrive at the realization of 
the amalgamation of maximodus , modus, lempus and prolatio (see p. 356). 
In those rare cases in which it is necessary to indicate the maximodus 
we shall use italic roman numerals, as for example: [III, II, 2, j\. x 

As a matter of curiosity, however, it may be mentioned that illustra- 
tions of modus, tempus, and prolatio may also be found in various com- 
positions of the classical period. A particularly interesting example is 
offered by the variations in Beethoven's pianoforte sonata op. ill, the 
rhythmic structure of which, in the language of fifteenth century theory, 
may be described as: modus maximarum imperfectus cum modo longarum 
perfeclo cum tempore per jeclo cum prolatione perfecta [II, III, 3, 3]: 




Here, if one considers the thirty-second-notes as the smallest unit {mini- 
mae), we find the four subsequent mensurations consistently employed 
for lengthy sections of the composition: 

(a) three thirty-second-notes to a sixteenth: prolatio per je eta 

(b) three sixteenths to an eighth: tempus perjectum 

(c) three eighths (beats) to a measure: modus perfectus 

(d) two measures to a phrase: maximodus imperfecta 

We turn now to a detailed consideration of the four combinations of 
tempus and prolatio. 



B. Tempus Imperfectum cum Prolatione Imperfecta 

This mensuration offers no great problems, since the notes are all 
binary and, therefore, stand in the same metrical relationship to one 
another as in modern notation. Using our scale of reduction 1 :/}., the 
modern equivalent of this mensuration is J-time. Each measure* con- 

1 By introducing these abbreviations we hope to achieve greater simplicity and precision than has 
heretofore been usual. For example, in F. Ludwig's edition of the works of Machaut (Machaut, 
Musikalische Werke, Leipzig, 1929, vol. in, p. 78) the above mensuration is expressed as follows: mo. 
ma. pf.j mo. mi. imp.; tp. imp.; pr. ma. 



Tempus Imperjectum 



101 



tains one B, transcribed as a half-note. It is, of course, possible to 
combine two such measures into one ^-measure, although cases are not 
infrequent in which this method necessitates the insertion of single \- 
(or, 3X4, i.e., 2-) measures. For the sake of clarity and consistency, 
4-meter is used throughout the book. 1 

To indicate that a note contains three units of the next smaller species, 
it is dotted as in modern usage. This dot, the so-called punctus addi- 
tionis, also appears in conjunction with ligatures (see p. 93). 

Aside from the reduction of note values, the modern notation differs 
from the old method chiefly by the arrangement of the parts in score, 
and by the use of bar-lines. Modern scholars have frequently raised 
objection against the latter device which they felt to be detrimental to 
an understanding of the polyphonic nature of early music. It also has 
the disadvantage of entailing a frequent use of tied notes, since values 
occurring in syncopated position form a characteristic feature of the 
style of the Flemish polyphony. In various recent publications attempts 
have been made to eliminate this drawback by replacing the bar-line by 
the 'Mensurstrich' (mensuration line) which is drawn not through the 
whole score or through the individual staves, but through the spaces 
between them. Following is an example illustrating both methods: 




It is doubtful whether the advantage of the second method — i.e., a 
greater similarity to the original notation — is considerable enough to 
compensate for its unfamiliar appearance and greater difficulty of read- 
ing. Moreover, it may be noticed that the 'Mensurstrich' cannot be 
used if different mensurations occur in various voices, as for instance, 
[3, 2] in the tenor against [2, 2] in the discant, a feature not uncommon 
in the masses and motets of the earlier Flemish masters. It seems to 
us that the best device of barring is the bar-line which is drawn through 

1 It goes without saying, but may be stated expressly, that the methods of transcription used in 
this book have been devised chiefly from the notational point of view, which means that they are de- 
signed primarily to clarify the important features of the original writing. For other purposes, 
scholarly as well as practical, certain changes or adjustments may be advisable. 



102 White Mensural Notation 

each stave individually. This method avoids the 'sectional' appearance 
produced by the long bar-lines of the modern score and yet allows for 
different barring in each part if necessary. It goes without saying that 
such bar-lines have only metrical significance, without necessarily im- 
plying the added modern meaning of an accentuated first beat. We 
say 'necessarily,' because a large portion of early music actually is 
'bar-line music' in exactly the same sense as music of Mozart and 
Beethoven — a fact which is usually overlooked in the discussions about 
the bar-line. To this field belongs the entire repertory of the thirteenth 
century, practically all Italian music of the fourteenth century, and the 
various types of sixteenth century chanson (chanson, frottola, villanella, 
etc.). 

We may now turn to a consideration of some examples in [2, 2]. Fac- 
simile 23 shows on the lower half of the page a three- voice chanson, Dona 
i ardenti , by Guillermus Dufay whose name is written in an enigmatical 
manner, the syllable fa being indicated by the note B-flat which, in the 
hexachordum molle (on f), is fa. 

Although the two lower parts carry a flat in the signature, there is none in the discant. 
This manner of writing is extremely frequent in polyphonic music from the early thir- 
teenth century through at least the beginning of the sixteenth. Its meaning has been 
the subject of several studies. 1 In an article on 'The Partial Signatures in the Sources 
up to 1450' {AM x; see also AM xi, p. 40) the present author has tried to show that 
the partial absence of a flat in the signature is an expression of a kind of bitonality, 
namely, of F-major (or D-minor) in the lower parts as against Lydian (or Dorian) in 
the higher ones. This difference of tonalities bestows upon the music a contrast between 
'dark' and 'bright,' between 'heavy' and 'light,' which forms one of the special charms 
of early polyphonic music and which should not be effaced by editorial accidentals. 2 
In fact, the chanson under consideration does not need any emendations, as far as the 
accidentals are concerned. 

The second note of the last ligature of the contra should read f, not g. For the signum 
congruentiae on staff 1 and 3 of the chanson, see p. 94. In transcribing the piece, the 
student will notice that these signs are not quite correctly placed. The beginning is 
transcribed in the appendix, No. 12. 

Facsimile 24 serves as another example of [2, 2]. These two pages 
from the Trent Codex no. 92 contain the Sanctus of a mass by Benet, 
which falls into five sections: (1) Sanctus Sanctus Dominus Deus Sabaoth; 
(2) Pleni sunt celi el terra gloria tua; (3) Osanna in excelsis; (4) Benedictus 
qui venit in yiomine Domini; (5) Osanna in excelsis. Of these, sections 
(2) and (4) are in two parts only, as is indicated by the rests in the 

1 See the above-mentioned article, p. 4. Also K. Jeppesen, Der Kopenhagener Chansonnier 
* (Copenhagen, 1927), p. lxiii f. 

2 This writer was glad to find his view supported by various transcriptions given by H. Besseler 
in his Die Musik des Mittelalters und der Renaissance, Potsdam 1931 (E. Biicken, Handbuch der 
Musikwissenschaji)\ see the examples 97, 109, 113, and others. 



Tempus Imperjectum 
Facsimile 23 



103 






71 



I 






i^N^'k \ t 



ffl* 




PI 



^*Tfw 4*&4 p«M» «~*«V». 



.f|=- «Vf.. 




5P 



4 j 1 



pjgp 



fiS~~& v 



: Nhi ■ TTA — 






WV / ^ U » 3» U»MUM« 



^T 






<3 







J±\m:x> • 



rv^H**. 



j K jj« -J 



u n .^.|H< 'V stfc 



■ ■ rg;.!,,"^ , 7o£jagL^ j ^ 



«e 



_$»«.«& 






AfWfe^ 



MS Oxford, Bodleian Library Canonici misc. 2/j (ca. 1450) 
Page 73 



1 04 Wh ite Mensural Notatio n 

contratenor. Sections (1), (2), and (5) are in [2, 2] and may be tran- 
scribed now. 

It will be seen that the two-voice section (2) comprises 16 B (16 
4-measures) plus a final L which is followed by a long vertical dash, 
the so-called finis punctorum. On the other hand, in the contra there 
are rests to the equivalent of only 16 B before the finis punctorum. As 
a matter of fact, the final L, which usually appears at the end of a piece 
or a section thereof, was not considered an exact value, but was supposed 
to be held until the leader of the chorus gave the sign for silence. It 
is therefore best transcribed as a half-note with a fermata. 

This piece is another example of partial signatures. However, the application of the 
principles explained in connection with the previous piece, fails to lead to a satisfactory 
result here. As a matter of fact, a literal rendering of the parts appears to be impossible 
from the melodic as well as from the harmonic point of view, since numerous tritones 
(f-b) and clashes such as bb-f'-b' would result. As has been pointed out in the above- 
mentioned article {AM x), there occurred, around 1450, changes of musical style which, 
owing to a greater emphasis of the harmonic point of view (triads in root-position) 
obviated the continuation of that bitonality which is frequently encountered in the works 
of the preceding period. Generally speaking, the melodic as well as the harmonic con- 
text now calls for a much greater use of B-flats in the upper parts than theretofore and, 
consequently, for a considerable number of editorials accidentals. The extent to which 
such accidentals should be added and the principles, upon which such additions should be 
based, represent what may well be called the most controversial and problematic topics 
of musicology. Until recently, editors have been inclined to eliminate, by a liberal use 
of added accidentals, features which are not compatible with the harmonic system of, say, 
the eighteenth century, e.g., the vertical and the horizontal tritone, cross-relations, the 
lowered seventh before the octave, etc. Their method was purely empirical or experi- 
mental, which means that editorial flats (and sharps) were added after the completion 
of the transcription wherever they appeared to be required by the context of the voices. 
In place of this rather unsatisfactory procedure another method has been suggested by 
the present writer (see the above-mentioned publication), a method which allows one to 
determine the flats and naturals a priori on a purely horizontal basis, i.e., from a consid- 
eration of the part itself. The following rules have been advanced: 

The B is natural when occurring in conjunct motion (seconds) from both sides, but 

is flat when it is connected by a leap with either the preceding or the foHowing note. 

The B occurring as a top-tone is flat. 
According to these rules, the B is natural in the combination a-b-c' or c'-b-a, flat in 
combinations such as g-b-c', d'-b-a, a-b-a, etc. The justification of these principles lies 
in the fact that a progression by leap, either of a third or a fourth, introduces a harmonic 
element into the melodic line, while a progression by steps alone remains within the 
boundaries of the (modal) scale. That there existed a differentiation between a 'melodic 
tonality' with an emphasis of the B-natural and a 'harmonic tonality' with a greater use 
of the B-flat appears particularly from the study of sixteenth century keyboard music 
(see pp. 8, 26, 34). The 'moderate bitonality' which results from the above method 
forms the transition between the earlier, more distinct, tvpe, and the 'monotonality' of 
the seventeenth and later centuries. 

It goes without saying that the rules given above do not constitute an infallible prin- 
ciple. They are useful, however, as a point of departure — if only, as a point of departure 
away from the biased misconceptions which prevailed in practically all the editions 
published until recently. If the principles here presented need revision or replacement — 



Temp us Imperfect urn 
Facsimile 24 



105 




°fc=: 






~5^ - 

O ol 

— OO 

-a « 

IS <" 

* SP 

4-1 rf 
c/) 



io6 



White Mensural Notation 



a possibility which this writer readily admits — this can only lead still farther away from 
the classical system of harmony, toward a still stricter adherence to the original. An 
indication of such a trend is found in the edition by D. Plamenac of the masses (i-viii) 



of Ockeghem, a publication in which progressions such as: 

"' T.Ff 

left intact, while, strangely enough, other combinations of a much less 'offensive' nature 
are corrected (see the Kyrie of the first mass). 

A few remarks may be added with regard to the second problem of musica Jicta, i.e., 
the sharped leading-tones in cadences. The closing measure of section (i) in Facsimile 24 
illustrates the problem presented by the three-voiced cadence typical of the Burgundian 

, MBi 4j „(tt)A - ^ 

and the early Flemish schools: 




Three readings of this cadence are possible: one without sharps, another with the 
sharped seventh (F-sharp), and a third one with both a sharped seventh and fourth 
(F-sharp and C-sharp). In the sources from ca. 1350-1450, the latter variety is fre- 
quently indicated expressly by sharps written in both parts (see e.g., Facsimile 26). 
However, the quaint charm of the resulting chordal combination (often called 'Burgun- 
dian cadence') should not lead to an unrestricted and injudicious application of editorial 
sharps. Certain considerations of a general nature would seem to corroborate the view 
that, in the Sanctus from Benet's mass, the version without sharps is preferable. As a 
matter of fact, there is ample evidence pointing to the fact that the Ars Nova (Machaut) 
and the Burgundian School (Dufay, Binchois) made considerably greater use of chro- 
matic tones than the early Flemish masters (Ockeghem, Obrecht) who obviously inau- 
gurated a new vogue of modal diatonicism. One may assume that the shift in emphasis 
from secular to strictly liturgical music, which is one of the most striking features of 
the change taking place around 1450, played a decisive role in the adoption of a tonal 
system which was much more conservative and 'Gregorian,' so to speak, than that of 
the previous periods. On the basis of this general view it would be proper to give 
preference to the sharped varieties of the above cadence in music (particularly secular 
music) of the Ars Nova and of the Burgundian School, as against the diatonic variety in 
sacred music of the ensuing period, at least through the end of the fifteenth century. It 
is interesting to note that this tonal change is in inner agreement with the shift from 
light to dark timbre, from high to low range, from a thin to a fuller texture, which ac- 
company the transition from the Burgundian to the Flemish style. It may also be 
noticed that in the cadence which closes the first phrase of the Sanctus the use of sharped 
tones is actually prohibited by the B-flat in the contra: 




In applying our rules regarding the B to the piece under consideration it will be seen 



Imperfection 107 

that they lead to satisfactory results, particularly in the section (4), Benedictus, which 
will be considered later (p. 118). In the section (2), P/eni, one will probably restrict 
their application to the obvious case of the tritone (f-b), without changing the B in the 
fifth measure (second staff of the original, shortly before the syllable 'sunt'), on account 
of its close proximity to a cadence on C. 

As a last example of imperfect mensuration the chanson Dangier tu 
trias tolln reproduced on Facsimile 25 may be studied. The third 
and fourth notes on the last staff of the discant are an example of the 
so-called minor coloration which will be explained later (see p. 128 ff). 
For the present purpose, it will suffice to say that the third note, a 
'blackened 6*,' has the same value as a dotted M. 

The clef on the last staff of the discant is a G-clef. The beginning of the discant is 
transcribed in the appendix, No. 13. 



C. Tempus Perfectum cum Prolatione Imperfecta 

In this mensuration, which in early practice is indicated by a whole 
circle or, in this book, by the sign [3, 2], the B equals three «?:B=***; 
all the other values are binary. The transcription into modern notes 
leads to ij-measures: oa^li^G »3|e)-IJJ"3 J! J-l 

Imperfection. Whereas in tempus imperfectum (and, of course, in mod- 
ern notation) the ternary value of a note is derived from the binary 
by adding one half, a reverse process takes place in tempus perfectum. 
This process, which leads from the ternary B to the binary and there- 
fore amounts to subtracting one third, is called imperfection. Generally 
it is not indicated by any external sign, but certain circumstances de- 
termine when the B remains perfect, and when it becomes imperfect or, 
as we take the liberty of saying, 'is imperfected.' 1 The following ex- 
amples illustrate the two principal methods of imperfection, namely, im~ 
perfectio a parte post {a p. p.)> i.e., imperfection by a following note, and 
imperfectio a parte ante (a p. a.), i.e., imperfection by a preceding 
note: 

a p. p. a*.|JJ| a p. a. ♦h=|JJ| 

The following rules must be observed : 

1 The use of 'imperfect' as a verb throughout this book seems justifiable both by the analogy 
with the verb "to perfect' and by the exigencies of this subject. 



io8 



White Mensural Notation 



Rules of imperfection (for [3, 2]) : 

1. A B is perfect if followed by another B or by a J5-rest. 
1. A B is perfect if followed by two or three S. 1 

.3. A B is imperfect if followed or preceded by one or by more than 
three S. 

4. If both imperfectio a p. p. and a p. a. are admissible, the former 
takes preference. 

5. A 5-rest can never be imperfected; however, a ^-rest may cause 
imperfection of a note. 

These rules may first be illustrated by the following examples: 




NB: In the examples to rule 2 the case of two S has not been illustrated because it 
calls for further explanation (see alteration, p. 112). 



It is unnecessary to mention that these rules are not strict laws, but 
guiding principles. They should be used, not from the standpoint of the 
mathematician, but from that of the singing or playing musician. In 
other words, the value of a given note should not be determined by a 
process of calculation, but by the comprehension of the musical context. 

Following are a few supplementary remarks regarding the above rules. 

To rule i: This rule is considered one of the most fundamental of the 
entire theory. It is frequently given in the form: similis ante similem 
perfecla, i.e., a note is perfect before another one of the same kind. 2 

1 For a possible modification of this rule and the next, see p. 114. 

* Although this writer has never encountered an exception to this rule, there is an interesting 
remark in Glarean's Dodekachordon of 1552 which shows that such exceptions may have been quite 



Imperfection 
Facsimile 25 



109 



r - — j=J 




V — r 




! 1 


■1 

<5 


V 






5 ' S 


1 ~;r 


r 


f i-.^ 




|H J 


^ 




PS 


fei- 


- £ 


Iftssi 


BL 




o 
U 

>^ ^ 

1-, ^*- 
-2 « 

i—l bo 

in, 

bo 



no White Mensural Notation 

To rule 2: The following example: 



shows that a B followed by three S may occasionally be imperfect, 
namely, by imperfeciio a. p. a. 

To rule 3: Although the above examples illustrating this rule show 
the normal grouping of 1, 4, and 5 S placed between two B, yet the 
grouping may differ occasionally, according to the context, namely, if 
the first B is imperfected a. p. a. In the following example, for instance, 
the group of four S must be divided into 3 + 1, instead of 1 + 3: 



In the following example the imperfection a. p. a. of the first B neces- 
sarily leads to the application of the same imperfection to the second 
and third B: 

The flexible character of the principles of imperfection may be illus- 
trated by the following passage from the Trent Codex 89 (p. 246'; see 
the facsimile in DTOe vn): 




The sharp-like sign after the second B (near end of the first staff) 
means four Z?-rests (two and two). After this follow five perfections 
(groups to the value of three S each; a punctus addilionis is missing 

frequent. Here is a translation of this passage (lib. in, cap. xir; p. 214 of the German edition of 
the Dodekachordon by P. Bohn, Leipzig, 1899): 'What shall I say about imperfection? Franchinus 
[Gafurius] states and maintains emphatically that under no circumstances can a note be imper- 
fected which stands before another of the same species. And yet how frequently does one see this 
rule broken, not only by mediocre musicians but also by Josquin des Pres, the king of singers.' 



Imperfection 



in 



after the ascending ligature), until we arrive at the first B of the second 
staff. Since this B is followed by a long series of £ (or their equivalents 
in smaller values) one would expect imperfection a. p. p. to take place 
(see below, version a). This, however, is wrong as appears from the 
fact that one S is lacking at the end of the phrase. Actually, the first B 
of the second staff is perfect, as is also shown by the context of the other 
voices (version b) : 




Properly, the perfect quality of the initial B should be indicated by a 
punctus divisionis (see p. 115). 

To rule 5: If a B is followed by two ^-rests, the scribe usually makes 
a slight but important distinction. When the two rests are on different 
lines of the staff the first is meant to imperfect the preceding B> whereas 
the second belongs to the next perfection. If, on the other hand, both 
rests appear on the same line, both belong to the same perfection, and 
the B remains perfect: 




The above rules and remarks explain the simplest and most important 
type of imperfection — the so-called imperfectio ad totum, i.e., 'imperfec- 
tion of the whole' (of the note). In addition, there is an imperfectio ad 
partem, 'imperfection of a part' (of the note), which is discussed at 
great length by theoretical writers of the period, and which is used occa- 
sionally in musical practice. Generically, this term refers to all those 
cases in which a note is imperfected by a note two (or more) degrees 
removed from it in value. In the present mensuration this situation 
occurs chiefly when an L is followed or preceded by a S. Here, the L is 
considered as being composed of two B, one or both of which may be 
imperfected. Thus, reduction of the L from six to five or four S results: 

^♦-UJdJI ^-IJJJJ.1 ♦^♦-IJ^yjl ^o-IJ^JJI 



112 



White Mensural Notation 



More specifically, these examples illustrate the so-called imperfectio ad 
partem propinquam (partes propinquas), in a contrast to the much rarer 
imperfectio ad partem remotam {partes remotas), i.e., the imperfection of 
a note by one (or several) of the third-following degree, for instance, 
* of an L by an M in [3, 2]: oai4l JJJJ~3| . 

The following example, the beginning of the discant of the Et in terra 
pax from Pierre de la Rue's Missa Uhomme arme {Misse Petri de la Rue, 
Petrucci, Venice, 1503), illustrates the problems one may encounter in 
this matter: 

h „,^Um> ftft 'lljll' »t>»lilljiUll!ilfc4Jtf 

1 fife terowtotfe* bone volrfttffe ItmkmmtttoMtimru JlZnmmu frxHcmfm fto 




=/ 



The rhythmic as well as the melodic design of the opening phrase would 
seem to suggest imperfectio ad partem remotam, i.e., imperfection of the 
L by the M: 



However, this is wrong, as one will notice as soon as he comes to the 
two B, near the end of the staff where he will find that there is one M 
too many. Actually, the L is imperfected by two M, as follows: 



In cases like this where there is a long series of small values between 
two long values (B or Z,), the quickest way of determining the proper 
rhythm is to work backwards from the final B, which — at least, nor- 
mally — will come at the beginning of a measure. This method, unmusical 
though it is, is frequently extremely useful. 

Alteration. In the above explanations the case of two S placed be- 
tween two B (see rule 1) has not yet been considered. In fact, another 
fundamental concept of perfect mensuration enters here, namely, alter- 
ation, which means, the doubling of the value of a note. The principle 
rule is as follows: 

6. If two S are placed between two B, the second S is doubled. 



Alteration 



"3 



Examples: 




(a) 



(b) 



One might wonder why in example (b) the two identical rhythms of 
measures 3 and 4 are not both expressed by means of imperfection as 
follows: hiobohb • This manner of writing, however, is not permis- 
sible since it would contradict rule 1, according to which a B followed 
by another B must always be perfect. It appears, therefore, that the 
principle of alteration is the logical corollary of this rule. It is the only 
way of expressing the iambic rhythm immediately before a B. 

If, on the other hand, this rhythmical combination is followed by 
another value, larger or smaller than the B> its rendering by means of 
imperfection a p. a. is possible and, indeed, was considered imperative. 
In other words, the rhythm J J was to be expressed by alteration ♦♦ 
only if its rendering by imperfection a p. a. ♦a was prevented by 
rule 1. Statements to this effect are to be found in practically all the 
theoretical treatises, and a strict observation of this principle is encoun- 
tered in the practical sources. Frequently the following rule is given: 

7. A note may be altered only if the succeeding note is of the next 
higher value. Therefore, the following renditions are correct: 

«*fl-IJcJ|J-|;«H».|JJ|J hoBq-UJUJcM 

The following two examples from the Odhecaton {Tandernaken, tenor) 1 
are instructive: 



The dot of these examples is the punctus divisionis, see p. 115. 

It must be noticed that occasionally the combination B S S B calls 
for an interpretation which does not conform with the above principles, 
namely, for imperfection: i\ J J| J J| . According to strict theory, such 
a meaning ought to be indicated by a punctus divisionis, as follows: 
bo-*b . However, examples calling for imperfection but lacking this 
dot are not unusual in musical documents. The ambiguity in this 
matter is explained as the result of an evolutionary shift. In the nota- 
tion of the thirteenth, fourteenth, and early fifteenth centuries the com- 

1 See the facsimile edition, published by Bolletino Bibliografico Musicals, Milan, 1932, p. 75. 



114 White Mensural Notation 

bination B S S B invariably calls for alteration. If in such a group 
imperfection was intended, this had to be indicated by a punctus divi- 
sionis. In the late fifteenth century, however, the iambic rhythm result- 
ing from alteration became obsolete and the principle of alteration 
gradually fell into disuse. At this time, therefore, two S placed between 
two B were understood normally to imply imperfection, even without 
the punctus divisionis. However, the new interpretation did not com- 
pletely supersede the old one; hence, one encounters a certain ambiguity 
in respect to this combination in the sources of the Ockeghem — Josquin 
period. The theorists definitely adhered to the old principle (Tinctoris, 
see CS iv, p. 69; Pietro Aron, see E. Praetorius, Die Mensuraltheorie 
des GafuriuSy p. 47). In the practical sources, however, the opposite 
interpretation seems to prevail. Two examples of the combination in 
question appear in the beginnings of the nos. 667 and 1418 of the com- 
plete list of contents of the Trent Codices, given in DTOe vu, p. 52 
and 76. A comparison with the transcriptions given in DTOe vu, p. 
266 and DTOe xxvn, p. 16 shows that they both call for imperfection. 
However, examples calling for alteration are also frequent. The 
question certainly deserves fuller investigation. It appears that, de- 
pending on the result of such an investigation, the fundamental rules 
(2) and (3) of imperfection (see p. 108) may have to be changed to run 
as follows: 

2a. A B is perfect if followed by three S. 

3a. A B is imperfect if followed or preceded by less or more than 
three S. 

Only in one case was the old principle of alteration never modified, 
that is, if the two S were written in ligature c. 0. p.: 

8. Two S in ligature c. 0. p., placed between two B, invariably call 
for alteration. 

It may be noticed that imperfection is automatically ruled out in the 
combination B S S B B, on account of rule 1, and that alteration is 
naturally impossible if the second of the two S is replaced by its valor, 
i.e., by smaller notes of the same value, as, for instance, B S MM B. 

The following example from Obrecht's Missa sub tuum praesidium 
illustrates both interpretations of the sequence B S S B. The first two 
S, written in ligature c. 0. p., call, of course, for alteration. The third 
and fourth S 3 however, must (according to the context of the other 



Punctus Divisionis 115 

voices) be interpreted as imperfection although the dot is missing: 1 



The following rule corresponds to rule 5: 
9. A rest cannot be altered but may cause alteration of a note. 

Example: Ofl^tf*^ = iU-lf JcJ Jl{ Jl . 

The impossibility of altering a rest brings about an unequivocal indica- 
tion of imperfection in the following combination: B S(S) B. 2 

Finally, it may be noticed that the principle of alteration comes into 
play also in the case of six S between two B. At first thought, such a 
combination would suggest two groups of three S each, so that the in- 
itial B remains perfect: b«««««oh= 4 |J- U JJ|JJJ|J-I • However, if rule 
3 is applied, the first S would imperfect the preceding B, and the last S 
would be altered: ^1 JJ| JJ J! Jj|j.| . The latter version would seem to 
deserve preference, but not to the entire exclusion of the former. As 
in the case of two S, alteration is impossible if the last S of the group 
is replaced by smaller values. Hence, in the following combination: 
BSSSSSMMB the first B of necessity remains perfect, because 
otherwise one S would be missing at the end of the phrase, before the 
final B. 

Functus divisionis. The above concepts of imperfection and alteration, 
ingenious though they are, do not prove sufficient for the clear rendering 
of every rhythmic combination. For instance, the following simple 
rhythm cannot be expressed in mensural notes by employing only the 
rules previously given: 2|JJ|JJ|J.| • Indeed, one might suggest either: 

Oaoood or: Ota^oHd . But the former version means |J-|JJJ|J.| 
(rule 2) and the latter |J.| J J|J.|J.| (rule 6). 

In this case as well as in many others of a similar nature the punctus 
divisionis (p.d.) is used. As the name suggests, this punctus is a sign 
of division and, indeed, serves somewhat in the same capacity as the 
modern bar-line. For instance, a pair of S, placed between two p.d., 
or between one p.d. and a B, is understood to constitute a perfection, 
demanding alteration of the second S. Thus, the above problem is 
easily solved by placing a p.d. after the first S: ao-ooa (a; see below). 

1 In this example, as also in subsequent ones, groups of imperfection are indicated by a slur, 
groups of alteration by a square bracket. 

2 Here and in subsequent examples, brackets around B, S, etc. indicate rests to the value of 
these notes. 



1 1 6 White Mensural Notation 

The p.d. is also needed in order to guarantee correct reading of the 
ambiguous combination B S S B. Indeed, b«-»h (b) clearly demands 
imperfection whereas in B-o*o (c) the dot emphasizes alteration. 

Early theorists, delighting in intellectual subtleties, made further dis- 
tinctions in this matter, introducing various names such as punctus 
alterationis, punctus per/ectionis, punctus imperfectionis, etc. Actually, 
they all amount to the same thing, i.e., a sign of division in perfect 
mensuration, and they vary only with regard to certain secondary effects. 
For instance, in the first of the above three examples (a) the p.d., in 
addition to its main function, causes alteration of the second S; hence 
it was regarded as a punctus alterationis. In the third example (c), its 
effect is to make perfect the first B which would otherwise be imperfect. 
For this reason it was called punctus per/ectionis. In the second example 
(b) it was called punctus imperjectionis because the two B become im- 
perfect. Since these distinctions are nothing but unnecessary complica- 
tions in terminology, we shall disregard them completely, and shall refer 
to the sign in question as punctus divisionis exclusively. 

The punctus divisionis, however, differs materially from the punctus 
addilionis (or augmentationis), which, as explained above (p. 101) is 
identical with the dot in modern notation. This punctus does not mark 
off perfections, but adds to a given note one half of its value. The 
essential difference between these puncti lies in the fact that the p.d. 
may be employed only in perfect mensuration, whereas the p.a. occurs 
exclusively in connection with imperfect notes. This may be illustrated 
by the following two examples: 

(a) oB.*a4|J.|Jcl| (b) cB-od-SUJJJIJI 

Although these two examples are identical not only in appearance but 
also in the metrical value of the individual notes, the dots serve two 
completely different functions. In the example (a) the first B is nor- 
mally ternary, and the dot merely prevents it from becoming binary. In 
the second example, however, the first B is normally binary and its 
value is augmented by the dot. 1 

x The writers of the fifteenth and sixteenth centuries attempted to simplify the system ot the 
numerous puncti, as it occurs in the treatises of the fourteenth century (see, e.g., GdM i, 103 fT; HdN 
I > 339)- Generally, three kinds of punctus are mentioned in the writings from 1480 to 1550, namely, 
the punctus divisionis, per/ectionis, and additionis. Gafurius goes even one step further and reduces 
their number to two; however, he does not identify the punctus per/ectionis with the punctus divisionis, 
but rather with the punctus additionis. Accordingly, this punctus may occur both in perfect and in 
imperfect mensuration, although it actually serves an entirely different purpose in one and in the 
other. Unfortunately, this twofold meaning of the 'point of perfection' has been perpetuated by 
Th. Morley, in his well-known Introduction to Practical Musicke (London, 1597) whence it has been 



Functus Division! s ny 

Of course, in the mensuration which we are considering, namely, [3, 2] 
both types of punctus may occur, the punctus divisionis referring to the 
lempus which is perfect, and the punctus additionis referring to the 
prolatio which is imperfect: op-o-ioop= *ld-l J-JJI J J I • 

There even occur cases in which both puncli coincide, as in the follow- 
ing example where the dot functions as a p.d. with respect to the tempus 
by marking off a group of perfection, and as a p.a. with respect to the 
prolatio by adding half to the value of the ^otao-ioon =il<J J[/3 J J|<J.| . 
For an example, see the beginning of the discant of Facsimile 27. 

Whether a given dot is a p.d. or a p.a. is generally apparent from 
the musical context. If a dot is a p.a., a note of the next smaller species 
must always follow which provides the other half of the increase. Some- 
times, the situation is obscured by the fact that this note does not 
directly follow the p.a., but is separated from it by notes of greater 
value as here: Ooo-oooin - At first sight, one might believe this to 
be a. p.d.; in such a case, however, there would be no place for the single 
M before the B. The interpretation as a p.a., with syncopation follow- 
ing, is evidently correct. 

In some documents of white notation the scribes distinguish between 
the p.d. and the p.a. by writing the former in a higher position or by 
giving it the shape of a check-mark: G a ♦*i-i*H ;ohV4o«h • This 
practice is observed, though not consistently, in Facsimile 30, in 
which the S is perfect {prolatio perfecta) and the M is, as always, im- 
perfect. 

Facsimile 26, containing a three-voiced Ave regina by Dufay, may be 
studied as a first example oi tempus per jectum. 

In the third measure of the piece we find an example of the 'Burgundian cadence' (see 
p. 106), with the sharped fourth and seventh. For the final cadence of the piece, a sharp 
is indicated only for the seventh (discant), not for the fourth (contra), while all the other 
cadences are without accidentals. Whether or not they should be modified according to 
the initial cadence, is a question which cannot be definitely answered. The champions 
of 'editorial accidentals' will, no doubt, argue that the sharps given for the first cadence 
are meant to indicate the intention of the composer with regard to all the cadences of this 
composition. The other school of thought will arrive at exactly the opposite conclusion, 

adopted into an article by S. T. Warner, published in Proceedings oj the Musical Association, London, 
191 8/19 (see also the article 'Notation' in Grove's Dictionary, 1938, vl. in, p. 654). 

In contrast to all these interpretations, it is interesting to note that as early as the first years of 
the fourteenth century an eminent theorist has defined the puncti exactly as we have done. In 
Joh. de Muris Ars discantus we read (CS in, 92): 'How many puncti exist in music? Two. Which 
are these? The punctus divisionis and the punctus augmentationis. . . . The punctus augmentation'^ 
cannot be used except in binary numbers of prolations, as for instance in the major or minor prola- 
tion, in reference to a note equal to two notes [of the next smaller species].' About the meaning of 
prolatio in the early fourteenth century, see p. 340. 



1 1 8 White Mensural Notation 

maintaining that the use of accidentals for three tones clearly shows that the other tones 
were meant to be diatonic. As a principle, this author inclines toward the latter view, 
because of its stricter adherence to the original. In the measure to the syllable 'sal-(ve)' 
there is a clear indication of a diminished triad b-d'-P. As a matter of fact, diminished 
triads are extremely frequent in music from the thirteenth through the fifteenth century. 
This composition also serves to illustrate the problem of text-underlaying in early 
music. Two facts can easily be seen: first, that the original frequently leaves considerable 
room for doubt and speculation as to the 'correct' placing of the words, as for instance in 
the initial phrase of our hymn; second, that in those cases in which the placement of the 
syllables is unambiguous, the result is frequently contradictory to the modern principles 
of 'good accentuation,' as, for instance, with the words radix, angelorum, regina. In 
general, it can be said that modern editors and interpreters are frequently misled and 
biased in this matter by ideas which actually did not prevail until the middle of the 
sixteenth century (musica reservata, Josquin and his pupils). 

A transcription of the beginning is given in the appendix, No. 14. 

As additional exercise, the transcription of Facsimile 24 may now be 
completed, by adding the first Osanna and the Benedictus [sections (3) 
and (4)]. In the latter section, which is in two parts only, a rest to the 
value of two B occurs, simultaneously in both parts. That this is not a 
slip of writing is shown by the fact that the total of 24 B (4-measures) 
for this section (exclusive of the final L) is also indicated by the number 
of rests in the contra. This author is at loss to explain this strange 
interruption from the musical point of view; it may, however, have a 
* liturgical significance. 

Finally, an example may be studied which illustrates with particular 
clearness the difference between tempus imperjectum and tempus perjec- 
tum. The first Kyrie from Pierre de la Rue's mass L'homme arme (Fac- 
simile 27) has tempus perjectum for the discant, tempus imperjectum for 
the alto, whereas the bass carries both signatures. This last manner of 
writing is indicative of canonic procedure. Actually two parts are de- 
rived from the bass line, the tenor in [3, 2] and the bass in [2, 2]. As is 
customary with the 'mensuration-canons' of this period, both parts start 
simultaneously, the tenor an octave higher, as is also suggested by the 
position of the question-mark-like signum congruentiae. The second of 
these signs indicates the end of the canonic voice (tenor) which, owing 
to the larger value of the B in [3, 2], does not consume the entire melody 
given for the bass. In the original edition {Misse Petri de la Rue y 
Petrucci, Venice, 1503) which is in four part books, the tenor (not repro- 
duced here) carries the inscription: resolutio ex basso. 

As has been pointed out previously (p. 1 17), the dot after the second note of the discant 
serves both as a p.d. and a p. a. In transcribing the piece it will be noticed that the final 
notes (L) of the various parts occur at different places. They must, of course, be held 
until the end of the piece. This practice, an example of which occurred already in our 



Examples of Tempus Perjectum 
Facsimile 26 



119 



4 







S 



IF 



if-i-a,. 



4Zp[ 



5*Lf 



">> «5^4 M& -^ **« ^wm *»£*&•*£ [<Ch* Vtffcg (V*« 



«c.^«* 



HDC 



P^E 



* 



^H- 



^^ 



-^ 



Ar...ft 






1 



^ .^Au "' 






:ezr 



fl-V 31 ^ 



3=± 



^s 



"° Eg " <hr 



A»^<fi>v-wm fi»«« vnS>«J. fXweH <g*u 



ih 



^~T B T 



-*-* 



•^TT 



* 



4, 



M-f 



J— == — ~ Lp s» 



j° 



F^ 



*t 



'ffwi^ **•»* . /«V.tT<. 



H 



1 



^-Vrfcr*^ 






4-H-4-- 



f-J 



/ V t / :t±r: 



gfe^ zj^ 






E=^k 



w- 



r«*«^ «p**<t 



TIJ& 



-fl— a- 



^? 



MS Oxford, Bodleian Library Canonici misc. 213 (ca. 1450) 
Page 62 



iio White Mensural Notation 

Facsimile 6 (see p. t6), obviates the use of a method which is frequently useful in the 
deciphering of difficult passages, that is, working backward from the end. See the 
transcription in appendix, No. 15. 

This composition illustrates that problem of musica ficta which is most prominent in 
the sources of the sixteenth century, namely, that of the sharped leading tone. Several 
times combinations such as d-c-d occur which raise the question as to whether the c 
should be sharped {subsemitonium, lower semitone) or not (subtonium, lower whole-tone). 
Even among the more 'reserved' scholars and editors the inclination toward the subsemi- 
tonium is so common that it may seem to be almost dangerous to raise a voice of doubt. 
It is true that the evidence which can be obtained from a study of the sixteenth century 
keyboard and lute tablatures (particularly the numerous intabulations of motets and 
chansons) is, on the whole, in favor of the subsemitonium, at least for the cadential endings 
of passages or sections (much less so for leading-tones in the middle of a phrase; see 
W. Apel, Accidentien und Tonalitat, p. 62 ff). On the other hand, there is the testimony 
of so distinguished a writer as Glarean (he cannot be considered a 'theorist' in the ordinary 
sense of the word) who in his most judicious and detailed analyses of the compositions 
of Josquin, Isaac, Mouton, and others never mentions the subsemitonium, but frequently 
refers to the 'whole-tone to be added below the fifth g-d', and similar formations (see the 
above-mentioned publication, p. 63, footnote). Summing up all the evidence available, 
a very cautious use of sharped sevenths would seem to be most proper for music prior to 
1550. For compositions from the second half of the century, the use of the subsemitonium 
will probably have to be increased, particularly, of course, in the secular literature (chan- 
son, madrigal, etc.). 

D. Prolatio Perfecta 

Prolatio perfecta may occur in combination with tempus imperjectum 
or tempus perfectum. In the former combination, indicated by G or, 
in the present book, by [2, j] the S equals three M (* = ili ) with all 
the other values being imperfect. All the rules given for [3, 2] are valid, 
with the understanding that L, B and S are replaced by 5, S and M. 
Only rule 8 is to be omitted since minims do not exist in ligatures. 

It may be noticed that imperjectio ad partem (and partes) which is 
quite rare in [3, 2] is not infrequent in the present mensuration: 

■ ii*iUU N ui-i* H IIJJ -hi J JiJENWJ J>IJ J>J>J IJ.I 

The combination S M M S, corresponding in prolatio perfecta to the 
ambiguous combination B S S B of tempus perfectum, is more likely to 
call for imperfection than for alteration since the former interpretation 
leads to a group of two perfect S:%\ J J* J>J| a rhythm that better conforms 
to the imperfect tempus than the group of three perfect S, which would 
result if alteration were applied: |J.iJ|J. . However, the latter possi- 
bility cannot be ruled out, particularly in earlier sources. 

The tenor of Facsimile 30 (p. 139) may serve as a simple example of 
this mensuration. Its melody is the famous L'homme arme. As will be 



Prolatio Perfecta 
Facsimile 27 



121 



\ 











V«3I 




— <• 




s 




— - 5 

c 




*~=^ 




' 




— < 
i 

si 

• - 
<>- 


■ 


• ' 




4 <►- 




\ i\. 




1 . *v 


11 _L 




122 



White Mensural Notation 



seen later (p. 138), its actual pitch is a fifth below the written notes (wrong 
* clef?). See also p. 164 for remarks concerning the meter and tempo of 
this piece. 

In tempus perjectum cum prolatione perjecta, a mensuration which is 
indicated by the sign O or, in our explanations, by the symbol [3, j>], 
the B equals three S(x~<><>* ) and the S equals three M(*-<^i), while 
all the other values are imperfect. 

The rules of imperfection and alteration apply without modification, 
both in tempus and in prolatio. However, the combination of two ternary 
groupings brings about certain complications which demand attention. 
Particularly the imperfectio ad partem (and partes) , i.e., the imperfection 
of the B by the M occurs more frequently and offers a greater variety 
of combinations than in the previous mensurations. 

Normally, the B equals nine M; but it may be reduced by imperfec- 
tion of various kinds to any number of M down to four. No further 
reduction is possible since a value equaling three M can be expressed 
by a S. The following examples are illustrative: 



siffpTfinccfrctcrifiP''wpTcfinrtctrrwf"i 

The perfect B is transcribed here by the sign cJ: which provides a simple and con- 
venient expression, lacking in modern notation, of a note equalling nine eighth-notes. It 
may be noticed that these two dots are used in the same meaning in an Ave regina coe- 
lorum from MS Selden B 26, f. 12' (reproduced in J. Stainer, Early Bodleian Music, I, no. 
lvi). 

Another peculiarity of this mensuration is the fact that an altered 
note may be imperfected. The following examples illustrate this point, 
the theoretical interest of which is greater than its practical importance: 




•irirrnin rnrppr crin rppirTrririri ppiiprrff triri 

In the first example, for instance, the second S is altered from 3 M to 
6 M in order to make up the equivalent of a perfect B between the first 
and the last B; simultaneously, however, this altered S is reduced from 
6 M to 5 M by the following M. In the last example, alteration is ap- 
plied to pairs of M as well as to pairs of S. All the dots in these 



Prolatio Perfecta 123 

examples are puncti divisionis. As a matter of fact, puncti additionis 
are not possible in this mensuration, except for the smallest values (M, 
Sm\ 

Examples of this kind are more prominent in the theoretical treatises 
(particularly of the late fourteenth century; see GdM 1, 126 ff.) than 
in the musical sources. On the whole, it must be noticed that pieces in 
[3>3] are very rare in the manuscripts of white mensural notation. Only 
the earliest among them contain a few compositions in this mensuration. 
Two examples from MS Canonici 213 of the Bodleian Library (Facsimiles 
31 and 32, pp. 141 and 143) will be studied later, in extenso. However, 
certain passages may be briefly considered here, in order to illustrate 
the above explanations. 

(H)ughe de Lan tins' chanson Ce ieusse fait (Facsimile 31) shows no 
time signature. However, tempus perjectum is clearly indicated in the 
initial phrase of the discant, while the single M's later in the course of 
this part, as well as the groups of three M and the combinations S M 
towards the end indicate prolatio perfecta. Here follows the transcrip- 
tion of the beginning: 



The rhythm of the measures 7 and 8 is exactly the same as that of our 
first example illustrating the imperfection of altered notes. In fact, all 
these examples can be notated in a simpler way, by replacing the altered 
S by a B y and by applying to this B the methods of imperfection illus- 
trated by our first examples of tempus perfectum cum prolatione perfecta. 

As a further example, the tenor of the three-voiced Vince con lena of 
Facsimile 32 may be studied. Whereas the rhythm of the group B S M, 
beginning with the eighth note, is clear, the following group B M S leaves 
room for doubt as to whether the M imperfects the preceding B or the 
following S, in other words, whether the transcription: IJJJJ-I or: 
I J. JJ| is correct. The former rhythm would seem to be more natural 
and indeed is the proper one, as appears from the context of the other 
parts. 

The music for this chanson consists of two sections, the second of which begins with 
the words Gia 'namorato of the discant, and is indicated in the two other parts by the 
inscription: S[ecund\a p[ar]s. Whereas the first section contains various notational 
devices which will be explained later, the second section is free from such and may there- 
fore be transcribed in full at this point in our study. The first measures are given in the 
appendix, No. 16. For the complete piece, see p. 151. 



124 White Mensural Notation 

E. Modus and Maximodus 

As has been pointed out previously (p. 99 )> modus and maximodus 
are mensurations which occur only in the 'Pfundnoten'-tenors of masses 
and motets. The metrical scheme to be observed with such a tenor is 
indicated by the length and arrangement of the rests which usually ap- 
pear at the beginning of the tenor, or else are found somewhere during 
its course. According to whether these rests cover two or three spaces 
of the staff, the modus is imperfect or perfect, while their grouping to- 
gether in pairs or in groups of three indicates imperfect or perfect 
maximodus: 

[7/,II] [77, III] [777,11] [777,111] 



The imperfect mensurations, as indicated by these signs, usually 
exist in theory only. Thus, the first sign shows that the L and the Mx 
are both binary, but does not necessarily imply a regular division into 
groups of two and twice two measures. Under the second sign we are 
likely to find (perfect) modus y that is, groups of three measures, but 
rarely any clear evidence of maximodus (groups of twice three measures). 
Examples of perfect maximodus (signs .3 and 4) are very rare. They 
occur only in the isorhythmic motets of Machaut and of some of his 
followers, such as Dunstable. The tenor of a Veni sancte spirilus by 
Dunstable from the Old Hall MS serves as an example: 1 



According to the mensuration [777, III] indicated by the rests, each 
L equals three Z?, and three L form a group equivalent to a Mx. Obvi- 
ously, a first group of three L ends with the p.d. which also implies im- 
perfection of the last L by the subsequent B. Another group of the 
same length is formed by the Mx and the 7-rest (it may be noticed that 
the Mx itself was not admitted to be ternary; in other words, its maxi- 
mum value was six, not nine, B). Between these two groups we find a 
ligature B B L which, although the second B will have to be altered, 
would yield only two L. In order to reach the necessary number of three, 
the L must also be altered. The construction of the second half of the 
tenor is identical with that of the first. Here follows a schematic tran- 

1 The notation of the Old Hall MS is in black notes (see p. 364 ff). 



Modus and Maximodus 



125 



scription of the first half in which the value of each note is given in 
figures indicating the equivalent number of B (rests in parentheses): 
(9) I 3 3 2 1 I 1 2 6 I 6 (3) J 3 3 3 |. Each B equals a (^measure of 
the upper parts. The sign at the end of the melody indicates that the 
melody has to be sung three times. 



III. COLORATION 

THE TERM coloration {color) first occurs in the fourteenth century 
to designate the use of red notes for certain variations from the 
normal values which, at that time, were written as black notes. In the 
later period of black notation, white forms were frequently used instead 
of the red ones. When, in the middle of the fifteenth century, the forms 
for the normal values changed from black to white ones, the special 
values expressed previously by white (or red) notes now came to be 
indicated by black notes so that the practice of 'coloration' became a 
process of 'blackening.' In current terminology, both terms are used 
synonymously. Much in the same way as the term 'white notes' com- 
prises some black forms (Sm, F, Sf), there is one white form among the 
'blackened notes,' namely, the Sm which, however, is of rare occurrence 
(no corresponding forms exist for the F and Sf ) : 

LB S M Sm 

White notes: H W * I I 

Blackened notes: *| M ♦ I ^ 

Although the 'white' M and Sm are identical in shape with the 'black- 
ened' Sm and M respectively, the context always discloses which note 
is meant by I and I . In the following combination, *l>il , all the 
notes are 'white,' namely, S, M, Sm, Sm; whereas in the following ex- 
ample, + li± , they are all 'blackened,' namely, S M Sm Sm, as appears 
from the form of the S. 

Coloration is employed to indicate certain changes in note-values and 
rhythm. The following two rules constitute the basis of this important 
concept: 

i. A blackened note loses one-third of its value. 

i. Blackened notes are always imperfect. 

According to rule i, we have: Msfl;»=5so . In other words, three 
blackened notes equal two white ones: iM-dO ;♦♦♦=** • According 
to rule 2, we have: *=♦♦;♦=!! . Due to the imperfect quality of 
blackened notes, none of the principles of imperfection or alteration may 
be applied to them. 

The explanations on coloration given by both early and recent writers 
are not altogether clear and satisfactory. A real insight into this matter 

126 



Coloration in Tempus Imperjectum 



127 



can only be obtained if a strict distinction is made between the coloration 
applied to imperfect notes and that applied to perfect notes. This dif- 
ference can easily be demonstrated in modern notation. If, e.g., two 
ordinary half notes are equalled by three notes, triplets result: |JJ| = | J<JJ| ; 
if, however, two dotted half notes are equalled by three notes, the 
result is not so much a change of note-values as a change of accent, 
inasmuch as the next-smaller values, namely, the quarter notes, remain 
unchanged :|J-J-|- Id J J|. Since this change of accent, which is equiva- 
lent to a change of meter from \ to I, is very common in the courantes 
of the suites by Bach and others, we may be permitted to refer to this 
type of coloration as 'courante-coloration,' as against 'triplet-coloration' 
for the former type. We shall now discuss the use of coloration in the 
various mensurations. 

A. Coloration in Tempus Imperfectum 
Cum Prolatione Imperfecta 

In this mensuration B, S and M (even Sm) may appear in groups of 
three blackened in the place of two white notes: 

si j 



(b) 

(c) 



capiM 



c ♦<>♦♦♦ = 



cUilio 



U J J I 
U J J I 

11 j n\shj\ 



ii j j 



(a) is called color temporis, (b) color prolationis y whereas a special case 
of (c), consisting of a blackened S and a blackened M, is known as 
minor color (see below, p. 128). The following quotation from Cypriano 
de Rore's Tutti i madrigali of 1577 (the earliest instance of the partitura, 
see p. 19) provides a particularly clear illustration, owing to the score 
arrangement of the parts: 




In this passage the blackened notes appear in groups of three «?, 



128 



White Mensural Notation 



whereas the following example from the Odhecalon (p. 95, Gentil prince, 
contra) shows the use of three blackened M: 



The figure 3 is added here for the sake of clarity because of the identity 
in shape between the blackened M and the four normal Sm preceding 
them. 

Particularly frequent is the simultaneous use of coloration in all the 
parts, as in the following final passage of Jo. Sthokem's (Stokeghem) 
Porquoy je ne puis dire (Odhecaton, p. 18'/ 19): 




Transcription of the discant: 




If such sections are of any considerable length, change of meter in 
transcribing i,s more convenient than the writing of triplets. If this 
method is used it is imperative to indicate clearly and accurately the 
time-relationship between the two meters, as in the following rendering 
of the above passage: 

J: 




A specially important case of coloration in lempus imperjectum is the 
so-called minor color ^ consisting of a blackened S followed by a blackened 
M — a combination which may also be considered as the half of a color 
prolationis (half of three blackened S). No doubt this sequence origin- 
ally indicated triplet rhythm, in conformity with the general meaning of 
coloration. In the later fifteenth century, however, its meaning changed 
into a dotted rhythm, identical with that expressed by a dotted M 
followed by an Sm: ♦i=[J J /J =J3 = ±.± . 

Throughout the sixteenth century both manners of indicating dotted 
rhythm are used interchangeably, without any difference of meaning. 
It is not uncommon to find them side by side, not only in the same 



Minor Color 



129 



source, but in one and the same piece. J. Wolf {HdN 1, 394) cites the 
following example from Obrecht's mass Si dedero: 



Other instances of the same practice occur in the contra of Facsimile 34 
and in the chanson Dangier tu ma tollu (Facsimile 25, p. 109, discant). 

Although the second note of the minor color agrees in shape as well as 
in value with the second note of its equivalent in normal notation, these 
two notes should not be considered wholly identical. In the coloration- 
group, this note is a blackened M whereas, in the dotted manner of 
writing it is a 'white' or, more properly, a normal Sm. In studying a 
passage like that from Obrecht's mass the reader should not fail to notice 
this difference, for instance, between the second and the third note. 

Minor color appears frequently in connection with half-blackened liga- 
tures c.o.p., as follows: \?i;\?i = o*i . See the exolanations on half- 
coloration, p. 142. 

Finally, as a curiosity we reproduce a passage from a late sixteenth 
century publication (Didier le Blanc, Airs de plusieurs musiciens, 
Paris, 1579; repr. H. Expert, Monuments de la musique Jrancaise de la 
Renaissance, Paris, 1924, vol. 111,78) in which the 'inverted' form of the 
minor color, i.e., with the M preceding the S y is used: 



Expert merely transliterates this passage into a rather obscure modern 
version: <t JJJJdl J «| JJ| . A proper transcription would be as follows: 




puis-san-ce 



fin - que mon coeur 



bles-se 



It is not without interest to notice in this song, not only the influence 
of the French humanism, with its novel but sterile ideas of 'correctness' 
in poetry and music, but also an early instance of the iambic rhythm 
which, under the names 'alia zoppa,' 'lombardic rhythm,' or 'Scotch 
snap,' is known as a characteristic feature of seventeenth century Italian 
and English music (Caccini, Monteverdi, Frescobaldi, Blow, Purcell, and 



13° 



White Mensural Notation 



others). Much rarer than the minor color prolationis, as the combina- 
tion S M might be called, is the minor color temporis, consisting of a 
blackened B and-a^adtejied^an. example of which is shown at the 
beginning of the following chanson from the Chansonnier Laborde (p. 21): 




Here, one might be doubtful as to whether to apply the change of 
rhythm from triplet to dotted notes. However, the fact that even meter 
prevails strongly throughout the piece would seem to constitute an argu- 
ment in favor of such a change: 1 




B. Coloration in Tempus Perfectum 
cum Prolatione Imperfecta 

In this mensuration coloration cannot be applied to the S 3 since this 
note already appears normally in groups of three. However, it may be 
applied either to the B or to the M. In the latter case it refers to an im- 
perfect note and, hence, is triplet coloration: ooiA.iilti =|| J J2 J^IJ.I . 

1 In the seventeenth century, the rhythmic clash caused by triplet-coloration, if used against 
normal values in other voice-parts, was no longer felt as an interesting subtlety but rather as an 
unnecessary disturbance. As a result, explanations occur in this period which interpret such a 

group in duple rhythm as follows: JJJ _ J^j (see, e.g., MuT, 16, referring to a treatise of Mel- 
chior Vulpius from 1641!). Jl^. 

It is not impossible to assume that this modification of rhythm made its appearance already in the 
late sixteenth century. However, it can certainly not be applied to compositions of Josquin or 
Isaac, as has been advocated by E. Praetorius who, in his Mensuraltheorie des Franchinus Ga/nrius, 
on the basis of the above interpretation, arrives at a 'neue Uebertragung' of such compositions (p. 
5 2 > 10 7), rejecting the traditional method as a 'rhythmisches Labyrinth' (p. 106) or 'rhythmisches 
Zerrbild' (p. 52). Such statements, resembling in character the familiar outcries over 'crude parallel 
fifths' and 'unbearable dissonances' hardly need to be refuted. Suffice it to state once more that 
throughout the fifteenth and sixteenth centuries coloration in tempus imperfectum calls for triplets, 
with the exception of the minor color. 



Coloration in Tempus Perfectum 131 

More important is the coloration of the 5, according to the equation: 
ac-iii . The blackened B may, of course, be replaced by smaller 
values, or two of them by a blackened L. The modern equivalent of 
uhmmm is: 2UU.IJ JJJ| • If two of the 4-measures are combined in one 
4-measure, the courante-character of this rhythm becomes still more 
evident: $|J.J.|J JJJI . This type of coloration {color temporis) is also 
known as hemiolia temporis or hemiolia major. 1 

If in the above equation the B are replaced by S we find that there 
are six on each side or, in other words, that the white S is equal in value 
to the blackened S y both being represented by a quarter note of our 
transcription. It should be noticed that this fact is not in keeping with 
the first of our rules of coloration, according to which blackening always 
entails a loss of one-third of the value. As a matter of fact, this rule, 
in its unlimited application, holds good only in imperfect mensuration. 
In perfect mensuration, however, it applies only to the largest value 
(i.e., the B in tempus perfectum, the £ in prolatio per/ecta) y not to the 
smaller ones replacing it. This point will be clarified by the following 
chart in which the L is considered the common point of departure, and 
is, for the sake of comparison, represented by the figure 24: 

24 0.) = 24(C) 

[ 2 J 2 \ + H = S + M + H a:«=«:6»3:2 

3 *0+*0 = 2 * ♦+♦♦+♦♦ *:*-6:4«3:2 

UU41U = UU-+UU+U'A4 W-.:.-3:a 

2*W - 24(L) 

[3> 2 \ U+H - % + H + M a:B-tt:s=s:2 

2 O <> + <► O ♦ - 2 * ♦ +♦ » +♦ ♦ 0:4 .4: 4- i:i 

The result of coloration in [3, 2] is usually described as a change from 
tempus perfectum (B = jS) to tempus imperfectum (B = 2S). However, 
it should be noted that not only does the tempus change but also that 
the modus simultaneously changes, namely from imperfect (L = 2B) to 
perfect (L = jB). Therefore the result is correctly described as a transi- 
tion from [II, 3] ([II, 3, 2]) to [III, 2] ([III, 2, 2]). 

Instead of the method of transcription given above, in which, for the 
passage in blackened B, two 4-measures are combined into one 2-measure, 
modern publications generally retain the original meter as follows: 
'IJJUJI. Although this rendition is, of course, mathematically cor- 
rect, it implies a syncopated effect which in our opinion is foreign to 

1 Hemiolia is Greek for one-and-half. 



132 



White Mensural Notation 



coloration. The meaning of coloration is not a jazz-like suppression of 
the strong beat, as in (a), but a change of accent, as in (b) : 

a) _ 




This point may be further clarified by the following consideration. 
There frequently occur passages in coloration the rhythm of which could 
easily be expressed in normal notes, and in which, moreover, the writing 
in white notes actually duplicates the notation in blackened notes. For 
instance, in the following example the values of the black notes are the 
same as those of the white notes, namely, 2, i, i, and i S: o«**« = oh«-«b . 
However, one should not jump to the conclusion that both progressions 
are plainly identical. There remains, indeed, the above explained dif- 
ference in phrasing or accent: (^♦♦K = l|<^ J J J| ;OH«-^B=4lJ J|JJ|=$y J J J| . 

This difference is obscured if 4-measures are used for the blackened 
notes. But it was undoubtedly this change in accent which the old 
masters wanted to stress by the employment of coloration. H. Beller- 
mann {MuT, p. 27) rightly points out that this rhythmical finesse still 
persists in the works of Bach and Handel, but was lost in the period of 
the Viennese classics. 1 As an example, he cites the following passage 
from Handel's Messiah in which coloration, although it is not notated, 
is clearly suggested by the original English text, but is obscured in 
Mozart's German version: 



glo-ry, the glory of the Lord shall Be re-vea - led 
Eh - re, die Eh - re des Herrn wird of - fen -bar 

What is true of Handel and Bach is certainly even more true of the 
masters of the fifteenth and sixteenth centuries, who still possessed a 
notational method of indicating this rhythmical effect. Unfortunately, 
in their case Bellermann fails to observe the principle which he expounds 
so clearly in his remarks concerning Bach and Handel (see, e.g., the 
passage from Dufay's mass Se la face ay pale, MuT> p. 33). 

Before transcribing a passage in coloration the student is advised to 

1 As is well known, it has been revived by Brahms. 



Coloration in Tempus Perfectum 



*33 



count the number of B involved. If there are three B (or their equiva- 
lent in smaller or larger values), as is normally the case, the passage will 
occupy exactly two 4-measures or one 2-measure, as in all the above 
examples. There are cases, however, in which the blackened notes are 
not sufficient in number to constitute a complete measure, for instance 
in the following passage from the same mass (see MuT, p. 34): 




Here, the group in coloration which comprises notes in the equivalent of 
only two blackened B> is completed by a group of white notes (S M M) 
in the value of a third B. The use of the white instead of the blackened 
forms is admissible because they have identical values (see p. 131). 

More interesting is a passage from Hughe de Lantins' A madame 
ptaysante y in which the coloration-group is split into two sections by an 
intermediate section in white notes (see the facsimile no. 4 in J. Stainer, 
Du/ay and His Contemporaries, London, 1 ! 



P^ 



3 






« 



.r»-ft^J»« 



If one transcribes this passage in f-meter throughout, one arrives at 
a result (a) which, although mathematically correct, is musically dull. 
However, the melody becomes alive and corresponds much more closely 
to the text (cf. the words 'ung chapelet') if the meter of the transcription 
is changed according to the notation of the original, as in (b) : 




vueil jedon- ner ung cha— pel-let 



These two transcriptions illustrate two different concepts of syncopa- 
tion, the first of which is based upon the idea of 'omitted strong beats in 



134 



White Mensural Notation 



unchanged meter,' whereas the second involves an irregular succession 
of strong beats due to change of meter. While the former meaning is 
the familiar one (particularly in modern jazz), the latter prevails in early- 
music (particularly in the fourteenth century, see pp. 395 ff, 414) as well 
as in the works of contemporary composers, such as Hindemith and Stra- 
* vinsky, who frequently mix measures of J, J, J, etc. 

A similar passage occurs at the beginning of the second staff of Fac- 
simile 23. The student is advised to transcribe the whole piece, Dufay's 
chanson, Queljronte signorilk^ which according to the inscription 'Romae 
ccmposuit' was the fruit of his trip to Italy. We suggest the following 
manner of transcription (beginning with the last two notes of staff 1): 




Slightly more difficult than Dufay's chanson is a motet, Anima mea y 
by Leonel [Power] 1 which is reproduced on Facsimile 28. The tenor 
as well as the contra show several complete groups of coloration (L B, 
B B B, B B S S) y each of which is the equivalent of a 2-measure. The 
single black B at the end of the first staff of the tenor has no particular 
significance; its value of 2 S could also be expressed by a white B, im- 
perfected by the preceding S. The last black B of the contra, however, 
is part of a split group of coloration, the other parts of which (S S B) 
are found shortly before. The rhythm of this passage is exactly the 
same as that from Quel fronte signorillz. 

Particularly interesting is a group of black notes: B M M S M which 
occur in the middle of the second staff of the discant. These notes, 
which together have the value of a perfect white B, must be read in 
[3, J>] and therefore, must be transcribed as a ^-measure or as triplets 
within a 4-measure (the B is reduced by imperfection to the value of 
4 M). A similar combination of notes occurs at the end of the third staff, 
but with two white M instead of the black S and M of the other group. 



J The composer's name is given in the MS Modena, Bibl. Estense, L. 471. 



Coloration in Tempus Perfectum 
Facsimile 28 



i3S 







s 




136 White Mensural Notation 

The blackened B MM of the second group can be interpreted in two ways, 
either in the triplet rhythm that is clearly indicated in the former group, 
or else as an example of minor color temporis, that is, in dotted rhythm. 
The relatively early date of the composition (ca. 1450) weighs in favor of 
triplet rhythm which is the original meaning of all coloration groups. 1 

The initial note of the tenor is a Mx, as is also the second note of the ligature near the 
middle of the next staff. A p.d. is missing at the end of the first staff of the discant. 
The Modena MS shows several sharps (evidently all added by a later hand) which would 
make the following tones B-naturals instead of B-flats: third note of the tenor; sixth 
note of the second staff of the tenor; fourth-to-the-last note of the second staff of the 
contra. The beginning of the tenor is transcribed in the appendix, No. 17. 

As a last example, Facsimile 29, containing a three-voice chanson 
* Monsieur, may be studied. 

This piece illustrates the special difficulties which, in some sources, arise from the care- 
less writing and from clerical errors. Following is a list of the most important ones: 

Discant: (1) The clef is missing; the melody begins on c". (2) The ninth note is prob- 
ably a plain 6" on c", not a dotted M on d". (3) The vertical dash near the middle of 
the second staff is not a B-rest, but a mere sign of demarcation, indicating the beginning 
of the second section; the same sign occurs in the tenor; however, both voices begin 
simultaneously with the contra in which there is no such sign. Tenor: (1) The first note 
of the second ligature is meant to be L. (2) The sixth note on the first staff of p. 23 
should be white. Contra: (1) The third note after the fermata is stricken out; (2) The 
next-to-last S should be c. 

Of special interest is the passage which begins with the eleventh note (e) of the third 
line (discant;, and which recurs on the first line of the right-hand page (beginning with 
the i6th-note). The original writing shows the combination S M . Sm £>'m Sm, which 
yields five M. From the context, however, it appears that this passage must fill in a 

whole measure, or six M. In other words, the meaning is not J J 1 . Jjj but J J_JJJJ . 
Apparently, this is not a clerical error but an emergency manner of writing necessitated 
by the fact that the latter rhythm cannot correctly be expressed in mensural notes. 

The use of coloration in tempus perjeclum persisted throughout the 
seventeenth century. In many courantes of this period the change from 
4 to 2 is indicated by blackened notes. Blackened notes are also fre- 
quently used in later sources (after 1550) for the expression of the iambic 
rhythm which was formerly indicated by alteration, e.g.: o***a**MH 
instead of: o**«H*-o^B . 

C. Coloration in Prolatio Perfecta 

Here only one type of coloration is practically possible, namely, that 
of the S: G <><>♦♦♦ =|| T'T'\TTT\ {color prolationis, hemiolia minor, hemiolia 

1 In the MS Modena both groups show the same notation, i.e., that of the second group in our 
MS. 



Coloration in Temp us Perfect urn 
Facsimile 29 



137 




<L> "1. 



c/) 



138 White Mensural Notation 

prolationis) . Aside from the shift to smaller values, the explanations 
given for tempus perfectum apply without modification. Again, colora- 
tion affects not only the prolatio, which changes from perfect to imper- 
fect, but also the tempus, which changes from imperfect to perfect. In 
other words, the result is a transition from [2, j] to [3, 2], or, in modern 
terms, from | to J. 

Facsimile 30, the tenor of which has already been studied, serves as 
an example. The coloration-group M M S S on the second staff of the 
discant (between 'cum gloria' and 'iudicare vi[vos]') begins in the middle 
of a ^-measure, so that the following succession of measures: jj, 4, f results 
in the transcription. 

In this piece not only the white form of the Sm (see p. 87) but also the white form of 
the F, with two flags, is used (e.g., discant, near end of the third staff). The distinction 
between the p.a. and the p.d. — the latter being placed higher or lower than the note — is 
rather consistently carried out. The tenor is erroneously notated a fifth too high, as has 
* already been pointed out. The beginning of the discant and tenor are transcribed in the 
appendix, No. 18. 

In [3, 3], triplet-coloration is of course impossible, due to the absence 
of binary values. Courante-coloration can be applied in different ways. 
In color temporis three blackened B will be equal to two white ones. 
Since a white B equals 9 M, the blackened B is worth 6 M; hence, if a 
blackened B is broken up into two S, each of these is worth three M 
and, therefore, equal to the white S. Example: 



II JJ J>|J. JJJ.J.J.IJ. Jl =11 U J)|g J. IJ.IJ.J.I1 J. J.I 

The latter transcription is preferable (three g-measures are written in- 
stead of one ^-measure). 

In color prolationis, three blackened S will be equal to two white 
ones, thus occupying two-thirds of a full measure. Since the white S 
equals three M, the blackened S will be equal to two M. If, in such a 
combination, two blackened S are. replaced by one blackened B, this B 
equals in value 4 M. Example: 

= §|JJ]J.JJ>|JJ>J.J>J l=|| J7JJ.JJ^IlXJi||^-JI 



Coloration in Prolatio P erf e eta 
Facsimile 30 



139 




cm' 

5 



*Q OO 

S 8 

u 

C 



140 White Mensural Notation 

It appears that the value of the blackened notes essentially depends 
upon whether they form a part of color temporis or color prolationis. 
Shorter groups, consisting chiefly of S, are likely to be color prolationis, 
longer ones, particularly a group of three B, are likely to be color tem- 
poris. In cases of doubt the proper evaluation must be derived from 
the context. 

Several instances of color temporis are found in Hughe de Lan tins' 
chanson Ce ieusse fait (Facsimile 31) which already has been considered 
in part (p. 123). In addition to various examples of the imperfection 
of the B from nine to five M (usually in the combination: S B M) there 
is, at the beginning of staff 6, an example of a L being imperfected by 
a preceding as well as by a following S which reduce its value from six 
to four S. 

The application of our 'rules of the B and B-flat' (see p. 104) is recommended for the 
discant of this piece which is another example of the partial signatures. Its beginning 
furnishes a remarkably early instance of the imitation in the fifth. See the transcription 
in the appendix, No. 19. 

The poetical-musical structure of this chanson is that of the mediaeval rondeau, as it 
originated with the trouveres of the thirteenth century. The music falls into two sec- 
tions, a and b (b begins with the words Je seroye plus, end of the first staff), which are 
repeated according to the scheme ABaAabAB (capital letters indicate # the refrain, 
i.e., repeated text). The underlaying of the full text is as follows: 

A l. Ce ieusse fait ce que ie pence — Et se jefusse en mon pays 
B 1. Je seroye plus que assouvis — D' avoir une telle chevance 

a 3. Car iay desyr de I'aliance — De la tres be'.le au doulx cler vis 
A 4. Ce ieusse fait ce que ie pense — Et se jefusse en mon pays 

a 5. Done ne Tames en oubliance— Si fort y ay mon cuer assis 

b 6. Et si luy plest que ses amis — Soie de tout iay souffisance 
A 7. Ce ieusse fait ce que je pence — Et se je fusse en mon pays 
B 8. Je seroye plus que assouvis — D' 'avoir une telle chevance. 

In the modern transcription, the distribution of the text can conveniently be indicated 
as follows (refrain in italics): 

a b 

1.4.7. C f * eusse 2 -8- J^ seroye 

3. Car iay 6. Et si 

5. Done ne 

Examples of color prolationis occur in the Vince con lena of Dom. 
Bartholomeus de Bononia (Facsimile 32). The coloration passage near 
the end of the third staff includes a full group of color prolationis, since 
it consists of notes to the value of three blackened S: 



AJ> J>= J> 1 



rs 



Coloration in Prolatio Perfecta 
Facsimile 31 



141 






v^r* 



$ 






rf^ m "^ <\c g 



^cfcw^ jrfi*"^ 



±^4 



r'-er 



HAS. .^ 3j 



f^'^y''^^^ ' 



-./ 









1 






°^ w g\ J 



T\^'<. gggg j 










ffi- 






tea ^H^a g 







wi 



mggeg < ^pr 




1 fy* ft>-Cf ^T 1 ^ 'Tf^Vc-iftrTj.w*., «*■ "ir *^*«^'«'»^4v~t S»wCt»v.p.^L 



MS Oxford, Bodleian Library Canonici misc. 213 (ca. 1450) 
Page 46 



142 



White Mensural Notation 



The two blackened S at the beginning of the discant are an incomplete 
group of coloration and, hence, bring about syncopated rhythm: 



For the full discussion of the piece, see p. 151. 1 

D. Half-coloration 

Half-coloration is applied to two-note ligatures, particularly c.o.p., 
and to single long notes. The former procedure, which has already been 
referred to on p. 129, simply means that of the two notes of the ligature 
one is normal, the other blackened. The contra (abbreviated ont[ra\; 
the initial C is missing) of a Quia respexit from Brussels, Bibliotheque 
Royale MS 6428, serves as an illustration: 




ylHll.^lW^ 



I 



The vertical dash through the circle indicates tempus perjectum diminutum (see p. 
148) which, however, in the present case has no different meaning from the ordinary 
tempus perjectum (see p. 191 f). 

The first and second passage in coloration are color temporis whereas, 
in the second line, there is an example of minor color. It is interesting 
to note that the dotted rhythm expressed by the latter is exactly the 
half of that expressed by the same notes (S and M) at the beginning of 
the second passage:*-!* ~ =l| s UpJii| ; . # U -IW^WI -*IJ.J3,J1 • 

Half-blackening is also applied occasionally to single notes of larger 
value: ^ «■ . Such a note may be considered as being equal to two 
notes of the next smaller value, the second of which is blackened. Thus, 

1 Blackened notes were also used in those passages, not infrequent in the compositions of Dufay 
and his successors, in which a single part is notated 'divisi,' i.e., with two simultaneous notes instead 
of a single one. For an example see the reproduction of the contra of Exultavit, p. 192. It is prob- 
ably this usage which accounts for the sixteenth century English practice of writing a middle part 
of a keyboard composition in blackened notes (see p. 12). 



Half -coloration 



H3 



Facj 



SIMILE -12 



9^ f+£-m fcfi~3 









z 1 



y i - m-^Sw. ^""vE^-gj* 1 ^ a m 



rf- V a jf 1 ')^^.^^'!^, , J *zb ' 






...... "re.. &3X*w?7,i*fiM£w^ 



^mmwm 



feaa 



a 









L/ 7 









rr-F-^a^ 



Oxford, Bodleian Library Canonki misc. 213 (ca. 1450) 
Page 135 



144 White Mensural Notation 

in tempus perfectum the Z., instead of equalling in value two white B of 
three S each, would be equal to one white B and one blackened B, with 
a total of five S. Similarly in prolatio perfecta, the half-blackened B 
would be equal to 5 M, instead of 6. Such notes occur in the Sanctus 
of Isaac's Missa Paschalis, which is reproduced on p. 43 of J. Wolf's 
Schrifttafeln and — together with a transcription — in his HdN 1, p. 420. 
Theorists also discuss the value of half-blackened notes in imperfect 
mensuration. Here, half-blackening would entail a loss of one-eighth 
of the original value, e.g., the half-blackened L would equal 4 + 3 M, 
instead of 4 + 4. Whether these speculations have practical significance 
this writer is not in the position to say (see HdN 1, 403). 



IV. PROPORTIONS 

A. History and Terminology 

THE USE of proportions, that is, of the diminution and augmenta- 
tion of metrical values in certain arithmetic ratios, is a characteristic 
feature of the Flemish music of the fifteenth and early sixteenth cen- 
turies. 1 Its history, however, goes back to considerably earlier periods. 
The first traces of this method are encountered in some of the clausulae 
of the period of Perotinus (ca. 1200), in which the liturgical melody 
serving as a tenor appears twice, the second time in half or double the 
values of the first appearance (see p. 245). The same procedure is 
normally found in the tenors of the motets by G. de Machaut (see p. 358). 
Here again, the second section of the tenor repeats the melody of the 
first in notes of half the value, each L being replaced by a J5, etc. In 
the later fourteenth eentury principles evolved which allowed one to 
indicate the reduction of value, not by actually using smaller notes, but 
by certain signs of diminution. It is this idea which is the basis of the 
proportions proper. 

The earliest mention of proportions is in the Libellus canlus mensura- 
bilis secundum Joh. de Muris (CS in, 58), a treatise of the mid-fourteenth 
century, in which diminutio (i.e., dupla) is discussed. Proportions are 
explained more fully by Prosdocimus de Beldemandis, in his Tractatus 
practice de musica mensurabili of 1408. He mentions proportio dupla , 
tertia, sesquiallera y sesquitertia and dupla sesquiquar/a, and indicates the 
signs designating them (CS in, 218). Guilelmus Monachus, in his De 
preceptis arlis musice libellus, (ca. 1460) expounds the entire system in a 
very learned manner, and illustrates it by numerous examples (CS in, 
277-288). The subject is treated most exhaustively by Tinctoris in his 
Proportionale musices, written around 1480 (CS iv, 1 53-177), and by 
Gafurius in his Practica musicae, Milan, 1497. In this period the system 
of proportions developed far beyond the bounds of practical application 
into the realm of pure speculation. Gafurius, for instance, does not 
hesitate to explain proportions calling for a diminution in the ratio of 
9:23. Needless to say, even the theoretical value of such extravagances 

1 Nonetheless, the term 'proportional notation,' which is frequently used as a name for mensural 
notation, is a misnomer. 

145 



146 White Mensural Notation 

is doubtful, to say nothing of their bearing on actual music. It will 
suffice to indicate only briefly these theoretical proportions in a general 
survey; then we shall proceed to an explanation of those which are of 
practical application. 

The mathematical foundation of the entire system of proportions as 
given in the above treatises goes back to Boethius. 1 Following his 
teaching the theorists of the late fifteenth century distinguished between 
five species of proportions, i.e.: genus multiplex, genus superparliculare, 
genus superpartiens, genus multiplex superparticulare and genus multiplex 
superpartiens. In terms of modern arithmetic, the first genus comprises 
all fractions the denominator of which is 1, e.g., proportio dupla=\; 
tripla=\\ quadrupla=T, etc. The second genus comprises all fractions 
the numerator of which is one more than the denominator. In Latin ter- 
minology, these fractions were indicated by the prefix sesqui- (semique-), 
which actually means addition of the half: 1 + \ = f . In conjunction 
with the terms -altera, -lertia, -quarta etc., it designates the fractions 
f, -f, f, etc. The third species includes fractions in which the numerator 
is two, three, etc., more than the denominator. For instance, proportio 
superbipartienle tertias means a fraction in which the denominator is 3 
{tertias), and the numerator is two (bi-) more than the denominator, 
i.e., f. Likewise, proportio supertriparliente quintas is the fraction f. 
In the fractions of the fourth species, which in a way is a combination 
of the first and the second, the denominator must be multiplied by a 
given number, before one is added. For instance, proportio tripla sesqui- 
tertias means a fraction in which the denominator 3 {tertias) has to be 
multiplied by 3 {tripla) and then augmented by one {sesqui-), i.e., V". 
Similarly, proportio quadrupla sesquiquinta is tt. Finally, in the last 
species (combination of the first and third) a similar process of multipli- 
cation is applied to the proportions of the third genus. For instance, 
proportio dupla supertriparliente quartas means that the denominator is 
4 {quartas), and that the numerator is 4 X 2 + 3 = 11; therefore, the 
fraction is :L t. The inverted fractions are indicated by the prefix sub-; 
for instance, proportio subdupla supertriparliente quartas means rf. 

These arithmetical proportions are used in mensural notation to dimin- 
ish or increase the value of a note in certain ratios. As will be explained 
later (p. 191 ff), the whole system of mensural notation rests upon the 

1 Boethius, the authoritative philosopher of the early sixth century, deals with the proportions 
from the standpoint of arithmetic. Musical theorists of the Middle Ages frequently used the 
terms to denote ratios of vibrating strings, i.e., intervals. For instance, sesquialtera is the fifth 
because strings sounding c and g are in the ratio of 3 to 2. 



Proportions 147 

principle of a fixed, i.e., unchangeable unit of time, the tactus, a beat 
in moderately slow speed (M.M. 50-60) which pervades the music of 
this period like a uniform pulse. The tactus (/) is normally represented 
by the S: S — /, with the other notes being multiples or fractions thereof, 
e.g., in [3, 2]: B = jt, M = \t, etc. These normal values of the various 
notes are called integer valor. If a note appears in proportion, its value 
is that part or multiple of its integer valor which is indicated by the 
proportion. Oddly enough, the proportions are used in mensural nota- 
tion in exactly the reverse meaning they would seem to indicate. For 
instance, proportio dupla (?) and tripla (1) do not indicate multiplication, 
but division of the values by two or three. In other words, all the pro- 
portions which are indicated by fractions larger than one (and only these 
are of practical significance) are diminutions. For instance, the value 
of a S in proportio dupla (1) is \ t, while the value of a perfect B in 
proportio sesquialtera (f) is I of 3/ = 2/. 

It goes without saying that these calculations are given here merely for 
purposes of demonstration. For the study of musical examples, appro- 
priate groups of notes rather than single notes should be considered. 
The general principle may be formulated as follows: In a proportion 
indicated by the sign ™, m $ equal n S of the integer valor. For 
instance, in the following example:0«*osoooo the four notes which 
follow the sign J occupy the same space of time as three S of the integer 
valory that is, the same time that is consumed by the three notes pre- 
ceding the proportion. Similarly, in proportio dupla or tripla, two or 
three S of the proportion will be equal to one of the integer valor. All 
these facts are easily retained if one understands that in a sign of pro- 
portion such as 3 or \ the denominator refers to the notes preceding the 
sign {integer valor), and the numerator to those following it (propor- 
tion). 

In addition to the fraction-like signs of the system just explained, 
certain special symbols were used for the simplest proportions. Proportio 
dupla, also called diminutio or diminutio simplex, is usually indicated 
thus: D ; Ct : C2 ; : 02 ; proportio tripla thus: C 3 ; O 3 . In certain early 
sources, around 14.00, the following modifications are used for proportio 
dupla: j? ; ■©- } 

Duple and triple proportion are not only the most frequent, but also, 
in a way, the most difficult ones. Since they have many features in 
common, it seems advisable to explain their general principles in con- 
junction. 

1 See Facsimiles no. 39, 71, and 88. 



i 4 8 



White Mensural Notation 



B. Proportio Dupla and Tripla in General 

The following equations may be considered as the basis for the appli- 
cation of these proportions to either tern-pus imperjectum or tempus 
* per jec turn: 

0)<t * ♦ «c* (!)([) n«oo 

(5)C3«0«sCO (4)03*00=0* 

These equations lead to the following scheme of transcription for a series 
oiS: 



C 
(D <t 
(3) C3 



J J I 

n n i 

JT2J72\ 

8 3 



jV 



o I J J J I 

(2) i n n n i 

u) 031 SJ1JT2JJ1 1 



Whereas in the two integer valor- mensurations the taclus falls on the S, 
it falls,' in the proportions, on a group of two or three S or, in other 
words, on an (imperfect or perfect) B. It is for this reason that the 
integer valor was called by Italian sixteenth century theorists alia semi- 
breve, and the proportion (particularly the dupla) alia breve. This name, 
together with the sign <t exists still today, the last vestige of the pro- 
portional system. 

It will be noticed that, in the case of (2) and (3), there exists a certain 
contradiction regarding the grouping of the S, insofar as different group- 
ings are indicated by the plain mensural sign and by its proportional 
variety. Indeed, whereas the semicircle suggests groups of two *S", the 
sign C 3 actually calls for groups of three; similarly, whereas the full 
circle would seem to indicate groups of three S, groups of two are actu- 
ally demanded by . Briefly, both signs of duple proportion, (1) and 
(2), must be read in tempus imperjectum (B = 2 S), and both signs of 
triple proportion, (3) and (4), must be read in tempus perfect um (B = 3 S). 




oul r r'piLLr llt - or: < r rv lu iljlt 



Proportions 149 

The schematic example on page 148, bottom, showing four proportional 
readings of the same melody, serves as a further illustration of this 
important point. 

It appears that with each of our four species the rhythm expressed 
by a proportional sign can also be expressed in integer valor, if the next 
smaller note values are used, as follows: 

(i) $ H * i i - c ♦ ^ 1 1 (2) <J> tl <> * p «o«44o 

Simultaneously with the shift of note values indicated by these equa- 
tions there occurs a displacement of the mensurations. That which is 
written proportionally as tempus actually is the prolatio of the integer 
valor, etc. In order clearly to indicate this important fact, it may be 
useful to introduce terms such as 'notated tempus' and 'actual tempus' 
In both proportions, then, the following displacements occur: 

notated modus = actual tempus 
notated tempus = actual prolatio. 

The observation of these facts is particularly useful in the two quasi- 
contradictory proportions (2) and (3). When it has been said above 
that the following sign, , calls for tempus imperjectum (in spite of 
the whole circle), we must now add that this tempus imperjectum is only 
illusory — that is, it appears merely in the writing; in reality, however, 
it is prolatio imperfecta. This same prolatio imperfecta is already present 
in the integer valoro, so that actually no change in mensuration occurs. 

On the other hand, the triple meter in the tempus of the integer valor 
is continued as modus in the proportion. As a matter of fact, in prac- 
tically all cases one will find that the passage in proportion contains 
groups of three B so that it may naturally be interpreted in the sense of 
modus perfectus. This perfect modus, then, actually preserves that per- 
fect mensuration which, in the integer valor, is represented by the 
tempus. Therefore, it is generally possible to maintain in the propor- 
tion the 4-meter used for the transcription of the integer valor. One 
might simply say — as the old theorists frequently do — that the whole 
circle refers, not to the (notated, imperfect) tempus, but to the (notated, 
perfect) modus, which, owing to the diminution, becomes the (actual, 
perfect) tempus. In this connection it is interesting to note that various 
theorists of the sixteenth century, by disregarding the reduction of the 
note values, adopt the sign as an indication for modus perfectus, al- 



ISO 



White Mensural Notation 



though without consistency (see the table of Ornithoparchus, HdN I, 

413)- 

The result of the above explanations may be summarized as follows: 
The four elementary proportions (£;(|);C3;03 are nothing but the four 

elementary mensurations C;0;G;0 , but written in the next-higher note 

values and performed with the tactus falling on the B instead of on the S. 

Their notational and actual significance appears from the following 

tabulation: 



Notated 



1 



<t [H,2] 

[111,2] 

C3 [II, 3 ] 

03 [HI, 3] 



Actual 
♦ I 
[2, 2] 

[2, j] 

[3>J] 



i 



As an illustration, we reproduce a well-known melody in what may be 
regarded as the modern equivalent of integer valor ( O ) and proportion 
(0): 



The following example shows the application of the four proportions 
to one and the same melody. The proportions start with the sign Z , 
the first three notes being in integer valor: 




After these general explanations, we now turn to the detailed study 
of the various proportions as they occur in the musical sources. 



Proportio Dupla 151 

C. Proportio Dupla 

An examination of the sources of the fifteenth and sixteenth centuries 
reveals interesting and significant changes in the practical application of 
this proportion. In the earliest manuscripts of white notation (as well 
as in the latest sources of black notation, see p. 404 f) the diminutio is 
used chiefly in order to introduce into perfect prolation short groups of 
duplets, which can be rendered in modern writing as under (a) or as 
under (b): 

.... <a)8|JJ>.TOlJ3J33|JJ3lJj>J.| 

(b)8UJ>J33iiJ]J33IJ.^I8JJ>J.I 

Examples are found in Facsimile 32 which already served as an illus- 
tration of coloration in [3, j]. Several times, groups of six S occur under 
the sign 3 . Such a group equals three S or, in other words, a perfect 
B, of the integer valor, thus filling in one complete s-measure of the 
transcription. It is interesting to consider the reason why the desired 
change of rhythm from triplets to duplets is indicated by a proportional 
sign, instead of simply changing from prolatio perjecta to prolatio imper- 
fecta, as follows:e^i^icii^ii-lli • 

Apparently, the reason is that this manner of writing may be misinter- 
preted, by considering the M as the unchanged temporal unit, instead of 
the S. Thus, the result would be as under (a), instead of as under (b) : 

(,) tiiminj \njm\ Mil }.m'\in}\njW\ 

The mensuration of the piece is [3, j] y ^-meter, with some passages 
in [2, j], g-meter. However, neither of these meters is always strictly 
observed. The section in [3, j>], middle of the second staff, includes 12 
M, instead of 9, and the section in [2, j] beginning near the end of the 
first line of the contra includes one half-measure (J) in addition to five 
full ^-measures. 

As has previously been remarked (p. 123), the piece consists of two sections, a and b. 
Its musical form is that of the ballata (the French virelai): A b b a A 

A: Vince con lena al periglioso scoglio (ripresa) 

b: Gia n'amorato a gli amorosi segni 1 , . ,■■. 

b: Anci divene costumi degni J P 1C 

a: Unde mie force tuo che voglio (volta) 

A: Vince con lena al periglioso scoglio (ripresa) 

For the repetition of the secunda pars {piedi) a seconda volta- ending is provided in the 



I 5 2 



White Mensural Notation 



short passage marked clus (ctuso, chiuso, French clos, 'closed'). The modern rendering of 
the discant would be as follows: 




For the distribution of the text the following scheme is convenient: 
a b 

i .5. Vince 2. Gia 

4. Unde 3. Anci 

The reader is advised to transcribe the entire piece, which is also reproduced in Stainer, 
* Du/ay and His Contemporaries, p. 60. A transcription of the end of the first section is 
given in the appendix, No. 20. 

The use of diminutio simplex described above explains an otherwise 
obscure remark of Gafurius according to which the sign D was used 
to indicate proportio sesquitertia y that is, diminution in the ratio of 3:4 
(Practica Musicae, lib. iv, cap. v; see HdN 1, 41 9). Indeed, the equa- 
tion: d ^iii=aiii shows that four M of the proportional sign are 
equal to three M of the integer valor. 

With the rise of a new, 'classical' style under Dufay and Ockeghem, 
the rhythmic complexities of the earlier period fell into disuse. Proportio 
dupla occurs now chiefly for passages which could just as well be written 
in integer valor (with the next-smaller note values), but which are notated 
in diminutio in order to bestow upon the composition an aura of learning. 
An example is the first piece (A) of Facsimile 2>2>-> which has diminutio 
dupla in one part (eontrapunctus) against integer valor in another {tenor). 
Two 6 1 of the former are worth one of the latter. If, in the integer valor, 
the S is transcribed as a quarter note, the S of the proportion becomes 
an eighth note: 






The twelfth note of the fourth staff is an Sm, not an M. 

More justified is the use of proportio dupla (as well as the other pro- 
portions) in the mensuration-canons, i.e., canons in which several voices 
are derived from a single written part, by the application of different 
mensurations. An example showing the simultaneous use of [3, 2] and 
[2, 2] has already been studied (p. 118). Below is an example by Josquin 



Proportio Dupla 
Facsimile 33 



*S3 



j# 



fAFnpt. 



if" 








yytibra 






PPf 








LJJ 






T Oei 







J. Tinctoris, Proportionate musices, MS Brussels, Bibl. Roy ale (c a. 1480) 
A: page 100; B: page 102; C: page 104; D: p. 106; E: page 102 



154 



White Mensural Notation 



in which [2, 2] is used in integer valor and mproportio dupla (from Sebaldus 
Heyden, De arte canendi^ Niirnberg, 1540). Both voices begin simulta- 
neously and at the same pitch. Under the upper sign, only the first half 
of the melody is sung, up to the first L. 

Exemplum Tertij Mod/, pet C cum 3 
Duo in unura Iofqufai* 




g g astpfli gi 



±tt 



Much more frequent than any of the above applications is the use 
of (t simultaneously in all the parts of a composition or a section 
thereof, that is, as a general time-signature. From the notational point 
of view, this method o/ writing presents no difficulties at all. However, 
it involves problems of tempo which will be dealt with later in a special 
chapter (p. 188 ff). 

As regards the proportio dupla of lempus perfectum y our explanations 
concerning its rhythm may be illustrated by the following passage, fro m 
Facsimile 38 (second staff of the tenor): 
If here the B were considered perfect, a rendering in #- (or | s '-)meter as 
under (a) would result, whereas, with the B being imperfect, a transcrip- 
tion in 4-meter as under (b) would be obtained: 



The context shows that (b) is correct (see the discussion of this piece, 
p. 172). 

It must be noted, however, that there are numerous cases in which 
the interpretation as under (a) is clearly indicated. The passage on 
page 155 (beginning of the cantus of Rompeltier, from Odhecalon^ p. 27') 
is a case in point. 

Obviously, the B is here perfect, the L understood to be imperfect, 
so that the diminutin does not entail any change of the rhvthmic structure 



Proportio Trip/a 155 




Cm pf trier 



of the ordinary tempus perjectum, but would only seem to double its 
speed. In other words, the (notated) mensuration is [II, 3], not [III, 2], 
and its equivalent in the next-smaller values is, therefore, [2, j], not 
[3, 2}. Hence the sign $ has the same meaning as O , namely, that 
of a substitute for G (see p. 195). Another example of tempus perfectum 
diminutum showing ternary grouping of the S, is the passage reproduced 
on p. 1 42 from the ^uia respexit. 

Actually, examples showing the 'ternary' interpretation are much 
more frequent in the sources than those for the 'binary,' because the 
former invariably applies if the sign in question is used as a time-signa- 
ture, that is, in all the parts simultaneously for the entire piece or a sec- 
tion thereof, whereas the latter usually applies if the sign is used as a 
true proportional symbol. See the chapter on Proportional Time-Sig- 
natures and Tempo (p. 188 ff). 

The meaning of diminutio simplex in connection with the signs of 
prolatio perfecta <X\§; I) ■ — rather rare combinations — will be explained 
later (p. 167). 

D. Proportio Tripla 

In proportio tripla of tempus imperfectum, C3 , the B must, as has 
been explained above, be read as a perfect note, or, in other words, the 
S must be read in groups of three. To avoid errors one must re-member 
that proportio tripla, like all the proportions, is — at least normally — 
based on the S and not on the B. This means that the fundamental 
equation is 3 S {prop.) = 1 S {int. val.), not 3 B {prop.) = 1 B {int. val.). 
As a matter of fact, these two interpretations are not necessarily identical. 
If, in the example c**'d«*^B > one considers the B as the unit of the 
proportion, then three B under \ are equal to one B of the integer valor, 
i.e., to two S of tempus imperjectum. However, if the £ is taken as the 
unit, we find that the three B under \ represent nine S which therefore 



156 White Mensural Notation 

equal three S of the integer valor. Thus two different interpretations 



toil J JIJ JEJ I toll J jlj JEIJ 



Only (b) is correct. An instructive example of this point is found in 
the piece from Tinctoris reproduced under (B) on Facsimile 23- Since 
here the tenor begins with B's, one may be tempted to contrast each of 
these notes by three B (or their equivalent) in the discant. However, 
the result, indicated below under (a), is evidently wrong. The correct 
interpretation is obtained if in the tenor each B is replaced by two S, 
to each of which correspond three S of the discant, as is shown under 
(b): 



discant: 



tenor: 



(b) *' £>«G3? IJ7J 
Mil j nm \nf 



iU 

j 



The version (c) of this illustration indicates another possible solution 
which would be obtained on the basis of the relationship 3 B = lB, if 
the 5 of the proportion were interpreted as being imperfect. Although, 
in the present case, this interpretation cannot be ruled out altogether, 
it is not likely to be the one intended (see the third measure of the piece). 
At any rate, it would be in contradiction with the general principles of 
proportio tripla. However, since in music of our period no strict obser- 
vation of these principles — or of almost any others — can be expected, it 
has been deemed advisable to call attention to the possibility of such an 
alternative interpretation, in which the proportio tripla refers to the 
(imperfect) B. 

More definite statements can be made with regard to the possibility 
of proportio tripla referring to the M. As a matter of fact, instances 
such as the following one are not rare in the sources of the sixteenth cen- 
tury: c*i!a*l*!li4*lcH • According to the general principles of 



Other Proportions 157 

proportio trip/a, the following transcription would be correct: 

1 1 J J3|«T3 Jl J33 jpiJI • However, this is not the intended rhythm, as 
one may gather already from the fact that unduly quick notes would 
result. Actually, in a case like this the sign 3 is likely to indicate, 
not proportio tripla> but proportio sesquialtera, with the result: 
ilJAI ^J/I^QJ/IJI • For an example, see p. 159. 
The triple proportion of tempus imperjectum is frequently indicated 
by the sign: $3 . Properly this would denote a combination of dupla 
and trip/a, i.e., proportio sextupla, particularly in analogy to the sign 

(U which always signifies proportio quadrupla (see below). However, 
it is not used in this meaning. In other words, the figure 3 does not 
combine with the dupla-stroke, but only modifies its meaning to indicate 
trip/a rather than dupla. 1 

The proportio trip/a of tempus perfectum, 03 , is the equivalent of , 
as has been previously explained. Theoretically, the difference between 

C3 and 03 is that, under the former sign, a passage consists of notes 
to the equivalent of a multiple of two perfect B {modus imperfectus), un- 
der the latter, of three {modus perjectus). However, the practical ex- 
amples of 03 usually show little evidence of notated modus perjectus 
(actual tempus per/ectum), but rather of notated modus imper/ectus (actual 
tempus imperjectum) , or else of no modus at all. A case in point is the 
discant of a piece from Sebald Heyden's Ars canendi, reproduced in 
MuT, p. 71, a passage of which, marked 03 , includes 13 i?, so that 
neither full ternary nor full binary measures can be obtained. In the 
bass of the same piece (see MuT y 72) there is another passage in 03 , 
which opens with two rests in the value of an imperfect L each. Obvi- 
ously the signature C3 would be more appropriate for this passage. 2 

E. Other Proportions 

Proportio quadrupla indicates a diminution in the ratio of 1 \\. The 
signs of this proportion are: };4;C?;C4; o\\ 04 , or combinations of two 
signs of proportio dupla: <t& 0f; 32-, Of-, 3<£; $ Since here the tactus falls 
on the Z,, this proportion is sometimes called alia longa. Proportio 

1 For an example, see J osquin's canon Agnus dei and Pierre de la Rue's Fuga quatuor vocum ex 
unica, p. 181. 

1 In the sixteenth century, proportio trip/a came to be regarded as the proportion par excellence and 
was frequently referred to simply as 'proportio,' 'proportionatus,' etc., while proportio dupla was 
called 'diminutio.' This special meaning also exists in the 'Proportio' or 'Proportz' of sixteenth cen- 
tury German dances in which it indicates variations in triple meter of the main dance (passamezzo, 
etc.); see, e.g., W. Merian, Der Tanz in den deutschen Tabulaturbuchern, p. -j-jf. 



158 White Mensural Notation 

quadrupla always calls for imperfect mensuration of the B (tempus im- 
per/ectum), even if applied to tempus perfectum (cf>2). Indeed, under 
this proportion groups of notated S really are groups of Sm (of the integer 
valor) which, of course, are always imperfect: 

c**n$*»«*i|-Hi] iijju iJS3J_unj 1 



Proportio sesquialtera signifies diminution in the ratio of 3 to 1. Like 
tripla it always calls for perfect mensuration of the B, i.e., for groups 
of three S. Each such group, then, is equal in value to a group of two 
S of the integer valor. For the transcription into modern notes the same 
method as that used in proportio tripla may be applied: 

C**4414ciH*-**Hl44l*4 

Since this proportion is the first example of the genus superparticulare 
we shall recall our previous remarks concerning groups of notes in the 
sections before and under such a proportion (p. 147). Apparently, the 
fundamental equation of sesquialtera, namely, 1 S {int. val.) = 3 *? 
(prop.) calls not only for ternary groups (tempus perfectum) in the pro- 
portion, but also for binary groups (tempus imperjectum) in the integer 
valor. Therefore, sesquialtera occurs usually in combination with tern-pus 
imperjectum, and an example such as this: ° ****oi*** = ilJJJI J JJJI is 
of purely hypothetical significance. This does not mean to exclude the 
use of Oi altogether. It is limited, however, to cases in which the 
proportion is applied to M' s, which are binary in [3, 2]. Example (C) 
of Facsimile 23 serves as an illustration. Three M of the proportion are 
equal to two of the integer valor. The sign at the beginning of the 
second staff is a g-clef. 

It appears that, in [2, 2], sesquialtera amounts to the same thing as 
coloration (hemiolia) : c*4-42*44*s* =c*4-4*44*K* • 

As will easily be seen, sesquialtera cannot be used in [3, 3]. 

It has already been mentioned (p. 157) that sesquialtera is frequently 
indicated, not by the sign i, but by the sign 3 which normally would 
call for proportio tripla. The following passage from Brumel's Missa de 



Other Proportions 



*59 



beata virgine (only altus and bassus; for the other parts see H. Expert, 
Les Maitres musiciens de la renaissance francaise, vol. viii, p. 19) illus- 
trates this usage: 



Altus: 



Bassus: 




Apparently, the figure 3 produces here the same effect that it has in 
the modern writing of triplets: three notes of the triplet-group equal two 
ordinary notes of the same kind. Familiar as this may be to the modern 
musician, it is difficult to explain within the proportional system, and 
must probably be understood as a mere matter of routine. The situation 
is somewhat simpler if the entire piece is written in tempus diminutum 
{alia breve, see p. 148). as in the following example (Janequin, La Guerre; 
see H. Expert, Les Maitres musiciens de la renaissance francaise, vol. vn, 
frontispiece; cf. the transcription in the same volume p. 36 ff, particularly 
p. 39) and many similar ones: 



f|tfc^£ft|l'|.*itl»lTlTrt'W'IV 



pits 



f eft en efowte* Bur eej fnkoye It ror/3Urme 

frfcOf* 



a Mm (a 



Here one could argue that, under the sign q; , two M equal one M 
of the integer valor, and that, under the sign 3, three M equal one of 
the integer valor; hence the equation (ti i =C3^ii , resulting in sesqui- 
altera. 

Proportio sesquialtera is frequently used in combination with diminutio 
simplex, as follows: <tl . Here, the 3:2-relationship of the former pro- 
portion is once more halved by the latter, so that the ratio of | X f = }, 
i.e., proportio tripla, results. This proportion was known as sesquialtera 
diminuta. The discant and bass of an example from Seb. Heyden, repro- 
duced on the next page, will serve as an illustration (for the other parts 
see MuT, 67): 



i6o 



White Mensural Notation 



j fe 4.iwrtlfrrt**i*tU^ 



Difouutu Integer 



Diarinutus 




^^ 1t ^Q!J ^pt^ty4 :: 



Ptoporttenatus 



!!l*'Ufl»."t*ii.« i«gJ 

g 



Baffin Dimiimtuf 



Proportfonatus 




Integer* 



Proportio quintupla, sesquitertia. Proportions other than those already 
considered are not likely to be encountered in the musical documents of 
white notation. However, two examples will be examined here in order 
to complete the presentation of the subject. Following is an example of 
proportio quintupla from Gafurius' Practica Musicae: 



CANTVS 



? k£fi%\.J^ 



^ ^#%rti 



P 



The sign \ indicates diminution in the ratio 5:1, so that 5 S of the pro- 



Other Proportions 



61 



portion are equal to one S of the integer valor, or of the tenor. This 
proportion is cancelled by the sign for tempus inperfectum. Once more, 
proportio quintuplet is introduced by ™ which is, of course, identical with \. 
For the transcription, one only has to mark off groups of five S, each 
of which has the value of one normal S. 




Facsimile 33D illustrates proportio sesquitertia or, as it is sometimes 
called, epitrita (Greek). The section in proportion, marked 3, contains 
two groups of four S each; each of these groups is equal in value to 
three S or to a perfect B of the tenor. For the transcription, the above 
method of indicating triplets, quadruplets, etc. may be used. 



Successive Proportions. If several proportions appear successively in 
the same part, their effect is cumulative, each of them referring to the pre- 
ceding ones, not to the integer valor. The cumulative result of two pro- 
portions is, of course, arrived at by multiplication; e.g., \ X % = f, 
which means that proportio sesquialtera in proportio dupla is proportio 
tripla. Facsimile 33E serves as an example. Here, the final passage 
signed 2 really is in proportio tripla of the integer valor, owing to the pre- 
ceding diminutio simplex. The blackened L and B at the beginning of 
this passage obviously equal 4 + 2=6 white S, which gives 9 «S* for the 
entire group; these, according to the proportion, are equal to three S of 
the integer valor, or, in other words, of the tenor (see the transcription 
in appendix, No. 21). A more complicated example illustrating this 
method is found in CS iv, 131-32. 

Occasionally, there occur, in the course of a piece, not only various 
proportional signs (figures, fractions), but also new signs of regular men- 
suration. The cumulative principle does not, as a rule, apply to these. 
For instance, in the following succession of signs,o--3--!-C3-2-$ , the 
first two fractions would accumulate, leading to proportio dupla 
(3X2 = 1); however, the following proportio tripla, being attached to a 
sign of mensuration (<$), does not multiply with the preceding pro- 
portio dupla — thus resulting in proportio sexlupla — but establishes, as it 



i6i 



White Mensural Notation 



were, a new beginning, cancelling automatically all the previous pro- 
portions. 

An example from Gafurius' Practica Musicae serves as an illustration 



CAOTVS 



aifetejg jj fflifefe 



§8 

■ ■ 



M^ 



i 



i a ^^"^^ i 



TENOR 



g^jgjfflpfe 




te$ 



ei 






The cumulative meaning of the signs is as follows: 

Signs: O i 2 J <t I I 

Meaning: O £ O J <t § <t 

A special difficulty of this example lies in the irregular length of some 
of the sections, which are not always adaptable to the tempus perfectum 
(J-meter) of the tenor. For instance, the section under \ which really 
is again tempus perfectum, contains four S y that is, one more than is 
required for one full measure. Thus the following section in sesquitertia 



Augmentation 1 63 

begins (and ends) on the second beat of a measure. The transcription 
of the upper part given in the appendix No. 22 may be compared with * 
that in HdN 1, 418. » 

F. Augmentation 

The proportions considered so far are all diminutions. Augmenta- 
tions are very much rarer, proportional signs such as \ and \ being used 
only for cancellation of previous diminutions. 2 There is, in fact, only 
one special type of augmentation which merits our attention because of 
its rather frequent occurrence, i.e., that indicated by the familiar sign 
of prolatio perfecta. The following principle must be observed: In pro- 
tat io perfecta the tact us is represented by the M, not by the S. 

This means that under the signs C and © the M takes the tempo- 
ral value which is normally indicated by the S. This principle is particu- 
larly important in the case of compositions written in prolatio imperfecta, 
except for one part, usually the tenor, which is notated in prolatio per- 
fecta. The singer of such a part determines the relative value of the 
notes according to the rules of prolatio perfecta, but gives the M the 
same real duration which the other singers give to the S. Obviously, 
the result is double augmentation. The prolatio perfecta actually becomes 
tempus perfectum, while the tempus (imperfectum or perfectum) indicated 
by the (semi- or full) circle in reality is modus {imperfectus or perfectus). 

Facsimile 34 illustrates this practice. Here, the tenor/containing the 
melody Lhomme arme, is notated in G , as against O in the other 
parts. The transcription, therefore, is not as under (a), but as under (b) : 

(a) (b) 




8 

In the C^mte-section all the parts are notated in prolatio perfecta; 

1 In this transcription the relationship 3 5" (int. vol.) = 4 S (prop.) is expressed, not 
by quadruplets, but by dotted notes, because of the fact that three half-notes are equal to four 
dotted quarter-notes. Wolf's rendering, though correct, makes rather awkward reading, and ob- 
scures certain peculiarities of rhythm, such as the varying measures of our transcription. After 
having read our explanations on the insertion-character' of late fourteenth century syncopation 
(p. 416) the student will realize that Gafurius, in this example, presents himself as the pupil — 
one of the last, no doubt — of the musicians of the period of 'mannered notation.' 

1 This usage still occurs in sources of the early eighteenth century, e.g., in F. X. Murschhauser's 
Protot\pon longo-breve organicum 11, 1707, in which the time-signature g 2 is cancelled by the signa- 
ture 12 (see DTB xvm, p. 154). It goes without saying that in this period the sign g 2 has no pro- 
portional meaning, but simply indicates measures comprising twelve eighfh-notes each. 



164 White Mensural Notation 

the entire section must be transcribed in the augmented values, i.e., 
in I (or J), not in g. The same procedure applies to the Et resurrexit 
of this mass which has been studied previously (p. 138, Facsimile 30). 
The student may have already noticed that, with this piece, the normal 
scale of reduction did not lead to a satisfactory result. Evidently, the 
notes are much too small to be sung in the speed suggested by our tran- 
scription. The reason for this failure becomes apparent now. In this 
composition, the M represents the beat and must, therefore, be tran- 
scribed as a quarter-note, not as an eighth-note. 

Under these circumstances, one may raise the question as to whether 
the same principle applies to the pieces on Facsimiles 31 and 32, both 
of which are in prolatio perfecta. However, as will readily be seen, the 
same considerations of tempo which, with the Et resurrexit, constituted 
a good argument in favor of the application of augmentation, speak 
strongly against this method in the present cases. This is particularly 
clear with the piece no. 31, which the principle of augmentation would 
cause to begin with a series of notes each equalling an entire 4-measure. 
Indeed, these compositions are not subject to the rule of prolatio perfecta, 
for the simple reason that they belong to an earlier period in which this 
principle had not yet become established. The following remarks repre- 
sent an attempt to clarify the 'history of prolatio perfecta' during the 
fifteenth century. 

Although Ramis de Pareia, in his Musica Practica of 148 2, is the earliest 
theorist to mention prolatio perfecta as a signum augentiae, an example 
of this practice occurs already in the Codex Chantilly, a collection of 
music written around 1400 (see Facsimile 88). However, this would seem 
* to be a rather isolated case. The musical sources of the earlier part of 
the fifteenth century (prior to 1475?) as we ^ as tne theoretical writings 
of this period show clearly that the interpretation in question was by 
no means common or universally accepted. Otherwise Tinctoris, the 
great authority, would not have failed to mention such a fact in his 
Proportionate (ca. 1475). That there existed, however, a great uncer- 
tainty and confusion regarding the meaning of the sign G , appears 
clearly from Tinctoris' explanations. According to him, three different 
rhythmic interpretations of this mensuration were in use among his con- 
temporaries, none of which, however, agrees with that of Ramis. With- 
out entering into a detailed consideration of his rather roundabout 
explanations, it will suffice to illustrate the intricate problem by the 
following table showing four different interpretations of one and the 
same example: 



Augmentation 
Facsimile 34 



165 







t>0 co 



1 66 White Mensural Notation 

Discant: oiio*H-ona Tenor: e**iioo 
Transcriptions: 

tun i j jioj jij l j I 

(a) IJ.JJJIJ* J-l ^ <* of disc. — ^ ♦ ♦ of tenor 

<b) u. m\j. J. i i- .,-,.. =1 .. .. 

(c) u. j j jij. J. i ilii.. .. =u.i.. .. 

( d ) u. j J jij. J. I lU ... - =1 .. .. 

A comparison of the number of measures in the various realizations of 
the tenor shows that (c) is the double of (a), that (d) is the double of'(b), 
and that (d) is the triple of (a). 

(d) is the interpretation called for by the above rule (threefold aug- 
mentation); (a), (b), and (c) are those mentioned by Tinctoris (CS iv, 
171). Of these, he disapproves of (a) {proportio sesquialtera, as he calls 
it with reference to the relationship of the M in discant and tenor) as 
well as of (c) (proportio subsesquitertia, again with regard to the M), con- 
sidering (b) the only correct solution. In a way, this interpretation is, 
indeed, the simplest and most plausible of all. It is based upon the con- 
sideration of the M, instead of the Sy as the common unit of time in C(0) 
and in G(0) . It appears that here two S under G are equal to three 
S under CO ; hence, Tinctoris calls it proportio subsesquialtera. As an 
example, he cites the following passage from Dufay's mass De Sancto 
Anthonio: 




Here, the M has the same value under both O and G . The result 
is simply a change from 4 to §, the reverse of the change expressed by 
coloration. 

Another example of the same practice is offered by Dufay's chanson 
Belle que vous, which is notated with a different mensuration in each 
voice-part (see page 167; cf. DTOe vn, p. 34, no. 119). 

In briefly summarizing the above explanations, we find that in the 
earlier period of the fifteenth century (Dufay) prolatio perfectciy if placed 
against prolatio imperfectciy indicates equal value of the M; in later peri- 



Augmentation 




i6 7 



ods (Ockeghem, Josquin) it calls for threefold augmentation (M = S). * 
However, in this later period, the augmenting significance of the prolalio 
perfecta could be cancelled by combining its sign with a sign of dimi- 
nution, in the following way: (f ;3;<J> . Under these signs, the former 
interpretation, version (b) of the above tabulation, based upon the equal- 
ity of the M, takes place. It was called prolatio perfecta diminuta. 

However, even in late documents a lack of correctness in this matter 
must be reckoned with. Particularly striking is the fact that Seb. Hey- 
den (1540!), although he clearly demonstrates the difference between 
C andd , fails to use the signs correctly in at least one of his examples, an 
Et in terra by Ockeghem. Below is the beginning of this piece (for the 
complete piece see MuT, 79) which calls for equal duration of the M 
in all the parts: 

Exemplum Qpfnti Tonf lobannis Ockegem * 




Et in terra, Altus fequft D/fcantu in Subdiateflaron. 




Baflus in Sabd/atcflaron incipientc Tenorem ,pfequif « 



The first part gives two voices in canon, a discant in [2, 2], starting on 
f, and an altus in [3, 2], starting simultaneously a fourth below {subdia- 
tessaron is the lower fourth). The second part also gives two voices in 
canon; again, the bass starts a fourth below the tenor. The rests written 
at the beginning of this part are valid, not for the tenor, which actually 
starts together with the discant and altus, but only for the bass which 
follows at the distance of four S, as is also indicated by the signum con- 



1 68 White Mensural Notation 

gruentiae. Since the bass is in [3, j], the initial 5-rest equals in value, of 
course, g M and, therefore, occupies one full ^-measure of the transcrip- 
tion. In the continuation of this part, however, there is no evidence of 
tempus perfectum (already the first B is made imperfect by the preceding 
^-rest), so that |-meter proves more convenient than J-meter. The be- 
ginning of the transcription follows: 




For the use of G as a general time-signature, see p. 195. 



G. Examples 

We now turn to the study of a few pieces which show to what a degree 
of complexity the proportional notation was used — or, occasionally, mis- 
used — in the fifteenth and sixteenth centuries. We begin with some ex- 
amples taken from Isaac's Chora/is Constantinus, in Formschneyder's 
publication (Nurnberg, 1550). 1 

(1) Ideoque quod nascetur (Facsimile 3$). The piece opens in [2, 2] in 
all the parts, the discant being silent throughout the first section 
(Ideoque . . . vocabitur), which comprises twenty measures. Towards 
the end of this section, the three lower parts have a passage in coloration. 
The remaining section (filius . . . del) is written in four different signa- 
tures: 0; D;C ;0 . Naturally, the proportio quadruplet of the alto renders 
the L y B, and S of this part equal to the S, M, and Sm of the tenor 
(integer valor). In a similar way, the S and M of the discant (pro- 
portio dupla) are equal to the M and Sm of the bass (integer valor). 
According to the proper interpretation of , the notated mensuration 
* of the cantus is [III, 2], its actual mensuration [3, 2]. In other words, 
the modern meter of this part is the same (4) as that of the bass, only 
written in the next greater values. Of course, the absence of larger notes 
(By L) makes it impossible to arrive at an unambiguous decision in this 

1 The original publication is in four part-books. 



Examples of Proportions 
Facsimile t>5 



169 




* Idea q> qu^dnafu'c 



tut cxte fanctum vo ca bi 



^b5±^s£p5S^S$ 



t^era 



bus 



Dei Dei. 



^ifciis 



Weo 9 ideo^ 




=4- 



filius 



W tur 



Ex re 6n clum voca 



Heinrich Isaac, CAorw/w Constanlinus. Formschneyder, Niirnberg, 1 



55o 



i7o 



White Mensural Notation 



question. In fact, the application of the 'secondary' interpretation of 
(notated [II, 3], actual [2, 3]) leads to the same note values, only- 
arranged in g-meter, instead of f-meter. In the transcription of the 
closing section, appendix, No. 23, both interpretations are indicated. 
(2) Piae vocis (Facsimile 36). This example opens in [2, 2] in the 
three upper parts, whereas the bass begins with two 5-rests in [2, 3]. 
According to the augmenting character of prolatio perfecta, each B of this 
mensuration is the equivalent, not of a g-measure, but of a J-measure, or, 
more conveniently, of two f-measures. Further on, this meter is intro- 
duced simultaneously in all the parts, but changes back to duple meter 
under C . Toward the end of the piece, the figure 3 introduces propor- 
tio /rip/a simultaneously in all the parts. The 'correct' interpretation of 
this passage, that is, according to the equation 3 S (prop.) = 1 S (int. 
val.)> leads to an unduly quick rhythm, as is shown below under (a). No 
doubt, the actual meaning of the figure 3 is proportio sesquialtera, applied 
to the M (3M = 2M),as in the instance from Brumel's mass, given pre- 
viously (p. 159). Therefore, the rendering as under (b) indicates the 
proper time-relationship between the integer valor and the proportion: 




ij) Dico ego (Facsimile 37, p. 174) shows prolatio perfecta diminuta in the 
discant, against tempus perfection diminutum in the other parts. Accord- 
ing to our explanations, the former sign simply means [2, 3] without aug- 
mentation, that is, 8 -meter (S = dotted quarter note). With the tempus 
perjectum diminutu'm, again the question arises whether it is the equiva- 
lent (written, of course, in larger values) of [3, 2] or of [2, j], in other 
* words of modern 4- or g-meter. In this example, an unequivocal deci- 
sion in favor of the latter interpretation is found in the blackened notes 
at the end of the alto (and bass). This coloration-group of three black- 
ened B is the equivalent of two white B and, therefore, suggests (notated) 
modus imperjectus and, consequently, actual tempus imperjeclum for the 
white notes. The following two renditions of the end of the alto (begin- 
ning with the last M-rest) illustrate this point; the 'triplet-coloration', as 
under (a), is one quarter-note too short, whereas the 'courante-colora- 
tion' as under (b) leads to a correct result: 

(b)| 




Examples of Proportion^ 
Facsimile ^ 



171 




TBI 

W-KI 

Ol I II 

Nil! 



IW 1 
lew l 1 

Itt I I 

n-WM l 

10m 

IKil 

1 m 1 1 
'til i 

t-KH 



■5 

to 

c 

<: 

O 

■8 




5j 



172 White Mensural Notation 

(4) De radice Jesse (Facsimile 38). This piece, which has repeatedly- 
been cited as the non plus ultra of proportional complexities, presents 
quite a few problems, although not nearly so intriguing difficulties as 
numerous pieces of the late fourteenth and early fifteenth centuries. 1 
The following table showing the modern equivalents of the various men- 
surations will facilitate transcription: 



c 


* ♦ 


= 


IIJ J 


1 





♦ ♦ ♦ 


= 


IIJ J 


j 1 


G 


♦ ♦ 


= 


1(1)1 J. 


j 





♦ ♦ 


= 


I (1)1 J. 


j 


(t(C2) 


1=1 W 


= 


fU J 


1 


02 


WWW 


= 


IIJ J* 


j 1 


<t2((t Djw W 


= 


11 n 


1 


3 


♦ ♦ ♦ 


- 


\m 





A few peculiarities may be noticed. The figure 3 signifies proportio tripla 
(as indicated in the above table), although it always occurs following 
upon proportio dupla. Properly, therefore, its value should be half of 
those shown in the table. Two explanations for this irregularity are 
open: either, that the cumulative process does not apply, or that the 
actual meaning of the figure 3 is, again, sesquialtera, which, by combina- 
tion with the dupla, would lead to tripla? A similar irregularity attaches 
to the figure 4 (near the end of the alto and of the bass). In both cases, 
it is preceded by a sign of proportio quadrupla ( (£ Z; <t ). However, it 
does not denote a reduction in the ratio of 1 :i6 (Z, = sixteenth-note), but 
only in the ratio of 1:8 (L-eighth-note). The blackened notes B S S B 
in the discant near the beginning of the second staff have exactly the 
same values as if they were written in white. They must be considered 
*a typographical error or else a peculiarity without meaning. The piece 
is transcribed in the appendix, No. 24. 

1 In MuT, 82, this piece is reproduced in mensural notation (after Glarean's Dodekachordon and 
with a different text) as well as in transcription. The latter, however, obscures practically all the 
notational features of the original. H. Riemann, in his Handbuch, n, i, 170, reproduces it from the 
same source, together with a much more adequate transcription. See also the transcription in 
DTOe xvi, p. 194. 

*In Glarean's version of the piece (see MuT, 82) most of these sections are, more correctly, 
labelled i 



Examples of Proportions 
Facsimile 38 



173 




iilsil^ 



De radicc 



Icf fc propa 



gnus 



iiiiiiiitg;sp:is 



cduxit I'd ucri lumi i\\& 



tunc 
nu fa picncia: fux tcmplum ^ 






De tadice 



IcfTc 



propaginis 



linis ma nu 



Sol vcri Luminis 



fapicnti* 



*ft|jEl 



tcmplum tern plum glo-- tue. 



sfc * g B -fej ^^r^r^rQjty t * 



Dc radicc Ic&e 



propagini* jhanc cduxit 



i^^^i Btk 1B 1 /J^^g^kg 



Sol 



luminis 



fapientiae 



foas tcmplum gloria; ' 



Heinrich Isaac, Chora/is Constanlinus. Formschneyder, Niirnberg, 1550 



174 



White Mensural Notation 
Facsimile 37 



I "Ul I 



09. 



W4-U 
(•1 1 1 1 

I0M-1 
11*11 

t I tit) 

i I 



6 t 



[♦I I 

n ii i 
01 1 1 1 

bM4i 

j HOH- 

1*4+) 

HHttl 
I l*H- 
HH01 
♦M-I 
f *» II 
(♦W-J 

Tl» 



tit 

if 

f 

Oil I 
1 1 1 1 1 





1 



I l-T-t-1 

i i?i i 

f-H$M 
I fcH I 



) 

♦I I I I 

W i i i 

mii 



mti 
rati 

•wr 
i«++j 

IWII 

IfchM 
1*4+]! 

fet-44 

1 "K» I 

!*++. 
I«4- 

trtu 

I M w 



I !*! J 
I U 



I 1 ) 
1 l 



f i i t » 






Examples of Proportions 



*75 



Finally, two pieces from the Canonici MS may be considered, which 
illustrate the use of proportions in the early part of the fifteenth century. 
The notational practice of this period differs in various respects from 
that of the later sources. In fact, the peculiarities of these examples 
can only be understood as the inheritance of that stage of black notation 
which, owing to its unique features of complexity, has been termed 
'mannered notation' in this book. Actually, their proper place would 
be in the chapter thus entitled (see p. 403), rather than here. However, 
since they are written (possibly, re-written) in white notes, they may 
stand here as a fitting climax to the student's efforts to cope with the intri- 
cacies of the proportional system. 






1 



335 



S2SS 



tndi^- 4. Wf Cc rvc *e m3V|cGm$ue 






enov-. <un<an£- 



i 



"'"^r'/V^^^^'^^'-'i'w 



(5) In Baude Cordier's Amans ames secretement we find nearly all the 
signs of mensuration, plain as well as in proportio dupla or tripla. The 
exact meaning of these signs (which, needless to say, must frequently be 
determined by experimentation) will appear from the following table in 
which all the values are expressed by a temporal unit designated e, which 
equals the M of the integer valor or the eighth-note of the transcription: 



£ Z O 
M = e e 
S = 3e %e 2e 


03 c er © 02 ©3 

e e 
e 2e e 3e 3 ^e e 


B = 6e 3e 6e 


3e 2e 4e 2e 9e 9 / 2 e 3e 



As appears from this tabulation, the relationship between the four 
plain mensurations is based upon the equality of the M, not of the S. In 
particular, the signs of prolatio perjecta do not call for augmentation. A 
transcription of the piece is given in the appendix, No. 25. 1 

1 A wrong transcription of the beginning of this piece (MS Oxford, Bodl. Libr. Canonici 2/j, 
p. 123) has been given in E. Dannemann, Die spatgotische Musiklradition in Frankreich und Burgund 
vor dem Aujtrelen Dufays (Leipzig, 1936), p. 106. 



176 White Mensural Notation 

(6) Our last piece, Hughe de Lantins' Je suy exent (Facsimile 39), is 
quite difficult to transcribe, but even more difficult is the proper explana- 
tion for some of its notational peculiarities. The piece begins in tempus 
* perfectum diminutum in all the parts. In contrast to its 'classical' mean- 
ing, this mensuration retains the perfect value of the B, as is clearly indi- 
cated by the punctus divisionis after the first S of the tenor, as well as by 
the coloration-groups at the beginning of the contra. In the later course 
of the piece, plain tempus perfectum appears simultaneously in all the 
parts (discant, near beginning of the third staff; tenor, beginning of the 
second staff; contratenor, before middle of the second staff). Notation- 
ally, this marks the beginning of a second section which may be consid- 
ered first because it shows the various mensurations in their normal 
meaning, and in relatively simple configurations. The tenor continues 
in [3, 2] throughout (4-meter). In the contra, the passage marked 2 con- 
tains 12 M, the value of which is reduced by proportion to 6 M or to one 
full measure of the tempus perfectum. The passage in O , towards the 
end, introduces a new rhythm: two B are equal to one (perfect!) B of the 
tempus perfectum. It will be noticed that this meaning of tempus imper- 
fectum diminutum is entirely different from that indicated by the sign -£ 
in the pievious piece. Whereas there the B of the proportion equalled 
two M of the integer va/or, it equals, in the present case, three M. Fol- 
lowing is the transcription of the close of the contra: 




A similar meaning attaches to the passage in proportio quadrupla, a- , 
of the discant (to the text [sou]/us). The L of the porportion has the 
same value as the B of the simple diminution, that is, half of the B of the 
tempus perfectum. Towards the end of the third staff, the sign G intro- 
duces change from [3, 2] to [2, j>], that is, from 4-meter to g-meter. To- 
wards the end of the discant, the sign 2 and the coloration-group of three 
M present a minor problem which, however, the student who has man- 
aged to steer safely this far through the notational labyrinth of the com- 
position will have little difficulty in solving. 

We now may turn to the study of the first section. Using the mensu- 
rations considered so far as a point of departure, one will naturally inter- 
pret the tempus perfectum diminutum of the opening as half of the 
tempus perfectum of the second section. Thus, three S would fill in a 
l-measure, instead of a 4-measure. Two such measures may be com- 
bined into one |-measure. The figure 3 found shortly after the begin- 



Examples of Proportions 
Facsimile 39 



177 



I 






¥4=3 



^7 



ggg= ^^^^^^^g 



to 



&**ttn« -wi-»v^ — * K f**) 



^wn- 






± 



" ^"fy'i fcf^ "f fry «» »•■>/ 



i 






jg ^h l ^^f « t |g§i J 



m-r^H'S j 






pp& 



fc**Pu\ J 



h ji0h^\ p 



j 



%%f 



£ 



MS Oxford, Bodleian Library Canonici misc. 213 (ca. 1450) 
Page 47 



i 7 8 



White Mensural Notation 



ning of the discant (and also in the later course of the contra) refers to 
the integer valor. In other words, with reference to the preceding dimi- 
nution it indicates, not proportio tripla, but proportio sesquiallera, so that 
three M take the place of two M, or of one S. Here follows the trans- 
cription of the beginning: 




The real problem presented by this piece lies in the fact that a satis- 
factory rendition of the first section is obtained only if the mensural 
signs D and G , which occur in the discant and in the tenor of this sec- 
tion, are interpreted as just half of what they represent in the second sec- 
tion. For instance, the B of D , which in the second section becomes a 
quarter-note (see the above transcription of the closing measures of the 
contra), must now be transcribed as an eighth-note. Following is a 
rendition of the second line of the discant (beginning with the first B) 
and the corresponding portion of the tenor in two versions: (a) according 
to the exact meaning of the mensural signs; (b) in the halved values 
which are required by the context of the parts (see the added contra). 



a) 




Canons 



179 



<b) 




Two ways are open for the explanation of this discrepancy. Either the 
signs 3 and £ are, in the first section, understood to be subject to the 
diminution indicated at the beginning of this section, whereas later they 
are understood to be in integer valor, being placed after the sign of plain 
tempus perfectum; or the sign of the first section has no proportional 
meaning, and indicates just simple tempus perfectum. In the latter case, 
the entire first section would have to be transcribed in the double values 
of those used above. No doubt, this choice is even less satisfactory than 
the first. From the musical point of view, the extremely long duration 
of the various L occurring with the text Je suy exent ('I am exhausted') 
would seem to represent a strong argument against the second version — - 
unless it is assumed that the composer wanted them to depict the state 
of mind of the despairing lover and perhaps — prophetically — that of the 
equally despairing reader of the above explanations. 



H. Canons 

In the music of the fourteenth through the sixteenth centuries, the 
term canon (i.e., rule) has a much wider significance than it has in the 



1 80 White Mensural Notation 

ensuing periods and today. It means any kind of prescription that con- 
tains a clue to the correct interpretation of music which would otherwise 
be obscure. Tinctoris, in his Diffinitorium (ca. 1500, see CS iv, 179) 
defines it thus: 'Canon est regula voluntatem compositoris sub obscuri- 
tate quadam ostendens' (A canon is a rule which shows the intention of 
the composer in an obscure way). 

Musicians of the fifteenth and sixteenth centuries certainly succeeded 
in making this definition come true. The Flemish masters spent no 
small amount of their ingenuity in devising enigmatical manners of sing- 
ing a part and in indicating them by inscriptions which, 'though osten- 
sibly vouchsafed for the purpose of giving the student some little insight 
into the secret of their construction, tend rather, as a general rule, to in- 
crease their perplexity' (Grove's Dictionary, 1938, vol. 11, p. 713). Their 
delight in these intellectual subtleties has brought them into grave dis- 
repute among the musicians and musical historians of a posterity that 
had completely lost living contact with the mentality of the Renais- 
sance, and who, being brought up in the tradition of musical romanti- 
cism, could not conceive of a composer combining artistic inspiration 
with clarity of intellect. A more sober and unbiased observer will not 
be misled into mistaking for a criterion of artistic quality what was 
merely the playful whim of a culture which followed the motto: Nihil 
humanum a me alienum puto. 

A relatively simple manifestation, but one which is of particular in- 
terest from the point of view of notation, is the mensuration-canon, i.e., a 
melody which is performed by various singers simultaneously under dif- 
ferent mensurations. Examples of this method occurred already in the 
tenor and bass of the Kyrie of la Rue's mass, Uhomme arme (Facsimile 
27), in Ockeghem's Et in terra (p. 167), and in a two- voice canon by 
Josquin (p. 154). On page 181 we reproduce a three- voice canon from 
the same composer's Missa Vhomme arme (from Dodekachordon, p. 442). 
The middle voice is in integer valor > (S = quarter-note); the lower in 
proportio dupla (S = eighth-note). In the upper voice, which is in 
diminutio tripla, three S equal one of the integer valor. The signa con- 
gruentiae indicate the stopping points of the two lower parts; since their 
tempo is slower than that of the upper part they both sing only a portion 
of the melody, which is sung in its entirety only by the discant. The 
entrances of the voices are here in the relation of tonic and dominant; 
they begin simultaneously on d, a and d' (see appendix, No. 26). 

The spirit of competition which is so characteristic a trait of the 
Netherland schools induced Pierre de la Rue to compose zfuga quatuor 



Canons 



181 



Exunauocc trcs^xciufde Io 

doci Mifla Lhomc armc fupcnioccs muficales. 




lis pecca ta mun 



di mi mifcre re 



i 



^ 



I&±>«-fe 



no 



ftri. 



ro<r«w w unica, which is easily the most interesting specimen of mensu- 
ration-canons. The piece is reproduced here from Dodekachordon, p. 445: * 



gi lig^^.lii^^^^ 1 ^ 



y ^ ^^^^iJiUM m ^M 



a' %*&B * {JdB**» H 'B » B »» q '' HV ' B — ~g 






The four voices start simultaneously on G, d, g, d'. The beginning is 
transcribed in the appendix, No. 27. 



1 82 White Mensural Notation 

Another type of canon is the use of proportional signs for the repeti- 
tion of a tenor melody. In fact, this is the earliest known use of propor- 
tions. Both Johannes de Muris {ca. 1325) and Prosdocimus de Belde- 
mandis {ca. 1400) assert that diminution and augmentation serve only 
to produce an extensive tenor from a shorter melody. 

The tenor of Obrecht's mass Si dedero (Facsimile 40) shows how this 
principle was utilized by the early Flemish masters. A single page 
suffices for the printing of the complete tenor (except the third Agnus 
Dei) of a mass, the discant of which covers nine pages. With each por- 
tion of the tenor two, three or four mensurations are given which, to- 
gether with the sign of repetition at the end, indicate that the musical 
phrase has to be sung twice, three or four times in succession, each time 
under a different mensuration. Two of these tenors may be studied 
here, that of the Crucifixus and that of the Sanclus. 

Four mensurations are indicated at the beginning of the Crucifixus. 
It is to be recommended that one begin transcribing the second and the 
third presentation of the melody, both of which are in integer valor. Con- 
trary to the rules of imperfection the initial B is perfect under O . A 
punctus divisionis, which ordinarily would indicate this, cannot be used 
here since it would be interpreted as a punctus additionis under C . The 
length of the rests preceding the notes also varies according to the men- 
suration. Under O they equal five perfect B or fifteen S (five 4-mea- 
sures); under C , five imperfect B or ten S (five 4-measures). Under 
the sign <t every note and every rest equals a half of its duration under 
C . Under the sign of prolatio perjecta each M equals a S of the sec- 
tions in integer valor. The initial rests are worth 5x6 = 30 M, which, 
owing to the augmentation, take the place of 30 S; therefore, in the 
transcription, the tenor begins with a rest of ten 4-measures. It may be 
noticed that, under this mensuration, the two pairs of M call for altera- 
tion, not imperfection (see appendix, No. 28). 

The construction of the tenor of the Sanctus is still more involved. 
This tenor consists of two sections of equal design which may conven- 
iently be designated as A and B. Each of these has three signs of men- 
suration. There result three different versions of A (Ai, A 2 , A 3 ) and three 
of B (Bi, B 2 , B 3 ), which have to be read in the following order: Ai Bi A 2 
B 2 A 3 B 3 . A 2 and B 3 , both of which are in [2, 2], are composed of six im- 
perfect B y inclusive of the two 5-rests at the end. In A 3 and B 2 these 
values are halved. In Bi the second B is imperfect, so that, as a result, 
the passage consists of only three (perfect) B, or of five with the inclu- 
sion of the rests. Finally, in A x the second B remains perfect, since a 
complete perfection, consisting of three perfect S, follows. There result 



Canons 
Facsimile 40 



183 




8 « 



184 



White Mensural Notation 



— with the rests included — five perfect B, the actual value of which is 
tripled by the prolalio perjecla as a signum augentiae (15 measures of 
2-meter). See the transcription in appendix No. 29, which may be com- 
pared with that in HdN 1, 422. 
* On Facsimile 41 we reproduce the other parts of the Sanctus^ in order 
to enable the student to make a complete transcription of this piece. 

The considerations and calculations involved in the reading of such 
tenors were not without their difficulties even for sixteenth century 
singers, not all of whom were so well trained in the intricacies of the pro- 
portional system as, for instance, the singers of the papal choir or of 
other great churches. This situation became particularly urgent in the 
case of printed books which, intended to reach a wide clientele, had to 
be designed in such a way as to accomodate a reader of merely average 
training and ability. It was for this reason that Petrucci, who was the 
first to publish printed editions of masses, frequently added to the pro- 
portional tenor a resolution that is, a transcription in plain mensural 
values. Following is the tenor of the Kyrie from Obrecht's mass Je ne 
demande, both in its canonic and transcribed version (from Misse Obrecht y 
Venice 1502): 



T yrte^cnf demands 



In accordance with the meter of the other parts, alia breve is used here 
for the resolutio; each S of the original becomes a B in the transcription. 
The reader may first transcribe the tenor in the familiar manner, and 
then compare it with the 'sixteenth century transcription.' 

Another method of writing proportional tenors is illustrated bv the 
following example, taken from Josquin's Miss a Di dadi supra naxagie 
(dadi — dice; naxagie = N'aray-je, a. chanson by Morton): 



Tcnoj 



CtaftdiSopranipffCc 




frte Uyfoii 

The black squares at the beginning signify augmentation in the ratio 



Canons 
Facsimile 4: 



85 



SJdrdfio 




fcltnf linr 




t.,.LW...il^ l » l liliMilii»ilillWli 




^^^^^fa^^y 
^^^^^^^^g . 



i i iiii% i iHf|iin!miiA ,i|ll "i if % jm, ^r 




Petrucci, Missarum diversorum autorum liber I. Venice, 1 qo8 
Superius, Altus, Bassus 



1 86 



White Mensural Notation 



indicated by the number of dots (doubling). Again, the student may 
compare his transcription with the resolutio: 



m^ v "' 



»*qH ,0,i <K) , .. » c £e^j 



I 



For the Crucifixus of the mass, the same melody is used in sixfold 
augmentation: 



P ..w(_. I 



C inciSnw 



fa i iifhf^ iB^ 




An example of considerably greater complication, found in the Old Hall 
MS {ca. 1 450) is discussed on p. 366 f. 

Only brief mention can be made here of the numerous canonic inscrip- 
tions which show the intention of the composer 'sub obscuritate quadam.' 

Among the simplest are those which direct the singer to read his part 
backwards. This indication was disguised under expressions such as: 
'A est O' (A [Alpha, the first letter of the Greek alphabet] becomes O 
[Omega, the last letter of this alphabet]), or: 'canit more Hebraeorum' 
(to be sung in the manner of the Hebrews, with reference to the fact that 
Hebrew v/riting is read from the right side to the left), or: 'Vade 
retro, Satanas' (get thee behind me, Satan), or by the more familiar 
'cancriza' (walk like a crab), or by the word tenor spelt backward: 
'Ronet,' or thus: / JOU9 X> if retrograde motion was to be combined with 
inversion. 1 

1 The inscription 'Ronet* appears on a four-voice Et in terra pax of the MS 5.? of the Library Kra- 
sinski, Warsaw, reproduced in SchT, 5. However, the present writer has been able to arrive at a 
satisfactory transcription of this abnormally difficult specimen only by disregarding the above in- 
scription and by allowing various other emendations in the notation of the two lower parts, namely: 
(1) both parts begin after a rest of 16 B (with the section 'Laudamus'); (a) both parts are repeated, 
beginning with 'Qui tollis'; (3) the last four L (two rests and two notes) of the tenor must be omitted; 
(4) the 6th and the 24th note of the tenor (not including the rests) is a L each. This author readily 
admits that these far-reaching conjectures are rather unsatisfactory; he would be glad to be informed 
about a solution which is more in keeping with the notation of the original. 



Canons 187 

An example is found in the chanson dolce conpagno by Dominicus de 
Feraria which appears on the lower part of Facsimile 32. The contra, 
bears the inscription: 'Et d[icitu]r eundo et redeundo,' that is: to be sung 
going forward and going backward. As a matter of fact, it will be seen 
that its length is the exact half of that of the discant, and that in playing 
it twice, the second time in retrograde motion, it combines satisfactorily 
with this part. However the resulting texture in two parts is not the 
complete composition, since a third part is indicated 'sub obscuritate 
quadam' in the text of the discant which reads as follows: 'O dolce com- 
pagno se tu voy cantare dyapason piglia senca demorare' — that is: 'My 
sweet companion, if you wish to sing, please sing the octave without hesi- 
tation.' This would seem to indicate that the singer of the third part 
should follow the discant in the (lower) octave, thus producing a succes- 
sion of consecutive octaves for the entire composition (see the transcrip- 
tion in J. Stainer, Du/ay and His Contemporaries, p. 160). Fortunately, 
this is not the meaning of the inscription. As H. Riemann has shown 
(ZIMG vi, 466), the 'companion' has to sing his part backward, begin- 
ning with the last note of the discant which actually is the lower octave 
of its first tone. 

As an example of the complicated tenor technique of the fifteenth 
century, the tenor of Dunstable's Veni sancte spiritus is reproduced below 
(from DTOe vu, 201; cf. also p. xxix of this volume): 



Canon: El dicitur prius directe, secundo subverte lineam, lerlio revertere 
removendo tertiam partem et capies diapente y si vis habere tenorem Sancti 

Spiritus. 

According to this inscription, the given meiody must be sung first as 
written, that is, in [3, 2], which is the mensuration of the other parts. 
For the first repetition, the direction 'subverte lineam' (turn the staff, 
i.e., upside down) indicates inversion, while for the third statement 
retrograde motion is indicated ('revertere') together with transposition 
to the (lower!) fifth ('capies diapente') and a reduction of the ternary 
values to binary values ('removendo tertiam partem') or, in other words, 
transition from [3, 2] to [2, 2]. Not only the 'inverted' but also the 
'retrograde' section is preceded by a rest of nine measures, as is suggested 
by the rests placed at the end of the melody, between the first and the 
second signs of repetition. A transcription is given in the appendix, 
No. 30. 

It goes without saying that with a canonic inscription like the above — - 



1 88 White Mensural Notation 

and there ar^ many which are much more 'obscure' — the exact meaning 
of the directions has to be worked out by experimentation, that is, on the 
basis of the transcription of the other parts which usually present no 
difficulty. H. B. Collins, in his edition of the Missa O Quam Suavis 
(Burnham, 1927) has used this method with remarkable ingenuity, an 
ingenuity which is certainly equal to that of the man who devised the 
really diabolical tricks encountered in this composition. The following 
tenor very nicely illustrates the mentality of the unknown composer 
whose work, by the way, proves him a great artist as well as a keen 
intellect: 1 

dia arte contract vs. 



The use of the smallest note-values for a tenor shows at once that the 
written values are fictitious. By induction, Collins has shown that 
their real values are nearly the reverse of those indicated in the writing, 
the B, S y My and dotted S equalling one, two, four, and six S respectively. 
Thus, the beginning of the tenor reads as follows: 




In this interpretation the tenor yields the exact number of 102 S which 
is required by the upper parts, as against 31^ S in the writing. The no- 
tation, therefore, actually is 'contracted' by an 'art' which, as Mr. Collins 
aptly remarks, the reader is free to interpret as 'divina' or 'diabolica.' 



I. Proportional Time Signatures and Tempo 2 

Our study of the proportions would be incomplete if we pass over what 
actually is by far their most frequent use, that is, simultaneously in all 
the parts of a composition or a section thereof. Practically all music of 
the sixteenth century is written with the alia breve sign C in all the 

1 The notation of the MS is in black notes. See p. xxi of the above-mentioned publication. 

2 Although, to the best knowledge of this writer, the above study is the first attempt to attack the 
problem of the tempo of Flemish music from a musical point of view, there exist several publications 
in which quotations from theoretical treatises are given, information which, of course, will have to be 
considered in a more exhaustive and definitive treatment than has been intended here. The most 
important of these publications are: A. Chybinski, Beitrage zur Geschichte des Taktschlagens (Krakau, 
1908); E. Praetorius, Die Mensuraltheorie des Franchinus Gajurius [Public ationen der Internationalen 
Musikgesellschaft II, ii, Leipzig 1905); G. Schunemann, 'Zur Frage des Taktschlagens und der 
Textbehandlung in der Mensuralmusik' (SIMG 1908). 



Time Signatures and Tempo 189 

parts, and the use of signs such as , etc. for shorter or longer 
sections of motets and masses is very common. From the strictly nota- 
tional point of view this usage is the least interesting, since, whatever 
the meaning of these signs be, it applies equally to all the parts. There- 
fore the transcriber may simply disregard them or, in order to appease 
his scholarly scruples, simply indicate them as they are given in the orig- 
inal, leaving it to the reader to find out what they mean. This method, 
together with the practice of using unreduced note values (S = whole- 
note, etc.) has been adopted in the great majority of scholarly publica- 
tions of early music (see the editions of the Trent Codices, of Ockeghem, 
of Lassus, of Palestrina, etc.). However, a serious objection must be 
raised against this method, namely, that it disregards (and, from the 
point of view of the modern reader, obscures) a fundamental feature of 
the mensural and the proportional signs: their temporal significance. 

There can be no doubt that throughout the history of music prior to 
1600 the notational signs indicated not only relative values, as do the 
modern notes, but also signified absolute temporal durations. This fact 
constitutes a basic contrast to the modern system in which the duration 
of a given note, e.g., a half-note, may vary from several seconds (in 
largo) to fractions of a second (in prestissimo). That the modern prin- 
ciple of unlimited variability of tempo is of a fairly recent date appears 
from a glance at the practice of the seventeenth and early eighteenth 
centuries in which the limits of the variability are considerably narrower, 
and in which the scarce use of tempo marks points strongly to the exist- 
ence of 'normal tempi' from which only moderate deviations were ad- 
missible. Such a line of development suggests the assumption that, in a 
still earlier period, the variability of tempo may have been practically 
unknown. This is exactly the situation that existed in music prior to 
the end of the sixteenth century. 

Before we turn to more detailed explanations it may not be superflu- 
ous to corroborate the principle of tempo-stability by some considera- 
tions of a general nature. In looking over, for instance, the works of 
Orlando di Lasso or Palestrina the uniformity of the notation is striking. 
There is nothing comparable to what we find in the works of Bach or, 
even more, those of Beethoven, in which one piece may be written chiefly 
in large values (whole to quarter-notes), the other in small notes (eighth 
to thirty-second-notes), a situation which becomes still more strange — 
not to say, 'artificial' — from the fact that the larger values are used for 
quick pieces, the smaller ones for slow compositions. The old masters 
followed a more 'natural' procedure, by writing all their pieces in the 
same note-values, chiefly brevis, semibrevis, minima, and semiminima, the 



190 White Mensural Notation 

fusa being used only in groups of two for a quick cadential ornamenta- 
tion in the character of a mordent. 

Additional evidence in support of the principle of tempo-stability is 
found in the fifteenth and sixteenth century theory of proportions, which 
is essentially based upon the idea of a fundamental and unchangeable 
unit of time, the tactus. In fact, the considerable complexities of this 
system would certainly present an insurmountable obstacle even for a 
well trained singer, if they were understood to refer to variable note- 
values such as prevail in modern music. Actually, the situation was not 
quite as complicated as the modern reader is inclined to believe. To the 
singer of this period proportia trip/a or proportio sesquitertia meant a 
definite and fixed tempo, derived from the integer valor, and familiar to 
him through his long training in a normal tempo which represented for 
him the natural pulse of music. 

The complete absence of tempo marks in the early sources is perhaps 
not a very strong argument, considering the general 'negligence' of the 
old masters in so many questions which are of vital interest to us. How- 
ever, it is interesting and significant that the first tempo marks occur in 
sources of music for a soloist. To the best knowledge of this writer the 
earliest remarks of this type occur in the lute pieces of Luis de Milan (El 
Maestro, 1536), according to whom certain sections of his lute fantasias 
must be played 'a priesa' (quick), others 'a espacio' (slow). That a 
single player was much more naturally disposed to free himself from the 
fetters of fixed tempo than the performer of ensemble music is obvious. 

More eloquent than the musical sources are the theoretical treatises of 
the sixteenth century. Practically every theorists gives longer or shorter 
explanations on the tactus as the unit of musical time, and although the 
positive information to be gained from these explanations is much less 
clear than we would wish, the important fact is that nowhere is a re- 
mark to be found which would give the slightest justification for the 
assumption that the duration of a note could be varied according to the 
text, the character or feeling of the piece, or whatever other romantic 
ideas a modern conductor may have in his mind if he chooses the 'right' 
tempo for a motet by Palestrina or by Byrd. In the sixteenth century 
there existed only one way of changing the temporal duration of a given 
note, that is, by proportions. Thus the proportional signs, if used si- 
multaneously in all the parts, represent the tempo marks, nay, the 
metronomic marks, of the fifteenth and sixteenth centuries. 

After this blunt statement, the situation may seem to be much simpler 
than it is. Actually, the establishment of tempo-stability as a principle 
of early music is only the basis for numerous questions of detail most of 



Time Signatures and Tempo 191 

which are bound up with evolutionary changes. It goes without 
saying that this principle does not imply stability of tempo throughout 
the entire early history of music, but only during certain periods, or in 
certain schools, or for certain 'standard' types of music. Even in this 
more limited sense the term should not be interpreted too rigidly, and 
should be considered as the indication of a guiding idea rather than as a 
strict law. 

The following explanations in no way attempt to present an even ap- 
proximately exhaustive study of the problem of tempo, a study which 
would certainly fall outside the scope of the present book. Only a few 
typical examples will be studied which serve to clarify the temporal 
meaning of the proportional signs. 

As has already been pointed out (p. 147), the fundamental conception 
of tempo in sixteenth century music was the tactus, a unit of time-meas- 
urement comparable to a slow to moderate beat which was represented 
(in integer valor) by the S. Although the indications concerning the dura- 
tion of the tactus, such as are found in various treatises, are much less 
clear than we would like them to be, yet they are sufficient to show 
that the tactus was a temporal unit equal to M.M. 48, more or less. 1 
Such a tempo, that is, S = M.M. 48, is indeed quite adequate for the 
major portion of the sacred music of the Flemish era, which is practically 
always written in B, S, M, Sm, and i 7 , the latter value being used only 
in groups of two as a quick 'cadential mordent.' The Kyrie's by 
Ockeghem and de la Rue, as well as the Sanctus by Benet (Facsimiles 34, 
27, 24) serve as examples. 

Another example, shown on p. 192 (from MS Florence, Magi. xix y 112 
bis), shows a section in C followed by one in <t . This change is accom- 
panied by a striking shift from the shorter to the longer values, the sec- 
tion <t being written mostly in B, S, and M. Evidently, the tactus 
which, in the first section, falls on the S, falls here on the B. Similar 
examples are frequent in the works of the late fifteenth and early six- 
teenth centuries, and may be studied in publications such as A. W. 
Ambros, Geschichte der Musik, (Leipzig, 1889), vol. v (e.g., pp. 4-5), or 
D. PI am en ac, Johannes Ockeghem , Sdmtliche Werke, Me s sen I -VII I 
(Leipzig, 1927). If, in these examples, the sign C is interpreted in its 
strict proportional meaning, the result is a change of the note values 
without any real change of tempo, the same durations (M.M. 48, 96) 
now being represented not by S and M, but by B and S. This interpre- 
tation is not wholly satisfactory, since it marks the sectional use of $ 

1 The number 48 has been chosen here as an average value because it is divisible by two as well 
as by three. 



192 



White Mensural Notation 






^.m^f V 






<£tt*S 



^^»gNg.Ujj)| .., =*£ 



w?*fcs) 



p^'^ll,^ 



ggg: 



4 



as a mere externality of writing without any real significance. We pre- 
fer to think that it really meant a different tempo, the reduction of the 
values being somewhat different from the exact halving. A possible 
explanation will be offered below. 

During and after the Josquin period the sign <t was universally 
adopted as a time-signature, to the almost complete exclusion of the 
signs of integer valor, C and O . We now find under this sign exactly 
the same note values, B to F, which formerly were used under the sign 
C , as a quick perusal of the editions of Lassus and Palestrina will read- 
ily show. Obviously, a real diminutio dupla of the temporal values, i.e., 
S = M.M. 96, leads to a tempo which is much too quick. The fact that 
the same note values appear here and in the Facsimiles 34, 27, and 24 
suggests the theory that there really was no change in tempo, the 5 hav- 
ing approximately the same value now under Cf as it had formerly 
under C . 

No attempt is made here to explain why the sign <t was so universally 
adopted throughout the sixteenth century, without any apparent signifi- 
cance and meaning. Possibly its adoption is bound up with the intro- 
duction of the tactus major and the tactus minor, terms which indicate, 
not different tempi, but different conductor's beats for the same tempo, 
the latter having two movements of the hand in place of one of the 
former. 

A similar situation is encountered in the case of the tempus perjectum 
diminutum . As has already been pointed out, this sign, if used as a 
common time signature, always calls for ternary mensuration of the B s m 



Time Signatures and Tempo 



193 



contrast to its correct meaning as a proportional sign. As regards the 
tempo of this meter, the same ambiguity exists as was previously en- 
countered. The following reproductions (from the Odhecatori) illus- 
trate this point. Obviously, a much quicker tempo is demanded for the 
'Rompeltier' than for the 'Est possible.' Whereas the latter is approxi- 
mately in the tempo of the integer valor (S = 48), the former is in double 
that speed, S — 96, or B = 32. 




& pOit'tUc (juelfeoiiupttilr 



In the latter interpretation which, no doubt, is the earlier and the 
original one (see our remarks regarding Facsimile 88, p. 425), we arrive 
at a new value, B = M.M. 32, for the brevis perjecta diminuta. Consid- 
ering the general importance of tempus perjeclum in the period of Dufay 
and Ockeghem, it is not impossible to assume that this value of the brevis 
perjecta diminuta was also used in tempus imperfectum diminutum. This 
would lead to the value S = 64 for <X , that is, to a really different tempo 
for the sections in diminution we have been considering previously. 1 

In turning to a consideration of proportio trip/a we find a somewhat 
simpler situation. The meaning of the signs C3 , or J, or simply 3, con- 
forms with their strictly proportional significance: three S (or a perfect 
B) consume the time which is normally allotted to the single S y thus lead- 
ing to the tempo: B (pf.) = M.M. 48. On page 194 is an example (from 
MS Modena, Bibl. Estense, L. 471). 

In the sources of the sixteenth century, the sign 3 occurs most fre- 
quently for shorter or longer sections in compositions marked 1 (for 
examples, see Ambros v, 106, 151, and numerous pieces in Lassus, 
Palestrina, etc.). Here it must be noted that as a rule the trip/a does not 

1 For an example, see Facsimile 71, p. 363. 



i 9 4 



White Mensural Notation 




b«n m# Ad U^jcmmt'^wV. 



| - u u a t H ^UUa» i iiH i 4rtHMMM^JtLik 



a 6 hi a 



I fiqrm* tttagm t«£i# cA* c a 



mM$c*Tn<|Mmtnm#c urn crof 



refer to the diminutio of the preceding section, but to the integer valor. 
In other words, three S of the tripla are equal, not to one, but to two S 
of the preceding section. Clear evidence of this is found in passages 
such as Ambros v, 112, in which measures marked <t and 3 alternate 
in both parts, or Ambros v, 76, where tripla is used in four parts against 
a cantus firmus in unchanged values. 

The use of (f , which largely predominated in the sources of the six- 
teenth century, was discarded to a great extent in the seventeenth cen- 
tury. In this period, pieces written in C frequently include sections 
marked 3 or ?, a designation which, of course, indicates exact triplication 
of the speed of the preceding section in integer valor. The following 
example (from G. MurTat, Apparatus musico-organisticus II \ 1690; repro- 
duced from A. G. Ritter, Zur Geschichte des Orgelspiels, II, 156) serves 
as an illustration: 




Passages of this kind are frequently a cause of fundamental errors on 
the part of performers and conductors who, mislead by the long notes 
occurring under these signs, usually take them much too slow, interpret- 



Time Signatures and Tempo 



195 



ing the sign \ as a mere metrical indication similar to the familiar 4, and 
overlooking its proportional significance. Below is a rendering which 
clarifies the temporal relationship between the two sections. It is inter- 
esting to note that in a document as late as this the notational principles 
of tempus perjectum are still strictly observed (see the use of undotted B 
for ternary, and of blackened B for binary values) : 







3 tr 


/?\ o: 


=J. 




J" "*- 


■*Ft4i 


!T 


"M r " 


t» 




. 


Ji J 


:/ 7 






1 — 0- — ^J 






1 rp t 



jfti-i Rfffj, 


Vi/ 


j j 


j j 1 


J ,'fT- 


r- etccst 

j j kj 


r r '- 


-W — ^_ 


1-^ g L 1 


1^ 1 







Turning back to the Flemish era, it may be noted that there existed a 
variety of proportional time signatures for quick triple rhythm, such as 

0»C3;C?:(tJ;^ • These were all used to indicate that meter and 
tempo which normally should have been denoted by G . Actually, 
however, this sign is practically never used after 1450 (1500?) as a time 
signature, on account of its then firmly established character as a signum 
augentiae. 

Considering the fact that some of the above proportional signs denote 
proportio dup/a> others proportio trip/a, it is tempting to speculate whether 
they might have signified different degrees of speed, possibly as follows: 





O 


0;(J: 


C3:CI 


Cf 


B: 


16 


32 


48 


24 


S: 


48 


9 6 


144 


72 



Some support of such a theory can be gained from a comparison of two 
related pieces by Ockeghem, reproduced in Ambros V, 12 and 18, to 
which the interested reader is referred. However, in this question, as 
well as in the whole subject of the temporal significance of the mensural 
and proportional signs, extensive special studies will be necessary before 
definitive statements can be made. 



PART III 

THE NOTATION OF ENSEMBLE MUSIC: 
BLACK NOTATION 



I. INTRODUCTION 

IN TURNING to a study of black notation one is confronted with a 
situation entirely different from that presented by white notation. 
Of course, the use of black notes instead of white ones is merely an ex- 
ternal difference. More notable is the fact that the signs and rules pre- 
vailing in the former system differ in many respects from those to be 
found in the latter. The chief contrast, however, is one of intrinsic 
structure, that is, the contrast between a phenomenon of a stable and 
one of an evolutionary character. For, whereas white notation is a 
consolidated system which, during its period of existence, underwent 
only slight modification, black notation must be comprehended as an 
historical process. Throughout the twelfth, thirteenth, and fourteenth 
centuries the mechanics of notation were in a state of continuous flux 
and rapid change, produced and paralleled by an evolution in musical 
style the progress of which lies mainly in the field of rhythm. The de- 
velopment leading from the entirely free and unmeasured rhythm of the 
twelfth century organa, through the rigid uniformity of the thirteenth 
century modal meter, to the singular rhythmic complexities of the 
late fourteenth century, brought about a continuous succession of nota- 
tional problems: as soon as one of them was settled, others arose and 
inaugurated a new phase. Naturally, under such conditions, it is diffi- 
cult to draw exact lines of demarcation. It is, therefore, with due reser- 
vation that the following classification is presented: 

I. Primitive notation (ninth through the twelfth century) 

II. Square notation (late twelfth and early thirteenth centuries) 

III. Pre-Franconian notation (middle of the thirteenth century) 

IV. Franconian notation (second half of the thirteenth century) 
V. French notation (ca. 1 300-1 450) 

VI. Italian notation (middle of the fourteenth century) 
VII. Mixed notation (late fourteenth century) 

VIII. Mannered notation (late fourteenth and early fifteenth 
centuries). 

Square notation is also called 'modal notation' (see p. 218). The systems IV to VIII 
are usually termed 'black mensural notation.' The term 'French notation' for the sys- 
tem V is not meant to suggest a contrast to the previous systems which, of course, are all 
of French origin, but to the contemporary Italian notation (VI). It should be noted that 

199 



2oo Black Notation 

the system of French notation, by the adoption of white notes, led, around 1450, to the 
white mensural notation. 

The treatment of this large field obviously demands an entirely differ- 
ent method from that used in the preceding chapters. In place of method- 
ical and systematic explanations, given frequently in the form of rules, 
we must treat the subject in a more flexible manner, and must approach 
it chiefly from the evolutionary point of view. More consideration must 
be given here to the theoretical writings, which in these early periods 
prove to be important and generally reliable sources of information and 
which, in spite of their aura of scholasticism, are closer to the musical 
practice of their period than the treatises of the late fifteenth and six- 
teenth centuries are to theirs. 

The following table provides a general view of the most important 
sources, both practical and theoretical, of black notation, together with 
references to modern publications. The chronological arrangement has 
been made on the basis of the notational characteristics rather than the 
date of completion of the manuscripts. The difference between these 
two dates may in some instances be quite considerable, especially in the 
case of manuscripts which are preserved only in copies from non-existent 
originals. 1 As a rule, the 'notational' date of a source will correspond 
with the position it occupies in the historical development, since the 
original system of notation was generally preserved even by later copyists. 

1 A case in point is offered by the Codex Wolfenbiitte! 6jy {W\) ol the School ot Notre Dame, 
which has been frequently accepted as having been written around or even after 1300 (see, e.g., the 
Introduction to F. H. Baxter, Av Old St. Andrews Music Book, p. xiii, and G. Reese, Music in the 
Middle Ages, p. 2gj). However, the present writer has always been skeptical about this late dating, 
and was gratified to find his view supported by no less an authority than Prof. E. K. Rand of Harvard 
University, who pointed out to him that the minuscule, rather than the majuscule, form of the 
final s, as well as the more regular a of minuscule Carolingian script, suggest a mid-thirteenth century 
date for the codices W\ and Fl, that is to say, only a few decades later than the period represented 
by their contents. 



Sources 201 



SOURCES OF BLACK NOTATION 

Musical Sources Theoretical Sources 

I. PRIMITIVE NOTATION ( 9 th-i 2th centuries) 

a. Syllables, Letters 

Musica enchiriadis, Scholia enchiriadis 
ca. goo (GS 1, 152, 173). 

Guido d'Arezzo, Micrologus, ca. 1000 
(GS 11, 2). 

yf*/ organum faciendum, nth cent. 

, T w . , (Coussemaker, Hist, de I'harmonie, 220). 

Ut tuo propitiatus, nth cent. v ' ' y ' 

(see p. 207). b cheironomic Neumes 

Winchester Troper, ca. 1050 (W. H. Frere, 
The Winchester Troper, 1894). 

c. Diastematic Neumes 

MSS of St. Martial, ca. 1150: Paris, B. N. 

lat. 1/39, 3719, 3549; London, Br. M. 

Add. MS. 36881. 
Codex Calixtinus of Santiago de Compos- 

tela, ca. n 50 (P. Wagner, Die Gesdnge 

der Jakobusliturgie, 1 93 1 ) . 

II. SQUARE NOTATION (1 175-1225) 

Four sources of Notre Dame, ca. 1250- 

1. Wolrenbuttel 677 (Wi); facs. in J. H. 
Baxter, An Old St. Andrews Music 
Book, London, 1931. 

2. Florence, Bibl. Laur. pluteus 29 codex 
1 {Ft); also known as Antiphonarium 
Mediceum. 

3. Madrid, Bibl. Nac. Hh 167 (Ma). 

4. Wolfenbiittel 1206 (W 2 ). 
London, Br. M. Egerton 2615 (LoA). 
London, Br. M. Egerton 274 (LoB). 
Paris, B. N. 13139 (formerly St. Victor 813). 
Paris, B. N. /re. 844, 'Chansonnier Roy' 

(R); facs. in J. B. Beck, l t Manuscrit- 
du Roi, Philadelphia, 1938. 
Paris, B. N. /re. 12613, Chansonnier 
Noailles' (N). 

III. PRE-FRANCONIAN NOTATION (1 225-1 275) 

Paris, B. N. lat. 1/266. Discantus positio vulgaris* ca. 1225 (CS 1, 

London, Br. M. Add. 30091. 94). 



202 



Black Notation 



Codex Montpellier, Montpellier, Fac. des 
Med. H 196 (Mo) fasc. II-VI; facs. and 
transc. in Y. Rokseth, Polyphonies du 
xiiie siecle, 4 vols., Paris, 1936-39. 

Codex Bamberg, Bamberg, Kgl. Bibl. Ed. 
IV. 6 (Ba); facs. and transcr. in P. 
Aubry, Cent Motets du xiiie siecle, 3 vols., 
Paris, 1908. 

Codex Torino, Torino, Bibl. Reale, man. 
var. N. 42. 

Codex Huelgas or Burgos, (Hu); facs. and 
transcr. in H. Angles, El Codex musical 
de Las Huelgas, 3 vols., Barcelona, 1938. 



Anon. VII, ca. 1250 (CS 1, 378). 

Joh. de Garlandia, the elder, ca. 1250 

(CS 1, 96). 
Pseudo-Aristoteles or Magister Lambert, 

ca. 1250 (CS 1, 269). 
Amerus, ca. 1275 (J. Kromolicki, Die Prac- 

tica Musicae des Amerus, Berlin, 1909). 
Dietricus, ca. 1275 (H. Muller, Eine 

Abhandlung iiber Mensuralmusik, 1886). 
Anonymous Sowa (H. Sowa, Ein glossier ter 

Mensuraltractat 1279, Kassel, 1930). 



IV. FRANCONIAN NOTATION 



Codex Montpellier, fasc. VII-VIII (see 

above). 
Paris, B. N. /re. 146 (Roman de Fauvef), 

ca. 13 1 5; facs. in P. Aubry, Le Roman de 

Fauvel, Paris, 1907. 



Franco of Cologne, Ars cantus mensur- 

abilis, ca. 1260 (CS I, 117). 
Walter Odington, ca. 1280 (CS 1, 235). 
Anon. IV, ca. 1280 (CS 1, 327). 
Robertus de Handlo, Regulae (CS 1, 383). 
Anon. Ill (CSi, 319). 



V. FRENCH NOTATION 



Codex Ivrea (Ivrea, Libr. of the Chapter). 
Machaut-MSS (G. de Machaut, 1300- 

1377): Paris, B.N. 22545/46, 1584, 1585, 

1586, 9221; MS de Vogue, Paris. See F. 

Ludwig, G. de Machaut, Musikalische 

fVerke, Leipzig, 1928, 11. 
Numerous French and English fragments; 

see AjMJV vn, p. 195 ff. and 219 ff; also 

GdM 1,176. 
Compositions contained in the MSS listed 

under 'Italian Notation.' 
Prague, Univ. Bibl. XI E 9; see F. Kam- 

merer, Die Musikstiicke des Prager Kodex 

XI E 9, Prag, 1 93 1. 
Codex Apt (Apt, Library of the Chapter), 

ca. 1400; transcr. in A. Gastoue, Le Manu- 

scrit . . . d'Apt, 1936. 
Cambrai, MS 6 (Cambrai A), ca. 1425. 
Rome, Bibl. Vat. Urb. tat. 141 1; see GdM 

1, 192. 
Bologna, Lie. Mus. cod 37; see GdM 1, 197. 
Bologna, Bibl. Univ. 2216; see GdM 1, 

199 ff. 



Joh. de Garlandia, the younger, ca. 1300 * 

(CS i, 389, 424). 
Ph. de Vitry, Ars nova, ca. 1325 (CS Hi, 

*>■ 
Joh. de Muris, Musica practica, 1321 

(GS in, 292). See also CS in, 46, 59, 68. 
Speculum musicae (by Jacobus of Liege?), 

ca. 1325 (CS 11, 322). 
Theod. de Campo, ca. 1350 (CS in, 177). 
Verulus de Anagnia, ca. 1350 (CS in, 129). 
Simon Tunstede, ca. 1350 (CS iv, 254). 
•Anon. V (CS in, 379). 
Prosdocimus de Beldemandis, Tractatus 

. . . , 1408 (CS in, 200). 
Joh. Ciconia, Liber de proportionibus, 

141 1 (see HdN 1, 333). 
Guilelmus Monachus, De preceptis. . . . li- 

bellus, ca. 1450 (CS ill, 273). 



Sources 203 

Old Hall MS (College of St. Edmunds., 
England); new ed. by A. Ramsbotham, 
3 vols., Burnham, 1 933-1938. 
(The last four sources date from the first 
half of the fifteenth century). 

VI, VII. ITALIAN NOTATION; MIXED NOTATION 

Rome, Bibl. Vat., MS Rossi 2/j, see J. Marchettus de Padua, Pomerium, ca. 1320 

Wolf in Jahrbuch Peters, 1938. (GS in, 121). See also CS m, 1 

Florence, Bibl. Nac. Pane. 26; see GdM 1, Anon. VII (CS in, 404). 

244. Ph. de Caserta (CS in, 118). 

London, Br. Mus. Add. 29987; see GdM 1, Anon. X (CS 111, 413). 

268. Antonius de Leno (CS lii, 307). 

Paris, B. N. ital. 568; see GdM 1, 250. Prosd. de Beldemandis, Tractatus . . . ad 

Florence, Bibl. Laur. Pal. 87, (Squarcial- modum Ytalicorum, I412 (CS in, 228); 

upi Codex); see GdM 1, 228. see C. Sartori, La Notazione Italiana del 

Paris, B. N.f.fr. nouv. acq. 677/, (Codex Trecento, 1938. 

Reina); see GdM 1, 260. 

VIII. MANNERED NOTATION 

Modena, Bibl. Estense L. 568 
Chantilly, Musee Conde 1047. 
Torino, Bibl. Naz. J II 9. 
Compositions contained in Paris, B. N. ital. 
368 andf.fr. 6771 (see under vi, vn). 

Bibliography: 

I: OH, 45-101 ; M. Schneider, Geschichte der Mehrstimmigkeit, Berlin, 1935, 

vol. 11. 
II: OH, 102-371 ; F. Ludwig, Repertorium organorum recentioris et motetorum 
vetustissimi stili, Halle, 1910, particularly p. 42-57; HdN 1, 198-237; G. Ja- 
cobsthal, Die Mensuralnotenschrift des 12. und 13. Jahrhunderts, Berlin, 1871 ; 
W. Niemann, Die abweichende Bedeutung der Ligaturen in der Mensuraltheorie 
der Zeit vor Johannes de Garlandia, Leipzig, 1902; H. Sowa, Ein anonymer glos- 
sierter Mensuraltraktat 1279, Kassel, 1930. 
Ill: HdN 1, 237-250; 

IV: HdN 1, 250-286; GdM 1, 37-62; 11, in, nos. 1-12. 

V: HdN 1, 330-362; GdM 1, 63-214; 11, m, nos. 13-37; F- Ludwig, in SIMG vi, 
607; H. Besseler, in AfMW, vn, vm. 
VI, VII: HdN 1, 287-329; GdM 1, 28-36 and 215-288; n, in, nos. 38-63. 
VIII: GdM I, 289 ff, 328 ff; n, in^nos. 64-70. 

For additional literature see: G. Reese, Music in the Middle Ages, p. 451 ff. 



II. PRIMITIVE NOTATION 

THE EARLIEST preserved documents of part music are the instruc- 
tive examples of parallel organum, contained in the Musica En- 
chiriadis (GS I, 152) and in the Scholia Enchiriadis (GS 1, 173), two MSS 
of the ninth century. 1 Here a staff of a varying number of lines (four to 
eighteen) is used, the interspaces of which represent the successive de- 
grees of the scale. Instead of using notes or similar signs, the syllables 
of the text are placed in the proper interspaces, as is shown in Facsimile 
42a (text: Tu patris sempiternus es Alius'). The pitch is further clari- 
fied by means of the signs of the so-called Dasia notation, written at the 
left of the staff. This system, which is a mediaeval imitation of the an- 
cient Greek notation, 2 utilizes four basic signs for the tones of the tet- 
rachord d e f g, and others (derived largely from these by changing their 
position from upright to horizontal, or their direction from right to left, 
as in Greek notation) for one lower and two-and-half higher tetrachords 
which repeat the basic tetrachord in exact transpositions of the fifth. 
There results a curious scale which avoids diminished fifths but, as a 
consequence, includes augmented octaves, as follows: 

^^yJ-^^SsCorSfV J S * "f ^> ^r» 

G A Bb c I d e f g I a b c' d' | e' f'# g' a' | b' c"# 

The letters / (or t°) and s, indicating tonus and semitonus (whole-tone and 
semitone) are added in some of the examples as a further clarification of 
pitch. It must be noticed, however, that their indications frequently 
contradict (or correct?) those of the Dasia scale proper. For instance, 
the example of Facsimile 42a contains, according to the fundamental 
scale, a B-flat in the lower part, while the letter / placed between the 
lowest signs would call for a whole tone above A: 



tupa-tris sempiternus es fi-li-us 

1 The notation of the Musica and Scholia Enchiriadis was first correctly interpreted by Ph. Spitta, 
in VjMW, v. See also HdN i, 31, and G. Reese, Music in the Middle Ages, pp. 126, 254, and Bibli- 
ography. For various details of the above explanations I am indebted to Mr. Lincoln B. Spiess who is 
preparing a study on 'Consonance and Dissonance from the Ninth to the Fourteenth Centuries.' 

2 See, for instance, HdN 1, 11 fF and various monographs on Greek music mentioned in the bibli- 
ography of G. Reese's book. 

204 



Primitive Notation 
Facsimiles 42a, 42b 



205 



^ 



z 



ftf tnCCtyifn*' \ Vj 



fe 



zT 



fl'einptthuT 



t 



X 



ef U 



y* 



\ 



b 



w 



iltffernpttmif' \ 



k 
4; 



u 



T 



h 



7Z 



trtffeirrptirwf 



f>r vr 



\ 



/ 



? 



tffep» 



i^S 



/4 w 
r 



T 



w 



k 



V* 



Musica Enchiriadis (9th century) 



Facsimile 43 



*rn*mcnm ualrti nilm.cU>rri o»nTuItrjfmma 







MS Oxford, Bodleian Library 572 (nth century) 



2o6 



Black Notation 



In Facsimile 42b, which shows a four-voice organum, the intervals are 
indicated only for the higher octave of the scale, probably in order to 
permit the singers of the two lower parts to introduce the necessary 
chromatic alterations: 




This is not the place to enter into a discussion as to what is the intended 
reading of these examples. It may be noted, however, that our two 
facsimiles (the only ones which were available for this book 1 ) are not en- 
tirely characteristic. More typical is the manner of writing illustrated 
by the reproductions given below, 2 in which only a small number of the 
Dasian signs are used and repeated in transpositions which are indicated 
by additional signs. 



<#\ 



J qA 



H J No/ qui vivimttfbenedicirou* 

f ZZZZZZZZZH 

/ . ?r< XL <J Ko/ q-ivivimus 

£ / ggv 

_7 °fl Or.VUl/ No/ quivivimuy 



He/ No/ 

I- 



qui vivirntt^ be^__iwu^ 



K 



J\ 0}J\ 



oft 



A<f Ko/ qui vivhmts htaedi chm# 

i___= 



Pt IIII. </ No/ quivivinmy 



$ 



1 See H. B. Briggs, The Musical Notation of the Middle Ages, London, 1890, pi. 17. 

2 For the complete reproductions, see GS 1, pp. 185, 186. 



Primitive Notation 



207 



For instance, in the first reproduction the signs for the segment d — b 
appear three times, while the letters A, H, and P, written in front of the 
sign for a, indicate that the three singers start with A, a, and a' respec- 
tively (for the meaning of the signs A, H, P see the explanations on p. 
21). In the second reproduction the same segment appears twice, and 
the three singers start, according to the roman numerals, on the fourth, 
eighth, and eleventh degrees of the scale (beginning with e), that is, on a, 
e', and a' (the letters Pr. and Or. designate the vox principalis and the 
vox organalis). The second tone of the organalis is F-sharp. 

A more advanced type of organum is represented by the curious illus- 
trations of another 'Hucbaldian' treatise (reproduced in CS 11, 74 ff) 
which — at least in Coussemaker's reproduction — look like an engineer's 
design for the construction of a bridge rather than like musical notation. * 
Small circles indicate the positions of the tones in the Dasian scale, and 
vertical or diagonal lines somewhat vaguely connect simultaneous sounds. 
Following are a few examples taken from Coussemaker (CS 11, 77) and 
their transcription: 




In the tenth century various systems of letter-notation were evolved 
(see p. 21). Such letters are used in the eleventh-century treatise, 
Ad organum faciendum 1 , for the writing down of organa in contrary 
motion ('new organum,' see OH 1, 74), for instance: 



cabGFecdcabG 
CDFDFEFGFEFG 
Alle lu ia 




Al-le 



A particularly interesting specimen of part music written in letter- 
notation (the only one preserved outside of treatises) is the famous Ut 
tuo propitiatus from the codex 572 of the Bodleian Library, Oxford 



1 E. Coussemaker, Histoire de P harmonic au moyen-age, Paris, 1852, p. 229. See OH 1, 77 ff. 



208 



Black Notation 



(Facsimile 43). This composition, although of a later date (eleventh 
century) than the one just considered, employs a more ancient system of 
signs, in which the letters a — p designate the tones of two octaves from 
A to a' (so-called Boethian notation; see the system II of the table p. 21). 
Following is a transliteration of the beginning of the piece: 

hgfg.hkln.hk lkh.higfgh. 

hhhg.hg?f.hg fgh.k?ihih. 

Ul tuo pro-pi-ti- a- tus {interventu Dominus nos pur- 

gatos a peccatis iungat coeli 

civibus) 

The question mark in the lower row stands for a sign, vaguely reminiscent 

of a 5, the meaning of which has been variously interpreted (see RHdM 

1, ii, 141 and OH 1, 92). We suggest interpreting it as indicating pro- 

* longed duration of the preceding tone: 




Despite the great authority which H. Riemann deservedly enjoys as a 
musical scholar, the reader must be expressly warned against his rhyth- 
mical version of the above piece — as well as against those of numerous 
other melodies reproduced in his Handbuch. These versions are the re- 
sult of his principle of 'Vierhebigkeit' (Hebung, i.e., accent), a theory 
according to which, throughout the history of music, all musical phrases 
comprise four accents, i.e., two or four measures or multiples thereof. 
Accordingly, Riemann forces the above melody into two J-measures, 
coordinating it to the four accents of the text: 'ut tuo propitiatus.' Ac- 
tually, 'Vierhebigkeit' is a principle which plays a basic and universal 
role only in the music of the eighteenth and nineteenth centuries. If 
applied to mediaeval compositions it usually leads to procrustean de- 
formities of which Riemann's rendition of the piece in question furnishes 
one of the most monstrous examples. 

A great number (over 150) of two-part organa are preserved in the 
eleventh century Winchester Troper. Unfortunately, they are written 
in cheironomic 1 neumes the deciphering of which is extremely dubious, 

1 Neumes are called cheironomic (staffless, in campo aperto) if their writing gives no clear indica- 
tion of pitch; otherwise they are called diastematic or heighted. 



Primitive Notation 209 

to say the least. A discussion of their notational problems is beyond the 
scope of the present book, since it would presuppose a study of the 
neumes. Suffice it to say that the organal parts are not written together 
with the liturgical melodies, but appear in separate sections bearing in- 
scriptions such as 'Incipiunt melliflua organorum modulamina super dul- 
cissima caelestia praeconia.' 1 

In turning to the sources of the twelfth century we enter upon more 
solid ground. A large repertory of two-part organa written in diaste- 
matic neumes is contained in the manuscripts from St. Martial at Limoges 
and in related sources. 2 A reproduction from the MS Paris B. N. lat. 
3549 (P- 1 5 I '/ I S' 2 ) ma Y serve as an example (Facsimile 44). 

With each line of the text, two rows of neumes of the x^quitanian (i.e., 
southern French) type are given, separated by a horizontal line. The 
neumatic signs are written on staff lines, which are scratched in the parch- 
ment and, therefore, barely visible in a photographic reproduction. 
They have been redrawn in our facsimile. 

The composition is a trope (i.e., inserted text and music) to the Christmas gradual 
Viderunt omnes fines terra (see Grad. Rom., p. 23)- Following is the complete text: 

Viderunt Hemanuel patris unigenitum 

In ruinam Israel et salutem positum 

hominem in tempore, verbum in principio 

urbis, quam fundaverat, natum in palacio 

omnes fines terrce salutare Dei nostri .... 
The second line of the poem is to be sung to the music provided for its first line; the 
continuation of the original text {omnes fines . . . ) is sung in plainsong. 

The pitch of the various tones is clearly indicated (clef-letters c, g, f). 
The writing of group signs in a strictly vertical position is a characteristic 
feature of the Aquitanian neumes; these signs must always be read from 
top to bottom. The contrapuntal coincidence of the two parts is some- 
what vaguely indicated by the alignment of the neumatic signs; in cases 
of doubt the observation of consonances provides a helpful clue. The 
main problem offered by this notation is that of time values and rhythm. 
F. Ludwig, in AHdM i, 179, gives a transcription of Viderunt Hemanuel, 
in which triple meter — apparently suggested by the modal rhythm of the . 
thirteenth century — is introduced for the beginning of the piece, while 
for the long melisma on '(iinige)ni-' irregular groups of eighth-notes are 
used in such a manner that frequently a group of three, four or five notes 
in one part is placed against a group of two, three, or four notes respec- 

1 See W. H. Frere, The Winchester Troper (publications of the Henry Bradshaw Society, vol. vm), 
plate 7. A number of transcriptions, necessarily of a tentative character, are given in M. Schneider, 
Geschichte der Mehrstimmigkeit, Berlin, 1935, vl. II. 

2 See the list of sources, p. 201. 



210 Black Notation 

tively in the other part. This rendition is open to several objections. 
The introduction of triple meter for the beginning of the piece is without 
foundation and is bound to lead to a misconception of the rhythmical 
context, even if this meter is treated freely, as is demanded by Ludwig's 
inscription: 'In rhythmisch freiem Vortrag.' On the other hand, the use 
of, e.g., four notes in one part against a group of five notes in the other is 
rather too vague an indication of how the two parts should be combined. 
Finally, the grouping of the notes and the vertical alignment of simul- 
taneous notes is frequently not in agreement with the writing of the 
original. 

The fact that a transcription presented by so outstanding and scrupu- 
lous a scholar as Ludwig is open to severe question only goes to illustrate 
the difficulty of the situation. The present writer is far from pretending 
to be able to offer a 'correct solution' of the problems presented by the 
piece under consideration. Properly speaking, no transcription into 
modern notes is possible for music of this kind, and even a rendering by 
means of the modern signs of Gregorian chant (Roman chorale notation) 
is not without its difficulties. One must content himself with a sort of 
clarified copy in which signs as similar as possible to those of the original 
are used. We suggest a method of transcription the details of which will 
become sufficiently clear from the following table: 

• f ' ■' f 9 5 • 
\ \ o •> 

The first three single signs are called punctum, virga, and apostropha. Their difference 
in meaning is rather problematic and need not concern us here. Even more obscure is 
the exact meaning of the ornamentations indicated by other symbols for a single note 
such as reproduced above. The group sign of the second line is the c/ivis, while the signs 
on the last line are a combination of the punctum and the apostropha, or else the liquescent 
form of the c/ivis, also known as cephalicus (see the explanation of the neumes in Liber 
usualis missae et officii, Rome, 1937, p. vii). 

The proper combination of the notes of the upper voice with those of 
the lower voice presents great difficulty. In the rendition given in the 
appendix, No. 31, the observation of consonances has been the main 
guide, together with the vertical alignment of the characters as they ap- 
pear in the original. This method has almost everywhere led to a satis- 
factory result, except for one or two places where a second (d-e) could not 
be avoided. However, it may be noticed that the use of this interval (in 
a weak position) is clearly indicated in the 'syllabic section' to the syl- 
lable '(tem)po(re).' For more information on the mediaeval theory of 
consonance and dissonance, see p. 244 f. 



Primitive Notation 
Facsimile 44 



211 



TT 



^t^tf 




X 



n^r 



-a_JE^ 



\bwmtJHi»*~ja&^ — 



T"? 



■*-=* 



^L 



JL 



£ 



1 « ******* 



^ill. 



c, - ; 



** 



.f- f ,f5 r 



<* twrn-JL^iltwiv 



*. • ^L_^ 2 3_ 

' ! ' -— - S 

— =— XT- *-, . * ■■ C ^ — 

*-> 

* _ - ^T £. 



m 






r~r » — » »l 



^dm^uunnr^aasm-ttr^^ 



,f' : 



MS Paris, Bibliotheque Nationale lot. 3549 (12th century) 
trom pages 151', 152 



212 



Black Notation 



From the standpoint of the technique of composition the use of chains 
of notes in the upper voice (duplum) against single notes in the lower 
voice (tenor) deserves our attention, particularly if considered in con- 
trast with the strictly syllabic treatment of the section 'hominem . . . 
pala(cio).' Here we find an early intimation of a differentiation in mu- 
sical styles which was bound to have far-reaching consequences, and 
which will play a fundamental role in the ensuing discussions of square 
notation — that is, the distinction between melismatic and syllabic style. 

Closely contemporary with the sources of St. Martial is the Codex Cal- 
ixtinus of the cathedral of Compos tela (northern Spain), a page of which 
is reproduced on Facsimile 45. l It contains, beginning in the middle of 
the first brace, a two-voiced Alleluia vocavit Jhesus, at the beginning of 
which the name Magister Goslenus, episcopus Suessionis, possibly indi- 
cates the composer. Each part is written in diastematic neumes of a 
type similar to those of St. Martial. Their reading, which may offer 
some difficulties to the novice, will be facilitated by the following trans- 
literation of the beginning, reproduced from P. Wagner's publication, 
into modern plainsong notes: 



jf-iyft— 


T6^- 


_•*• a*J a t 


■ Sc 31 


3i Si •» ■ _, 


* \ :^ •• ^ 


■% a N. ♦ 


• V«.3rf 




•Si 


1% 


1 


Al- - - 


le- - 


- - lu- - ia. 


\\ Vo- - ca- 


- - vit 












j 1 


a • 


■ ■ 1 


1 ■ 


1 PL ■ 


5 — J 




1 


1 g 


1 Ik 



■ 


jt 






a 


■ ■* J I 


t" \% 


■ ■ ■ 


■ fmm 


•V r, ]» j 


■ -1 ■ r 


i 


* ' V *. 


% a a % J 


■V J^V 


1 • a 1 , 


■\3 ■ 




1 » ' •♦ r k 

Jhe-sus Ja- - 


•• ' * 


co- - bum, 














af 


1 


■ 


• 1 


■, 




% 


■ 


• 


a 


— — *-■ — $- 



Certainly, these twentieth century 'neumes' are a very convenient — in 
fact, the most satisfactory — means of 'transcribing' pieces of this early 
period, the free melismatic rhythm of which would necessarily be de- 
stroyed by the signs of measured notation. 2 There is only one point 
which does not become sufficiently clear from the above transliteration, 
that is, the coincidence of the upper part with the lower part, if the latter 

1 From P. Wagner, Die Gesdnge der Jakobusliturgie %u Santiago de Compostela, 1931. 
2 Cf. Handschin's measured transcription of a three-voice Congaudeant Catholici from the same 
MS in ZfMW viii, 336. 



Primitive Notation 
Facsimile 45 



213 



f x jt - ^JjU. t 1 ' ! > y l^ 



-^r^ 



r^ y^^l^ ^ XX ^ 



K5 



7X 



title 



Jin y r-r j 



T-r, 



Iftr 



-r^r 



c-d&nr 



t+Ji 



H^t — ZJZ 



■JH-fo 



-f- 



^•j' fo } 



mr 



CA\ utc -— ^ tfv fttf U. co !n«rt 



«-/W-:-t/ 



~ ... _. ~ 1 ■ " ~« ~l j "*"""? ^ 



v-^|. 



-*n— ^-^— *~y*~ 









VVl . . , i r r 



a B / 



^3~E5 



< tut: tc 



^r : ^tri: 



:/ 



«»f§(l ..f»j0* 



&&*-*<*-& u* «*fcl 



bo a' 



' ^.7 fcr -*■**" 






j^"^ 



~4 



*?'— 3>" 



^— •— 'TUT $rf 



------ r! r 



jfc 



3fi 






'Z--± 



&■ uC om m cvt a -vox e - ■ - 



f— - --,1 — • — - 



Icyfim 



Codex Calixtinus. Cathedral of Santiago de Compostela (12th century; 

Pages 189', 190 



2I 4 



Black Notation 



is written in group-characters. For instance, already with the opening 
'measure' of the Alleluia the question arises how to align the two notes of 
the tenor with the ten notes of the duplum. There is, apparently, no 
hard and fast rule for this. However, the guiding principle will be 
quickly understood if the composition is viewed from the point of view 
of two singers performing it. Obviously, the singer of the duplum will 
take the lead, and the singer of the tenor will follow suit, beginning simul- 
taneously with the first note, and changing to the second note somewhere 
in the middle of the melisma (always with the first note of a group sign, 
of course), where a suitable consonance 1 occurs. As an illustration, 
there follows the 'transcription' of some measures in characters which 
will make easier reading to the student not familiar with the signs of 
modern plain-song notation: 




g-es 



Naturally, there is quite a considerable latitude in the question of the 
vertical alignment. The student will notice that the above arrangement 
brings about rather bold 'appoggiaturas' which could be avoided if the 
notes of the tenor were postponed to coincide with the end of a melisma, 
rather than with its initial note, for instance: 




This method has been used by H. Angles in his transcription of a Bene- 
dicamus from the Codex Calixtinus (see his El Codex de las Huelgas, in, 
47). Although it gives satisfactory results, as far as the consonances are 
concerned, it leads to a very uneven distribution of the notes of the tenor, 
or else, to fermatas at the end of the phrase which interrupt the flow of 
the musical line. It is for this reason that the other method, as a rule, 
would seem to deserve preference. 

1 See the explanation of consonances, p. 244. 



III. SQUARE NOTATION 

A. General Characterization 

THE LATE twelfth century is a highly important period in the his- 
tory of polyphony. The then newly constructed cathedral of Notre 
Dame at Paris became the center of a musical activity of greater inten- 
sity and of more important consequences than that of any previous 
period. In striking contrast to the extremely slow progress of poly- 
phonic music during the preceding centuries, there now begins an era of 
precipitate change. A significant feature illustrating the importance of 
this period is the fact that here, for the first time, musical activity steps 
out of the obscurity of anonymous and collective creation, and enters the 
stage of individual achievement and personal contribution. Magister 
Leoninus, 'optimus organista,' (greatest composer of organa) and Ma- 
gister Perotinus Magnus, 'optimus discantor et melior quam Leoninus,' 
(greatest composer of discant, and greater than Leoninus) — as they are 
called by the English Anonymous 1 — are the leading figures of the School 
of Notre Dame. Leoninus was the creator of the Magnus Liber Organi 
which represents a complete cycle of two-part organa {organa dupla) for 
the ecclesiastical year. His successor Perotinus {ca. n 60-1235) rewrote 
this repertoire in a more 'crystallized' style which is characterized by a 
greater rhythmic preciseness (modal meter) and by the increase of the 
number of parts from two to three and, occasionally, four (organa tripla, 
quadrupla). He also added a large number of short compositions, mostly 
in two parts, the so-called clausulae ('Ersatzklauseln') which were de- 
signed to be used as substitutes for certain sections of the complete or- 
gana. For instance, to the organum Audi filia (et vide et inclina aurem 
tuam quia concupivit rex) which is preserved in W\, p. 19', 2 there exist 
clausulae for the sections 'fili-,' 'filia,' 'et inclina,' and 'concupivit rex' (in 
Ft, p. 168; reproduced in SchT, p. 14). Naturally, the complete or- 
ganum as well as the clausulae use for their tenors the liturgical plain- 
song melody of Audi filia, which is the verse (¥) of the gradual Propter 
Mcritatem for Assumption (see Gr. Rom. s p. 561). 
in strong contrast to the liturgical organa and clausulae there is a 

*CSl, 34 2. 

2 Page references are always to the modern pagination of W\. 

215 



2i 6 Square Notation 

third type of composition, namely, conductus. A conductus has no re- 
lationship to pJainsong, either textually or musically, but is simply a 
musical setting of a Latin poem. In the period under consideration, 
these poems are usually religious lyrics, addressed to the Virgin, a Saint, 
or dealing with other religious matters. Later examples frequently re- 
fer to social conditions or to political events. A great portion of the ex- 
ceedingly large repertory of conductus is purely monophonic (conductus 
simplex). Here, we are interested only in the conductus in two, three or 
four parts (duplex, triplex, quadruplex). 

As regards the musical style, as well as the notational methods applied 
to these forms, there exists a fundamental distinction resulting from the 
fact that the text can be treated in two different ways: either syllabically, 
i.e., with one note to each syllable; or melismatically, i.e., with ex- 
tended groups of notes to each syllable. This distinction exists, of 
course, already in Gregorian chant, in which the psalm tones are in a 
simple syllabic style, while the graduals, alleluias, etc. are for the most 
part in a highly ornate melismatic style. The same distinction occurs 
in early polyphony, as appears from Facs. 44 (p. 211), where the section 
'hominem . . . pala-' is syllabic in both parts, while the closing passage, 
on 'ci-o,' is melismatic. 

In the School of Notre Dame the distinction between these two methods 
gains considerably in clearness and importance. Melismatic and syllabic 
style, which formerly were used side by side, now become rather completely 
segregated, the former being used mainly for organa and clausulae, the 
latter for conductus. The organa of this period are based on (untroped) 
graduals and alleluias, as well as on the Benedicamus Domino}* salutation 
used at Vespers. The plainsong melodies of these chants consist of 
passages in 'group style' (one to four notes to a syllable) in alternation 
with others in 'melismatic style' (ten to forty notes to a syllable). This 
distinction entails an important difference in polyphonic composition. 
The passages in group style were transformed into tenor sections consist- 
ing of single prolonged notes each of which serves as a sort of 'pedal 
point' for an extended complex of notes in the upper part or parts (duptum, 
tripium, quadr upturn). The melismatic passages, on the other hand, were 
transformed into tenor sections of continuous motion, by organizing the 
plainsong melisma in a strictly metrical pattern, according to one of the 
rhythmic modes. The upper parts added to these sections contain only 
slightly more notes than are found in the tenor, for instance, three against 
one. A good illustration of these methods is found in the Benedicamus Dom- 
ino of Facs. 49 (p. 247) . The plainsong melody consists of a passage in group 
style, 'Benedicamus,' which is followed by a highly melismatic passage, 



General Characterization 



217 



'Domino.' Consequently the organum consists of a first section with 
widely spaced tenor notes, and of a second section showing continuous mo- 
tion in the tenor. Sections of the latter type are called clausulae, while the 
term 'organal style' is used for sections based on sustained notes. 

Although syllabic treatment almost completely disappears in the 
strictly liturgical music, it becomes clearly established, in compensation, 
as the main style of the polyphonic conductus. The reason for this dif- 
ference of treatment is clear enough. In genuinely liturgical music — 
plainsong as well as polyphonic music — the text has a mystic significance 
which elevates it beyond criteria such as 'clear pronunciation' or similar 
requirements of modern singing. Its existence, like that of God, is eternal 
and independent of actual apperception on the part of men. With the 
conductus — as well as with other extraliturgical texts (tropes) — the situ- 
ation is entirely different. Here the words express new thoughts of in- 
dividual minds and are meant to convey a new message to the audience. 
Here audibility and clear pronunciation are matters of prime impor- 
tance. Hence, syllabic treatment is most suitable. 

The development of forms and styles that has just been outlined is 
paralleled by one of notational signs and methods. A comparison of the 
sources of the School of Notre Dame (chiefly the four more or less com- 
plete copies of the Magnus Liber Organi: W Xi Fl y fV 2i and Ma, — see the 
table p. 201; Facsimiles 46-50, etc.) with those of the preceding period 
(Facsimiles 44, 45) shows in the first place a striking difference of the no- 
tational characters. Towards the end of the twelfth century, the Aqui- 
tanian neumes assumed more definite shapes, characterized by the use of 
square forms. Thus they changed into what were later to be called notes 
and ligatures, e.g.: 

• r p. ,r r* 
■ 1 > 3 TS 

It is the use of these new shapes which led to the adoption of the name 
square notation (German: Quadratnotation 1 ) for the notation under 
consideration. 

In conformity with the above dichotomy of styles — syllabic and 
melismatic — there evolved two fundamentally different systems of no- 
tation, one in which the tones are represented primarily by single signs, 
and another in which the tones are written in group-characters, i.e., 
ligatures. They may fittingly be called syllabic and melismatic nota- 
tion. Theorists of the thirteenth century frequently refer to these two 

1 The term has been introduced by F. Ludwig. 



ai 8 Square Notation 

types of notation by the terms 'notatio cum litera' and 'notatio sine 
litera.' A particularly clear description is found in Anon. IV (CS i, 343;: 

Notandum est quod differentia est dicendo cum litera et sine litera quoniam 
sine litera fiat ligatio punctorum . . . quantum plus poterit. . . . Cum 
litera vero quandoque fit ligatio quandoque non; sed in majore parte plus 
distrahuntur quam ligantur. 

A difference is to be noted between singing with and without text. When 
there is no text, the notes are bound in ligatures as much as possible. But 
when a text is present, the notes will be partly bound in ligature and partly 
not. But they will more frequently be written separately than in ligature. 

A glance at the Facsimiles 46 and 53 will readily show the difference be- 
tween notatio cum litera and notatio sine litera. The remark of Anon. IV 
regarding the use of ligatures in syllabic notation refers to the occasional 
use of groups of two or three notes in place of a single note. 

Further distinctions must be made within the field of melismatic style 
(and notation). One of the most influential innovations of the late 
twelfth century is the introduction of modal rhythm. The long chains 
of notes in the duplum which, in the period of St. Martial, were sung in 
free plainsong-like rhythm (see our transcription of Facsimiles 44, 45) 
are now subjected to an extremely rigid rhythm characterized by the 
regular alternation of long and short notes. Whereas previously the 
vertical alignment of the parts (duplum and tenor) was regulated by a 
sort of sympathetic understanding between the singers, it now is based 
upon strict meter or, in other words, upon those principles which, in 
thirteenth century theory, are referred to as discantus (J. de Garlandia; 
see CS 1, 106): 

Discantus est aliquorum diversorum cantuum consonantia secundum 
modum et secundum equipollentis equipollentiam. 

Discantus is the consonant alignment of different parts according to a 
(rhythmic) mode and to the equivalence of equivalent values. 

This discantus style is most clearly expressed in those works which 
must be ascribed to Perotinus, the 'optimus discantor,' and his contem- 
poraries, that is, in the organa tripla and quadrupla, and in the numerous 
clausulae. However, the transition from the freely flowing rhythm of 
St. Martial to the rigid modal meter of the Perotinus-era was by no 
means sudden and without intermediate steps. In fact, the earliest 
sources of square notation {W x and, to a certain extent, Ft) contain a 
large number of organa and certain shorter pieces (chiefly polyphonic 
settings of the Benedicamus Domino) for which the applicability of modal 



General Characterization 



219 



rhythm must be considered extremely doubtful, to say the least. These 
pieces are, of course, all in two parts, with a quick duplum over sustained 
notes of the tenor. In fact, the addition of a third part (triplum), simi- 
lar in rhythmic design to the duplum, was possible only on the basis of 
strict meter, that is, of modal rhythm or discantus. 

There exist, therefore, two different types of melismatic polyphony: 
an earlier one, presumably connected with Leoninus, which is always in 
two parts and which clearly shows traces of the free style of St. Martial; 
and a later one, introduced by Perotinus, which admits of two, three or 
four parts and in which all the parts are regulated by modal meter. * 
This stylistic distinction leads to a similar dichotomy of notation, for 
which the terms duplum notation and modal notation will be used in the 
present book. 

In the last period of the School of Notre Dame, probably around 1225, 
occurs the rise of one of the most important musical forms, the motet. 
As is well known, the earliest motets are exact imitations of clausulae, 
the only difference being that the upper part, originally a melisma sine 
litera (vocalisation), is provided with a full text. This important inno- 
vation was accompanied by a notational change, that is, transition from 
modal notation to syllabic notation for the upper part or parts. Thus, 
at the end of the. development we see the two styles, which formerly had 
become clearly differentiated from each other, combined in a new form. 
Our discussion of square notation, therefore, falls into four sections: 
syllabic notation (simple conductus); duplum notation (organa dupia 
of the earlier, Leoninus period) ; modal notation (organa and clausulae of 
the Perotinus period); and motet notation (earliest motets). In order 
to clarify ideas, there follow four short examples illustrating these four 
types of polyphonic style: 

J j - 1 j 1 3 

(b) 




(c) 



Cru - ci - fi - gat om-nes 


TJLk I Kl k|J J^J^JjQ J-JH 


8 






8 




y\)H * t — 1 **~ ♦ 1 J.-— ^-77 **^—H 




GO 



EIUS 



22o Square Notation 

These are taken from the following sources: (a) Reproduction p. 264; 
(b) Facs. 49, p. 247; (c) Facs. 46, p. 229; (d) Facs. 55, p. 275. 

B. Modal Notation* 

We first turn to a study of modal notation which holds a central 
position within the entire field of square notation. 

The Rhythmic Modes. Modal notation is based on two values, a long and a 
short, called tonga and brevis. These occur in certain stereotyped rhyth- 
mic patterns which are called modi. The complete system of the rhyth- 
mic modes, as explained in the theoretical writings of the thirteenth cen- 
tury (Discantus positio vulgaris, Joh. de Garlandia, Franco, Odington, 
etc.) comprises six modes, namely: 

First mode: pattern L B Fourth mode: pattern B B L 

Second mode: pattern B L Fifth mode: pattern L L 

Third mode: pattern L B B Sixth mode: pattern B B B 

A voice written in a given mode repeats the pattern of that mode sev- 
eral times. Thus, a melody in the first mode would have the following 
rhythm: L B L B L B 

The first mode was, no doubt, the earliest, as it is also by far the most 
frequent one. Its pattern, L B L B . . . or, in modern notes JJJJL. , 
established that ternary meter which became the basis of the entire sys- 
tem. -The second mode shows the reverse order of values. It should, 
however, not be understood as a first mode with an upbeat; the accent 
falls here, not on the L but on the B: i J J* J ... . The third mode would, 
on the basis of the same values for the L and the B, lead to duple meter: 
J JiJJV'... . However, in order to be combined with the two other 
modes, its rhythm had to be adapted to ternary meter. This was done 
by making the L a ternary value, and by doubling the value of the second 
B, as follows: J JJJ.JJ,... . 2 It is here that we find the root of three 

1 The subsequent explanations on modal notation represent the first attempt to give a detailed 
description of the subject. The earliest studies in this field, such as G. Jacobsthal's Mensuralnoten- 
schrijt des 12. und /j. Jahrhunderts (Leipzig, 1871), and W. Niemann's Ueber die abweichende Bedeu- 
tung der LigatUren in der Mensuraltheorie der Zeit vor Johannes de Garlandia (Leipzig, 1902), are 
concerned exclusively with the theoretical writings of the thirteenth century. The explanations in 
HdN 1, pp. 202-237, deal only with the fundamentals of modal notation, chiefly with the notation 
of the six modes. Much more informative is the concise study contained in the chapter 'Exkurs II: 
Ueber Quadratnotation und modale Rhythmik' of F. Ludwig's Repertorium organorum recentioris 
et motetorum vetustissimi stili (Halle, 1910), from which various fundamental considerations have 
been borrowed for the present study. 

1 Much speculation and controversy has been caused by the fact that several thirteenth century 
theorists refer to an early tradition in which the L was equal, not to three, but to two B, as for 



The Rhythmic Modes ii\ 

important concepts of mensural notation, namely, perfection, alteration, 
and imperfection. In the complete system of the modes, the ternary L 
of the third mode was considered the normal value and termed perfect 
(see p. 96), whereas the binary L of the first two modes was called im- 
perfect. The term alteration (from Latin altera, second) refers to the 
fact that it is the second of the two B which is doubled. It goes without 
saying that the rhythmic formula for the third mode must be read in %- 
meter, not — as has occasionally been surmised — in 4-meter. Obviously, 
the latter interpretation would bring about a rhythm which is not com- 
patible with the g- (or %-) meter of the first and second modes. 

The three remaining modes present no new features. The fourth mode 
merely inverts the pattern of the third. The fifth consists of a succession 
of ternary L; and the sixth comprises only B, in groups of three. Here 
follows a table of the six modes in modern notation : 

••ilJJUJHJJ* 2 -f|i>JJ>JlJ>J a- ilJ.JUIJ.JUU.JU I 
4-SlJ)JJ.|J>JJ.|J>JJ.| 5- 2IJ.-J.I-J. 6 4\J72JJl\ni I 

One might well ask why, in this table, g-meter has been used for all the 
modes instead of only for the third and fourth mode for which it is nat- 
ural. The reason is that, in modal notation, the other modes normally re- 
peat their I- pattern an even number of times, so that the musical phrases 
naturally fall within the scheme of «- measures. The use of this meter 
usually facilitates the task of transcription. There are, however, a number 
of cases in which this meter cannot be applied (see pp. 245, 251 f). 

Another question suggested by the above scheme is that of the modern 
note values chosen for the transcription. That a reduction of the an- 
cient values is necessary, is apparent. Even the most 'conservative' 
editors have never gone as far as transcribing a composition in the first 
mode in L and B: tjBtjo . In older books (Coussemaker, Wooldridge) 

instance Walter Odington in the following remark (CS 1, 235): Tonga autem apud priores organistas 
duo tantum habuit tempora' ('the L equalled only two beats with the early composers of organa'). 
H. Riemann, with his well-known propensity for the even numbers in rhythm and in phrasing, was 
quick to seize upon these remarks and to surmise a pre-modal era in which duple time was prevalent, 
possibly as the result of some folk-like influence. Leaving aside the latter argument, which has too 
frequently been misused as a compliant deus ex machina, it can easily be seen that Riemann's theory 
is based upon a wrong conclusion, namely that a binary L necessarily entails binary meter. Such 
a conclusion is correct only with the third and fourth modes, but not with the first and second, in 
which the alternation of a binary L with a B results in triple time. Odington's remark, therefore, 
gives only additional evidence of the chronological order, outlined above, of the appearance of the 
modes. 



222 Square Notation 

a reduction I '.4 (whole and half-notes) is chosen for the rendering whereas 
more recent writers prefer a reduction 1:8 or even 1:16. The last is 
used here because it corresponds with our general principles of tempo- 
transcription, according to which that note which represents the beat of 
the music — in the present case the L — , is rendered by the modern 
quarter-note. 

Brief mention must be made of a nomenclature derived from the iden- 
tification of the six modes with certain metric feet of Greek poetry, 
namely (in the above order of the modes): trochaic -\j, iambic »-» -, 
dactylic -ww, anapaestic w^-, molossic , and tribrachic: \juxj. Al- 
though this terminology is widely used in modern writings, it has little 
historical significance and justification. The only mediaeval theorist to 
mention these terms is Walter Odington who also goes in for such schol- 
arly terms as proceleumaticus and pyrrichius (CS 1, 240O. It is perfectly 
clear that his references to Greek poetry are the result of personal anti- 
quarian studies, and that, in contrast to a wide-spread opinion to be 
found in Wolf's HdN (vol. 1, p. 202) as well as in many books on music 
history, they do not offer the slightest evidence of the rhythmic modes 
having developed from the poetic meters of the ancient Greek. 

The application of the modes to melodies of various length leads to a 
further concept of modal theory, i.e., ordo (pi. brdines). The ordo refers 
to the length of a musical phrase, indicating the number ot times the 
modal pattern is repeated before a rest: 

Primus ordo Secundus ordo Tertius ordo 

1. IJJ>J rl IJ J>JJ>IJ f IJj>JJ>IJJ>Jr| 

2. |JU J>r?| lJUJU|J>n 1J1J JUIJU.M 

3- IJ. J>J IJ-HU. AH J. AJIJ-H IJ. JUIJ. JUIJ. JUI J. M 

4- IJU J. IJUHIJU J- IJUJ. IJU*I IJU J. |JiJ J. IJUJ.IJUU 

5- |J. J. IJ.MIJ. J. IJ. J. u.jj |J. J. |j. J. |j. j.U.t-i 

6- |JJ3J>nl IJUJ^iJrr IJEJ33I JJJJVrl 

* Every ordo is followed by a rest, the duration of which is determined 
by the mode; it equals one B (eighth rest) in the first mode, two B in the 



The Rhythmic Modes 223 

second, etc. As may be inferred from our previous remarks regarding 
the use of ^-measures for all the modes, the second (fourth, sixth) ordo 
of the first, second and sixth mode are relatively rare. 

Certain thirteenth century theorists considerably broaden the above 
system of modes and ordines by the introduction of the so-called modi 
imperfecli in addition to the above modi per jecli. The various ordines of 
the imperfect modes are derived from those of the perfect modes by the 
omission of the final note, e.g., terlius ordo primi modi imperfecli: 
I J J*J «N J J*$.| ■ These imperfect modes, which are treated in great 
detail by Anon. IV (CS 1, 329 ff) and others, have no practical significance 
and may be completely disregarded by the student. # 

In turning to a study of the manner in which these modes were used in 
actual music and expressed in writing it must first be said that the theo- 
retical system does not in every respect conform with the actual data. 
If considered from the standpoint of the musical sources of this period, 
it proves to be too complicated in certain respects and too much simpli- 
fied in others. The latter point will become apparent in our discussions 
of exlensio modi and /radio modi, while the former point is illustrated by 
the fact that only four of the six modes, namely, the first, second, third 
and fifth are commonly used, the fourth and the sixth being extremely 
scarce. 1 Of the four modes commonly employed, the first mode is not 
only by far the most frequent, but also almost the only one to appear 
with all those rhythmic modifications and variants which constitute the 
real problem of modal notation. 2 

The Ligatures. In the previous explanations of the modi we have pur- 
posely indicated the metrical values by modern notes and have avoided 
using early forms for the L and B, such as ^" . The reason is that 
modal notation, although essentially based upon these two values, does 
not employ notational signs for them, but for combinations thereof, such 
as occur in the modal patterns; and these are the ligatures in their earliest 
stage oi development. This fact may seem surprising at first; but it will 
easily be understood when it is realized that modal notation is a melis 
matic notation which developed from the melismatic passages of the 
organa of St. Martial. 

The ligatures used in modal notation form the starting point of a de- 
velopment the final phase of which is well known to us. The various 
stages of this development can conveniently be described by the use of 

1 With regard to the fourth mode, Dietricus remarks: 'but it is not in use' ('sed non est in usu'). 

2 Two examples written in a free modification of the second mode are discussed at the conclusion 
of the study of modal notation. 



224 Square Notation 

the terms proprietas and perfeclio. In modal notation all the ligatures 
are cum proprielate and cum perjeclione; in pre-Franconian notation liga- 
tures sine proprielate and cum opposita proprietate are added, occasion- 
ally ligatures sine perfectione; and finally, in Franconian notation all the 
forms are used with equal frequency, and their rhythmical value is de- 
termined clearly and unambiguously by definite rules which persisted 
until the end of the sixteenth century. 

The following table shows the more common ligatures of modal nota- 
tion, all the binariae and ternariae ^ as well as some quaternariae. It also 
includes some of the varieties known as conjuncturae (marked c) which 
are frequently preferred for notes of the descending scale, particularly 
for combinations of four to six and more notes: 

Binariae Ternariae Quaternariae Quinariae 

In addition to the ligatures single notes are used, but very sparingly 
and only for special purposes. As in conductus notation, they occur 
usually with a short stem which in some cases is missing. Occasionally, 
a single note with a head of about double length is found. This is the 
so-called duplex tonga (D) which later becomes the maxima. 

In order to provide a simple and short designation of these signs Fried- 
rich Ludwig in 'Exkurs II' of his Repertorium organorum recentioris et 
moletorum vetustissimi stili has introduced a system of abbreviations as 
follows: 2 li for a ligatura binaria (two note ligature); 3 li for a ligatura 
ternaria (three note ligature) etc.; 1 si for a single note; 2 si for a group 
of two single notes, etc. For the present purpose we propose a somewhat 
simplified system, i.e.: / for each single note; 2 for a ligatura binaria; 3 
for a ligatura ternaria, etc. Thus, 1333 means a single note followed by 
three ligaturae ternariae. 

For the writing down of the modes these ligatures are used in certain 
standard combinations each of which is characteristic of one of the 
modes (see p. 225). 

From this illustration it appears that the value of the notes of a given 
ligature is by no means invariable, but depends entirely upon the mode. 
The lernaria, e.g., has the value J U in the first mode; J" J J in the 
second mode; J*J J. in the third mode; and J.J.J. in the fifth mode. The 
binaria is always B L (either J'J orJJ)in the examples given there. 
However, it will be seen that it is likewise capable of various other mean- 
ings, under special circumstances. 



Repeated Notes 



225 



Example 



Transcription 





Combination 

1. J 2 2 2 2 

2. 2222 J 

3- '333 

4- 333* 

5- 333 
6. 433 



The small vertical stroke which appears at the end of each ordo is the 
so-called divisio modi, which indicates a rest. 

Repeated Notes. For obvious reasons of writing, two successive tones of 
the same pitch (unison) can never occur in ligature. Therefore, when- 
ever the melody would call for repeated notes within a ligature, this lig- 
ature must be broken up into single tones or smaller ligatures (see p. 
91 0. 

The following examples show some of the deviations caused in the first 
mode by repeated notes: 





«*3 y y 



S !<■) fli pi 

2\ r- 



J -^p- 



There are, of course, no set rules for the writing of these anom- 
alous combinations. In the sources the same melodic and rhythmic 
phrase may be found expressed in several different ways, as, for in- 
stance: 



It may be noticed that as a result of these anomalies the ligatura 
binaria appears in a new metrical meaning, namely as L B. 



226 Square Notation 

The Plica. The plica ('fold') is an important auxiliary symbol of square 
notation. It is indicated by downward or upward dashes attached to a 
note. These dashes occur in connection with single notes as well as with 
the final note of ligatures. The original form of the nota plicata is ex- 
plained as the square-shaped modification of the liquescent neumes, 
epiphonus and cephalicus, from which the plicas developed: 

V {epiphonus) = U {plica ascendens) 

p {cephalicus) = fl {plica descendens) 

While these single plicas are frequently used in syllabic notation (see 
p. 260), in modal notation the plica occurs chiefly as ligatura plicata. 
Here it is indicated by an upward or downward dash added to the right 
side oit\\tfinalis. If the Jinalis is in ascending position and, consequently, 
written above the preceding note, the plica-dash is difficult, if not im- 
possible to attach. This problem was solved in two different ways. Either 
a single nota plicata was written immediately after the ligature; or the 
head of the finalis was turned to the right side, so that the dash could be 
added. Following are all the forms of the binaria plicata, and some 
examples of ternaria and quaternaria plicata: 

(a) ^ pj rf| J sn *) «] 

00 3" J u fS" jC" 

The plica sign indicates an ornamenting tone, somewhat in the char- 
acter of a grace note, to be inserted between the note to which it is 
attached and the next written note. According to the direction of the 
dash this ornamenting tone is above or below the written note. 

The explanations of the plica by the theorists are not entirely satisfac- 
tory. The following passage from the treatise of Magister Lambert 
(Pseudo-Aristotle, CS 1, 273 a) is typical: 

Unde notandum est quod plica nihil aliud est quam signum dividens sonum 
in sono diverso per diversas vocum distantias, tarn ascendendo quam de- 
scendendo. videlicet per semitonium et tonum, per semiditonum et ditonum, 
et per diatessaron et diapente. . . . Fit autem plica in voce per compo- 
sitionem epiglotti cum repercussione gutturis subtiliter inclusa. 

. . . the plica is nothing but a sign indicating that a tone is divided into a 
different tone, in various intervals both ascending and descending, such as 
half tone and whole tone, minor and major third, fourth and fifth. . . . 



The Plica iz-j 

The plica is performed in singing by the partial closing of the epiglottis com- 
bined with a subtle repercussion of the throat. 

As regards the performance of the plica, a problem somewhat irrelevant 
to the purpose of this book, one must be content with the information 
given in the above and in similar statements. Evidently the plica, 
which is derived from the liquescent neumes (cephalicus), belongs to the 
same species of ornaments as, e.g., the French 'aspiration' or the Ger- 
man 'Nachschlag.' More relevant to our study is the problem of deter- 
mining the pitch and value of the extra tone indicated by the plica. For 
the sake of clarity we shall carefully distinguish between plica-note and 
plica-tone. The former term refers to the written note to which the 
plica-dash is attached; the latter to the extra tone called for by the dash. 

The pitch of the plica-tone depends upon the pitches of the plica-note 
and the next-following note. If these two notes are the same, then the 
plica-tone is the upper or lower second, depending on the direction of the 
stem. If the interval between the two notes is a third, the second in be- 
tween is meant to be filled in. If it is a second, one may have to choose 
the upper or lower third. In many cases, however, the second will prove 
more satisfactory, causing anticipation of the subsequent note. In re- 
gard to the larger intervals, the instructions of the theorists are even less 
clear than in the previous cases. Apparently, the interpretation was 
governed chiefly by the musical context which, indeed, rarely leaves 
room for doubt. 

Concerning the second question, that of the metrical interpretation, 
the general principle is that plica-note and plica-tone together consume 
the same time as that to be assigned to the note if it were written without 
plica. Since, in actual application, this note always turns out to be a L 
(last note of a ligature), there are only two possibilities: either this L is 
imperfect, in which case the plica-tone gets the half of the full value; or 
it is perfect, in which case the plica-tone is allotted one-third of the full 
value. On this point Magister Lambert speaks with perfect clarity 
(CS i y 2 73 ): 

[Plica perfecta] habet autem omnem potestatem, regulam et naturam 
quam habet perfecta longa, nisi quod in corpore duo tempora tenet et unum 
in membris . . . [Plica imperfecta] . . . continet unum tempus in corpore 
et reliquum in membris. 

The perfect plica has the same function, value, and nature as the perfect 
longa, except that it contains two tempora in the note {corpus), and one in 
the tone (membrum). The imperfect plica contains one tempus in the note 
and the rest in the tone. 1 
1 Tempus denotes in the thirteenth century the duration of the B. See p. 283. 



228 



Square Notation 



It appears that the plica-tonz was not a sort of a short grace-note, 
but had a definite metrical value, comparable to that of the normal notes. 
It was only the special manner of singing (see p. 235) that distinguished 
it from them. Therefore, transcriptions in which the p/ica-tone is ren- 
dered by the modern symbol t (see HdN 1, 225) are misleading, as are 
others in which they are transcribed as ordinary notes without any dis- 
tinction. We suggest the use of small notes, as illustrated in the follow- 
ing examples: 




That the plica-tont has the full value of a £ is confirmed by the fact 
that, according to various theorists, />//V<z-ligatures could be used to ex- 
press the sixth mode. Joh. de Garlandia gives the following example 
(CJ 1,101): 




This manner of notating the sixth mode has been misinterpreted by 
both Niemann and Wolf. 1 In HdN 1, 232, Wolf cites the following as 
illustrations of the sixth mode: 



The two examples in modal notation, however, do not mean the same 
thing, as Wolf assumes. The transcription which accompanies them is 
correct only for the first example, whereas the second would result in the 
following much longer melody (using Wolf's scale of reduction) : 



At the beginning of a composition or a section thereof one frequently 
finds a single note followed by a.p/ica-note of the same pitch: «n . This 

1 See A. Michalitschke, Thtorit des Modus, Regeruburg, 1923, p. 6a. 



Examples of Modal Notation 
Facsimile 46 



229 



.jju^^ j " : '\^ = ^^M 



''^^^^A,, ' 



3=4 









Mf 






*f 







lofCUu5 c 



f§§^lp§2ffii|i|j|j|/ 



= ^^^ 



^S^M ^f^ ^ / 



MS Florence, Biblioteca Medicea-Laurenziana^>/#/. 29.1 

(13 th centurv) 

From pages 11, 11' 



230 



Square Notation 



combination usually indicates a plica duplex longa. There is an obvious 
similarity of appearance between this sign and forms given in the second 
row (b) of the illustration of ligaturae plicatae (p. 226). However, in 
these forms the use of a separate plica note is a mere expedient of pen- 
manship and does not, as a rule, indicate duplex longas. 1 

Examples. The principles of modal notation just explained may be il- 
lustrated by a few relatively simple examples. 

( 1 ) Facsimile 46 (p. 229) contains a three- voice clausula Go, the tenor of 
which is taken from the verse (V) Vir-go Dei of the gradual Benedicta es 
et venerabilis (see Gr. Rom., p. [99]). 2 The liturgical melody appears 
twice, beginning for the second time with the eleventh ligature (the ini- 
tial ligature is the ternaria written slightly to the left of the letter G). 
The two upper parts are in the first mode, and show various examples of 
unison-writing and of plica ligatures. The tenor is evidently in the fifth 
mode. Every two ordines of the tenor correspond in length to one ordo 
of the upper parts: 




1 1 am greatly indebted to Mr M. F. Bukofzer for pointing out the correct meaning of these forms 
of ligaturae plicatae. The (b)-forms (as we may call them with reference to the illustration) are 
probably the earlier ones, since they are the only ones used in W x . In F and JV 2 both forms occur, 
the (b)-form being preferred when the Jirtalis is a L, the (a)-form when it is a B. See, e.g., Facs. 47 
(P> 2 33)y second column, second staff, next-to-the-last ordo; and Facs. 46 (p. 229), seventh staff, 
end of fourth ordo, and eighth staff, middle of sixth ordo. 

2 We seize this opportunity to emphasize the importance of tracing the liturgical tenors of the 
organa, clausulae and motets back to their original sources, that is, to the melodies of the Gregorian 
chant. This task is greatly facilitated by F. Ludwig's standard publication, Repertorium organorum 
recentioris and motetorum vetustissimi stili (Halle, 1910), which is an invaluable aid in all research 
connected with the School of Notre Dame. The strictly scientific character of this book, which is 
written in the form of a detailed catalogue of all the sources of this period, makes it difficult to read; 
however, a study of its somewhat cryptic language and its complicated system of abbreviations 
amply repays the effort. As a guide to such a study, it may be remarked that the above clausula 
Go is listed on p. 61, and that the sign M 32 given there refers the reader to the complete index of 
the Magnus liber organi de Gradali et de Antiphonario contained on pp. 65-75. The organa de 
Antiphonario are marked Oi - O 32 (O = Office), those de Gradali M 1 — M 59 (M = Mass). 
Under M 32 (p. 72) the reader finds listed the gradual (Gr) Benedicta with its verse (V) Fir-go dei 



Examples of Modal Notation 



231 



The fourth, seventh, and ninth ordo of the upper parts contain ir- 
regular combinations of ligatures which indicate extensio or fractio modi 
(see p. 234ft*; particularly p. 237). 

(2) The conductus Hac in annijanna (Facs. 53, p. 259) closes with a 
three-voice vocalization on (acti)-'o' (beginning after the first divisio 
modi of the last brace), which is written in a mixture of the third mode, 
1 3 3 3> an d the second mode, 222. Here follows the transcription: 




(3) Facsimile 47 (p. 233) contains an organum triplum Descendit de 
celis from JV 2 . In order to facilitate orientation, the various sections of 
the composition have been marked by letters. Several of these sections 
show the normal combinations of ligatures explained previously. Thus, 
the sections (a), (0, and (h) are in the first mode (j 2 2 . . . ), (b) and 
(e) in the third (/ 3 3 . . . ), (d) in the second (222...). 

The vertical strokes usually are signs of divisio modi, indicating rests 
the length of which depends on the mode, according to the previous ex- 
planations (see p. 225). Some of them, however, have a different meaning, 
that is, to call the singer's attention to a change of syllables in the text. To 
this category belong the sixth stroke of brace 1 (change from 'Des' to 
'cen') and the second stroke of brace 2 (change from 'cen' to 'dit'). F. 
Ludwig, who was the first to call attention to these syllable dashes (Silben- 
striche; see Repertorium, p. 49), rightly pointed out that they give proof of 
the vocal (vocalizing) nature of the organa in all their parts. It will be 
noticed that in most of these cases the interpretation of the dash as a rest 
is prohibited by the appearance of plica notes which naturally call for im- 
mediate joining with the following note. The practical result of these con- 
siderations is that the quaternaria at the end of section (a) is not preceded 
by a rest, but follows immediately after the binaria plicata, filling 

which is the source for the tenor of the above clausula. The full texts and the liturgical melodies of 
the graduals, alleluias, etc. are found, of course, in the ritual books of the Catholic Church, either in 
the Antiphonarium Romamim (complete service for the office) and the Graduate Romanum (com- 
plete service for the mass), or, more conveniently, in the Liber Usualis which contains the most 
important chants from both books. 



232 



Square Notation 



a measure in the rhythm B B B L (fractio modi). A similar case occurs on 
the right-hand column, first brace, where the next-to-the-last stroke is 
not a divisio modi, but a syllable dash indicating change to 'ce.' These 
signs may be reproduced in the transcription as breathing marks. 

The section (d) shows the familiar groups of the second mode, particu- 
larly in the middle part (duplum) which has the final ternaria required in 
this mode. Since the triplum closes with a binaria, the first note of this 
ligature would have to be extended from a B into a L {extensio modi). 
Section (i) finally, notated in ternariae, would seem to indicate the fourth 
mode. The fact, however, that the triplum begins with / 2 suggests an- 
other interpretation, that is, to start in the first mode and to continue 
thereafter in the sixth mode. The musical design of this section, with its 
extensive use of short sequential patterns, would seem to lend itself more 
naturally to the continuous motion of the sixth mode than to the halting 
rhythm of the fourth which, moreover, is very rarely used (see p. 223). 

For the major part the transcription of the organum presents no diffi- 
culties, once the correct start is made. In order to facilitate transcription 
some of the crucial measures are shown below. 




Examples of Modal Notation 
Facsimile 47 



m 



11 imri 


: 










% •?* "V * : 




■a ' "- ; 3 ,ir ,;: 






: ' r 


2 iL =1 =r r 1; 








« Sr i SI ltt 


•nrvfeui n i 1 






i?r rtii i °i"8ii mifti r 


■ L 1 n r , - 1 « 1 - l 


; a: -r r ;Sr "j V s w * 

;l - ri *i ;^ .. % ii ?- f 



234 Square Notation 

In Fl y which is another source for Descendit de cells (see the facsimile 
in OH, p. 208), the second tenor note, c, for the syllable 'cen' appears 
right after the first note, d, at the beginning of section (b), not at its end, 
as in fV%. We have adopted the version from Fl because it eliminates 
some strongly dissonant combinations such as d-f-c' and d-e-a which occur 
in Wi. This may be the place to remark that the exact placement of the 
tenor notes in the organal sections is often uncertain. For instance, the 
note to the syllable 'cen' could just as well be placed on the second beat 
of the measure, coincident with the final notes of the upper parts. 

The preceding explanations cover all the sections of Descendit except (c), 
(g), and (k). It will be seen at a glance that these differ from the others by 
their shortness and by the irregular groups of the ligatures and conjuncturae 
found in them. Furthermore, they all occur immediately before a change 
of syllable, that is, at the end of the main divisions of the organum. These 
are the so-called copulae, which are described by various theorists of the 
thirteenth century as a separate species of polyphonic music, side by side 
with discantus and organum (Joh. de. Garlandia, CS i, 175a). Garlandia 
(CS i, 114a) also tells us that 'discantus cannot be considered as perfect 
without having connecting copulas (nisi mediante copula), and that 
'copula forms the connection {est inter) between discant and organum.' 
In spite of their shortness these passages offer many problems (see p. 241). 

If the normal pattern of the rhythmic modes were always strictly ob- 
served in the compositions of our period, their interpretation and tran- 
scription would present little difficulty. Actually, examples of this pure 
type are relatively rare and uncharacteristic. Usually the elementary 
pattern of the mode is modified by either omission or addition of tones, 
modifications which are expressed in notation by irregular combinations 
of ligatures. It is these anomalies which present the chief problems of 
modal notation. 

Extensio modi. This term is used here to denote the occasional omission 
of a B (eighth-note of the transcription). Such a modification of the 
modal pattern is very frequently used at the end of an ordo. Below are 
a few typical examples: 



(a) and (b) are first mode; (c) and (d) are second mode. 



ExtensiOy Fr actio Modi 



*35 



Most of the ordines of Facsimile 46 show this type of extensio. The 
following examples illustrate the omission of a B in the middle of an ordo: 
(1) Fl, p. 7', Mors (beginning of the upper part): 



(2) W\, p. 50, clausula Ta (from the Alleluia, Ascendens Christus [in 
altum captivam duxit captivi-ta-tem . . .]): 




Fractio modi. 1 This term signifies the opposite procedure of extensio 
modi, that is, the breaking up of the normal pattern of the modal rhythm 
into smaller values, preferably of the L into two B. It may be illus- 
trated by the following example {IV 1, p. 22, third brace): 




An already familiar means of introducing />vz<:/z'<9 modi is the plica. In 
fact, many examples exist showing that the plica and the above nora- 
tional method were used interchangeably for the introduction of passing- 
notes. For instance, a comparison of our Facsimile 47 with the repro- 
duction of the same piece from Ft given in OH 1, 209, reveals the follow- 
ing variants of notation (fourth ordo from the beginning): 



See Anon, iv, CS i, 336-339. 



236 



Square Notation 



The following passage from JVi p. 162 (middle of the fifth brace) shows 
the simultaneous use of both methods: 




Occasionally, the breaking up of the normal pattern may be carried to 
even smaller values, equivalent to sixteenth notes in the transcription, 
for instance {JV X p. 21, Notum fecit) \ 




A comparison of the above examples of /radio modi with those of 
extensio modi shows that there is no clear notational distinction between 
these two opposite modifications. It is chiefly this lack in clarity which 
makes modal notation difficult. As a matter of fact, the same combina- 
tion of ligatures may denote two, and sometimes even more, different 
rhythms, resulting in different lengths of the phrase, for instance: 



3 23 



wirpf pir* r p ir- 1-\ 
(b)irTfiwr 'i 



wirpfpir r pirrpirfrpm-i 
32 2 =-((b)irTf fipor ir"pf pTr fr y \ 
wiiTr fipcTpcxTf p? vTr >• 1 

No definite rules can be given concerning the application of one or the 
other interpretation in a given case. The main consideration in this 
matter is the coordination of the parts according to the thirteenth-century 
principles of consonance and dissonance (see p. 244). Naturally, the tenor 
should always be transcribed first. In compositions with two (or three) 



Extensio, Fractio Modi 



237 



upper parts a clue to the correct coordination is often found in what may- 
be called the "rule of corresponding ligatures." In fact, a ligature in the 
duplum usually corresponds in position to one in the triplum, except 
for such deviations as are caused by repeated tones, extensio modi, etc. 
Although it cannot be applied strictly, this rule often proves helpful. 
The student is now prepared to complete the transcription of the 
clausula Go (Facs. 46, p. 229). The fourth ordo has fractio 
modi in the triplum, while extensio modi would seem to be 
indicated for the close of the duplum [see Figure, (a)]. However, the 
version given under (b) is probably preferable, if only from the point 
of view of corresponding ligatures. 




At the end of the seventh ordo we find three single notes each of which 
equals an L (dotted quarter-note). It is interesting to notice in this ordo 
(duplum) a clear tendency to distinguish between a brevis-\\ke and a 
/onga-Wke shape for the single note. The former occurs at the beginning 
of the ordo for unison-writing, the latter for extensio modi: 

--'--J /J. -m-JJJ. 

The end of the clausula presents some difficulties, owing, to the great 
number of notes in the upper parts. The following transcription (begin- 
ning in the tenor with the eighth ordo of staff 6) would seem to be correct, 
in spite of the dissonance in meas. 5. The upper parts close with a copula 
(coda) showing the ligatures of the second mode. Although the mode 
never changes within the main part of a clausula, examples suggesting a 
change of mode in the coda are quite frequent (see the close of 'domino* in 
Facs. 49, p. 247, and of Sanctus and Sancte spiritus in Facs. 51, p. 255). 




238 Square Notation 

Our facsimile also includes a three- voice clausula Flos filius est, which 
will be considered later (p. 251). 

Facsimile 48 contains a number of textless pieces, evidently instru- 
mental dances in two parts, from the slightly later MS, Brit. Mus. Hart. 
978. The two parts are marked 'cantus superior' and 'cantus inferior.' 
The first three lines of the page are occupied by the lower part of a piece, 
the higher part of which is given on the preceding page (see the complete 
reproduction and transcription in HdN 1, 224). The cantus inferior, 
which is evidently in the first mode, shows a few simple cases offractio 
modi) for instance in the last ordo of the first staff: 



There follows on the page a piece with a remarkably regular rhythm 
and structure. Each part consists of eight ordines, each of which com- 
prises eight perfections (seventh ordo) and, therefore, yields four f-meas- 
ures in the transcription. The piece (as well as the others of the fac- 
simile) belongs to the class of ductia, a mediaeval type of dance music 
consisting usually of four short sections each of which is repeated: aa bb 
cc dd. The present example shows an even simpler structure, since the 
third and fourth phrases reiterate the first and second, but transposed a 
fifth above and transferred from the cantus inferior to the cantus su- 
perior. The basic scheme of our ductia is therefore: 

Cantus superior: (counterpoint) a a b b 
Cantus inferior: a a b b (counterpoint) 

In every ordo some deviation or other from the normal scheme of 
ligatures, 322222, occurs. Some of these deviations, e.g., the writing 
/ 2 (instead of 3) at the beginning of the first and second ordo of the cantus 
inferior, are obviously caused by repeated notes and, therefore, do not en- 
tail a modification of the basic rhythm of the first mode. Others, e.g., the 
sequence J* 2 3 2 2 (superior, first ordo) indicate extensio modi: | L B L' B 
\V LB \ L . B L B\V — j, while the sequence 3 22232 (superior, third 
ordo) indicates fractio modi: I L B V B \ V B V B \ B'B BU B\V—\. 
More problematic is the rhythm of the sequence 3 2331 (inferior, third 
ordo). Here it is only by comparison with the rhythm of the upper part 
that the solution is found, namely: \LBVB\VLB\B y BBL\ 
L' — /. The first three ordines of the upper part are given in transcrip- 



Extensio, Fractio Modi 
Facsimile 48 



239 






6. 



^V^Ai 




^ r V^^:^^V^h,l 



Twptir 



S j^^^fe iS 






gjj > 



frpmyg 



Wj*ft)*/>U 



uSSr 



MS London, British Museum Harlelan 978 (13th century) 



iaP Square Notation 

tion in the appendix, No. 32. For a discussion of the second piece, see 
p. 2 4 2. 

Conjunclurae. Particularly vague and equivocal symbols are those 
many-note ligatures which appear in the form of conjuncturae or cur- 
rentes, that is, of a single note or a binaria {ternaria) followed by a series 
of three to seven or more isolated notes of the descending scale, written 

in a form like that of the later semibrevis: T% ]V 3*% (""S**^ . 

Already the name currentes (from currere, to run) indicates that quick 
notes are involved here. However, the question as to their exact rhyth- 
mical meaning has caused considerable confusion as early as the late 
thirteenth century, because the diamond-shaped notes were mistaken 
for real semibreves which, in that period, had already become established 
as independent values. Originally, these shapes have nothing to do with 
semibreves i but are transformations of the dots characteristic of the 
neume climacus: ?•-. . 

We have already pointed out that the simplest conjunctura^ that is, 
the conjunctura ternaria, is identical in meaning with the ordinary liga- 
tura tervaria. Very informative in this respect is the section (i) of 
Facsimile 47. As additional evidence, the following passage from the 
Ms Madrid Hh 167 {Ma) may be quoted: 



As far as the conjuncturae with four, five, etc. notes are concerned, 
their value is much more variable. The following rule, which is sup- 
ported by evidence from theoretical as< well as musical sources, may 
serve as a point of departure: 

In every ligature the last note is an Z,, the next-to-last note is a B y and 
all the preceding notes are equal to one L (see Anon. IV, CS 1, 34 1, 
Omnis figura I i gala . . .). 

Examples illustrating this rule are given below under (a). However, 
the context often requires certain adjustments, such as are indicated 
under (b), (c), and (d): 



(a) 
(b) 
(c) 
(d) 



Ternaria 
3 

IJ JiJ.I 

bJUl 

J>IJJ I 



Conjuncturae 
Quaternaria Quinaria 



241 



Senaria 



IJT3J.I 
It J3JJ.I 

J>IJ J>J.I 



IJ3J1J 

lr JE3J 
J>IJOT 

J>IJ71J. 



IJ3333J.I 



J>IJ37JJ.I 

For the interpretation of symbols composed of both ligatures and cur- 
rentes the following examples may serve as a guide: 



(^ J>i m 

(b) J> I J31 



3*» 

)imj.i 

J>IJ3T] 1 



u j>jtju. 1 

U J>J3T3l 



Modern scholars have frequently been misled by the semit>revis-\ike 
characters of the conjuncturae. The following passage from Ma> to- 
gether with its transcription by Aubry (Iter Hispanicum, Paris, 1908, p. 
11) and the (approximately) correct transcription, may serve as an 
example: 




The cadential sections (e), (g) and (k) of the organum Descendit (Fac- 
simile 47) illustrate the highly equivocal character of the conjuncturae of 
many notes. Several variants of transcription are deliberately given 
in the appendix (No. 23), some of them based on the notational variants 
found in other sources. They are meant to warn the reader not to ex- 
pect a 'correct solution' of problems of this type. He will derive the 



242 



Square Notation 



greatest benefit by trying to tackle these passages, and by comparing his 
results with our transcriptions, as well as with those given in OH 1, 209 ff, 
where the whole organum is transcribed. A comparison of our facsimile 
with the reproduction of the same piece from F/, given in the same book, 
as well as with that from fV u to be found on p. 76' of J. H. Baxter's pub- 
lication {An Old St. Andrews Music Book) will reveal to him the impor- 
tance of consulting different sources whenever these are available. A 
fourth source for this organum is the MS Brit. Mus. Egerton 2615 {LoA) y 
p. 82/ Following is a reproduction of the final passage (k) from this 
manuscript: 




A rhythmic variant suggested by this manner of writing is given in the 
appendix, No. 33. 

A special type of conjunct ura which occurs in some later documents of 
modal notation is the following, characterized by a diagonal stem at- 
tached to the left side of the initial note: /*♦♦ . This symbol indicates 
shorter notes than the normal conjunclura ternaria; in fact, it has the 
same meaning as the later ligature cum opposita proprietate: S S B. It 
occurs repeatedly in the last dance piece of Facsimile 48, the beginning 
of which is transcribed here: 




The transcription of this piece presents few difficulties, owing to the 
fact that it falls into regular phrases of eight perfections each, or, of four 
8 -measures of modern notation. The binaria plicata at the end of staff 6 
means B + L plicata, while the similar form occurring simultaneously in 
the cantus inferior (third-to-the-last sign of staff 7) means B + D plicata. 



Conjuncturae 2 43 

Another notational peculiarity of interest is the use of single notes in 
the diamond-shaped form of the semibrevis (see the closing ordines on the 
last two staves). Actually, these notes are not S y but represent a pecu- 
liar manner of writing the B which is found in various sources of English 
origin. The first to point out this peculiarity was H. E. Wooldridge, in 
his detailed discussion of Sumer is icumen in to which the reader is re- 
ferred. 1 The same shape occurs in the last fascicle of W x (see p. 191' 
and others of the facsimile edition), the English origin of which has been 
pointed out by J. Handschin. 2 Following is a transcription of the close 

of our dance piece (upper part) : 




Our lengthy explanation of modal notation may seem very unsatisfac- 
tory to the reader, who naturally expects to obtain concise information 
and a reliable clue to the problems of this notational system. It cer- 
tainly will appear even more annoying when, upon trying to make tran- 
scriptions of his own, he finds himself confronted with many questions 
for which our explanations contain no answer. Unfortunately, this situ- 
ation cannot be remedied since vagueness and ambiguity is an inherent 
characteristic of modal notation. As early as the late thirteenth century 
musicians were fully aware of this fact. About 1275 Anon. IV very ade- 
quately summarizes the situation in following sentences (CS 1, 344): 



. . . in antiquis libris habebant puncta equivoca nimis, quia simpliciama- 
terialia fuerunt equalia, sed solo intellectu operabantur dicendo: intelligo 
istam longam, intelligo illam brevem, et nimio tempore longo laborabant, 
antequam scirent bene aliquid quod nunc ex levi ab omnibus laborantibus 
circa talia percipitur mediantibus predictorum, ita quod quilibet proficerit 
in una hora quam in septem ante quoad longum ire. 

Maxima pars cognitionis antiquorum fuit in predictis sine materiali 
significatione . . . prout habebant respectum superioris ad cantum in- 
feriorem, et docebant alios dicendo: audiatis vos et retineatis hoc canendo. 
Sed materialem significationem parvam habebant, et dicebant: punctus 
ille superior concordat cum puncto inferiori, et sufficiebat eis. 

In the old books the signs were all too equivocal because the fundamental 
signs [B and L?] were alike. The singers proceeded only by their intellect, 
saying: I see that this one is a long, that one a breve. Thus they labored a 
long time before they learned something which today anybody can easily 
learn by means of the above explanations if he wants to do so, so that 

1 OH i, 3i6ff. See also M. F. Bukofzer, Sumer is icumen in (1944), p. 83fT. 

1 ZJMW 193a. See also pi. 10 (p. 55) in A. Hughes, Worcester Mediaeval Harmony (Worcester, 
t 9 28). 



244 Square Notation 

today every student will achieve more in one hour than formerly in seven. 
The knowledge of the ancients was chiefly oral tradition without written 
fixation. They paid attention to the relationship between the upper and 
the lower part and taught by saying: listen carefully and remember it by 
singing. But they had little notational fixation and merely said: this note 
of the upper part coincides with this note of the lower part; and that sat- 
isfied their needs. 

Weighing these pertinent remarks, the student will realize that only by 
long experience and patient practice may he expect to acquire some facil- 
ity in this field of study. As a further aid to this goal, there follow a few 
remarks of a more empirical nature, as well as a number of additional 
examples. 

Consonance and Dissonance. As is intimated by the words of Anon. IV, 
a knowledge of the early thirteenth century principles of consonance and 
dissonance is of foremost importance. These principles call for conson- 
ances on the strong beat although, between these, dissonant combinations 
are admissible. The consonances of this period are, according to the 
theory of the time, the unison, octave, fifth, and fourth. In musical 
practice, the third as well as the augmented fourth (diminished fifth, tri- 
tone, e.g., f-b) also are admitted as consonant intervals, although they 
appear much less frequently than the others. The sixth is regarded as a 
dissonance in theory as well as in practice. It must be borne in mind, 
however, that a strong dissonance, such as a second, is admissible even 
on the main beat if it is immediately resolved into a consonance, e.g.: 




Various examples of this practice occur in our Facsimile 47 (Go, tran- 
scription, meas. 18, 19 etc.). An interesting and adequate explanation 
of these appogiaturas of the thirteenth century is given in the following 
remark by Johannes de Garlandia (CS 1, 107a): 

Sed duo puncti sumentur hie pro uno, et aliquando unus eorum ponitur in 
discordantiam, propter colorem musice. Et hie primus sive secundus; et 
hoc bene permittitur ab auctoribus primis et licenciatur. Hoc autem in- 
venitur in organo in pluribus locis et precipue in motetis. 

However, two notes may be put in the place of one, and sometimes one of 
them is treated as a dissonance, in order to add color to the music. This 
tone may be either the first or the second. This method is fully approved 



Notation of the Tenors 245 

and permitted by the best authorities and it is to be found repeatedly in 
organa, and especially in motets. 

The observation of consonances is practically the only reliable clue in 
transcribing pieces in modal notation whenever, as is frequently the case, 
writing of the ligature fails to indicate clearly the rhythm. The student 
is strongly advised never to consider a transcription satisfactory unless it 
conforms with the principles of consonance and dissonance. The ob- 
servation of consonances is helpful also in determining the pitch of tones 
in ligatures written carelessly. 

Notation of the Tenors. It is advisable always to start with transcribing 
the tenor which, owing to the greater simplicity and regularity of its 
rhythm and notation, gives a desirable basis for the interpretation of the 
duplum and triplum. The chief types of tenor-notation are as follows: 

1. All single notes, for instance: |M^M«mh«<hi«m| • This nota- 
tion evidently indicates the fifth mode. Usually the ordines contain a vary- 
ing number of notes. Examples showing regular groups of, e.g., 4 L are 
rare, except for the very frequent pattern of 3 L which, however, is usually 
notated in ligatures (see p. 248, under Ic). Tenors consisting of irregular 
groups of single notes (Ludwig, in Repertorium, p. 43, calls them Simplices- 
Gruppen and uses the abbreviation ay) occur chiefly in compositions of 
the Leoninus period and, therefore, represent the oldest type of modal 
rhythm used for the tenors. Examples are found in Facs. 46 (p. 229), Do; 
Facs. 49 (p. 247), 'domino;' Facs. 50a (p. 249), Scio; and Facs. 51 
(p. 255), Et occurrens. Owing to the varying numbers of L found in these 
groups the g-meter cannot be insisted upon in the transcription. Usually 
the divisio modi indicates a rest to the value of a B (eighth-note), so that, 
in the case of 3 (or 5) L an extra g-measure (or a g-measure) results. 

2. The notation of the tenor in single notes sometimes indicates values 
of double length, namely, the duplex tonga (D). There is hardly any 
clear notational distinction between the L and the D; however, the pres- 
ence of the latter will generally be suggested by the greater distance of 
one sign from the other which is caused by the greater number of corre- 
sponding notes in the upper parts. An interesting example is the final 
section of an organum Benedicamus domino^ which is reproduced on 
Facsimile 49. Here, the plainsong for the syllable 'do-' occurs twice: 
first (end of the fourth brace) in the following grouping: dfdc/dfgd/ 
e c / . . . , then (beginning with the next-to-last ordo of the fifth brace) 
in different ordines: dfdcd/fgd/ecd/ . . . . Whereas, for the 
second presentation, the single notes of the tenor represent ordinary L, 
to be transcribed as dotted quarter-notes (see below, b), those of the first 



2 4 6 



Square Notation 



section must be given the double value (see below, a), in order to account 
for the considerably greater number of notes in the discant: 1 

(a) _ 




Sometimes the decision on this point is not easy, due to the equivocal 
nature of the upper part as well as of the tenor. On Facsimile 50a, a 
two- voice Scio cui credidi from the slightly later MS Paris, B. N. lat. 
15139 (also known as St. Victor, 813) is reproduced, the upper part of 
which shows the familiar ligatures of the third mode. In order to make 
the tenor conform with the discant, its single notes must be interpreted 
as D: 




However, in the present example it is also possible to read the discant 
in the sixth mode and the tenor as a succession of L. In fact, this probably 
is the correct version since in this Ms the D is often indicated by slightly 
enlarged heads (see the end of Alleluya on Facs. 50, p. 249). l 




1 In this connection it may be pointed out that the anonymous treatise from 1279, which has been 
edited by Sowa, contains interesting information about the possibility of reshaping a piece in a 
different mode, a procedure which was called 'transmutatio.' See Sowa's edition, p. xix ff, and his 
article in ZJMIV xv. 



Notation oj the Tenors 
Facsimile 49 



247 



gii|§|l§§j| |f 



? = %Bm 



m* if 



m 



im n& 



ym^F!,& 



! 



• ^ 



n^ 



^» 






ai 



^ 



•*f- 



ca 



; ^=^g^^' W^/^y/« \^^ 






at 



muf 



^tx> 



^"\.^ :V '^^Aw^^ 



♦— - — *-+ 



1 V T %/* ■ ■ . ',>■ 5 S ,- o / ^^s?i 






MS Florence, Biblioteca Medlcea-Laurenziana plut. 29.1 

(13th century) 

From pages 87', 88 



248 Square Notation 

An interesting detail are the numerous deviations from the normal 
pattern of ligatures, / J 3 J, for instance at the end of the first and the 
second ordo, as well as within the third ordo, where 3 is replaced by 2 r. 
These deviations are conditioned by the change of syllables, as indicated 
in the tenor. The ordo 'depositum' contains more notes than can easily 
be accommodated by the four L of the tenor. A possible solution is 
given in the appendix, No. 34a. 

On Facsimile 50b we reproduce an Alleluya from the same source. The 
tenor is one of the few examples showing regular groups of L. The upper 
part goes even further than that of Scio in the direction of quick motion, 
and represents an interesting attempt to utilize the restricted means 
of modal notation for the rendering of lively rhythms. Some details, 
particularly in the final copula^ remain doubtful. See appendix, No. 

34b. 

3. Frequently, the tenor is written in ternariae^ either exclusively or in 
connection with L. These combinations usually indicate the fifth mode, 
as under (c); occasionally, however, they must be read in the quicker 
rhythm of the first mode, (a) or possibly the second (b). The following 
groupings are the most frequent ones: 

I. ,IalJJ>J 7 |J JlJr|JJiJr| 

ia'i3 13 hbijij Jwju jyjyjg 

'lc|j. J. |j. }. |J. J. |J. J. |J.J.Ij.).| 



n. 

11 13 111(3 I 



HalJ. JrlJ J>J,|J- JrUJ>Jrl 
IIb|J. JwlJ>J JVrU. JVrlJ>j JVrl 

(nc|J. I J. *• IJ. J. I J. HJ. |J.*.lj.J.|J.H 

In lie the first of the two single notes is actually a D. 
An example of Ic is the tenor of the clausula Go, Facs. 46, p. 229. The 
following beginning of another clausula Go (F/, p. 165) illustrates lb: 



_ img 1 Bl - m 1 fc i air 



Notation of the Tenors 
Facsimiles 50a, 50b 



249 



S^MS jgE 




MS Paris, Bibliotheque Nationale lat. 15139 ( T 3th century) 
From pages 285', 283' 



250 



Square Notation 



The ligatures of the upper part clearly indicate second mode which, 
therefore, must also be assumed for the tenor. The following transcrip- 
tion reveals a rhythmic peculiarity which is more frequent in the com- 
positions of our period than one might expect it to be, that is, an overlap- 
ping of the phrases of the two parts, caused by the fact that an ordo of 
the discant begins in the middle of a ^-measure: 




The same cross-rhythm occurs even more consistently in the following 
clausula, (F/ y p. 165') the tenor of which is an example of la: 



■^ V \jj'*«>l* 







In determining the rhythm of the upper part (the first ordo belongs to 
the preceding piece) one will have to rely chiefly upon the principle of 
consonances (octaves, unisons, fifths, fourths), since another clue, fre- 
quently useful, completely fails us here, namely, the principle of the 
vertical alignment of simultaneous sounds (particularly on the second 
brace). Towards the end of the piece the transcription is not without 
difficulties, and remains to a certain extent dubious (see the appendix, 
No. 3S y 

The following Regnal (F/, p. 167) shows the combination II in the 
tenor. Since the duplum has about the same number of notes as the 
tenor, only the rhythm of the first or second mode, i.e., Ha or lib, comes 
into question. The ligature-writing of the duplum once more suggests 

1 A derivative motet exists in Mo, No. 194 (facsimile and transcription in Y. Rokseth, Polyphonies 
du XI lie siecle, i and iii). 



Notation of the Tenors 



251 



second mode. In the second statement of the tenor two ordines, corre- 
sponding to the last two ordines of the first line, are missing. 






ffl 7 



^V^fc^^^ ,, ^/^|l,l^/Hi^ | l 






Transcription of the beginning: 




In the following Regnat (Fl, p. 167) the tenor is in the fifth mode (lie) 
as appears from the considerably greater number of notes contained in 
the duplum: 






v^ 




Finally, the three- voice clausula Flos filius from Facsimile 46 (p. 229) 
may be considered. This example is interesting because it clearly shows 
that the normal scheme of g-measures cannot always be insisted upon. The 
tenor, after an initial ordo of two Z,, has the combination j 2, i.e., the 
secundus ordo of the first mode. From the context of the parts it ap- 



252 Square Notation 

pears that this combination comprises only three perfections (three 
groups of the value of | each), without a fourth perfection being supplied 
by a g-rest. The modern equivalent of each such ordo is a g-measure, so 
that the rhythm of the beginning is as follows: \% J. Jy||J J>J JJy| J J*J J* J >- 1 ... . 
The transcription of the upper parts is not without difficulties. The 
student is advised to transcribe first the duplum, then the triplum, al- 
ways paying attention to the consonances. A particular problem is 
presented by the concluding measures, in which it is difficult to reconcile 
the rhythms suggested by the notation of the different parts. Evidently 
a free performance, involving some sort of ritardando, is intended here. 
The beginning of the triplum is transcribed in the appendix, No. 36. To 
tackle this piece will be particularly rewarding for the student because he 
will encounter it again in the later course of this study in the form of 
two derivative motets, Quant revient — V autre j or — Flos filius (Facs. 54, 
p. 273) and Candida virginitas — Flos filius (Facs. 57, p. 285). 

Notation of the Upper Parts. The following examples are given in order 
to clarify certain peculiarities of the writing of the upper parts. A 
clausula Et gaudebil from W\ (p. 45) is interesting as an illustration of the 
comparatively high degree of rhythmic freedom — within the bounds of 
modal meter, of course — which could be expressed by the rather primitive 
means of modal notation: 



^^^ ^ ^^^^m^ 







^% i yJ v '^ A ' ' /1% ' 



In the tenor, the liturgical melody Et gaudebit (from the Alleluia^ Non vos 
relinquam; see Gr. Rom. 268) appears twice, the repetition beginning 
with the fourth ordo of the second staff of the tenor. The rhythm of 
the tenor obviously is lie of the above tabulation. With a transcrip- 



Notation of the Upper Parts 



*S3 



tion of the tenor as a basis to start with, the interpretation of the duplum 
presents few difficulties if the principles of consonance are observed. In 
the first half of the piece the rhythm is that of the first mode with extensio 
modi being used frequently. The single notes always indicate L. Be- 
ginning after the first division stroke of the second line the writing of 
ligatures, / J J . . . would seem to indicate the third mode, that is, a 
change from the trochaic to the iambic rhythm. Since, however, the 
fundamental rhythm does not change within a clausula (see p. 237), the 
ternariae represent ^x/^wj/o-patterns of the first mode. In the tenor, the 
group of three single notes which closes the first representation of the 
liturgical melody (third ordo of line two) signifies three D y not L. Here 
follows the transcription of the beginning of the second brace: 




An interesting and (as far as this writer's experience goes, very excep- 
tional) irregularity of notation occurs at the beginning of the last brace. 
The writing of the duplum would clearly seem to suggest the first mode, 
with alternating L and B. However, in order to make the passage con- 
form with the tenor the notes must all be read as L> similar to those of 
the preceding ordo: 




The arrows point to the initial notes of the two staffs which, as is fre- 
quently the case, do not sound simultaneously. The penultimate note 
of the tenor (B) must be extended to cover two measures. 

It would, of course, be possible to interpret the passage under consid- 
eration as being in the first mode, if in the corresponding section of the 



254 Square Notation 

tenor the rhythm of the fifth mode (He) were replaced by the doubly 
quick rhythm of the first mode (Ha). Although such a quickening of 
rhythm is not uncommonly applied to the second! presentation of the 
liturgical melody, it would seem to be rather out of place here where it 
would occur only with the last few measures of the second presentation. 
In fact, definite proof supporting our first interpretation will be found 
later (p. 280). 

Examples. We now turn to a consideration of Facsimile 51 which shows 
a number of clausulae, contained on p. 174/ /T75 of the Florentine Codex. 

(1) Et occurrens. The tenor (beginning with the fourth note on the staff") 
is written in L which appear in irregular groups ('simplex groups,' 
see p. 245). Groups with an uneven number of L call for an extra %- 
(§-) measure. Naturally in cases like this ^-measures may well be used for 
the entire transcription. The duplum (beginning with the ternaria f-e-d) 
is in the first mode. 

(2) Et gaude — bit. The entire tenor is written in the grouping // / / 
3 /, which must be read in the fifth mode (lie). The duplum is in the first 
mode, with the initial ternaria of several ordines broken up into / + 2 y 
because of repeated .tones. At the beginning of the duplum we find a 
single note (f) followed by a plica note of the same pitch, another example 
of the plica duplex longa. Several ordines (end of the second brace of the 
page, middle of the third brace, show the grouping 1333. . • sug- 
gestive of the third mode. Actually, they indicate extens io-pa.tterns of 
the first mode, as in the clausula Et gaudebit (p. 252O. In the present 
case definite proof for this interpretation exists in a derivative motet, 
Quant florist — Non orphanum — Gaudebit y which is notated in the un- 
equivocal symbols of pre-Franconian notation. 1 

The student will have already noticed that in the pieces under consid- 
eration the vertical alignment of the written characters unfortunately 
does not always exactly correspond to the vertical alignment of the tones 
which are to be simultaneously sounded. Neither do the entire lines 
necessarily end with simultaneous notes. For instance, in the third 
brace the last note of the tenor sounds, not with the last note of the 
duplum, but with the first note of the next line. Several measures of 
this piece are transcribed in the appendix, No. 37a. 

1 Mo, no. 42 (Rokseth, Polyphonies) and Ba, no. 67 (Aubry, Cent motets). It is interesting to note 
that in both these sources the conjunctura quaternaria in the second ordo of staff 5 appears, not as 
three shorts followed by a long (see p. 249), but as a long followed by three (in Ba four) shorts (see 
Polyphonies i, p. 77, staff 1, and Cent motets i, p. 43, staff 1 : 'cum iero'). This is one of many ex- 
amples indicating that at the time of the composition of the motet (1250?) the conjuncturae had 
lost their original meaning and were interpreted as what was suggested by their shape, that is, as a 
long followed by several short notes. 



Examples of Modal Notation 
Facsimile 51 



*55 










u Pi 




256 Square Notation 

(3) Reuo/vit. This short clausula (from the Alleluia Angelus Domini) 
has duplex longae in the tenor. The duplum starts with two L, 

(4) Ta. The tenor has the rather unusual combination / / / j / 
throughout the first statement of the c.f., / j / in the second. The begin- 
ning is transcribed in the appendix, No. 37b. 

(5) Sanctus. The ternariae of the tenor indicate the fifth mode. The 
duplum is in the first mode. The ternariae in the middle of several 
ordines always indicate extensio modi. The piece closes with a short 
copula whose notation suggests change from the first to the second mode, 
as in the almost identical copula of the clausula Go (Facs. 46, p. 229; see 
the remark on p. 237). 

(6) Hodie perlustra — vit. Both duplum and tenor are in the second 
mode. Each ordo of the tenor consists of three perfections, corresponding 
to a g-measure. The irregular notation of the tenor to the syllables '-die 
perlustra-' is caused by the change of syllables, which also accounts for 
the numerous dashes in this passage. Actually the basic tenor rhythm, as 
indicated by the regular ordines, 2 j, continues without change. The 
duplum is one of various examples showing that modal notation, although 
often proving a surprisingly pliant medium of notation for the rhythmic 
variants {extensio and f radio) of the first mode, is much less adapted for 
similar variants of the second mode. The notation of such parts often re- 
mains uncertain and doubtful in many particulars. The main guide is, as 
always, the principle of consonances. Occasionally the rule of correspond- 
ing ligatures (see p. 237) proves helpful in making a decision between 
various alternatives. See the transcription in the appendix, No. 37c. 

(7) S ancle spiritus. The duplum begins with a single plica on d'. 
Whether the ordines of three perfections should be transcribed as two 
8 -measures or as one ^-measure, cannot be determined. At the end there 
is a cadential passage similar to that of Sanctus. 

(8) Amo. Tenor and duplum begin with two single notes. The 
rhythm is similar to that of El occurrcns. 

(9) Vado. The two ternariae at the end of the first and second ordo of 
the duplum evidently call for /radio modi. 

A page similar to the one just considered is reproduced in HdN 1, 228, 
and another one in SchT, p. 14. Both are strongly recommended for 
study. 

We close our study of modal notation with the consideration of some 
clausulae showing certain notational irregularities not encountered in the 
previous examples. In the clausula Mulierum of Facsimile 52a the tenor 
daac'c'... appears twice (the initial d, to the syllable 'Mu-,' is omitted 
in the second statement), first in ternariae, then in the combination 



Examples of Modal Notation 
Facsimiles 52a, 52b 



257 







^=^r 



K 



W 7 ' * M> 







. ^VV^^M 



a=a« 



Sggplg gjj = A ,, mi, ;j1 i/ 



I |§§|| g§l|§ 




tmno 



MS Florence, Biblioteca Medicea-Laurenziana, ^/«/. 29. 

(13th century) 

(a) From page ^4; (b) From pages 88', 89 



258 Square Notation 

I t 1 1 3 I . The Ms erroneously omits two complete ordines (tenor notes: 
/fef/dec/)at the end of the first brace. They are included in the 
version of /Fi, p. 45. 

The great number of notes in the duplum clearly suggests the fifth mode 
for the entire tenor (Ic and lie). The duplum is conspicuous for its ex- 
tended use of repeated notes which, moreover, show a distinction between 
notes with and without the dash, or, as we may say, between L and B. 
Repeatedly these signs occur in the combination L B B L (according to 
Wi y where the B are written in the lozenge-shape of the later S, a B is 
missing at the beginning of the seventh ordo, and the fourth note of the 
ninth ordo should be a L). These groups suggest interpretation in the 
second mode, with alteration of the second B. Toward the end of the 
duplum (middle of the third brace) we find the characteristic ligatures of 
the third mode (/ 3 3 . . . ), whose rhythm is closely allied with that of 
the second mode. Various passages of the piece are transcribed in the 
appendix, No. 38. 

Facsimile 52b shows two clausulae Domino the first of which (desig- 
nated Do) is an extremely difficult specimen of modal notation. The clue 
to its transcription is that the tenor pattern is lib (see p. 248), and that 
the duplum is in the second mode, with frequent /r<2<r//o-modifications 
(sixteenth-notes). Even with this information as a basis there remain 
many uncertainties which it would be difficult to settle definitely without 
some outside help. Fortunately, this exists in the form of a derivative 
motet, Ne moubliez mie — Domino, which is preserved in Mo (ed. Rokseth, 
No. 236). The student is advised to transcribe the piece along the lines 
indicated above, and to compare the transcription with that of the motet 
(ed. Rokseth, III, p. 60). 

The second Domino is less difficult. The tenor is in the pattern of Ha 
(with the reversed arrangement, / 3 / / / /), and the duplum is in the 
first mode. The last ternaria of the tenor probably has to be read as 
L L L y not L B L, as is the case with the other ternariae. 



C. Syllabic Notation 

The principles of this notational system may be explained in con- 
nection with Facsimile $%, containing a conductus Hac in anni janua. 
Three parts are notated on what seems to be a single staff of thirteen 
or more lines, but is in fact a contraction of three different staves, each 
with its own clef-letter c (see p. 8). Actually, all the parts move within 
about the same range, quite different from what the arrangement in 
writing suggests at first sight. 



Syllabic Notation 
Facsimile ^ 



259 




1 \ j j-jtz zz JA « J ii 



< . 1 ■> /T ? 



acm flam lAnufr foe tn t&mfrtt toftftnutf aS 



333 1 ' AiL^nj 



S5tt 



j^tiaurrtitnm\(UVft>wa*ttbia tat ttumiA 



X^ 



£ P Z 1 »f *W^ »±5 







MS Wolfenbiittel, Herzogliche Bibliothek 6jj y formerly Helmstedl 62S 

(13th century) 

Page 71 



260 



Square Notation 



The music is notated essentially in single notes, each of which belongs 
to a syllable of the text. Occasionally plica notes are used (for instance 
near the beginning of the middle part), and frequently ligatures {binariae 
and ternariae) appear in the place of a single note. These, of course, 
mean that two or three tones should be sung to the syllable to which 
they belong. 

It will easily be seen that, in each part, the number of notational signs 
(single notes or ligatures) corresponds with the number of syllables 
which, in the present case, is seven for each line of the poem: 



Hac in anni janua 
hoc in januario 
tendamus ad ardua 
virtutum subsidio. 



Gaudia sunt mutua 
muto facto vitio 
reproborum fatua 
reprobatur actio. 



Following is the transcription of the beginning: 







t 






/?> 










3 




*- 


/?\ 


8 

firm 3 








/C\ 


1 - 












I i 


8 
Hac in 


an - 


ni 


ja - 


nu - a, 


hoc 

i I i 


i 


n 


J a " 


nu - 


a 


- ri - 






In accordance with the poetic meter of the text, the last note of each 
phrase has been prolonged by a pause, a procedure which is actually 
prescribed in notation by the 'doubled plicas' in the lowest part. 

The last line of our facsimile is occupied by a cadential vocalisation 
{cauda) to the final syllable — V. Automatically the notation changes 
from syllabic to modal notation (see p. 231). 

Judging from these explanations the system of syllabic notation is 
simplicity in itself. But this simplicity is deceptive. A transcription 
such as given above is only the point of departure for various consider- 
ations of a more or less controversial character, and for questions which to 
the present day have not been definitely answered. 

The first question that arises concerns the evaluation of the groups of 
notes represented by the ligatures which often occur in the place of a 
single note. Many conductus show a considerable number of groups of 



Syllabic Notation 



261 



two and three notes, and often a group of two notes occurs in one part 
against one of three notes in another part, as repeatedly in Hac in anni 
janua. It seems highly improbable that cross rhythms such as would 
result from the simultaneous occurrence of two and three notes can be 
admitted in a period which more than any other is characterized by the 
rigidity of its rhythmic concepts. Proceeding from the premise that the 
single notes of syllabic notation represent each a longa (a premise which 
actually is the most controversial of all; see p. 262), the notes of a ligature 
naturally suggest interpretation according to the system of modal 
rhythm, based on the ternary division of the L. This means that the 
notes of a ligatura ternaria represent three B of equal value. In the case 
of a ligatura binaria either the first or the second B will have to be 
doubled, in the pattern of either the first or the second mode. Since the 
first mode is the much more frequent one, the former alternative appears 
as the more natural solution. For groups of more than three notes the 
rhythmic formulae given on p. 241, first illustration, under (a), may 
serve as a model (disregarding, of course, the final dotted quarter-note 
which, in syllabic notation, would be represented by a separate note). 
Following is a new rendition of Hac in anni janua, according to the 
* principles just outlined: 




The rhythmic interpretation of the smaller note values, as just out- 
lined, is only one of several possibilities. Various other methods have 
been used in transcriptions of conductus, as appears from the table 
on p. 262 (all values are reduced to the same scale, L ^quarter-note). 

The interpretation, used by Wooldridge, Handschin, and Ellinwood, of 
the binaria as an iambic pattern (second mode) is suggested by the basic 
meaning of this ligature, that is, B L. In many cases this rendition seems 
preferable because it leads to a quicker resolution of a dissonance between 
the first note of the ligature and the simultaneous note of the tenor (e.g., 
e' - d' against d). There are, however, other instances (possibly less 
numerous) in which the second tone produces the dissonance (e.g., d'- e' 



binaria 


ternaria 


quaternana 


J J> 


j n 


J Jf3; J5T3 


J>j 


J £ 


j js 

3 


J-3 


J~H 




jVj 


JT1 




J> J 


^J 




j.j. 
J> j,J>ij 


JSJJ. 


^4 "^ 


J~J~3 


JJ J J 



262 Square Notation 



Coussemaker (Histoire de 
Vharmonie, Traduction, no. 23) 

Woolciridge (e.g., OH, 254^ 
'commiserans ..considerans') 

Riemann {RHdM i. 2, p. 211) 

Handschin (in A. Einstein, 
Short History of Music, Ex . 6) 

Handschin {ZjMW vi, 554) 

occasionally 

Ellinwood (M^xxvii, i8 9 fF) 



against d) and in which, therefore, the rhythm L B would give a better 
result from the point of view of consonance. The obvious solution, that is, 
to choose between both possibilities, would imply a change of modal 
patterns within one and the same composition which one might hesitate 
to admit. If such a change is ruled out, the decision in favor of the first 
mode becomes almost imperative, owing to the frequent occurrence in 
syllabic notation of plica notes, symbols which it is practically impossible 
to interpret as B L. (An example showing the simultaneous use of a plica 
note and a binaria is found at the beginning oiHac in annijanua, syllable 
'an-'.) 

While the uncertainty that exists with regard to the evaluation of the 
ligatures may appear as a somewhat irrelevant question of detail, a much 
more fundamental problem is presented by the single notes of syllabic 
notation. All the preceding explanations are based on the assumption that 
these single notes indicate values of equal length or, to put it differently, 
are to be read in the fifth mode. As has been previously intimated 
(p. 261), this theory, favored by some scholars (Wooldridge, Handschin, 
Reese, Ellinwcod) is contested by others (Ludwig, Aubry, Gennrich, 
Bukofzer) who maintain that these notes actually represent alternations 
of longs and shorts, usually in the rhythm of the first mode. This means 
that modal rhythm is introduced by the single notes, not by the ligatures 



Syllabic Notation 263 

which now appear only as fractio patterns. Here follows a 'modal' 
rendition of Hac in anni janua: 1 

J J 1 J J J 1 

-3- 




What are the reasons in favor of this interpretation? The most obvious 
argument is the versification of the text which, with its alternation of 
accented and unaccented syllables, naturally suggests a conforming 
alternation of long and short values. Another argument exists in the fact 
that modal rhythm is, beyond doubt, required for the upper parts of the 
early motets, parts which are notated in exactly the same manner as are 
all the parts of the conductus (see the explanations under Motet No- 
tation, p. 27 iff; also Facsimiles 54, 55, 56). Particularly impressive is the 
evidence furnished by the so-called conductus-motets (see p. 274, fn. 1), 
compositions in three (or occasionally four) voices, whose upper parts 
are, for all practical purposes, undistinguishable from a two- (or three-) 
voice conductus, as appears from Facsimile 55 (p. 275). 2 These examples 
clearly show that modal interpretation of compositions or of voice-parts 
written in the uniform symbols of syllabic notation was part and parcel 
of the musical practice of that time. 3 

Champions of modal interpretation have also called attention to the 
fact that occasionally conductus of the period under consideration occur 
in later sources in a more advanced type of notation (pre-Franconian), in 
which there is a clear differentiation between longa and brevis. Following 

1 For the sake of short reference the two methods of interpretation may be designated as 'isochron- 
ous' and 'modal,' although the former also falls within the general frame work of the rhythmic modes. 

2 W\ contains several 'conductus' (e.g., Serena virginum, p. 9) which actually are motets, the 
tenor (in the present case, 'Manere') being omitted in this source, but found in others (e.g., Fl, p. 
235). See Repertorium, p. 35 {Serena virginum), p. 39 {Latex si/ice), p. 40 {Deo confitemini, Laudes 
re/erat, Gaudeat devotio), and p. 41 {Qui servare). 

3 In this connection it may be mentioned that, the method of modal interpretation has also been 
applied to the monophonic songs of the troubadours and trouveres, and is, at present, generally 
accepted as the correct interpretation of these melodies, all of which are transmitted in syllabic 
notation. See, e.g., P. Aubry, La Rhythmique musicale des troubadours et des trouveres (Paris, 1907); 
also HdN i, 201 ff and AHdM i, i89ff. It has also been used for the monophonic conductus (see 
AHdM'x, 187), the Spanish cantigas {AHdM'x, 213) and, occasionally, the songs of the Minnesingers 
(see AHdM i, 204). However, recent investigations have considerably shaken the foundation of 
this theory, except in the case of the songs of the trouveres (see the author's review of H. Angles, 
La Musica de las Cantigas . . . (1943), in Speculum, July 1947, p. 458ff, and J. Handschin's 
review of U. Sesini, Le Melodie trobadoriche . . . (1942), in AMxx, 1948, p. 62. 



264 



Square Notation 



is the beginning of a conductus, Crucifigat omnes y in two versions, from 
W\ (p. 71) and from the Codex Hue/gas (p. 97): 



H P f % ti « a C 




W7 ^ 



J* LL 



^^M- 



ftr4 p >tt ^^Unmi5^AcrWnx«vi u 




mciftyAfr 0f*net 'vtwiinx cn& &\to** n*»&xpi{U aut 



Finally, recent investigations have brought to li^ 
number of conductus there exist musical relations 
between the syllabic and the melismatic passages, 
casionally the same music that appears at another 
sition in syllabic form. Since there can be no doubt 
rhythm of the melismas, the obvious conclusion 
sections are also in modal rhythm. 

No doubt, these considerations constitute strong 



rht the fact that in a 
and correspondences 
the latter using oc- 
place of the compo- 
regarding the modal 
is that the syllabic 

evidence in favor of 



1 See M. F. Bukofzer, 'Rhythm and Meter in the Notre-Dame Conductus' (Bulletin of the American 
Musico/cgicai Association, 1948, p. 63). 



Syllabic Notation 265 

modal interpretation. The main argument against its universal acception 
lies in the fact that in many cases it leads to versions of a rhythmic com- 
plexity far exceeding the limitations of thirteenth century style. Such 
versions result in all those cases where the single notes are to a large 
extent replaced by ligatures, particularly if these ligatures include groups 
of three or more notes. Using a terminology familiar from Gregorian 
chant, we may distinguish between conductus in 'syllabic style' and 
others in 'group style.' While examples of the former type, for instance, 
Crucifigat omnes (p. 264) lend themselves very well to modal interpre- 
tation, this method leads to much less satisfactory results if applied to 
a conductus like Hac in anni (p. 259) with its numerous groups of three 
notes, many of which fall on the weak accent of the text, hence on the 
short value of the modal pattern, thus leading to a very uneven rhythmic 
texture. Even more awkward is the result in the case of examples show- 
ing groups of four, five, or more notes, as for instance in the three-voice 
conductus Relegentur ab area (Fl, p. 202'), a section of which follows on 
p. 266 in facsimile reproduction and two transcriptions, (a) isochronous 
(fifth mode), and (b) modal (first mode). 

It should be noticed that the version (a) makes the rhythmic contrasts 
disappear to an even greater extent than the written score suggests, since 
it admits (and probably calls for) a certain flexibility of tempo in actual 
performance, including a slight prolongation of the syllables having ex- 
tended groups of notes. Modal rhythm, on the other hand, by its very 
nature is incompatible with flexibility of tempo. 

Obviously, an argument in favor of modal interpretation of conductus 
in group style could be established if it could be shown that the groups of 
notes appear preferably on the strong, that is, on the presumably longer 
beat. Actually this is not the case, as the examples clearly show. In 
some instances, however, better results can be obtained by applying an- 
other mode than the one that seems natural at first. Thus, a considerably 
smoother version of Hac in anni janua results if it is transcribed in the 
second mode. 

In weighing all the evidence pro and contra, one will probably arrive 
at the conclusion that, first of all, a distinction should be made between 
conductus in syllabic style and conductus in group style. For the former 
type modal interpretation appears to be not only admissible but probably 
preferable. In this connection it may be noticed that the conductus-like 
upper structure of motets such as Laus Domino — Eius or Homo quo 
vigeas — Et gaudebit (Facsimiles $$, 56, pp. 275, 281) are definitely in 
syllabic style, and that in the Huelgas version of the Crucifigat omnes 



266 



Square Notation 



(p. 264) the upper part, which contains several groups of notes, is omitted. 
For conductus in group style the isochronous rendition (fifth mode) 
appears proper, unless a modal pattern can be found which leads to a 
reasonably even rhythmic texture. 










S*A.|*' TT,I V'''V^K,~ 




; l/^v'il^^/j:i5I^.i. 



w---A 



le^twmrabArcafiJJd^amibmtirluturalana- 




[Re] - le-gen - tur ab a - re - a Ki-de-lis con-sci - en - ti - ae 



Duplum Notation 267 

D. Duplum Notation 

The organa dupla represent the earliest repertory of the School of 
Notre Dame. Their development, associated with Leoninus, the 'optimus 
organista' (second half of the twelfth century) forms the transition 
between the school of St. Martial (see p. czoofT) and the organa tripla 
and quadrupla of Perotinus, the 'optimus discantor.' 

The notation of the organa dupla presents even greater problems than 
that of the conductus. While in syllabic notation at least the basic 
principles are obvious and incontestable, the very foundations of duplum 
notation are uncertain. As we shall see later, the knowledge of this 
system (if it ever was a 'system') was lost as early as the thirteenth 
century. Theorists of this period often speak of organum duplum as 
a miraculous thing of the past, extolling it as the most beautiful and 
noble kind of music, but without being able to describe it in the technical 
language of their day. From the historical point of view this uncertainty 
is readily explained by the fact that the organa dupla of the Leoninus 
period stand between periods representing two diametrically opposed 
concepts of rhythm, the free, 'Gregorian' rhythm of St. Martial and the 
rigid system of the rhythmic modes. Rarely in music history has a 
development of a half a century brought about such a radical change 
of methods, and the very distance between the two points makes it 
difficult to determine the position occupied by the organa dupla of 
Leoninus. 

The problem presented by the notation of the organa dupla is illus- 
trated by the Benedicamus Domino of Facs. 49 (p. 247). This consists 
of an 'organal' section, 'Benedicamus,' with long held notes in the tenor, 
and a clausula on 'Domino.' The latter is, of course, in modal notation 
and, in fact, served as an example of this system (p. 245). The former 
shows the characteristic traits of duplum notation, that is, ligatures 
and extended conjuncturas in irregular combinations which fail to sug- 
gest — let alone to indicate clearly — modal rhythm in any of its varieties. 
The difficulty of determining the rhythmic meaning of these signs is 
considerably enhanced by the fact that the tenor of these sections 
consists of sustained single notes, each serving as a pedal point for a 
great number of notes of the duplum. Thus, one of the most important 
clues of modal notation is missing, that is, the simple and relatively 
unequivocal rhythm of the tenor. Evidently, "the notation of this section 
differs radically from that of the clausula. On the other hand, it shows 
an unmistakable similarity to the notation of the Alleluia vocavit Jhesus 



268 Square Notation 

from the Codex Calixtinus, reproduced on Facs. 45 (p. 213), as appears, 
for instance, from a comparison of the second ordo on staff two of the 
Benedicamus with the third 'ordo' on staff two of the Alleluia. The 
question, then, is whether the organal section of the Benedicamus should 
be interpreted in a rhythmic style similar to that of the organa of St. 
Martial and Compostela, or in a more advanced style midway between 
free rhythm and strictly modal patterns. 

As regards the interpretation in free rhythm, there are several theorists 
of the thirteenth century whose remarks about organum duplum (also 
called 'organum purum,' 'organum speciale,' 'organum proprie sumptum,' 
'organum non rectum ,' 'organum per se') could be quoted as supporting 
evidence. Thus, Walter Odington says (CS i, 245b): 

There is one type of organum in which only the coherence of immeasurable voice-parts 
(vocum immensurabiliuni) is observed, and this is called organum purum. And this is 
the oldest, and is in two parts only. 

Anonymous of 1279 (H. Sowa, Ein anonymer gloss ierter Mensuraltraktat, 

p. 127): 

In this chapter the author deals with organum speciale, also known as organum duplex; 
which, if it is found as such, 1 proceeding (gradiens) in its own manner, does not hesitate 
to transgress or interrupt the regular divisions (regularum metas) as distributed in a 
definite series of notational signs {figurarum) and temporal values (temporum), thus 
leading to an irregularity [which appears] upon careful observation {irregularitas subtiliter 
intuenti). 

Anonymous de la Fage (De la Fage, Essais de diphterographie musicale, 
1864, p. 358): 

In an organum the parts sound together, not by the equivalence of notes (equalitate 
punctorum; with reference to discant style), but in an infinite multiplicity and an almost 
miraculous flexibility. 

The language of these quotations leaves little doubt that the compo- 
sitions thus described were rhythmically free and unmeasured. The 
difficulty is that we have no way of knowing whether these descriptions 
refer to the organa of Leoninus as preserved in W\ and Fl, or to unknown 
compositions of a somewhat earlier period in the development of the 
school of Notre Dame. It could even be argued that they refer to the 
organa of St. Martial, although this surmise is somewhat unlikely in 
view of the fact that this school was located in southern France (Limoges). 
It is doubtful whether, under then prevailing conditions, a provencal 
repertory from ca. 11 50 was still known in Paris about 1270, the time 
when the above quoted theorists wrote. 

*per se post turn;' see the explanation in fn. 1, p. 269. 



Duplum Notation 269 

Most scholars are inclined to consider the organa under consideration 
as examples of a more advanced rhythmic style, that is, in triple meter, 
but without strict modal patterns. The basis for this interpretation 
is provided by the fact that several of the most important theorists (all, 
by the way, of a somewhat earlier period than those previously quoted) 
expressly refer to the use of longae and breves in organum duplum. Par- 
ticularly clarifying are the explanations of Johannes de Garlandia (De 
Musica mensurabili positioy c. 1250; CS i, 114a [some obscure or relatively 
irrelevant sentences are omittedl) : 

There are two special types of organum, per se and cum alio. 1 Organum per se is that 
which is performed in modus rectus or in modus non rectus. By modus rectus we mean 
that type of modus which is used for discantus. In modus rectus longae and breves are 
taken principally in the first mode proper (debito modo primo et principaliter). In modus 
non rectus, however, the longae and breves are [also] in the first mode, but incidentally 
{ex contingenti) . 

These remarks suggest an interpretation of organum duplum in the 
first mode, this mode being applied strictly in the clausulae, freely in the 
organal sections. Taking this rhythmic style as a basis, there arises the 
question as to the evaluation of the ligatures in modus non rectus. 
Judging from the relatively few transcriptions of organa dupla that 
have been published, 2 the guiding principle seems to be to interpret each 
ligature in its basic meaning, that is, the binaria as B L, the ternaria as 
L B L, and the ligatures with more than three notes as fractio-modi- 
fications of the ternaria, 3 all normally in the first mode, but occasionally 
(in spite of Garlandia's statement) with changes into the second mode. 
However, an examination of the available transcriptions shows that the 
ligatures are often interpreted differently, in order to obtain a smoother 

1 The most likely explanation of these terms is that per se means 'in two parts' (organum duplum) , 
cum alio, 'with a third part' (organum triplum). 

2 Judea et Jherusalem: OH, i88ff (facsimile); RHdM, i.2, 156; Handschin, in ZfMW x, 15; Sowa, 
in Ein . . . Mensuraltraktat, p. XXXVIII. — Hec dies: AHdM i, 217 (Ludwig); H. Besseler, 
Musik des Mittelalters und der Renaissance (1931), p. 99f (facsimile); A. T. Davison and W. Apel, 
Historical Anthology oj Music i (1946), No. 29. — Alleluia Pascha nostrum: Ludwig, in ZfMlVv, 448. 
— Crucifixus in came: Handschin, in AjMW vii, 161. — Propter veritatem: H. Angles, El Codex 
musical de Las Huelgas (1931), ii, No. 47. — Tanquam sponsus: OH, 195. — Virgo Dei genetrix: 
OH, 201. — Benedicamus Domino: Davison-Apel, Anthology, No. 28c. 

Special studies of organum duplum are found in OH, pp. 175-187, and in Sowa, Ein . . - Mensu- 
raltraktat, pp. XXVII-XXXIX. 

3 Anon. VII (CS i, 381a): 'And be it known that any ligature with more than three notes should 
be reduced to a ternaria.' Similarly Anon. IV (CS i, 341b: 'Omnis figura ligata') with reference to 
the 'libris antiquorum ... in tempore Perotini Magistri.' 



270 



Square Notation 



result. As an illustration there follows a transcription of the begin- 
ning of the Benedicamus Domino (Facsimile 49, p. 247). In the main 
text an attempt has been made to follow the above rules, while the 
small notes illustrate modifications such as are found in modern 
transcriptions. 1 




Obviously, this method of transcription (if it can be called a method) 
is very unsatisfactory. It leaves so much room for arbitrariness that one 
might hesitate to accept it as the final answer to our problem. Possibly 
a clue toward a more satisfactory solution exists in certain statements 
made by several thirteenth-century theorists which deserve more careful 
attention than has been given them so far. These statements all empha- 
size the importance of consonance and dissonance as a regulating factor 
in the organa dupla. Joh. Garlandia, after his remarks about modus 
rectus and modus non rectus (see p. 269) continues as follows: 

The longae and breves are recognized as follows: through consonance, 
through the form of notes (Jigura) and through [the rule of] the penulti- 
mate. Hence the rule: Whatever occurs by virtue of consonance, is con- 
sidered as longa. Another rule: Whatever has the form of a longa y is long. 
. . . Another rule: Whatever occurs before a long pause or before a perfect 
consonance, is considered as long. 

Similar rules are given by Franco (CS i, 1340* By far the clearest 
and most detailed explanation, however, is found in Anon. IV (CS i, 
362fT). Essentially he tells us that the consonances are unison, octave, 
fourth, fifth, major and minor third, and that in every ligature a note 
is long if it is in consonance with the tenor, short, if in dissonance. Ac- 
cording to these principles, one and the same combination of ligatures 
is to be read in a different rhythm, depending upon the pitch of the tenor 

■w- 

Additional rules are that each penultimate note before a rest is long, 
and that the currentes always descend quickly, but are preceded by a 
long note. 

^he transcriptions by Riemann should be disregarded. 



Motet Notation 271 

As appears from the above illustration and even more so from the prac- 
tical application of these rules, they entail the abandoning of triple meter 
as the basic rhythm. Long and short notes follow in free succession, lead- 
ing to a rhythmic style very similar to the one that has long been con- 
sidered by many scholars 1 as the correct interpretation of Gregorian 
chant. Very likely, the 'principle of consonance' would not apply to pas- 
sages written in regular groups of ligatures, such as the ordo immediately 
after *ne' in the Benedicamus. These then, together with the clausulae, 
would indicate the intrusion of modal rhythm into polyphonic music, and 
would make the organa dupla of Leoninus to appear as a plausible link 
between those of St. Martial and the organa tripla of Perotinus. 2 Follow- 
ing is a new transcription of the Benedicamus. 



J J=3 




E. Motet Notation 

As has been pointed out in our brief historical survey of the forms of 
the early thirteenth century, the motet originated around 1225 by the 
addition of a full text to the upper parts of the clausulae. Concomitant 
with this change are two important notational innovations, the transi- 
tion from melismatic to syllabic notation in the texted parts; and the 
abandoning of score arrangement for arrangement in single parts, a 
method of writing which was to last continuously in ensemble music un- 
til the advent of the seventeenth century. 3 

The main sources of the early motet are the Florentine Codex {Ft) and 
the Codex Wolfenbiittel 1099 (rV 2 )y both of which contain numerous 
motets in separate fascicles. Additional sources are the manuscripts 
Brit. Mus. Eg. 2615 {LoA) y Paris, B. N./rc. 844 (Chansonnier Roy, R) y 
and Paris, B. N. 12615 (Chansonnier Noailles, AO. 4 From the notational 
point of view, these sources are clearly marked off from the well-known 
later collections of Montpellier, Bamberg, etc., by the fact that, as is the 

The so-called 'mensuralists,' Dechevrcns, Wagner, Dom Jeannin, Bonvin, Jammers (see G. Reese, 
Music in the Middle Ages, p. 143; Harvard Dictionary of Music, p. 309a). 

'For a detailed study of this question see W. Apel, 'From St. Martial to Notre Dame' {Journal of 
the American Musicological Society, vol. ii, No. 3, 1949). 

*The only exceptions to the universal adoption of part arrangement for the writing down cf 
ensemble music are certain conductus-like pieces encountered in English MSS of the fourteenth 
and fifteenth century. See, e.g„ H. E. Wooldridge, Early English Harmony 1, plates XVI, LVH, 
and the explanations on the Old Hall MS, p. 364. 

4 The main contents of the last two MSS are monophonic melodies of the troubadours and trouveres. 



1J2 



Square Notation 



case in the entire field of square notation, only one character exists for 
the single note, that is to say, there is as yet no notational differentiation 
between the longa and the brevis. 

Facsimile 54 shows a number of motets from the Chansonnier Roy. 
The music is arranged in two columns. On the left-side column, after 
the closing portion of a motet beginning on the preceding page, there fol- 
lows a texted duplum (or, as it is called, motetus) : Hut main au doh mois 
de mai> at the end of which the tenor Hec dies is written. The almost 
spectacular incongruity between the length of the two parts sufficiently 
explains why score arrangement is abandoned. It would have been a 
waste of the valuable parchment to assign full staves for the few notes 
of the tenor, to say nothing of the difficulty of aligning vertically the 
compact ligatures of the tenor and the widely spaced notes of the motetus. 

After this two-voice motet there follows in the manuscript a texted 
part, Quant revient et joille etflors, without tenor, and a part, U autre jor 
men alai par un destor, at the end of which there is the tenor Flos filius. 
Together they form a three-voice motet which may be studied here. 

The writing of the tenor shows the familiar features of modal notation. 
After two singles notes, there follow eleven ordines written (normally) 
3 2, which evidently are in the first mode. As each ordo contains three 
perfections {secundus ordo) the question as to the length of the closing 
rests arises: (a) SIJ J>J1I J.t-I ; (b) J| J J>JJJ y\ . The context of 
the other parts readily shows that (b) is correct, and that the g-meter 
must be abandoned for g-meter, except for the first ordo. 

The notation of the upper parts (the duplum L 'autre jor may be con- 
sidered first) in no way differs from the syllabic notation of the conduc- 
tus. However, it goes without saying that the rhythm of these voices 
must be accommodated to the modal rhythm of the tenor. Most fre- 
quently the upper parts show the regular alternation long-short of the 
first mode. The value 6f the ligatures depends, of course, upon whether 
they take the place of a L or of a B. The following transcription of the 
beginning serves as an illustration: 



8 Quant re-vientet foille et flor con-tre la dou-cor d'es-te, 




L - au-tre jor m'en al-lai par un des - tor; en un jar- din 



FLOS FILIUS 



Motet Notation 
Facsimile 54 



273 



BE 



± 3EZ£ 



in 



HtJ: 



^L.|L.LijLt: 



-tie u &uu • to urn Aineta • lu tturaot & 



V 



-teat 




**=pqc: 






ttu »)Ktue-m4it<gc it mW &>toJf-tnoh- 



\n mam an &£ twwf fc nut. 
I 1 



ictunr Ic (Weill launr o> 



Axtgtcr men cmwi • 5ct<nifte vn pin -vxr 



-T-* " ' ■ 

tounrome pitcde ttimui-ioftf cnaUaiir- 



±±± 



tatftwtnuftcrfu- define ,1 , nwupn- 

{ i »-5 ■— • T t 

"8c we tttyonta • Jtnot tutondxm wf u-cfir 



d«f. 




^RV 



Vanr nruicnr cr rotllt er ft?T f 



OatU 



kite ^cyafcjc" 



.mc ton cttr awuarf, qui wa tar iaf cotm 
ic crdNitecftr-tnour 4tm fen ftaef- qtu 



Anem-biettferljwioiffcihvafimjn*. 




=34*^ 



E3£ 



annc w: men aiat wr m 



fettw - en^m >trtm mm en 



ten pj cneatr fl« -Same ntatCmr 



It 



X=3t 



i^ 



"uai ♦ ^ cottns &MW - ctter or oai - ft own 



.t wrcBjonr cfmai • amcrfat q nen frra 

— r O :> — 



-Hv-.- 4 - 



=F 



<fifr to ftnf qnc <ntf nuf Mejammt 

p . ... , Jl"»i*l/n A *»NA i t il Jtrr^i flri " 
1 fD \t* tt*1r*rr m - '^|jttt gil_JLk.l 

fulfil**. , , iL . 




s^ 



jtifftmw Citwi (tit (bttew" 






•mcfcuctf Ctttttr. 5cy fw «t Iwtn tattr. 



qiunr metct tie mtifenn -cnunr 



4S 



Chansonnier Roy 
Paris, Bibliotheque Nationale/r^. 844 (13th century) 
Pages 206 ' 



274 Square Notation 

This is the place to refer the reader back to the three-voiced clausula 
Flos films from Facsimile 46 (p. 229), which is tne modei for the present 
motet, the music being identical save in a few minor details. It is inter- 
esting to note in this case, as in. many similar ones, that the earlier nota- 
tion is considerably more precise and unequivocal than the later system 
(see also Homo quo> p. 279). Not until the introduction of the pre- 
Franconian system did this situation change (see p. 284). 

Another example illustrating the principles of motet notation is the 
motet Laus domino — Eius of Facsimile 55. This piece belongs to a spe- 
cial class of motets the superstructure of which consists of two or occa- 
sionally three parts with the same text, notated in the score-arrangement 
of conductus. 1 The determination of the rhythm of the tenor as well as 
of the upper parts proves more difficult here than with the previous ex- 
ample. To start with, a clue may be gained from a rough calculation of 
the number of notes contained in the different parts. Since there are 30 
notes of the tenor against 79 notes of the duplum (or triplum), the ratio 
is almost 1 r}, so that, in the average, three notes of the duplum will be 
placed against one of the tenor. This result suggests that the single 
notes of the tenor are duplex longae, and that the rhythm of the texted 
parts is the third mode. The latter conjecture is supported by a consid- 
eration of the text whose accents naturally conform with this rhythm: 
Laus domino resonet omnium jubilo. As has been remarked by J. Beck 
{Die Melodien der Troubadours ', Strassburg, 1908), a frequent occurrence 
of trisyllables in Latin texts usually indicates the third mode. 

Once these results are obtained, the actual transcription presents no 
real problems. The transcription of the last ordo is given in the appen- 
dix, No. 39. An emendation is necessary for the close of the triplum. 

It should be observed, however, that many motets of the period under 
consideration present even greater difficulties than the above two ex- 
amples may lead the student to expect. These difficulties are generally 
due to one of the two following factors: either the inadequacy of the syl- 
labic notation for the clear indication of rhythmic modifications of the 
modal patterns; or else the obscure and corrupt writing of the tenors. 

The latter fault occurs particularly in the two chansonniers R and N. 
The motet Hut main — Hec dies of Facsimile 54 is an example in point, 
though one of relatively minor difficulty. The ligatures of the tenor fail 
to suggest any of the modal schemes. Under such circumstances, the 

1 In view of the fact that such 'conductus-motets,' as one may call them, occur in great number 
in the sources of Notre Dame (Ft, Ma, W 2 ) but are absent in the later MSS (Montpellier, Bamberg), 
they must be considered the earliest type of motets. See F. Ludwig in AHdM i, p. 236. 



Motet Notation 
Facsimile SS 



*75 



Jflltfc 



5 r 

3 r 




tu 



1 



|B 



:5i 







W 



? I 



,0 ^' 



s - 
_oPh 



276 Square Notation 

clue for the solution must be sought for in the upper part, the text of 

which suggests the first mode: 

Hui main au dolz mois de mai 
A consideration of the consonances readily shows that the notes of the 



tenor are plain L: 



However, a satisfactory rendition of the remaining portion of the motet 
is not possible without some emendations. In order to check the correct- 
ness of the tenor one will, of course, revert to its plainsong, which is the 
beginning of the gradual Hec dies (see Gr. Rom. p. 221). A comparison 
shows that the authentic' melody is correctly given in the ordines 1 — 4 
of our tenor, except for a final note a which is missing: 




The ordines 5 — 7 of the tenor of our motet repeat the plainsong, but 
less accurately. We find five repetitions of the tone c, as against the 
correct number four; furthermore, three tones, g-a-a, are missing at the 
end. Assuming, then, that the deviations of our MS are clerical errors, 
we arrive at a tenor which can be satisfactorily combined with the du- 
plum, as is shown in the appendix, No. 40. 

It is interesting to note that there exists another version of the same motet in the 
Codex Montpellier, no. 184 (f. 234' of the original), which is notated in the much more 
definite symbols of the pre-Franconian notation, that is, with a clear distinction of L and 
B in the duplum and with single L in the tenor. A comparison shows that the two dupla 
are practically identical. The tenor, however, represents an interesting 'secularization' of 
the liturgical melody, in a form reminiscent of and apparently derived from that of the 
mediaeval rondeau: A A A B A (A includes the first eight notes; B the following eight 
notes; the last two, or three, notes, g-a-[a], are missing). Actually, this secularized 
tenor combines much more easily with the duplum than the 'authentic' tenor of our 
motet 1 — a fact which may make one suspicious as to whether the latter may not, after 
all, be the result of a fundamental error on the part of a scribe. The only reason against 
this conjecture is the fact that the tenor of the Chansonnier Roy with its simple repetition 
of the plainsong follows a common practice of the early thirteenth century, whereas the 
more complicated rondeau-like structure of the tenor from the Codex Montpellier suggests 
a later date, and one which is probably too late for our source. At any rate, a comparison 

1 See the transcription in Y. Rokseth, Polyphonies du xiiie siec/e, hi, 8. 



Motet Notation 277 

of the two versions throws an interesting light upon the adaptability of the thirteenth cen- 
tury technique of composition. 

Still more irregular and obscure is the notation of the tenors in the 
Chansonnier Noailles. 1 Below is a reproduction of the upper part of 
page 191' of this manuscript (the first staff is from the bottom of p. 191): 



B 



fto-UutC jwteGntftoUuC'ic nxtmw ttiAtvtttoiici mm* 



* i g " ; 1 V 



^ ^T^ll 1 1 * , , , , I 

■h i 




1=1 



ala^ 1 * 1 *** 



<oouT snaficf tnu timf ^ouf cnii . 

The first piece contains few notational difficulties. Its chief interest 
lies in its formal structure, which shows a liturgical tenor of strictly 
binary form (the melody Quia concupivit rex appears twice, with a dif- 
ferent ending for the second time) combined with an asymmetrical mo- 
tetus written in the shortened form a A a b A B of the rondeau (A is 
the melody to the text 'C'est la jus par desous l'olive,' B that to the words 
'or charoles'). The notation of the tenor suggests the first mode, with 
extensio modi in the ordines containing only two notes (3, 10, 11, 13), and 
with the ordines 2 and 9 containing three perfections ("-meter). In or- 
der to make the upper part fit, an extra rest of one L must be inserted in 
the tenor between the first and the second statement of the melody (end 
of the seventh ordo). The rhythm of the upper voice is less clearly in- 

1 See Repertorium, p. 285-287 (N). 



278 



Square Notation 



dicated. Following is a transcription of the sections A and B of the 
rondeau which will enable the reader to piece the fragments of this inter- 
esting quodlibet together: 




The upper parts of the next pieces in our reproduction are merely short 
refrains, combined with liturgical tenors. Possibly they represent 
abridged versions of rondeaus of which only the sections A and B are 
notated. In spite of their brevity the rhythmic interpretation of these 
miniature pieces presents great difficulty. The following transcriptions 
are offered with due reservation: 



Renvoi-si-e-ment i vois a mo n a -mi, en-si doit a-ler a son a - mi. 



HODIE 








"*|^ n g m ^ 






mours a 


• — * 
- me-rai; 

») * 


nevous ma - ri - es mi 


e, te-nes 


vous en-si. 


1 r 













The proolematic character of these pieces clearly appears from a com- 
parison of the above transcriptions with those contained in F. Gennrich's 
philological publication, Rondeaux, Virelais und Ba/taden, vol. 11 (Got- 
tingen, 1927). 1 His rendition of Renvois iement is shown on page 279. 
Apparently, Gennrich's basis of interpretation is the declamation of the 
text, and in this respect his rendition is a model of correctness. How- 

1 See pp. 21, 22 of the publication. The rondeau C'est la jus is transcribed in vol. i, p. 21 of the 
same publication (Dresden, 1921). Another motet from Noailles is reproduced in HdN 1, 227. 
Wolf's transcription may be compared with that by Gennrich (vol. 1, p. 18). 



Motet Notation 



279 



Ren-voi-si-e-menti vois a mon a- mi, en-si doit on a-Ier a son a - mi. 



HODIE 

ever, one is entitled to question how strictly applicable to thirteenth cen- 
tury music modern principles of correct declamation may be. From the 
notational point of view as well as from a consideration of the conso- 
nances his renditions are certainly open to objections. 

As a final example, the motet Homo quo vigeas — El gaudebit from JV 2 
may be considered. Its beginning is found on Facsimile $$> the com- 
pletion on Facsimile 56. Although it follows immediately upon the 
motet Laus domino — Eius and is very similar to this in appearance, it 
presents quite a different problem. A comparatively simple question is 
that as to the mode of the tenor. A calculation of the type suggested 
previously is scarcely necessary in order to show that the fifth mode (lie 
of the tabulation p. 248) is correct (the tenor begins on staff 7 of the 
right-hand column of Facs. 56, with the notes f-g, and continues 
underneath on the eighth staff). The real problem of the piece lies in 
the coordination of the upper parts to the tenor. The student is strongly 
advised to try his hand on this, if only for the sake of the experience thus 
gained. Even the most persevering efforts, however, will result in fail- 
ure, judging from this writer's experience. 1 In fact, the problem would 
be hopeless were it not for the fact that there exists a related piece the 
rhythm of which is more clearly expressed in its notation, namely, the 
clausula from which the motet in question is derived. This clausula, a 
two- voiced setting of the liturgical tenor El gaudebit y has been studied 
previously (p. i$if). A glance at our reproduction shows the identity of 
its parts with the tenor and duplum of the motet. All we have to do is 
to underlay the text and to add the triplum in the same rhythm as the 
duplum. 2 

There are, of course, certain variants between the two dupla. Most of 
them need not be mentioned here, since they are rather obvious and in- 
consequential. Only towards the end of the piece does the duplum of 



1 1 am indebted to Mr Lincoln B. Spiess far his calling my attention to this interesting specimen. 

2 This is another example showing that modal notation is clearer than motet notation (see p. 274). 
If no clausula exists, one will have to resort more or less to experimentation, in which case the princi- 
ples outlined in Ludwig's Repertorium, p. 526°, will prove helpful. 



28o 



Square Notation 



the motet vary considerably from that of the clausula, owing to the in- 
troduction of two notes for one [(a) clausula; (b) motet]: 

(a) 




sinonfe-ce - ris damp-na-be- ris. Hac invi - a mi-li-tans 



The final passage of the motet, beginning with the words 'hac in via 
militans,' constitutes the proof previously alluded to (p. 254), that the 
corresponding passage of the duplum of the clausula is not in the hrst 
mode — strongly suggested by the notation — but in the fifth. 

The addition of the triplum of the motet, although without any diffi- 
culties from the notational point of view, raises a stylistic problem, on 
account of the rather strong dissonances which result. Combinations 
such as f-c'-e', b -f'-c', g-d'-a (the tones are named in the order tenor — 
duplum — triplum) occur repeatedly on the first beat of the measure. 
Theorists of the period accounted for such discords and admitted them 
as being composed of two consonant intervals. For instance, the e' of 
the first chord was considered legitimate because it formed a consonance 
with the c' of the duplum, though not with the f of the tenor. A closer 
study of the piece shows that the tenor and duplum, i.e., the original 
clausula, as well as the duplum and triplum, i.e., the conductus-like su- 
perstructure, each form a pair of strictly consonant voices, whereas the 
combination of all three parts produces the above-mentioned dissonant 
chords. 



Motet Notation 
Facsimile $6 



281 




!■ 



% 

I 

life ira 



3=r 



■Hisa 




i 



&3 






1 

1 



~a 




o 0+ 



PQ 



IV. PRE-FRANCONIAN NOTATION 

THE NOTATION of the thirteenth century, if compared with that 
of other periods of equal duration, exhibits a unique picture of great 
changes and rapid development. Every two or three decades new ideas 
of form and style appeared which necessitated the introduction of corre- 
sponding notational innovations. Thus the system of square notation 
was soon followed by another which we shall call pre-Franconian nota- 
tion. It may be considered as falling approximately between the years 
1225 and 1260. 

The transition from square notation to pre-Franconian notation may 
be briefly summarized in the statement that the number of notational 
signs is increased and, consequently, the ambiguity of the interpretation 
of the signs is lessened. The rhythmic modes remain the basis of music 
and of notation, but they are more freely used, more clearly expressed, 
and better distinguished from one another. In fact, it is not until this 
period that all the modes are used equally, whereas in the sources of 
square notation two modes prevail: the first mode in the upper parts and 
the fifth mode in the tenors. 

The following are the chief characteristics of the new system: 

1. Notational distinction between longa and brevis. 

2. Introduction of the semibrevis. 

3. Introduction of ligatures sine proprielale, sine perfectione and cum 
opposita proprietale. 

4. Change from the divisio modi to rests of different lengths. 

5. Establishment of the brevis as the musical beat. 

The first four points will be dealt with in the subsequent study of the 
sources of pre-Franconian notation. As regards the final point, the 
reader is referred to the general explanations given in the chapter on 
French Notation (p. 34 1 fF). Here it will suffice to say that, henceforth, 
a reduction in the ratio of one to eight will be used instead of the former 
reduction one to sixteen, so that the B becomes the quarter-note of the 
transcription. Properly speaking, this scale of reduction should be ap- 
plied only to those motets which are written in the 'tempus medium legit- 
imum' of Anon. IV, that is the motets in which groups of two to three 
smaller notes (semibreves) are used in the place of a B> while motets lack- 
ing these groups are in the older 'tempus minimum' and therefore should 

282 



Pre-Franconian Notation 



283 



be transcribed in the scale of reduction that has been used for the pieces 
of the previous period. However, such a procedure would bring about 
a rather undesirable discrepancy which it has been deemed better to 
avoid. The thirteenth century term for the duration of the B is tempus, 1 
a term which has remained associated with the B throughout the ensuing 
development of mensural notation, although changing its connotation 
from the temporal to the mensural (tempus perfectum y tempus imperjec- 
tum). 

The pre-Franconian notation — and, as a consequence, all the later 
systems — developed from the motet notation of the preceding period, a 
circumstance easily explained by the fact that of all the forms of this 
period only the motet survived. Whereas, apart from the special type 
of the primitive conductus-motet (see p. 274), the motets of the School 
of Notre Dame had been mostly in two voice-parts, now the three-voice 
motet becomes the normal type. Its parts show rhythmical as well as 
textual independence, a feature clearly distinguishing this motet from 
the three-voice conductus-motet in which the two upper parts have iden- 
tical rhythm and text. 

The increased number of independent parts as well as the increase in 
length of all the parts lead to new methods of allotting them on the page. 
The following sketches show the typical arrangements either on two op- 
posite pages, or else on one page: 

I II III 



1 Z 

-~3- 



1 z 

1 3 Z~~ 







1 1 1 


1 2 1 


1' 


2' 


I r l 


1 r 1 


1311 3' 


11 r 1 







1: triplum; 2: duplum (motetus); 3: tenor 

The advantage of these arrangements is that they make it possible for 
three singers to read their parts simultaneously from the same page. If a 
motet covers several pages the parts are always so written that the sing- 
ers arrive simultaneously at the end of their parts, immediately before 
the page is turned. The third of the above drawings illustrates the ar- 
rangement used with shorter pieces. Such a page may contain the end 



For instance, Joh. de Garlandia (CS 1, 97): 'Recta brevis est que unum tempus continet. 



284 Pre-Franconian Notation 

of a motet A (1,2, 3), a complete motet B (1', 2', 3'), and the beginning 
of another one, C (1", 2", 3"). 

Before turning to a study of the two main sources of pre-Franconian 
notation, the Codex Montpellier and the Codex Bamberg — both com- 
piled towards the end of the thirteenth century, an example from the MS 
Brit. Mus. Add. 30091 may be considered, a source which, although less 
well-known, is important because the date of the MS (ca. 1275?) ' s much 
closer to that of the compositions contained therein than is the case with 
the MSS Bamberg and Montpellier. In this source, the above-described 
arrangement of the parts, which makes it possible to use the manuscript 
for practical performance, is not yet observed. For instance, p. 1 of the 
MS contains, after a complete motet Maria — Nostrum, the beginning 
of the duplum of a motet Candida — Flos filius, while the rest of the 
duplum and the entire tenor follow on the reverse side of p. 1. 

Facsimile 57 shows these two pages (1 and i')- The most striking 
feature of the notation, if compared with that of the motets considered 
previously, is the clear indication of the rhythm of the upper part, by 
means of L and B. The advance thus achieved becomes particularly 
apparent by a comparison of the motet Candida — Flos filius with the mo- 
tet Quant revient — L autre jor — Flos filius from the Chansonnier Roy, 
(Facsimile 54; p. 273), the duplum and tenor of which are identical with 
the two parts of the piece reproduced on Facsimile 57. It will be recalled 
that the motet from Roy, in turn, comes from the three-part clausula 
Flos filius y reproduced on Facsimile 46 (p. 229). Thus, these examples 
show one and the same composition in three different stages of elabora- 
tion and of notation. 

A. The Codex Montpellier, fasc. II-VI. 

The Codex Montpellier (Montpellier, Faculte des Medecins H 796; 
abbreviated Mo) is the most extensive and most important source for the 
thirteenth century motet. It has been the object of repeated investiga- 
tion. E. Coussemaker, in his L Art harmonique aux xiie et xiiie siecles 
(Paris, 1865) was the first to call attention to its importance, including 
in that book reproductions and transcriptions of fifty pieces. This pub- 
lication was the basis of further studies by O. Koller ('Der Liederkodex 
von Montpellier,' VjMW, iv) and by F. Ludwig ('Studien uber die 
Geschichte der mehrstimmigen Musik im Mittelalter,' SIMG, v), who 
offered criticism of Coussemaker's explanations and transcriptions, as 
well as of Koller's theory regarding the dates of the various fascicles. 
Recently the entire codex has been published in facsimile and transcrip- 



The Codex Montpellier 
Facsimile 57 



285 




1 -a 




286 Pre-Franconian Notation 

tion, with a commentary, by Y. Rokseth under the title: Polyphonies du 
xiiie siecle, 4 vols. (Taris, 1936-39). 

The codex contains 345 compositions which are arranged in eight 
fascicles, according to types. Fascicle I contains organa and conductus 
from the Notre Dame period; II contains 17 four-voices motets; III con- 
tains 11 three-voice motets with Latin motetus and French triplum, as 
well as 4 two- voice Latin motets; IV contains 22 three- voice Latin 
motets; V contains 9 hockets and 104 three-voice motets which have, 
with few exceptions, French texts in both upper parts; VI contains 75 
two-voice French motets; VII contains 39 three-voice motets of various 
kinds; and VIII contains a conductus and 42 three-voice motets of vari- 
ous kinds. 

The first fascicle may be excluded from the following study since it 
contains organa written in modal notation (arrangement in score, liga- 
tures in the upper voices). The fascicles II to VI, which represent a 
unified whole, comprise the most extensive collection of motets of the 
middle of the thirteenth century; they are written in pre-Franconian 
notation throughout. The last two fascicles are evidently a later addi- 
tion, as may be seen from the following considerations: (1) the hand- 
writing is of a different, more decorative character; (2) the systematic 
arrangement to be found in the fascicles I to VI is not carried out; (3) 
Franconian notation is used exclusively, along with certain even later 
elements of notation, which are associated with Petrus de Cruce (see 
P-3i8ff). 

Our immediate concern is with the fascicles II to VI; first we shall 
treat the notation of the tenors, then that of the texted parts. 

Notation of the Tenors. The notation of the tenors (notatio sine 
litera) in Mo II -VI shows no fundamental advance over that in the 
earlier sources. The same combinations of ligatures and single notes 
occur, the groupings I and II of our previous survey (p. 2,48) still being 
by far the most frequent. The only difference to be noted lies in the 
clearer distinction in the writing of the single signs, for which three 
shapes are now available: ■ brevis (B), 1 longa (L), and "J duplex 
longa (D). The most frequent form is, of course, that which signifies 
theL. 

The following tabulation gives a survey of the most common types 
of tenor-writing. 1 The figures in the column to the right indicate the 
number of times each combination occurs in the fascicles II-VI. The 
tabulation takes note only of those instances in which the type in ques- 

J A complete tabulation of the tenors of Mo is given in Rokseth's publication, vl. iv. 





Symbol 


I. 


Ij| 


II. 


\n\3\ 


III. 


\J2 . . . 2\ 


IV. 


\22 ■ • ■ 3\ 


V. 


\i3 ■■■3\ 


VI. 


|//7| 


VII. 


III . . ./I 



The Codex Montpellier 287 

tion is continued strictly, or with minor deviations only, throughout 

the course of the piece. 

Example Number 

* 69 

mii*i niiii 59 

iarh-Ai 16 

HHJ-ai 2 

mil 10 

HT-11 11 

What rhythms are represented by these types? In the case of the 
types III to VII the situation is clear and unequivocal. Type III rep- 
resents the first mode, type IV the second, type V the third and type 
VI the fifth mode in the first ordo. Type VII belongs also to the fifth 
mode, yet includes ordines of various length. Types I and II offer more 
difficulty since they are used to represent various modes, as we already 
know from our study of square notation (p. 248). Of the 69 examples of 
type I we find: 

Type I: 

Mode Number 

(la) First: I J J |J £ | 15 (e.g., nos. 58, 101, 221, 226) 

(lb) Second: I J d I J £ £ | 17 (e.g., nos. 37, 59, 102, 220) 

(Ic) Fifth: I J. I J. I J. I _.| 37 (e.g., nos. 41, 57, 107, 227) 

Type II represents a similar situation as appears from the following 
survey: 

Type II: 

Mode Number 

(Ha) First: U-U*|JJ|J*| 22 (e.g., nos. 24, 

43, 141, 240) 

(lib) Second: I J- I J U\ J J I J U I 20 (e.g., nos. 64, 

94, 14^ 2 39) 

(He) Fifth: lJjJ.|J.|..|J.|J.|J.|..| 17 (e.g., nos. 23, 

42, I35» 2 40 



288 Pre-Franconian Notation 

The ambiguity of these two types raises the question of how one may 
arrive at a correct interpretation in a given case. Here a consideration 
of various other notational features will prove decisive. Frequently a 
clue is provided by that deviation of writing which arises from repeated 
tones (unison) and which, as in modal notation, necessitates the splitting 
of the ligatures. If, in such a case, a ternaria is replaced by a B fol- 
lowed by a binaria, the second mode is intended; if it is written ■'saZ, 
followed by a binaria, the first or fifth mode is clearly indicated: 

.3-IJJIJ | si a-UJ|J|or|J.|J.|J.| 
Other useful clues are derived from a consideration of the upper 
voices, regarding both length and rhythm. As a matter of fact, since 
the fifth mode produces exactly twice the number of measures as the 
first or the second mode, one can sometimes find out, by simply esti- 
mating the number of measures of an upper voice, whether the fifth 
mode or one of the two others comes into question. Frequently the 
rhythm of the upper voices provides the clue to that of the tenor. In 
fact, a rhythmic relationship often exists, particularly between the tenor 
and duplum. This relationship is explained and described by Anon. 
VII as 'convenientia modorum,' i.e., rhythmic conformity of the modes 
{CS i, 379). For instance, the first and fifth mode combine well to- 
gether, as do the second and third, or third and fifth: 

Mode 1 and 5 Mode 2 and 3 Mode 3 and 5 

IJ JIJ JIJ JIJ \\ IJJIJJ|JJIJ))| IJ.IJJIJ.IJJI 

IJ. u. U. U- 1 u. IJJU. 1 j J 1 ij.ij. ij.ij. 1 

The first and second, however, will never be found simultaneously in 
the same motet, nor will the first and the third. Therefore, if the second 
(or third) mode is indicated in one of the upper parts, the first mode is 
not likely to occur in the tenor. Another point which must be mentioned 
here is the use of the duplex longa (D) which appears in the example II 
of our table. One would naturally expect the shape of this note to be 
a reliable means of distinction between the fifth mode on the one hand 
and the first and second mode on the other, since only in the former 
case does the initial note actually have the value of a D. Unfortunately, 
this is not the case. The slightly lengthened form of the initial note is 
found in all three modes. This statement is true particularly for the 
first two fascicles; in the later fascicles one can more clearly detect the 
attempt of the scribe to differentiate between the first (or second) and 
the fifth mode by distinguishing between the L and the D. 



The Codex Montpellier 289 

Examples. The above explanations may be illustrated by a few ex- 
amples. Facsimile 58 1 contains a three-voice motet Ave beatissima — 
Ave Maria — Johanne, and the beginning of a three-voice motet Salve 
virgo — Ave lux — Neuma. The tenor Neuma (as much of it as is written 
on this page) consists of six ternariae and one binaria. In the first or 
second mode this would lead to 6 X 2 + 1 =13 measures (| each). 
In the fifth mode, however, there would be 6 X 4 + 2 = 26 measures 
of the same length. A superficial examination of the upper voices tells 
us at once that they are much longer than thirteen measures, since 
fifteen L alone appear in the triplum, to say nothing of the many B. 
Therefore the tenor must be in the fifth mode. 

To follow out a similar process in the case of the first motet of our 
facsimile, Johanne, may present more difficulty to the novice. How- 
ever, he may base his estimate on the fact that as a rule a single line 
of a triplum or duplum contains an average of eight perfections. Thus, 
we arrive at a total of approximately forty measures (4) for the entire 
piece. Since the tenor contains 22 groups of ternaria, only the first or 
the second mode are possible. 

In the present instance this method of reckoning is not really neces- 
sary, since the use of the B as an initial note of a split ligature plainly 
points to the second mode (see the first ordo, above the initial letter, 
as well as the ordines 9 and 15). 

A comparison of the two tenors shows that the division strokes of 
Neuma are somewhat longer than those of Johanne, probably corre- 
sponding to the longer rests of the fifth mode as compared to those of 
the second mode. Unfortunately, unlike the Bamberg Codex (see p. 302), 
this distinction, which would provide a simple clue to the determination 
of the mode, is not carried out consistently in the codex under con- 
sideration. 

Finally, the tenor of the motet Diex je — Amors qui ma — El super 
(Facsimile 59) may be studied. The first three L of the lowest line of 
the page belong to the preceding motet, together with the top lines on 
the left- and right-hand pages. The tenor of our motet begins with ten 
temaria-ord'mes; at the end the notation shows a greater variety of 
combinations. The appearance of two ordines each containing three L 
(beginning of the right-hand page) might suggest that the whole tenor 
is in the fifth mode. In such a case, however, it would be hard to ex- 
plain why these two ordines are not written in ligature, as are the others. 
Moreover, a quick calculation shows that the assumption in favor of 
the fifth mode for the whole tenor would produce more than 70 measures, 

1 The original pagination means: 4 x 20 + 14 = 94. 



290 



Pre-Franconian Notation 



a greater number than that of the upper parts (40-50 measures). One 
must assume therefore that the tenor is in the first mode (the second 
mode is excluded, cf. the unison writing in the ordines 3, 5, 8), with the 
rhythm changing twice to what seems to be the fifth mode, but what 
more correctly should be considered an extensio variety of the first mode. 
Following is a transcription of the second half of the tenor, beginning 
on p. 142 of the original: 




Besides the more or less regular tenors given in the above table, there 
exist, naturally, a great number which show a free rhythm in triple 
meter. Below is an example: 

In seculum (f. 231): 



JUp it fcmUiJ ' I ' 

This tenor is in the second mode, as appears from the unison-writing. 
As with the tenor El super, groups of three L are interspersed, causing 
extensio modi. It should be noted that, according to strict theory, the 
last of these single notes should be a B, as the divisio modi takes two 
tempora in the second mode. Rather than to reduce the L to a 5, we 
prefer to consider this tenor as an argument against too strict an interpre- 
tation of the divisio modi (see p. 299). Besides the short strokes the 
tenor contains several dashes which extend through the entire staff. 
This is the so-called fin is punc/orum which indicates a rest in the value 
of a perfect L (three tempora). Below is the transcription of the begin- 
ning and the end of the tenor: 




Duple Meter. A unique specimen is the tenor of the motet no. 164, 



The Codex Montpellier 
Facsimile 58 



291 




■M 



<L> ^ 

•^ On 

^ <* 

C/5 <U 

OJ tlO 



292 Pre-Franconian Notation 

Je ne puis — Flor de lis — Douce dame, which is notated entirely in B: 



t 



This tenor not only represents the sole example in the tenors under 
consideration of what seems to be the sixth mode, but — still more re- 
markable — it is the first example of binary rhythm or duple meter. In 
fact, the B are not to be arranged, as they should be in the sixth mode, 
in groups of three: |2JJJ|JJJ|J*| but in groups of two: \\ J JIJJUJI J'l , 
as the context of the upper voices clearly indicates. This piece is there- 
fore our first example of what was called later modus imperfectus. 

Compositions like this (we shall encounter several more in the Bamberg 
Codex) are indicative of an innovation in the musical thought of the 
thirteenth century, indeed of a real revolution, the magnitude of which 
we today can scarcely appreciate. There is an interesting remark in 
Magister Lambert's (Pseudo-Aristotle) treatise which not only refers to 
this innovation but also indicates the strength of the opposition it met 
(CS 1,271 a): 

Unde considerandum est, quando [longa] imperfecta fieri nequit nisi medi- 
ante brevi sequente, seu precedente, quoniam longa et brevis, et e converso, 
semper unam perfectionem faciunt. Unde si querat aliquis utrum possit 
fieri modus sive cantus naturalis de omnibus imperfectis sicut fit de omni- 
bus perfectis; responsio cum probatione, quod non, cum puras imperfectas 
nemo pronunciare possit. 

From this it appears that an imperfect longa can be executed only in con- 
nection with a following or preceding brevis, since a longa and a brevis (or a 
brevis and a longa) together always complete a perfection. Therefore, if 
someone were to ask whether a mode or a natural song can be formed 
by imperfect longae exclusively just in the same way as it can be formed 
by perfect longae, the approved answer is: no; since nobody cart sing a 
succession of pure imperfect longae. 

Indeed, to the mind brought up in the tradition of the early thirteenth 
century, music in duple meter must have appeared to be something 
quite obviously impossible, being based upon a rhythm which had 
'beginning and middle,' but no 'ending,' an 'imperfect' rhythm in the 
true meaning of the word. However, evolution did not stop because 
of such scholastic thought. Here was the first impulse of the movement 



The Codex Montpellier 
Facsimile 59 



293 




294 Pre-Franconian Notation 

which shattered the 'classical' system of the six modes and led to the 
teaching of the fourteenth and fifteenth centuries, which recognized only 
two modes — the modus perfectus and the modus imperfeclus (see p. 99). 
As a matter of fact, by the year 1300 the characteristic distinctions 
between the six modes had become so irrelevant that they all appeared 
essentially the same — that is, as subtypes of one single mode, in which 
the L was equal to three B, the modus perfectus. In addition to this 
the modus imperfectus appeared, first as the equal, but soon as the pre- 
dominant. 1 It is not without interest to notice the striking similarity 
of this development to the change from the system of the church modes 
to the later major and minor. Again in this case we find, although sev- 
eral centuries later, the same transition from many modes to two, from 
varied to limited tonal resources. 

Notation of the Upper Voices. The pre-Franconian notation of the 
upper voices [notalio cum litera, syllabic notation) shows a considerably 
greater advance over the previous system than does the notation of the 
tenors. Whereas in the syllabic notation of the conductus and of the 
early motets, the upper parts are written without any notational dis- 
tinction between longs and breves, we now find the rhythm clearly indi- 
cated by means of two different signs, the L with a tail, and the B 
without a tail. The evaluation of these signs is governed by the prin- 
ciples of modus perfectus, practically the same principles which are 
known to us from the consideration of tempus perfectum and prolatio 
perfecta in white notation. As a curiosity, we quote here the rhymed 
hexameters of M agister Lambert (CS 1, 270, 271): 

Ante vero longam, tria tempora longa fatetur 
Si brevis addatur, duo tempora longa meretur. 

Inter perfectas si bis brevis una locetur 
Temporis unius fit prima, secunda dupletur. 

Therefore: 

1. L before L is perfect 

1. L is imperfected by a following (or preceding) B 

3. If two B are found between two L, the second B is doubled. 

1 This change has been studied by A. Michalitschke in his Theorie des Modus, Regensburg, 
1923, p. 80 ff. Unfortunately, this little book is written in an almost unintelligible, over-ripe and 
artificial type of prose, and is overloaded with that 'weltanschauliche Vertiefung' and 'schicksalhafte 
Verkniipfung' typical of the German post-war literature. 



The Codex Montpellier 295 

Magister Lambert gives further rules for three, four, and five B be- 
tween two L. These may be illustrated by the following examples: 

y.y-UUJJUJ 1 ...- r IJJ|JJJ|J.| 

...... ...... T .....^U.|JJJUJU.| 

The little stroke which appears in the last two examples no longer 
indicates a rest {divisio modi), but serves to mark off perfections. It is 
supplanted later by the punctus divisionis. 

As regards the application of these rules to the sources under consid- 
eration, there are rather frequent violations of the first rule. One finds 
numerous cases in which the third mode is written as follows: ^" ■ ^"^ n . 
However, the correct manner of writing occurs too: 1""!""1 • 

Besides the L and B, the S appears as a new type of note in the manu- 
script under consideration. It never occurs, however, as an isolated 
note but always in groups of two or three which are equal in value to a 
B. The principle of replacing a B by a group of smaller values was 
called 'equipollentia' (equivalence). The appearance of the S in groups 
of two and of three raises the question as to the values to be assigned to 
them in modern transcription. From the modern standpoint the sim- 
plest solution would be to transcribe a group of two S as two eighth-notes 
(♦ * = /3), and a group of three S as triplets ( ♦♦♦ = JT3 ). As a matter 
of fact, this method has been adopted in some recent publications, e.g., 
in the transcriptions given by Rokseth. However, it seems very doubt- 
ful whether conflicting rhythms such as would result from this interpre- 
tation, are in conformity with the rather rigid concepts of mensuration 
in this period. 1 Barring this possibility there remains a choice of two 
interpretations, one of which is based on a ternary division of the B y the 
other on a binary: 





2S 


3s 


as ternary: 


P'r 


3 

Of 


as binary: 


u 


£U 



The fact that groups of two S are by far the more frequent (especially 
when one includes the instances in which they are indicated by ligatura 

1 Examples are not infrequent in which a group of two S and one of three £ appear simultane- 
ously in different voices, as, e.g., at the beginning of the motet Portare from Ba, Facsimile 60. 



296 Pre-Franconian Notation 

cum opposita proprietate) points to the binary interpretation as the most 
likely one. Moreover, the name semi (-brevis) indicates in itself that the 
B was originally divided into two equal halves. 1 If this view is accepted, 
Franco of Cologne's reiterated statement demanding the ternary divi- 
sion of the B (see p. 311) would represent, not a confirmation of a tradi- 
tional practice, but a deliberate deviation from it. This interpretation 
would certainly be in keeping with the fact that most of his rules are of a 
decidedly novel character, intended to establish a new practice. A final 
argument in favor of the binary division can be derived from the fact 
that, in the pre-Franconian sources, groups of three S are practically al- 
ways written in a conjunctura-\\ke formation: *«^ . Hence, our binary 
interpretation of such a group would be in accordance with the principle 
that in a conjunctura the last note is the longest of all. Naturally, all 
these arguments do not constitute a clear proof. Throughout the thir- 
teenth century, the evaluation of the S was a flexible and controversial 
matter, as may well be expected to be the case, considering their short- 
ness of duration. 2 

Ligatures. The ligatures which appear in the texted parts have the 
same function as in the conductus and early motets, that is, to introduce 
two or three notes in the place of one. However, their rhythmic mean- 
ing is more clearly indicated by the introduction of those varieties which 
are known as sine proprietate ', sine perfectione, and cum opposita proprie- 
tate (c.o.p.). As for the metrical value of these new types, it appears 
that we are in a transitional stage between the great ambiguity of square 
notation and the unequivocal exactitude of the Franconian system. It 
would be a futile task, we believe, to work out a set of rules for the vari- 
ous types of ligatures and conjuncturae used in the period. Instead, the 
following table may be given which will provide the clearest insight into 
the prevailing relations. It will be noticed that the value of most of 
these signs depends upon the value of the neighboring notes, i.e., whether 
the ligature in question stands in place of a perfect L (3 tempora), an im- 
perfect L (2 tempora) or a B (1 tempus): 

1 Both Franco (CS i, 136) and Anon, vn (CS 1, 381) explain semis as 'quod est dimidium' (that 
which is the half), and Dietricus writes: 'semibreve, quia duo talia cum tanta celeritate proferuntur 
sicut unum breve recte scriptum' (semibreve, because two of them are sung in the same speed as one 
ordinary breve). On the other hand, Magister Lambert (CS 1, 270) explains semis as meaning the 
same as imperfect: 'semis, sema, semum, quod est imperfectum.' This etymology, however, aside 
from being doubtful on philological grounds, certainly cannot be considered a satisfactory explana- 
tion of the word semibrevis since the idea of an imperfect brevis did not arise until half a century 
later, at the earliest. 

2 See p. 320 ff. 



The Codex Montpellier 



297 



Type 



Forms 



1 tp. 



Value 
2 tp. 



3 tp. 



3 
3 s 
°3 



r- s 


- 


J J 


JJ(JJ) 


h ' 


- 


J J 


- 


"4 J 


- 


- 


JJ 


^ Lf 


J^ 


- 


- 


(V ^ 


- 


jj.j 


JJJ(J^J) 


N /Af 


- 


ji j 


... 


; 19 ^< 


- 


j? j 


- 




- 


(J3-T3) 


J^ JJ 
JJ^J 



In this table the following abbreviations are used for a short and simple designation of 
the ligatures: 

2, j: lig. cum proprietate and cum perjectione 
2 s , 3 s : lig. cum proprietate and sine perjectione 
s 2, s j: lig. sine proprietate and cum perjectione 
°2 y °j: lig. cum opposita proprietate 

From this survey it will be seen that the various forms of binaria liga- 
tures are already quite clearly differentiated from one another, while no 
such distinction is to be found with the ternaria or quaternaria forms. 
The peculiar form of the s 2 is worthy of note. It appears only in the 
Montpellier Codex and was later discarded (see the Franconian form on 
p. 313; for a similar form in white notation, see p. 93). The forms •♦♦ 
and ♦♦♦ are easily confused, since often the square notes are not clearly 
written. Furthermore the following frequent form, H\ # , must be dis- 
tinguished from that of a descending quaternaria; it represents the con- 



298 Pre-Franconian Notation 

nection of a L with a descending ternaria and has the following value: 
U-|J3.J|(cf. Mo, no. 119, p. 163/4). 

Plica. The plica also undergoes a remarkable change of form and 
meaning. P/z'oz-ligatures, so common in square notation, now occur in- 
frequently. Instead, single plica notes appear in great number and con- 
stitute an important element in notation up to the time of the Ars Nova. 
By the theorists they were considered an integral part of the system and 
were grouped at the very beginning of the explanations together with the 
simple forms. Thus Joh. de Garlandia says (CS 1, 177b): 

Longarum triplex est modus: quia quedam est longa recta, quedam duplex longa, que- 
dam plica longa. . . Similiter brevium triplex est modus. Quedam dicitur recta hrevis, 
quedam semibrevis, quedam plica brevis. 

There are three kinds of longa: the normal longa, the duplex longa, and the plica longa. 
In the same way, there are three kinds of brevis: the normal brevis, the semibrevis, and the 
plica brevis. 

As may be seen from these remarks, one must distinguish between two 
kinds of plica notes, the plica longa and the plica brevis. The forms of 
the plica longa have a short stroke on the left and a long stroke on the 
right side; in the ascending form the stroke on the left side is sometimes 
missing. The forms of the plica brevis have the longer stroke on the left, 
or else the strokes are practically of equal length: 

Descending Ascending 

Plica longa m j j 

Plica brevis P H L U 

The rules of Magister Lambert previously mentioned (p. 227) are valid 
for the measuring of the plica longa. This is therefore to be transcribed 
either as 4j or as «J , according to whether it stands for a longa per- 
fecta or a longa imperfecta. Nothing is said by that theorist regarding 
the value of the plica brevis, i.e., about the measuring of its principal and 
auxiliary note. According to our above explanations of the semibreves, 
the most natural interpretation would be as two equal (eighth) notes. 
The plica brevis, then, differs from two cV written out or from an s 2 only 
in its peculiar mode of performance, which Magister Lambert describes 
as 'compositio epiglottis cum repercussione gutturis.' 

Examples. We shall now consider a few examples in the study of which 
further details will come to light. The first example is the motet Salve 
virgo — Ave lux — Neuma, the tenor of which we have already considered 



The Codex Montpellier 299 

(Facsimile 58). The third mode is easily recognizable in the two upper 
voices. Occasionally the related second mode enters (e.g., triplum, first 
line, 'sola christi'). Whether one should interpret the various ternartae 
as three equal quarter-notes or as two eighths followed by a half-note is 
difficult to decide. Since the latter version would fit the iambic rhythm 
of the third and the second mode somewhat better we shall choose it in 
this instance. The long strokes indicate rests of the value of a perfect 
L. At the beginning of the second line of the duplum a short stroke ap- 
pears which represents a B-rest. Immediately following that there is an 
even smaller stroke which is not a rest but the punctus divisionis in its 
older form. It prevents the preceding L from becoming imperfect. The 
beginning of the motet is transcribed in the appendix, No. 41. 

The other piece of the same facsimile may serve as the second example. 
We have already seen that the second mode prevails in the tenor (p. 289). 
Therefore, one may assume that iambic rhythm appears also in the upper 
voices. This is especially clear in the triplum: 




The short stroke after the qualernaria will have to be interpreted as an 
eighth rest, as indicated above. In the remainder of the triplum the fol- 
lowing details may be noticed: the two binariae at the beginning of the 
second line are each B B, since they and another B complete a perfection; 
the note above gau-' is a plica brevis, as is also that above 'ha(bitacu- 
lum)'; two syllables later appears the short conjunct ura *♦♦ , which is 
not to be confused with the form "% at the end of this ordo; in the last 
line one finds again the 2 s = B B, as well as various forms of ternaria, all 
signifying B B B. It is noteworthy that the final note of the ordines is 
nearly always written as a L (with a slightly shorter stroke than a L 
appearing within an ordo), although the second mode should properly 
end with a B. Apparently this final tone is meant to be held somewhat 
longer than a strict correspondence to the modal rhythm would demand. 
The same type of a L appears also in the fifth ordo of the tenor. Whether 
one should transcribe this note as IcUl or as |JH| is difficult to say. 
A compromise would be IJ-^I; this, however, is perhaps too fastidious. 
We shall choose the version with the half-note in order to follow the orig- 
inal as closely as possible. 1 

1 Rokseth's publication holds to the strict modal interpretation, which also has its justification. 
In any case, the performance of motets in the second mode should avoid that cut-up rendition which 
is suggested by the use of two quarter-note rests in modern transcription. 



3°° 



Pre-Franconian Notation 



The duplum of this motet begins with a. plica tonga perfecta 'cum reper- 
cussione' (see p. 238). As regards the B above < ma(ria),' there may at 
first be some doubt as to whether it makes a perfection with the preced- 
ing or the following conjunctura ternaria. The context of the voices leads 
one to a decision in favor of the latter. 

In the fourth line the relationship of the voices shows that the binaria 
on 'ex(ora)' is perfect (B — L). As a result the ternaria on '(exor)a' 
which follows immediately is rendered imperfect by the preceding B. 

The close of the motet displays a peculiarity which may be seen in 
numerous compositions of the codex — namely, a sort of ritardando which 
is fully written out in notes. Following is a transcription of the last ordo 
(the tenor begins with the last note of the third from last ternaria): 




(Note: We have interpreted the last ternaria of the fourth line as "3.) 

It appears that the triplum is one note too long as compared with the 
other voices. Apparently the motetus and tenor are supposed to follow 
the triplum freely. In the tenor this is indicated by the use of a some- 
what lengthened note in the middle of the last ligature. Naturally, a 
certain liberty must be admitted in the interpretation and transcription 
of such irregularities. We suggest using a 4-measure for all the parts. 1 
The transcription of the beginning is given in the appendix, No. 42. 

The motet of Facsimile 59 is a more difficult example. We have al- 
ready considered the tenor which is in the first mode, with groups of per- 
fect L interspersed at the end (p. 289 f). In transcribing the upper voices 
one will do well to begin with the duplum (right-hand page), the rhythm 
of which is clearer. 

The ternaria at the very beginning, on 'qui,' is to be interpreted as °J, 
since otherwise its value would be too great to complete a perfection. 



1 In Rokseth's edition the transcription of these final cadenzas is always carried out strictly in 
4-time and is marked 'ritardando.' This seems to us to leave a great deal too much freedom to the 
players and singers of today. One can imagine what performers who do not know the original 
notation might do with such a ritardando. 



The Codex Montpellier 

The first note of the next ordo, on 'de,' is a plica longa imperfecta. 
lowing is the beginning of the motetus in transcription: 




301 
Fol- 



In front of the last note of the first line there appears a flat (B-flat) 
which is repeated at the beginning of the next line. The fifth character 
of the third line is a plica longa {imperfecta) , the last character of the 
same line is a plica brevis. The ordo which begins in the middle of the 
fifth staff ends exceptionally with a B instead of a L. Toward the end 
of this staff is another ternaria meaning °j. The close of the motetus is 
found at the end of the bottom line. 

Let us turn now to the transcription of the triplum, the beginning of 
which is as follows: 




The last note of the first line is an ascending plica longa, which is im- 
perfected by the first B of the second staff. The quaternaria on 're(dout)' 

must be reduced to two beats: 

The quaternaria in the third staff (on '-mant'), on the other hand, con- 
tains three beats; as an exception, however, it begins with an up-beat: 
J"3 I J J . The last note of the fifth line is a poorly written plica longa — not 
a plica brevis. The ternaria at the beginning of the next staff, on 'es- 
(longuant),' is again °j. At the close is another written-out ritardando 
which again is best transcribed in \ time: 




In the appendix, No. 43, the transcription of the middle section is given 
(beginning with the third staff of the triplum; with 'li regars' in the 
duplum; and with the eighth ternaria in the tenor). It contains some 
bold appoggiaturas. 



3<D2 Pre-Franconian Notation 

B. The Codex Bamberg 

The Codex Bamberg (Bamberg, Ed. iv. 6, abbreviated Ba) contains 
ioo motets in its main section; with the exception of no. 92 (four voices 
with two tenors) all are for three voices. An appendix, written in the 
same hand, contains three additional motet-like pieces and a few com- 
positions without text (In seculum longum, In seculum viellatoris, etc.) 
notated in score in the older manner. 

The arrangement of the voices is that indicated by the first sketch 
on p. 283, i.e., with all the parts written on the same page. Three motets 
(nos. 52, $3, 54, pp. 31 '-34) are arranged in a peculiar manner, namely, 
in three parallel columns of equal width on one page. This arrange- 
ment is explained by the fact that in these pieces the tenor also bears a 
text. Therefore all the voices require approximately the same space. 

The notation of Ba is, in principle, the same as that of Mo ii-vi. How- 
ever, considerable progress in the direction of clarity and exactness is 
evidenced in various particulars. Owing to this progress the pieces of 
Ba are far easier to understand and to transcribe than those treated in 
the previous chapters. Perhaps the most important innovation consists 
in the fixing of exact values for the divisio modi or, as it may hereafter be 
called, for the rest. Indeed, this sign is no longer a stroke of indefinite 
length, drawn carelessly through the staff, but is written very accurately 
and appears in four different lengths, namely: 



i tempus (S) 1 tempus (B) 1 tempora (L imp.) 3 tempora (L perf.) 
Example (In seculum breve, Ba, p. 64) : 



This manner of writing the rests is in keeping with the teaching of 
Magister Lambert (CS 1, 278), while Joh. de Garlandia, although prob- 
ably somewhat earlier in point of time, already uses the Franconian sys- 
tem of rests in which the 5-rest covers only one space, the imperfect L- 
rest two, and the perfect L-rest three (CS 1, 104a). It may be noted 
that the notation of Ba corresponds in almost all details (especially in 
regard to ligatures) to the system described in the little-known but very 
important treatise by Dietricus. 1 

1 Dietricus' presentation is distinguished by unusual clarity and conciseness. Cf. H. Mueller, 
Eine Abhandlung iiber Mensuralmusik in der Karhruher Handschrijt St. Peter pergamen. 29a (Leip- 
zig, 1886). 



The Codex Bamberg 



303 




Notation of the Tenors. Even though the tenors of Ba employ the 
same ligatures and combinations as Mo ii-vi, the rhythmic relations are 
much easier to discover, since the rests make clear at once the prevailing 
mode. Indeed, the second of the above rests (1 tempus) indicates the 
first mode, the third type (2 tempora) the second mode, and the fourth 
type (3 tempora) the third or fifth. Three examples may serve to illus- 
trate: 

1. Victime, p. 46 1 

2. Pro patribus, p. 56 

3. Brumans est mors, p. 

The first example is L B L / . . . , the second B L B / . . . , the third 
LB BL I . . . . 

A confusion of the fifth mode with one of the others is all the less likely 
since the fifth mode is regularly written entirely in L, i.e., without liga- 
tures. The second mode is distinguished from the others not only by 
the use of the 2-tempora rest, but also by the persistent use of s j-ligatures, 
to denote B LB (see the tenor Pro patribus). The tenor Optatur (p. 57') 
reproduced below shows the use of s 2 in the meaning of L B (the reverse 
of 2) as well as that of j s in the meaning of B B B. It may be noticed 
that in Ba the shape of the s 2 is that of the Franconian system (and of 
all the ensuing periods), whereas in Mo a peculiar form is used (p. 297). 
At the beginning of the third ordo of the example the form 2 s is used 
in the meaning of B B. 




It does not seem necessary to treat the ligatures of Ba systematically, 
since on the one hand their meaning becomes easily clear from the con- 
text, and on the other the principles involved give way very shortly to 
the Franconian system. 

As a curiosity we mention two tenors which are written in modus im- 
perfectus, namely Proh dolor (p. 19 , no. 35) and Aptatur (p. 54', no. 86). 



1 The page references are to the facsimile volume (vol. i) of P. Aubry's Cent motets du xiiie siec/e; 
see the survey of source material, p. 201 ff. 



304 Pre-Franconian Notation 

Proh dolor 



Notation of the Upper Voices. The notatio cum litera of Ba scarcely 
differs from that of Mo ii-vi. However, the clearer writing does much 
to make the transcription easier; and even more does the fact that 
in Ba any given staff of the triplum is always composed of the same 
number of bars and beats as the adjoining, i.e., corresponding staff of the 
motetus. This means that the initial as well as the final notes of two 
such staves sound simultaneously. Since these staves are rather short, a 
great number of points of coincidence are provided by the observation of 
this fact. 

Single semibreves, that is, those which are sung to separate syllables, 
occur, as in Mo, only in groups of two. Groups of three S occur also, but 
these are always sung to one syllable and therefore are written in the 
form of a conjunclura. As has been explained previously (p. 296), this 
usage supports our theory that in pre-Franconian notation the B is 
binary, not ternary. Therefore: ♦♦ = J^ ; s^-J32 • 

The writing of the descending ternaria as a conjunctura, "* # , which 
occurs so frequently in Mo ii-vi, is not to be found in Ba. In its place 
one finds frequently the form *♦. (Facs. 60, right column, beginning of 
line 5), which always means °J:JHJ . This notational variant is of 
interest since it evidences the tendency towards identifying the diamond 
shaped characters of the conjuncturae with the S, a significance which, 
as we know, they did not have originally. It should be noted that the 
symbol in question represents exactly twice the value of ♦♦♦ = J^ • 

Facsimile 60 shows a motet Mou[l]t meju grief — Robins m aimme — Por- 
tare. In spite of its apparent plainsong derivation, the tenor has the 
structure of a secular song. It consists of two short melodies, A (from c' 
to f) and B (from a to c') which are repeated according to the scheme: 
A B A' A B A B (A' denotes the first half of A). This scheme is an in- 
complete variant of the form of the thirteenth-century rondeau: A B 
a A a b A B. Tenors 'ad modum rondelli' are not infrequent in the 
sources of the late thirteenth century. 1 A fourteenth century example 
is G. de Machaut's motet Trop plus — Biaute paree — Je ne suis, which is 
reproduced in SchT, p. 23. Here, the tenor consists of two short melo- 
dies A, ('Je — amie'), and B, ('mais — amis'), which are to be repeated ac- 
cording to the full scheme of the rondeau. 

1 See the reference to such a motet from Mo, p. 276. 



The Codex Bamberg 
Facsimile 60 



305 




*-*+■ 



W'tucgncruaquynrfaT 



ft ' ' ' S J 

jjfiuumctx u tote mi dcv ifif gtu 



o^= 






tid* vcrmcmccc ami* iwflr 








MS Bamberg, Bibliothek, Ed IF 6 (13th century) 
Page 52' 



306 Pre-Franconian Notation 

C. The Codices Torino and Huelgas 

The Torino Codex (Torino, Bibl. Reale Var. N. 42), which has been 
little investigated, shows a striking resemblance to Ba in its notational 
details as well as in its graphological appearance. The most important 
difference exhibited by our Facsimile 61 is the Franconian writing of the 
rests. Evidently, the rests covering two spaces equal two B, as against 
one in the Bamberg Codex. The transcription presents no difficulties. 

The Codex Huelgas, which has recently been published in full by H. 
Angles (El Codex musical de las Huelgas) contains a very motley reper- 
toire, including monophonic chants as well as various types of polyphonic 
music among which are the earliest known settings of the ordinary of the 
mass (two- voiced Kyries> etc. in conductus style). The notation, too, 
is anything but uniform and suggests a scribe who was not too well in- 
formed in this matter. It is scarcely worthwhile to point out the many 
peculiarities of notation to be found here. Perhaps the most interesting 
notational detail is the writing of the ligatures of the tenors. The forms 
used here show the attempt to clarify the meaning of the ligatures, and 
may be regarded as indicative of a transitional stage between the purely 
'modal' forms of pre-Franconian notation and those introduced by 
Franco. The following reproduction, showing the beginning of one and 
the same tenor Alleluia from (a) Bamberg (p. 59') and (b) Huelgas (p. 
106) illustrates this point: 



(a) 



^iTT^ff »3ig8 



In Franco's system, the dashes at the end of the descending ligatures 
would have to be omitted. 

A comparison between Huelgas and Bamberg (or Montpellier) also 
reveals interesting examples of 'transmutatio,' i.e., rewriting of motet in 
a different mode (see p. 246, footnote). For instance, the motet In omni 
Jratre tuo — ^ tenor), which is notated in Huelgas (p. 96/96') in the third 
mode, occurs in Bamberg (p. 27 ff, Moul me grief — In omni fratre — In 
seculum) in the shortened rhythm of the sixth mode, i.e., with jL B B Lj 
replaced by IB B B B/. 

Finally, brief mention may be made of the semibreves caudatae which 
occur on several pages of the MS. They are, without doubt, not a fea- 
ture of the original writing but represent the attempt made by a later 
hand to remodel the thirteenth century notation according to the prin- 



The Codices Torino and Huelgas 
Facsimile 6i 



307 



\V 



V#i« 



i^ — L " - | i - g . ~ zz 



-en&'opBlatf 



1 : jZPEi 

IZt-tit 



ntctagattt toutetna 



I 



^ 






g£^ 



T 



EEJ^J Sg 



quat-neiuusttrnteirfijlas 






4mittJ at uaiurt&crr 



! cti 



ncftula* y 



ttuelSnta 



UCtJjl&li 



S=? 



te 



amftomc temouife 



pitta Xcgtt&nfc enfit gUut 



tiaialtiajpal axarabrfiT 
t~: — 



J pot mate pas ne 



! H : 



M^i^^p 



MS Torino, Biblioteca Reale mss. varii 42 (13th century) 
Page 40 



308 Pre-Franconian Notation 

ciples of the early fourteenth century. The following reproduction (from 



p. 1 06') serves as an illustration: 1 — %- 



*♦ 



E 



For a more detailed study of the MS the reader is referred to the above- 
mentioned publication which also contains numerous transcriptions from 
W x and Fl. It must be mentioned, however, that Angles' versions are 
not always convincing. Perhaps the most striking example is his ren- 
dering of an Et in terra pax (Facsimile 62), in which the clear rhythmic 
meaning of the notational characters is completely disregarded. Here 
follows the beginning of Angles' version (a) together with what undoubt- 
edly must be considered the correct transcription (b) : 

(a) 




Another point is Angles' inconsistency in transcribing pieces written 
in the third mode {/L B B L/). Whereas the motets, p. 113, 114, 114/, 
are transcribed in modal meter (L = 3 B)> duple meter {modus imper- 
fectus, L = 1 B) is used for the above-mentioned motet on p. 96/96' as 
well as for another one on p. 87. Possibly, a reason for this procedure is 
given in the introductory volume (I) which, unfortunately, is written in 
the Catalan language. 

1 For a similar case of greater interest, see the explanations on the Roman de Fauvel, p. 325 ff. 



The Codices Torino and Huelgas 
Facsimile 62 



309 



— — — 1 — 




£ 



■J"% ,■, ! .»' 



^ 



=3 



V\jt m terra "pa? tpmwwm* "We \ w>Wi 




Codex Huelgas 

Monastery Las Huelgas,near Burgos (13th century) 

Page 4' 



V. FRANCONIAN NOTATION 

A. The Franconian System 

AROUND 1260 there occur those decisive changes in notation which 
by all subsequent writers are coupled with the name of Franco. 
Apparently two men, both bearing this name, lived at the same time and 
accomplished much the same thing — a Franco of Paris and a Franco of 
Cologne. They are mentioned in the important historical account of 
Anon. IV (CS 1, 342a) as 'Franco primus et alter Magister Franco de 
Colonia.' The title 'primus' as applied to the Parisian Franco may best 
be construed as meaning earlier, elder. It cannot be accepted as an esti- 
mate of value, since by far the most important of the various Franconian 
treatises — the Ars canlus mensurabilis (CS j, 117) was written by Franco 
of Cologne. 

Since the principles evolved during this period form the basis of nota- 
tion until the sixteenth century, and in some respects up to our own time, 
they will be given here rather completely but in as concise a form as pos- 
sible. In general it may be said that Franco introduced no new signs of 
notation. For that reason his achievement was all the greater: the 
building, out of the equivocal symbols inherited from a previous age, of 
a system which for the first time was free of ambiguity. 

Single notes. Franco enumerates the following 'figurae simplices' 
(tp = iempus) : 

Longa Brevis Semibrevis 



Duplex perfecta imperfecta recta altera major minor 

1 1 1 " " ♦ ♦ 

6 tp 3 tp 2 tp 1 tp 1 tp \tp \tp 

The rules ('ordinatio figurarum'), which concern the various combina- 
tions of L and B i are virtually those which we already know from the 
treatise of Magister Lambert (p. 294). Briefly summarized they run as 
follows : 

A L is perfect if followed by another L, or by two or three B. If it is 
followed by one or by more than three B, then the first B imperfects the 
L and the remainder are grouped together in groups of three (perfections). 
If in such a case two B are left over, alteration of the second occurs; if 

310 



The Franconian System 3 1 1 

only one remains, it imperfects the following L. If an exceptional 
grouping is desired, the 'signum perfectionis' in the form of a short stroke 
('tractulus') is used. 

Of the greatest importance is the principle, expressed several times, 
that the same rules govern the relation between the B and the S: 'et nota 
hoc idem esse judicium de brevibus et semibrevibus' (note that the same 
principles are valid for the B and the S); or 'de semibrevibus autem et 
brevibus idem est judicium in regulis prius dictis' (the rules just given 
apply equally to the B and the S; see CS 1, 119 and 122). 

Here the S is recognized for the first time as an independent note value 
which theoretically may occur in any number and combination. More- 
over, the relationship between the B and the S is governed by the same 
principle of ternary mensuration which forms the basis of the relation- 
ship between the L and the B. In fourteenth century terminology, in 
addition to modus perfectus there now exists tempus perfeclum. It will 
be noticed that this principle differs from that prevailing in pre-Fran- 
conian notation where the mensuration of the B is binary. 

The rests of Franco's system are those known to us from white nota- 
tion: the Z?-rest covers one space, the L-rest two or three spaces, accord- 
ing to whether it is imperfect or perfect. His writing and evaluation of 
the plicas show no difference from the system that has been previously 
explained (p. 298). 

It must be noted, however, that the practical sources of the late thir- 
teenth century are much more conservative with regard to the use of 
semibreves than one might expect on the basis of Franco's statement; 
nor is it likely that Franco himself was aiming at a complete analogy be- 
tween the use of L and B on the one hand, and between the B and S on 
the other, an achievement which did not take place until the Ars Nova 
(Philippe de Vitry). There are at least two important differences be- 
tween the use of B and that of S. The first difference is the fact that 
a single S never occurs, in other words, the B is never imperfected by a pre- 
ceding or following S. The second difference consists in the fact that 
groups of more than three S, which appear occasionally in the later 
motets of the period, call for a particular interpretation different from 
that to be applied to groups of B. According to Franco they are to be 
arranged in pairs with alteration or, if they are uneven in number, in 
pairs with a final group of three, for instance: 1 

■♦««».-! ij-jvaju. • ♦♦♦.. -gu.jg.rji.mj.jj 

1 Pieces of the Franconian period are usually transcribed in 4-meter with eighth-note triplets. 
Since, however, the ternary measurement of the B (quarter-note) is an integral feature of the Fran- 
conian notation, a rendering in g-meter ([III, 3]) is at least equally appropriate. 



312 Franconian Notation 

Examples of these Franconian 'chains of S' (as one might call them in 
contrast to the later 'groups of S' of Petrus de Cruce) are not very fre- 
quent in practical sources. We may well understand that they attained 
little practical importance since they offered no possibility for rhythmical 
variety within a series of S. Apparently another device had to be in- 
troduced in order to allow for combinations such as B SSS SS B or B SS 
SSS'SS B. This advance in the notation of the smaller values was made 
by a younger contemporary of Franco, namely, Petrus de Cruce. It 
will be discussed later (see p. 318 ff). 

Ligatures. Franco's principles in the writing and the evaluation of 
ligatures are virtually the same as those which we already know from 
white notation. It may not be superfluous, however, to summarize 
them once more with special emphasis on the historical point of view. 

The fundamental dictum is contained in the following sentence (CS 1, 
124): 

Item ligaturarum alia cum proprietate, alia sine, alia cum opposita pro- 
prietate. Et hoc est a parte principii ligature; a parte autem finis, alia cum 
perfectione, alia sine. Et nota istas differentias essentiales esse et spe- 
cificas istis ligaturis. 

Furthermore there are ligatures cum proprietate, sine proprietate and cum 
opposita proprietate. These characteristics refer to the initial note of the 
ligature. As for the final note, a ligature may be cum perfectione or sine 
perfectione. These differences are real and specific properties of the 
ligatures. 

This sentence contains two new thoughts of great importance: first, 
that proprietas has to do exclusively with the initialis, and perfectio ex- 
clusively with the finalis of a ligature; second, that these features are 
essential and characteristic, in other words, that they fully and unam- 
biguously determine the value of the ligature which no longer depends 
upon the context (i.e., on the mode or the value of the neighbouring 
notes). The practical realization of these principles was achieved by the 
establishment of the following rules: 

The initialis is B in a lig. cum propr.; L in a lig. sine propr. 

The finalis is L in a lig. cum perf.; B in a lig. sine petf. 

The first two notes are S each in a lig. cum opp. propr. 
These rules are supplemented by the following statement: 

A parte autem medii ligaturarum nulla essentialis differentia invenitur. 
. . . Per quod patet, positionem illorum esse falsam qui ponunt in ternaria 
aliqua mediam esse longam, in omnibus autem aliis fore brevem. 

As for the middle notes of a ligature, there is no difference between them. 



The Ligatures 



3*3 



. . . Therefore it is obvious that they commit an error who maintain that 
in a certain ternaria the middle note is an L, but in all the others a B. 

Indeed, according to Franco all middle notes are always B. 

The indication in writing of the various types of proprietas and perfec- 
tio is governed by principles explained below by means of two tables, the 
second of which also includes some modifications to be found in sources 
of the fourteenth century: 



WRITTEN 

ascending descending 



VALUE 



initialis without 

stroke 
initialis with 

stroke 
finalis turned 

toward left 
finalis turned 

toward right 
opp. propr: initialis with 

upward stroke 



cum propr; 
sine propr: 
cum perf: 
sine perf: 



initialis with initialis B 

stroke • 
initialis without initialis L 

stroke 
finalis square 



finalis oblique 

initialis with 
upward stroke 



finalis L 

finalis B 

first and sec- 
ond notes S 



BINARI A 



TERNARIA 



type 


/ 


\ 


2 


a -ji (W 


> 


*2 


■(&) ■«» B(b) 


1 


2* 


J 


h 


e 2 B 


j(a) ■ (a) 


s 


°2 


if V 


kk 






- 



value 
B L 
LL 
BB 
LB 
S S 



type 


/ 


\ 


s\ 


N/ 


3 


; X' 


rv 


A 


iwr 


B 3 


■(d) m& Kb) 


\ 




w 


3 s 


S 


% 


J* 


r^ 


S 3 S 


J0) J(« 


\ 


AX 


c 


°3 


; u* 


< 


^ 


taur 


°3 S 


y 


< 


L* 


^ 



value 

BBL 

LBL 

BBB 

LB B 

SSL 

S SB 



Remarks: 

(a) Franco mentions two manners of indicating sine proprietate for an ascending 
ligature, that is, with the dash to the left or to the right side of the initial note. The 
second, which he calls 'magis proprium,' was the only one to survive after 1300. 



14 



Fran con tan Notation 



(b) In earlier times this form expressed the binaria (ternaria) plicata (see p. 236), and 
Franco mentions it as still having this meaning (CS 1, 125b). However, as the plica 
ligatures continued more and more to lose their former importance, this character was 
adopted in place of the older form of the ascending ligature cum perfectione, probably 
because this is awkward to write when the lines of the staff are close together. The 
downward stroke at the end of a ligature thus changes its meaning from that of a plica- 
stroke to the sign of a tonga. The new form appears (beside the older form) as early as 
the Codex Huelgas. 

A comparison of this table with that of the pre-Franconian ligatures, 
given on p. 297, shows that the system has been broadened by the intro- 
duction of ligatures sine proprietate and sine perfectione (*2*, s j s ) 3 as well 
as of ligatures cum opposita proprietate and sine perfectione ("J s ). 

The progress made by the Franconian system of ligatures over that of 
the pre-Franconian period is apparent from a comparison of Franco's 
teaching with that of Dietricus which, as we have said, corresponds to 
the notation of the Bamberg codex. According to Dietricus, the ternaria 
cum proprietate is L B L (first mode), the ternaria sine proprietate is B L B 
(second mode). The transition from this purely modal interpretation to 
that of Franco may be glimpsed in Dietricus' remark that under certain 
circumstances the ternaria cum proprietate is B B L, namely when a L 
precedes (third mode). Franco's contribution consisted in making this 
last interpretation the exclusive one. As a result, all ligatures cum pro- 
prietate (binaria and ternaria) begin with a B. Therefore Franco could 
make the decisive statement that the quality cum proprietate did not 
concern the entire ligature but only its initialis. And herein lies the 
chief difference between his system and all the earlier ones. Once this 
step was taken, it was a simple matter to relegate the quality cum per- 
fectione to the last note, which, of course, had to have the value of a L in 
order to complete a perfectio with the initial B (in the binaria). Having 
assigned proprieta s to the initialis and perfectio to thtfna/is, all the pos- 
sibilities of differentiation were exhausted. The middle notes, therefore, 
had to have a value independent of these distinctions: 'A parte autem 
medii ligaturarum nulla essentialis differentia invenitur.' In order to 
illustrate the difference between the Franconian and the pre-Franconian 
systems, we give here a table of the chief modes in both notations. 

I II III V 

Pre-Franconian: 322 223 ^333 3 (L L L) 

s n- n- *>+* i^a; WW 

Franconian: s j 2 2 2 2 2 B ^33j( s 4 3 3) L L L 

*%> an- ] ■ ir* a;c\3a;j m 



Examples 315 

In the first mode a *J must be used since the initial note is a L. In 
the second mode the J must be divided, since a media can never be a L. 
The third mode needs no modification; however, Franco prefers a '4 in 
place of L + J, following the principle: ligare quantum possibile est ('to 
use ligatures as much as possible'). In the fifth mode ligatures cannot 
be used: 'vehementer errant qui tres longas aliqua occasione, ut in ten- 
oribus, ad invicem ligant' (he makes a serious mistake who, under any 
circumstances — e.g., in tenors — writes three L in ligature). We have 
seen that this older manner of writing was virtually abandoned even 
before Franco. 



Examples. Compositions written according to the principles of Franco 
occur, though sparingly, in the fascicles VII and VIII of Mo, in the Codex 
Torino, in Paris, Bibl. Nat././r. 146 {Roman de Fauvel) y and a few other 
MSS of the late thirteenth and early fourteenth centuries. A motet 
Huic ut—Huic ut — (tenor) (Facsimile 63) may be studied as a first ex- 
ample. The tenor begins in the middle of the staff, after the empty in- 
terspace. It is written in the first mode: 'J 2 2 . . . The last ordo is 
identical with the first and, in fact, is written out only in order to indicate 
that the entire melody must be repeated until the upper voices have 
finished (four times; the motet closes on the next page of the Ms). 
The motetus (right-hand column) starts with an extended vocalization 
on the syllable 'Hu-', and continues with seven lines of music to which a 
full text is underlaid ('huic ut . . . mira potentia'). Exactly the same 
two passages occur in the triplum, but in reversed order, resulting in 
Stimmtausch (interchange of parts). Both parts continue with a vocali- 
zation on (potenti) 'a-', in which groups o( S-(S) frequently sound against 
groups of (S)-S in the other part, leading to hocket effects. The S-rests 
[(<?)] are written as small dashes irregularly placed below, above, or across 
a staff line. The strictly Franconian interpretation of this motet would 
make it necessary to double the ^-rests in the groups S-(S). In order to 
avoid this rather awkward consequence, it may be better to transcribe 
groups of two S as equal notes. 

In the appendix, No. 44, are shown the beginning of the first and of 
the third section in transcription. 

Facsimile 64 illustrates the use of the Franconian 'chains of S.' The 
S appear always in even number, that is, in groups of two, four, six etc. 
According to the above principles, they are to be arranged in pairs. The 
tenor Aptatur is written entirely in ternariae sine perfectione, each of 
which equals B B B. Since each ligature is followed by a 5-rest, groups 



316 



Franconian Notation 
Facsimile 63 



f 1 1 i m 1 fi li f iff 


iliMUimiffl 1 ifli 4 





On 

S 



v(U CO 
5 ON 

ft M 

T3 bo 

"3 






Examples 
Facsimile 64 



317 



\ * 


■ r S« 




■"it 


lit 


B 




(U (U 
T3 bfl 



fe 



318 Franconian Notation 

of four B result which obviously indicate modus imperfectus. Here is the 
beginning of the duplum in transcription: 




B. The Innovations of Petrus de Cruce 

As mentioned above, compositions in true Franconian notation are 
rather scarce. The greatest shortcoming of Franco's system was the 
lack of rhythmic variety in the realm of the small values, and it was in 
this matter that new contributions were soon made. Important prog- 
ress was made by Petrus de Cruce (ca. 1280?) who actually inaugurated a 
new trend in thirteenth century music and notation. Since the nota- 
tional devices introduced by him are sharply distinguished from Franco's 
principles it seems appropriate to refer to them by a special name, i.e., 
Petronian notation. 

Petrus de Cruce's innovations are often mentioned by theorists of the 
early fourteenth century. Robertus de Handlo, after explaining the 
Franconian principles of semifrreves-notation, continues (CS 1, 387): 

Securius tamen et verius . . . addatur punctus inter duas et duas vel inter 
tres et tres. . . . ut ponit Petrus de Cruce 

For the sake of greater accuracy and truth ... a punctus should be added, 
between two and two, or three and three S, . . . as is done by Petrus de 
Cruce. 

Jacobus of Liege, in Speculum Musicae, says (CS 11, 401 a): 

Petrus de Cruce primo incipit ponere quatuor semi breves pro tempore 
perfecto 

Petrus de Cruce was the first to introduce four S within the span of a 
perfect tempus. 

According to the first writer, Petrus de Cruce introduced the punctus 
divisionis in order to mark off groups of 6" neighbouring on other similar 
groups. Thus, combinations such as B SS.SSS.SS.SSS.SS B, which are 
not possible in Franconian notation, could easily be formed. This in- 
novation, however, was only the point of departure for another one of 
greater significance, namely, the introduction of four, five, six or seven S 
in the place of a B {perfecto). In Montpellier vn, vm are found a num- 
ber of motets which embody this innovation (e.g., nos. 253, 254, 255, 



The Innovations of Petrus de Cruce 



319 



262, 289, 293, 297, 298, 299, 317, 332 etc.). A famous motet by Petrus 
de Cruce, Aucun ont trouve chant, the beginning of which is cited by vari- 
ous theorists, may serve as an example (Facsimile 6$). The tenor 
Annun{ciavii) is in groups of three (perfect) L throughout. The motetus 
is notated chiefly in L and B> with occasional groups of three S in con- 
junctura, and of two S in ligatura c.o.p. The triplum, however, displays 
a remarkable advance in rhythm. It is written chiefly in S which appear 
in groups from two to seven. The beginning or the end of a group is 
indicated either by a longer note (L, B) or an equivalent rest, by a liga- 
ture, or by the punctus divisionis. Two S, written as a binaria c.o.p., do 
not rombine with preceding or following S y but occupy the value of a B 
by themselves. Disregarding, for the moment, the question of the 
rhythmic organization within a group of S } the following transcription 
of the beginning results: 




Obviously, the replacement of a B by more than three notes results in 
practice in the introduction of values smaller than the S, i.e., the minima 
(or even the semiminima). However, in the Petronian teaching and 
notation these smaller values still appear under the guise and under the 
name of semibrevis, and a considerable time elapsed before the M was 
recognized de jure as an independent type of note. 

The main problem presented by the groups of more than three S, char- 
acteristic of Petronian notation, is that of the metrical values within 
such a group, i.e., the question whether they simply indicate notes of 
equal duration, or whether they call for some sort of rhythmic organiza- 
tion similar to that of a series of S in Franconian notation. This prob- 
lem may be illustrated by two transcriptions of the beginning of our 
motet: (a), Coussemaker, U Art harmonique, no. XI; (b), Wolf in GdM 
in, no. 1, and in HdN 1, 266 (see p. 320). 

Both Coussemaker and Wolf interpret the ^-groups on the basis of 
strict triple meter or, in fourteenth century terminology, of temp us per- 
fection (B = 3 S). Furthermore, Wolf applies prolatio perjecta and in- 
troduces an iambic grouping (alteration) which is similar to that called 
for by the Franconian 'chains of $.' 

These two versions may be compared with the preliminary transcrip- 



22Q Franconian Notation 

igJvj m rn^j rrm J>j ,j^ ^J>j j. j jjjjj i 

(a) ' 



1 Jr 3 °^T tT 


iOOOiu 


3 


,M iW-.B-. 


, |Q m i 








T T~ 


i hTu- 




T T' f 




JJ J-J J 


J-J -hJ /J 

u. «i t T 


'Igftll l"°"l | A *WJp°p°'"|" rn |" | |i| ~R|" || ~[*~ ['E=| 



(b) 



The small notes indicate the rhythm in the reduced note values used in the present study. 

tion given above which conforms with the transcription given by F. 
Ludwig {AHdM i, 254). l 

The question as to which interpretation is correct is certainly not an 
easy one to answer. 2 In three treatises of the mid-fourteenth century — 
namely, Theodoricus de Campo, Anon. Ill, and Anon. IV of the third 
volume of Coussemaker's Scriptores — one finds explanations which 
would seem to support the theory of a strictly measured interpretation 
of the groups of S. These writers deal chiefly with the notation of the 
Ars Nova, which is distinguished from the notation under consideration 
by the use of the so-called semibreves signalae, semibreves caudatae, or 
semibreves cum proprietate, i.e., special types of £. characterized by an up- 
ward or a downward dash: I semibrevis maior; ♦ semibrevis minor •; j 
semibrevis minima or, briefly, minima. The same writers, however, ex- 
pressly refer to earlier practice and give as its chief characteristic the 
failure to distinguish between these forms and the use of the punctus 
divisionis. They also give detailed explanations regarding the values of 
the various notes within a group of £ which are not signalae. It will 
suffice to illustrate their principles by the following table: 

Tempus perfectum Tempus imperfectum 



iS 


J>J 




J - 3 


3S 


m 




JT3 or: JTJ 


4 S 


jttj 

3 


s 


J li : or: J-J J-J 


s$ 


nn: 


or: J-J J-J J 


J5J73 or: JttJJ 



1 Stiil another interpretation is used in Rokseth's transcription, Polyphonies, ill, 81 flf. 

2 This problem has been studied particularly by J. Wolf in GdM I, 7 and 21, and in HdN 1, 264. 
His explanations in GdM (1904) are based largely upon the theory that, in the late thirteenth cen- 
tury, Italian.music and notation was sufficiently developed to exercise a strong influence upon French 



The Innovations of Petrus de Cruce 
Facsimile 65 



321 






CO 3 



3- 




111 



1- 



!,: 



322 Franconian Notation 

These detailed explanations, made with reference to an earlier practice, 
seem to support the interpretation by Coussemaker and especially that 
of Wolf. The only remaining problem, then; would be the question as 
to which of the two mensurations mentioned by the theorists should be 
applied, tempus perjectum or tempus imperfectum, and whether trochaic , 
or iambic rhythm should be preferred for the notes in prolatio perjecta. 

It would be lost labor to search for an answer to these questions. In- 
deed, the very futility of this task raises suspicion as to the admissibility 
of the whole issue. Fortunately, another theorist — and one of much 
greater weight and authority — namely, the author of the Speculum 
musicae? comes to our assistance. In his extensive and unusually in- 
formative explanations he repeatedly touches upon the problem of the 
semibreves. The following remarks are especially clarifying (CS n, 429): 

Quod si moderni multis distinctionibus, multis nominationibus utantur in 
semibrevibus, quidquid sit de figuris antiqui, quantum ad rem, uti videntur 
pluribus. Nam cum pro eodem et equali tempore, pro brevi recto impor- 
tato, nunc duas semibreves ponerent inequales; nunc tres equales, nunc 
quatuor, quinque, sex, septem, octo vel novem, cum duas ponebant, 
vocari ille poterant semibreves secunde, . . . ; cum tres semibreves tertie 
. . . ; cum quatuor semibreves quarte . . . ; cum quinque semibreves 
quinte, . . . cum novem, semibreves none. Cum tot distinctionibus in 
semibrevibus uterentur, numquam eas in figuris distinxerunt, nunquam 
eas caudaverunt, et tamen eas suffkienter ab invicem per puncta 
diviserunt. 

The modern musicians use numerous distinctions and names for the semi- 
breves. Whatever variety there may be in shapes, the old masters in reality 

music. This theory is untenable, as has been shown by F. Ludwig (A/MJV v, 289) and H. Besseler 
(AjMW vii, 177). In particular, Ludwig has shown that the date 1274 for Marchettus de Padua's 
Lucidarium, which was a cornerstone of Wolf's conclusions (see GdM i, 16), is erroneous, being at 
least fifty years too early. In his HdN (1913) Wolf has quite rightly given up the idea of an Italian 
influence upon the notation of the early French Ars Nova. Instead, he gives a detailed account of 
the information contained in the writings of Walter Odington, Johannes Hanboy, Robertus de 
Handlo, Joh. de Garlandia the younger, W. de Doncastre, Robert Trowell and other theorists of the 
period of transition from the Ars Antiqua to the Ars Nova. It has not been deemed necessary to 
dwell here upon this subject as our knowledge about it is practically limited to its theoretical aspect 
which has been fully expounded by Wolf. 

1 The Speculum musicae is not only by far the most extensive treatise on medieval music, but 
also the most penetrating and informative one. Only the last two of its seven books have been 
published, (CS. 11, 191-433). In Coussemaker's Scriptores as well as in many books of more recent 
date the Speculum has been attributed to Johannes de Muris; however, H. Besseler has shown that 
this theory is untenable (AfMJVvu, i8orT). The author of this treatise is one Jacobus who probably 
lived in Liege. At any rate, the author of the Speculum was an extremely conservative musician, 
whereas Johannes tie Muris was a close friend of Philippe de Vitry's and an ardent champion of the 
Ars Nova. 



The Innovations of Petrus de Cruce 323 

had a larger variety. For one and the same tempus, namely, that of the 
brevis recta, they used two semibreves unequal in value, or three, four, five, 
six, seven, eight and nine equal semibreves. Thus, in the case of two semi- 
breves, one might speak of semibreves secundae, . . . ; in the case of three, 
of semibreves tertiae ... ; in the case of four, of semibreves quartae; in the 
case of five, of semibreves quintae ... in the case of nine, of semibreves 
nonae. Although they used such a variety of semibreves, they never dis- 
tinguished them in shape, never provided them with dashes; yet, nonethe- 
less, they discriminated them from one another sufficiently by puncta. 

In order to attach the proper importance to these remarks one must 
realize that the whole extensive treatise of Jacobus is designed to show 
the superiority of the Ars Fetus over the modernistic innovations of the 
Ars Nova. In the present case, he justifiably points out that the appar- 
ently revolutionary changes introduced by the 'modern' composers (de 
Vitry, Johannes de Muris) actually are not an enrichment, but rather 
an impoverishment in comparison to the varieties of rhythm possible in 
the late thirteenth century. First, he calls attention to the fact that the 
introduction of the minima (or, in other words, of tempus with pro I 'at io) 
amounts to nothing but the expression of the old rhythms and values by 
other signs. This statement becomes clearer upon realizing that the in- 
troduction of the apparently smaller notes was accompanied by a length- 
ening, in fact, an exact triplication of the duration of the B and L, 
as will be seen subsequently. Thus, there is no difference ad rem be- 
tween the 'modernistic' *i or ■♦ and the 'old-fashioned' 1" . After 
having demonstrated this the author of the Speculum justly points out 
that the followers of Franco, first among them Petrus de Cruce, actually 
succeeded in introducing into music and notation a variety of metrical 
values not to be found in the practice of the Ars Nova. As a matter of 
fact the introduction of the Petronian groups of more than three S not 
-only leads to values resulting from a repeated bipartition and tripartition 
(i, i B), but also means the creation of essentially new fractions such as 
t, i, y, and | of a B {semibreves quartae, quintae , septimae, octavae). 

Jacobus' explanations, if viewed in the light of this general situation, 
are perfectly clear and unambiguous. It appears, therefore, that the 
Petronian groups of S must be interpreted according to the following 
scheme: 

B 26' 3 S 4 S $S 6S yS 

j. ^j m sm ffm mm msm 

A correct transcription of the beginning of the motet is given in the 



324 Franconian Notation 

appendix, No. 45. A comparison of this transcription with those of 
Coussemaker and Wolf immediately shows that the question of tempo, 
and consequently that of the proper scale of reduction, plays a decisive 
role in this matter, as it also does in many others. Indeed, a great num- 
ber of misinterpretations and controversies could have been avoided if 
this point of view had been properly considered. The transcriptions in 
Coussemaker and in Wolf's GdM illustrate the complete neglect of this 
viewpoint, a neglect which is a common characteristic of almost all the 
earlier editors (except H. Riemann); indeed, under the pretext of 'sci- 
entific exactness* it still continues to exert its detrimental influence in 
many recent editions of early music. The transcription in Wolf's HdN 
(p. 266) shows a better understanding of this matter, since the reduction 
there chosen suggests a tempo in which the beat falls on the S. How- 
ever, although the problem has at least been faced, it is not answered 
correctly. There is sufficient evidence to show that throughout the Ars 
Antiqua, to which no doubt Petrus de Cruce still belongs, the normal 
musical pulse is represented not by the S but by the B, except for the 
earliest period (School of Notre Dame) in which it is represented by the 
L. Ample proof of this exists in the repeated remarks of the author of 
the Speculum musicae^ who always extols Petrus as one of the great mas- 
ters of his beloved ars veterum, and who on the other hand is one of the 
many theorists to inform us about the fact that in the old art the beat 
(tempus) was represented by the B in contrast to the modern art (Ars 
Nova) in which it falls on the *S\ If, then, a composition of this period is 
sung in its proper speed ( ■ • J- M.M. 60-70), it becomes immediately 
clear that no differentiations of temporal values are possible within a 
group containing four, five, or more S. Such groups are performed either 
as quick coloraturas or else, if underlaid with a full text, like rapid speech 
not dissimilar to Italian parlando or an English patter song. 

In the light of these considerations it appears that the explanations of 
Theodoricus de Campo and the various anonymi mentioned above rep- 
resent the attempt, made in the second half of the fourteenth century, to 
interpret the notation of the Petronian period according to the concepts 
of speed and rhythm which prevailed in their day. Some people went 
even farther and changed the notation of the earlier MSS by adding up- 
ward or downward dashes to those semibreves which they considered to 
be shorter or longer than the others. There exist at least two MSS in 
which these attempts at remodelling have left traces. One of these, the 
Codex Huelgas, has already been briefly discussed. The other, which is 
the more interesting and more important one, is the so-called Roman de 
Fauvel. 



The Roman de Fauvel 325 

C. The Roman df Fauvel 

This MS (Paris, Bibl. Nat././r. 146), which contains motets and mono- 
phonic songs inserted in a continuous narrative 1 and which was com- 
pleted in 13 14, represents the last extant document of the Ars Antiqua. 
Its chief notational interest lies in the fact that, in addition to the plain 
S y so-called semibreves signatae or caudatae occur, i.e., S with a downward 
or upward tail or with other characteristics designed to indicate differ- 
entiation of values within the realm of the smaller notes. For instance, 

the combination ♦♦♦ would indicate that the first note is longer than 

the second, and this (in turn) is longer than the third. The exact inter- 
pretation, of course, would still depend on the mensuration, i.e., on 
tempus and prolatio. In the above example the following renditions 
would seem to be possible: 

L3,ji: iiij^ni [*,ji: &irT3i [2,* 41 Jin I 

B=J: B=J. B=J 

Like the plain S of the Petronian motets the semibreves caudatae of the 
Roman de Fauvel have been the subject of divergent interpretations and 
controversial utterances on the part of various scholars such as Cousse- 
maker, Wolf, and Ludwig. But once more, as in the previous case, the 
whole issue is futile. An examination of the MS shows easily that none 
of the indications of semibreves signatae are part of the original writing, 
but that all are later additions. In fact, they appear as extremely short 
dashes, timidly and furtively drawn, which in many cases are clearly out 
of the center of the note (see the illustration p. 326). 

The unauthentic quality of the semibreves signatae in the Roman de 
Fauvel is particularly evident in the case of the form with an upward 
dash, the semibrevis minima (the minima of the later system). The pres- 
ence of these forms in the piece tyuare Jremuerunt (f.i ; see the reproduction 
on p. 326) has led J. Wolf to a rendition in tempus perf,ectum cum prola- 
tione perfecla (GdM in, No. 4), whereas F. Ludwig, in his criticism of 
Wolf's publication (SIMG vi, 624) advocates the application of tempus 
imperfectum cum prolatione perfecta. Actually, in this case the contro- 
versy is particularly futile, not only because the 'minima' -strokes are 
barely visible and are used without any consistency (cf. the beginning of 
the second and the end of the third staff), but also because the piece in 
question, which appears on the first page, is the only composition of the 
whole codex to show these pseudo-minimae. The conclusion is inevit- 

1 See the list of contents in GdM i. 40 ff. 



326 



Franconian Notation 









$s 



£tkml 



F=F^g^ 









pv vvTuy ' fj , 



>', , '.♦ i \ 



J> ?*ft|ii t yftF 













Qiiare fremuerunt (Tenor enlarged) 

able that a revisor of the manuscript tried to remodel it after the princi- 
ples of Ars Nova style and notation, but soon gave up, becoming aware 
of the futility of his task. He was more persistent in the application of 
the downward dash which appears throughout the manuscript, appar- 
ently indicating semibreves of a somewhat longer value {semibrevis major). 
However, a glance at our Facsimile 67 (e.g., left and right column, staff 
8) will readily show that they bear the same appearance of being a later 
emendation as the upward dashes mentioned previously. The final con- 
clusion, then, is that this MS was originally written in true Petronian 
notation and that, in all probability, its groups of S must be interpreted 
according to the principles set forth above. 

The application of this theory to the Qiiare jremuerunt leads to the fol- 
lowing transcription, to which for the sake of comparison two other in- 



The Roman de Fauvel 



3V 



terpretations have been added, one (a) according to J. Wolf (see GdM m, 
p. 8), the other (b) according to F. Ludwig (see SIMG vi, p. 625): 



U)I§JJJ)|J^J^J33]U.J.^U: u.JTKJj J>iJ>J J- 

(b)\ijji\fi2nsshu jjmu. u hhnin j - 




We now turn to a more general discussion of the notation of the poly- 
phonic compositions of the Roman de Fauvel. 

The Tenors; Modus and Maximodus. The notation of the tenors follows 
the Franconian principles, as is illustrated in the following two examples, 
both of which are in modus perfectus: 
Fur non venil (f. 7) : 



Ruina (f. 



The modus imperfect us is much more frequent now than in the earlier 
sources. Sometimes it is explicitly indicated as in the motet Nulla pestis 
(f. 3), the tenor of which bears the inscription 'Vergente ex imperfectis' 
(i.e., tenor Vergente performed with imperfect L). 2 In this case the re- 
mark would appear to be superfluous since the use of L-rests covering 
two spaces unmistakably points to imperfect modus: 





The situation is less clear in the case of the tenor Displicebat of the 
motet Quasi non ministerium (f. 6'), 3 where there is no such remark nor 

1 See GdM n, 6. 
*SeeHdNi, 281. 

» See GdM n, 10. 



3 28 



Franconian Notation 



any rest. Here it is the duplum and triplum from which the correct 
mensuration, namely modus imperfect us, must be derived: 



Imperfect modus is particularly frequent in the tenors written without 
ligatures. Among nine tenors of this type four are in perfect modus and 
five in imperfect, namely, Superne malris (f. 2), Imperjecte canite (f. 13), 
Heu me tristis (f. 30), Merito hec patimur (f. 42), and Alleluia benedictus 
(f. 43). The last-named tenor is reproduced on Facsimile 66. Follow- 
ing is the beginning of the transcription: 



This tenor is also indicative of another broadening of the system of 
mensurations. While in the earlier sources the combination of the longa 
and the duplex longa — or, as it was called in the fourteenth century, 
maxima (Mx) — always leads to groups of two L, e.g.: /Mx/L L/Mx/L Lf 
Mx/ (see the tenors Ruina and Vergente), in the present example there re- 
sult groups equalling three L:/L Mx/L Mx/L (L) (L)/. In this may be 
seen the germ of the modus maximarum [maximodus, see p. 124) which 
became of practical application in the motets of the early Ars Nova and 
of Machaut, and which was perpetuated in the theoretical writings of the 
fifteenth to the seventeenth centuries. Like any of the other mensura- 
tions the maximodus was either perfect or imperfect. It must be no- 
ticed, however, that the Mx itself was never admitted to be ternary; it 
was only the grouping of the L's — with or without the binary Mx — 
which caused the maximodus to be either perfect or imperfect by implica- 
tion. 

Whenever the maximodus is clearly perceptible in a composition it 
should be indicated in the transcription by heavier bar-lines or some 
similar means. In the above transcription of the Alleluia-tenor, such 
bar-lines should appear, then, after every three measures. Another pos- 
sibility would be to combine three ^-measures into one 2-measure. 

Red Notes. In the Roman de Fauvtl are found the earliest examples of 
red notes which are used to signify transition from modus perfectus to 
modus imperfectus in the tenor. 1 They occur in two motets one of 
which, Garrit gallus — In novafert, is reproduced on Facsimile 67. That 
the black and red notes have the meaning just indicated appears from 

1 In Aubry's facsimile edition of the Roman de Fauvel the red notes appear as ordinary black notes. 
Thus an important feature of the notation is obscured. 



The Roman de Fauvel 
Facsimile 66 



329 



i 
■ 
■ 



til I * ^ ■-fit 



./"I • 



2J *? 



1 > **fi ■ -M4J • Hi ft 


li 




i > 


Ij i.fWi'i II -e flN^t 


IE: 11 



I 



u 



^h 






*-.*■-.?¥ 




fil 

14 
r 



It 




J I OKU 






1 

I 

I 

I 

•f 

.a 1 
jJ, a . t 



5* 

tLiJ 



I 

m 

i 



(».-. 



5 J--IU :j 



; 



i 



i 



> ^s t 

3 R - 

TO *-< 

cZ p 



330 Franconian Notation 

the length of the rests which cover three spaces in the passages written 
in black notes, two in those notated in red ones: 

J=J 



This tenor is also remarkable as one of the earliest examples of that 
fourteenth century extension of the modal scheme which is known as 
isorhythmic construction (isorhythmic motet). In fact, the elaborate 
rhythm of the above passage appears three times in succession, much in 
the same way as, in a thirteenth century motet, the simple scheme of a 
modal pattern is repeated a number of times. 

Notation of the Upper Parts. The ^-groups of the upper parts have 
already been discussed. Normally they will have to be interpreted on 
the basis of the scheme worked out for the Petronian groups in the Codex 
Montpellier. In two motets, Servant regem — Rex regum — Philippe 
(p. 10-12) and Detractor est — Qui secuntur — Verbum iniquum (p. 4), one 
finds two small dashes, similar to the *S*-rests of Mo, written before the 
first notes of the parts, e.g. (see GdM 11, p. 6 and 13): 



Since real rests cannot be meant here, J. Wolf {GdM 1, 57) interprets 
these signs as indicating tempus imperfeclum in contradistinction to the 
tempus perjectum prevailing normally. This plausible interpretation 
would mean that in these pieces groups of two and of three S must be 
read in binary meter as follows: ♦♦■ J"3 ; ♦♦♦ = J73 • The rhythm of 
the more numerous groups of S naturally remains unaltered. Binary 
mensuration of the B may also be preferred in pieces which, although not 
marked in the above manner, show a distinct prevalence of groups of 
two S. An example is the motet Firmissime — Adesto — Alleluia benedic- 
tus (Facsimile 66), 1 in the upper parts of which groups of two and four S 
are much more numerous than groups of three. As a matter of fact, in 
this case we possess definite evidence in the following remark of Philippe 
de Vitry, made in his Ars nova (CS in, 20; see also GdM 1, 47): 

Modus imperfectus et tempus imperfectum continentur in Adesto, quia 
ibi duo tempora pro perfectione qualibet accipiuntur et quodlibet tempus 
non partiturnisi in duas partes aequales semibreves 

1 The queer appearance of our Facsimile is explained as the result of its having been pieced to- 
gether from different pages of the MS. 



The Roman de Fauvel o o l 

Facsimile 67 



jfoin^fliunfl- niflir fiJHiuOfant <£ ( .uuTW twin ftoifcini ° 0ii1kiiii. i .. r tuii.yu en i mfanu I. , I,, 

W&r ifvv ,ftr rei " -""Wit \Ju ftiuutCir ft jpir ftmr cr t u&m "?«. fwuu" yr fiuwcl mem cii 

; j"3» ouj^ur iw iiwr .ini«Kftft» CjctSbn C^S^mqnir, tcfvnfcii . C\ i ,t'n. ■ »ifl "«n timfrrt 

^;cnii«<»tu mnr fcfinir'ujGir f j& uann arSxtix <Pioai*uu tv<- ii ht,.$c\cx£>\*m<t*i«c i >f*' 

fe\ „ j v, Tvu.'v'-' 7 J '- n 



irnini* inii.iPiii aiifl* ictru 



ytfr : t- : — = , 

$p a&tS "ft &(■» « <"ft«» fro"" *ffa« *^ uufiw 0%f mH'i «• »"ium >iucn ofcra 



«.)» &.(uif w«at«a^uaA < &C««tt* Abfti jpm 1 itunt.n tut ^Itftauir iniWucf mrlinn* iuct.H-T.iCii iiiunirw 

. .. ,. ...t-' 1 ' " gg ' '«• ' , '.' : ^r 7 T^ T 

<fi0rdcard(Rjtiui tuPV- cor Imnfe (ill JUj^Hnnry <ift. »x?in.i m t . ul'ioo ^u%nc Amtbia m« fit-mio 

g ,..-»7 ,,,t 5 ■ """•rv^ 

fuM^twurMn iu <> ikAucm OTraiuit uof femur" nwV'oj- ^binlw amumie flifrvHW unit* miluvi m'fW 

= '■" "' 't*,y '■'"'■' 

i- f'-. 1 "" 1 l] 

te^xtu^Q^Li^^bxaayne c.na'.ttmaAfiidinuc mum Snuir m vidian liiur.inio .uiMi ciiiik* litimnc f-i 

~ ♦ '< t i ■ * ♦ > . . - i ? | i « t 1 ) 1 ■'' ♦ '♦ 1 ♦ t4 « P 

j«i/ V' ' -=-*+•!♦."• h-^ . c M'Mi\.' f f == = 

fjv&uu* ananw fr.rn. moiinita o nufbuiu cruliim im iumv fos>it£r im»r<iriir mitr ouc>* 0' w? r *" u f* 

*T^f t . #. jjj jgl t "'" v, - , '""-> , -'> ^^. 

^uw ogpfcni i ivtn'ii* *ibCn# a« faiiw aatao fi* OaanioR.ii fiio^p< «ui« alar iTjttr .ft iranuf 



i . - .■ -^ J 



offhnti P..mVt wtit.iuifi-w |^Hm» «uk> flifhu» a i« Pno non i;inr uc yuBiv hut uc a cv 
fiifVnwne enme niflnauo alue fifi/ctflfeurq^lvi (i imi cr^m >T>fl» anjJkwt iu- %i a>m 

G» fmiMu (^ mar mfli.nmo tni9i« uAmffcu tn«r- 



m m S 



Roman de Fauvel 

Paris, Bibliotheque Nationale/ow^j/rf. /^<5 (ra. 13 10) 

Page 44' 



332 Franconian Notation 

Modus imperfectus as well as tempus imperjectum are found in the motet 
Adesto, because two tempora (i.e., brews) are contained in a perfection (i.e., 
tonga), and because each tempus (i.e., brevis) is divided only in two equal 
semibreves. 

Naturally, there are quite a number of motets in which a decision is 
difficult, if not impossible, to reach. It would seem that the blame for 
this must be laid, not upon our lack of knowledge, but upon the vague- 
ness of early fourteenth century musicians themselves in the matter of 
the small note values. Much in the same way as the organa dupla of 
Leoninus form the transition between the plainsong-like rhythm of St. 
Martial and the modal meter of the thirteenth century, so the motets of 
the Roman de Fauvel indicate the gradual change to the new rhythmic 
concepts of the Ars Nova. In both cases, the intrinsically transitional 
character of the period forestalls any attempts to arrive at 'the correct 
solution.' In both cases it seems advisable to incline to the less rigid 
notions of the earlier period rather than to the more strictly regulated 
principles of the development to come. It is particularly this general 
consideration which causes us to pass over the hair-splittings encoun- 
tered in the treatises of the fourteenth century (as well as in modern 
writings) — mindful of the wise remark which was made by a contempo- 
rary with a view to this particular situation and which appears as a motto 
on the dedication page of the present book. 

Semibreves Signatae. This remark applies particularly to the semibreves 
signatae {caudatae) which have already been discussed briefly. That the 
strokes are later additions there can be no doubt. Whether they repre- 
sent an authentic clarification of the original intentions or an unauthentic 
remodelling of the rhythm according to principles of a later period re- 
mains to some extent an open question. The following points, however, 
should be observed, in view of the great importance which J. Wolf, F. 
Ludwig, and others have attached to these signs: 

(i) The semibrevis minima (with an upward stroke) appears only in one 
short piece {$uare fremuerunt) on the first page. It is clearly a subse- 
quent addition to which no importance whatsoever need be attached. 
(2) The semibrevis maior (with a downward dash) occurs only in groups 
of two or three S, never of four or more. This fact clearly supports our 
former contention that the groups of four or more S must, at any event, 
be read in the Petronian style as groups of equal notes. (3) The semi- 
brevis maior appears only in the following two combinations: f** s f ♦ . 
Both are capable of being interpreted in tempus perfectum (a) as well as 



The Roman de Fauvel 



333 



in tempus imperfectum (b), as appears from the following table which 
may serve as a basis for the transcription of the upper parts: 

■ ♦♦ ♦ ♦ ♦♦♦ t ♦ ♦ ♦♦♦♦ ♦♦♦♦♦ 

w j. j>j j j> m j n rm ra 

Conjuncture, and Plica. If several £ are to be sung to the same syllable, 
they are naturally grouped closely together, as* for instance at the begin- 
ning of the duplum of Facsimile 67 {In nova fert). These groups, of 
course, have nothing to do with the old conjunctura to which they bear a 
certain resemblance in appearance. More closely related to the conjunc- 
tura is the following character, ft^ , which occurs quite frequently, e.g., 
at the beginning of the duplum Adesto of Facsimile 66. This sign takes 
the place of a L, usually an imperfect one, the only question being as to 
whether it indicates a long note followed by two short ones (a), or the 
inverse rhythm (b), conforming with that of the old conjunctura: 



(a) 
(b) 



Tp. pf. 

IIJ. JU I 
IlJtJ J. I 



Tp. impf. 

IIJ ill 
II/3J I 



J. Wolf, in GdM 1, 52, admits both versions, but in his transcriptions 
from the Roman de Fauvel {GdM in, nos. 2-10) always uses (a). Ludwig, 
in SIMG vi, p. 627, criticizes this method, contending that the character 
must be read in the old manner. His view is strongly supported by the 
following passage from the motet Favellandi vicium (p. 1 of the original; 
see the reproduction in GdM n, no. II, third staff), in which the version 
(b) certainly deserves preference on account of the better consonance * 
with the tenor: 

jn j n 
JJJj.J I.JJ3J.J 



The Roman de Fauvel shows a striking increase of the plica, shortly be- 
fore its final disappearance in polyphonic music. The shapes are the 



334 Franconian Notation 

familiar ones of the p/ica longa and the plica brevis in their ascending and 
descending varieties. The ascending plica longa usually has only a long 
dash to its right side, the short dash to the left being missing. Nothing 
need be added to our previous explanations on the plica, as far as the 
questions of pitch and performance are concerned. As regards the tem- 
poral value allotted to the plica-tone, all theorists of the early fourteenth 
century agree that it is reduced to a short passing tone, immediately be- 
fore the following note. This meaning is clearly expressed in the follow- 
ing remark of Hieronymus de Moravia in his explanations on 'flores,' i.e., 
ornamentations (CS i, 91): 

. . . sed flores subitos, non alia quam plica longa. Inter quam et immediate 
sequentem note brevissime ponuntur ob armonie decorem. 

The flos subitus (rapid ornamentation) is nothing but the plica longa. A 
very short note is placed between this and the following note, for greater 
refinement of the sound. 

More concrete and, hence, more useful for our purpose, are the explana- 
tions of Marchettus de Padua (Pomerium, see GS in, 181), according to 
which the plica's are to be executed as follows: 

Tempus perfectum Tempus imperfectum 

Plica brevis §|JJ> | J|J^ | ||J3 | || | 

Plica longa ||jj^| 9|JJ^| ||JJ3| 1 1 J^jg | 

Examples, (i) Quare fremuerunt (p. 326). The problem of the semi- 
breves, ordinary as well as signatae, has already been fully discussed 
(p. ^S)- The modus is perfect, as appears from the fact that on the 
second staff there is a group of nine B (or their equivalents) between two 
L. In contradiction to the rules of Franco the former of these two L 
(last note of the first staff) remains perfect. As a matter of fact, imper- 
fection of this note would entail alteration of the last B, a procedure 
which is impossible since a group of four S occurs instead of this B. For 
the same reason the initial L {longa plicata) as well as all the other L of 
the piece remain perfect, except those which are followed by a single B- 
rest (e.g., the last note of the second staff). 

An interesting feature of this piece is its conductus-like texture, the 
tenor being in almost exactly the same rhythm as the upper part. It 
clearly foreshadows the 'ornamented conductus style' of Italian four- 
teenth century music. 

Another point of interest offered by this piece is its form which is that 



The Raman de Fauvel 



33$ 



of the French ballade, namely, A A B. The repetition of the first section 
(A) is fully written out in the discant where it begins with the third line. 
In the tenor, however, A is written only once and, therefore, must be re- 
peated, as is indicated by the rest-like dash after the first L of staff seven. 
Moreover, there is a different ending for the prima volta and the seconda 
volta or, as it was called then, for ouvert and clos. In repeating the sec- 
tion one has to continue after the brevis e-flat not with the group d-e-d-c 
— d, but with the group d-e-d-b — c. 1 See the complete transcription in 
GdM in, 8. 

(2) Firmissime — Adesto — Alleluia benedictus (Facsimile 66). As we 
already learned (pp. 328 and 330), this motet is in imperfect modus and 
tempus, with perfect maximodus [III y II, 2], a mensuration the modern 
equivalent of which is 4-meter with groups of three measures each (or 2- 
meter). The upper parts contain various instructive examples of con- 
junctura (first staff of the duplum), plica longa (same staff) and plica 
brevis (second staff). The fifth staff of the Iriplum shows a plica longa 
and a plica brevis in succession. The character above 'ut' on the fourth 
staff of the triplum, however, is not a conjunctura, but a L followed by a 
group of four S. Below is a transcription of the beginning of the motet: 




(3; Garrit gallus — In nova fert (Facsimile 67). The tenor, with its 
alteration of black and red notes, that is, of modus perfectus (4) and 
modus imperjectus (4), has already been discussed (p. 328). As regards 
the upper voices, the foremost question is whether to interpret them in 
iempus perjectum or in tempus imperfectum. Since groups of two, three, 
and four S are freely mingled, it is impossible, we believe, to arrive at a 
definite conclusion from internal evidence. It is only on the basis of 
certain general considerations that preference may be given to tempus 
perjectum. These considerations are chieflv based upon the fact the 

1 See the explanation of ouvert and clos, p. 349 ff. 



336 Franconian Notation 

Pranconian teaching established the ternary division of the B as the only- 
possible one and that, therefore, a deviation from this scheme may not 
reasonably be assumed unless it is clearly indicated. The very fact that 
with two or three motets of our MS such an indication is given (see p. 
330) is a strong argument in favor of the assumption that these are the 
exceptions from the rule, as may also be those motets in which groups of 
two S appear in the majority. As there is no such evidence in the present 
composition we prefer to transcribe it in tempus perfection (see appendix, 
No. 46). However, for the sake of instruction, a rendering in tempus 
imperjectum has also been indicated. 

Another problem presented by this piece is that of the evaluation of 
the various L in the duplum and triplum. The context shows that some 
of them equal two B y others three, although the notation fails to indicate 
any such distinction between perfect and imperfect values. One might 
expect to find a clue to this problem in the mensuration of the tenor 
which constantly alternates between modus perfectus and modus imper- 
fecta, the obvious assumption being that the upper voices would follow 
the same scheme. This, however, is not the case. Nor can the upper 
parts be interpreted throughout in either of the two modes. In several 
places their notation indicates groupings which differ from those of the 
tenor, as, e.g., at the end of the first staff of the duplum (text: *[for]mas 
draco'), where a ternary L (imperfected by a 5-rest) is followed by two 
binary Z,, whereas the simultaneous passage of the tenor begins with two 
binary L and ends with a ternary L (see the transcription of the begin- 
ning, appendix, No. 46). The tenor, as written, covers only one half of 
the motet; it must be repeated in its entire length. 

A feature worth noticing is the peculiar underlaying of the text which results in the 
most absurd declamation to be imagined. Students of the humanities will notice par- 
ticularly — and, no doubt, with horror — the alteration of Ovid's elegant hexameter (the 
words In nova fert animus are the beginning of Ovid's Metamorphoses) into a distorted 
stammering which is one of the most striking illustrations of the indifference of mediaeval 
* composers in the underlaying of text. 

For further studies of the Roman de Fauvel the reader is referred to 
the reproductions and transcriptions in GdM 11, in, nos. 2-10, and in 
HdNi, p. 279. Since Wolf's transcriptions are based on principles which 
have been partly rejected in our previous explanations, some indications 
are given below as to what we consider to be a more appropriate render- 
ing: 1 

1 1: GdM, no. 2 (ending); 2: GdM, no. 6; 3. GdM, no. 7; 4: GdM, no. 10; 5: HdN I, p. 279. 



The Roman de Fauvel 



337 



s De-us mi-se - ri-cor - di - e, ad-hibe hie con- si - li - urn. 



8 ro-ys princes contes dus; om- mbus sunt ta-les f u - g-i-en-di 



iT=i /*> 



j'j> 




8 Qua-si non mini-steri - urn creditum fitpas-tori - bus. 




8 Ser-vant regem miseri-cordia et uni-tas nee non dementi - a 




8 Nul- la pestis est gra-vi - 



or quam hostis famili. 




All these examples are taken from the tripla of the motets. The ver- 
sions (a) and (b) illustrate the application oi tempus perfection or tempus 
imperfectum. The small notes above the staff refer to the variants indi- 
cated by the semibreves signatae. 



VI. FRENCH NOTATION 

A. The Innovations of the Ars Nova 

THE CHIEF contribution of Franconian notation was the establish- 
ment of clear and unequivocal relationships in the notes of larger 
values, the longa and brevis. In this respect Franco arrived at definite 
results which were taken over essentially unaltered by later centuries. 

Concerning the smaller values, however, the chief problems had still 
to be solved. Here Franco took only the first steps, when he introduced 
groups of two or three semibreves in place of a brevis. With the innova- 
tions of Petrus de Cruce notes smaller than the semibrevis were admitted 
de facto, although they had still to be recognized de jure and to be ex- 
pressed clearly in notation. 

In the Roman de Fauvel we have found evidence of a first attempt to- 
wards the differentiation of small values, namely, the addition (by a 
later scribe) of a downward or an upward stem for values larger or smaller 
than the normal S. Apparently, numerous other forms were invented 
around the turn of the century, for, as Walter Odington says, 'There are 
as many inventors of new signs as there are scribes'; 1 and Jacobus of 
Liege complains 'And thus in this matter as well as in others, everybody 
disapproved of what the other did.' He continues however: 'Most of 
them agree in that they distinguish the semibrevis minima by an upward 
stroke.' 2 

As a matter of fact, the semibrevis minima or, as it was later called, the 
minima (M) is the only form which found acceptance in French practice 
and consequently in the mensural notation of later periods. The follow- 
ing remark from Anon. I of CS in (p.336) clarifies its origin: 'The minim 
was invented in Navarre and was sanctioned and used by Philippe de 
Vitry, the finest figure of the entire musical world.' 3 

1 SeeHdNi, 271. 

2 CS 11, 409a. 

3 According to Johannes Hanboys (CS i, 424) the 'inventor' of the minima and of the semibreves 
signatae in general was the younger Johannes de Garlandia who flourished around 1300, and who was 
an important link between Petrus de Cruce and Philippe de Vitry. The kingdom of Navarre, situ- 
ated north and south of the Pyrenees, was one of the most important cultural centers of the thir- 
teenth century. From 1201-1255 it was ruled by Thibaut, Roy de Navarre, who was one of the 
foremost trouveres and after whom the Chansonnier Roy was named. 

338 



The Innovations of the Ars Nova 339 

Philippe de Vitry, whom we now encounter for the first time, is the 
leading personality in the development of French notation of the four- 
teenth century. Even if he did not invent minima^ he played an im- 
portant part, if not the decisive role, in its adoption as a basic element 
of the new notation and of the new rhythm. For it is a new rhythm 
which makes its appearance in the works of the Ars Nova. In this re- 
spect the following remark from the Speculum musicae is informative 
(OS 11, 417 b): 

. . . antiqui . . . habebant pro consuetudine primam minus, secundam 
magis tenere, motu forte ex imitatione nature que fortior est in fine quam in 
principio. Dicunt autem moderni istud non esse necessarium cum e con- 
verso possit fieri, scilicet quod prima semibrevis amplius teneatur quam 
secunda, sicut ipsi nunc observant; . . . dicunt etiam quod non oportet 
ut ars semper naturam imitet. 

. . . the old masters always made the first [semibrevis] shorter, the second 
longer, a rhythm full of strength and harmonizing with nature which is 
always stronger at the end than at the beginning. The modern musicians, 
however, maintain that this is not obligatory and that it may be done 
in the opposite way, namely, with the first being longer than the second, 
as they actually do it nowadays . . . They also say that it is not necessary 
for art always to follow nature. 

These words are, indeed, a very apt description of that fundamental 
change by which European music for the first time ceased to aim at being 
the image of divine law and nature, and began to turn to emotionalism 
and refinement as sources of artistic inspiration. 1 

With the introduction of the S as an independent, and of the M as a 

1 In putting the blame for the change from 'naturalness' to 'artificiality' at the door of 
the 'moderni,' Jacobus was either insufficiently informed or, more likely, forgetful of the fact that 
these modernistic tendencies had made their appearance in a considerably earlier period. Already 
in the anonymous treatise from 1279 (edited by Sowa, p. 51) we find the following interesting remark: 
'Sed figura binaria per oppositum figurata recte brevi proportionaliter equipollet, ergo frustra in ea 
inequalia habenda, quod verum est. De quorum dispositione contingit similariter dubitarem eo 
quod quidam dicunt in ilia figura minorem semibrevem procedere et maiorem sussequi vel paritus 
e converso promutua cantantium voluntate. Et isti opinioni videtur maxima pars canentium adhere' 
('The Ugatura binaria c.o.p. equals a brevis recta [i.e., not altered]; therefore its parts must be per- 
formed unequally, as is the truth. At the same time, however, one may be doubtful about their 
order, since certain authorities say that in this ligature the shorter value proceeds and the larger one 
follows, or just as well the other way around, according to the pleasure of the singers. It seems 
that the majority of the singers share this opinion'). Although this remark clearly confirms our 
contention that in the notation of the late 13th century a group of two S must be read in ternary 
rhythm, it simultaneously introduces another element of choice into the interpretation of the music 
of this period. On the basis of the date of the above treatise, the option between the iambic and 
trochaic reading of a group of two S would apply to all pieces written in Petronian notation, includ- 
ing those from the Roman de Fauvel (see e.g., p. 337, no. 3). 



34-0 French Notation 

new note value, prolatio appears in addition to tempus and modus. It 
may be well to note here that the term prolatio originally was used in a 
broad sense, namely, as a general expression for any variety of mensura- 
tion. Johannes de Muris, for instance, begins his Libellus cantus men- 
surabilis by saying: 'There are five elements of prolatio, namely, maxima, 
longa, brevis, semibrevis and minima' Nevertheless he uses the same 
term in the more restricted sense as well:' . . . the semibrevis equals three 
minimas in the prolatio maior (i.e., perfecta), two in the prolatio minor 
(i.e., imperfecta). 1 Still another meaning is encountered in the 'quatre 
prolacions' which are mentioned by various writers as an invention of 
Philippe de Vitry, 2 and which are identical with the four combinations of 
tempus and prolatio. Anon. VI (CS i, 369) describes the same combinations 
as four different types of breves namely: brevis perfecte perfecta ([3, j]) y 
brevis imperfecte perfecta ([3, 2]), brevis perfecte imperfecta ([2, j]), and 
brevis imperfecte imperfecta ([2, 2]). 

This leads us to a second important advance made by Vitry, namely, 
the de jure recognition of the equality of perfect and imperfect mensura- 
tion. The Franconian system rests entirely on perfect mensuration. 
We have seen, however, that imperfect modus already appears in some 
of the motets of the Montpellier and of the Bamberg codices, and more 
frequently in the Roman de Fauvel. Once more — as in the case of the 
minima — all that was necessary was to recognize and legitimatize an 
accomplished fact. This is credited to Vitry, who not only considered 
perfect and imperfect modus as having equal rights, but also applied the 
same dichotomy to tempus and prolatio, each of which might be either 
perfect or imperfect. Another innovation of Vitry which, however, was 
not readily accepted by his contemporaries, was the use of signs to indi- 
cate mensuration. He introduced the circle and the semicircle for 
tempus perfectum and tempus imperfectum respectively. The modus can 
be recognized by the rests, the modus perfectus being indicated by the 
'pausa triorum temporum' and the modus imperfectus by the 'pausa 
quarum quelibet valet duo tempora.' None of these signs were adopted 
in common use before the fifteenth century. 

It should be noted that prolatio and the metric combinations resulting 
from it are not yet treated in the Ars Nova in the same systematic 
fashion as the combinations of tempus and modus. They appear instead 
under the guise of various species or modifications of tempus. According 
to Vitry tempus perfectum can be minimum, medium, and majus, while 

1 CS m, 4 6, 47. 

2 Rigles de la seconde rectorique; cf. GdM i, 65, also AHdM 1, 16$. 



The Innovations oj the Ars Nova 341 

tempus imperjectum may be minimum or majus. The tempus perfectum 
minimum is nothing but the Franconian metrum ('tempus minimum pos- 
uit Franco'). It actually means tempus perfectum without pro/atio, i.e., 
with only three (or, occasionally, four) notes to the B, but with the 
modus (per/ectus or imperfectus) as an additional factor of mensuration. 
The other four kinds of tempus prove to be identical with the above-men- 
tioned 'quatre prolacions' or, in other words, with the four combinations 
of tempus and prolatio •} 

Tempus perfectum Tempus imperfectum 

Minimum Medium Majus Minimum Majus 

[HI, 3], [II, 3] [3»*1 [3, 3] [*,*] [2,3] 

A further important characteristic of the new epoch is the lengthening 
in duration of the large values which occurred automatically as the result 
of the introduction of smaller values. Anon. I speaks of this when, 
looking back at the Franconian (Petronian?) period, he says: 'At that 
time the longa and the brevis were sung as quickly as is the tempus imper- 
jectum today.' 2 Jacobus of Liege speaks even more clearly of this matter 
in his Speculum musicae. Chapter XVII of Book vn, entitled 'Anti- 
quorum excusatio et dictorum suorum expositio' {CS 11, 400) contains so 
many interesting remarks that we quote it in translation at consider- 
able length, particularly since it has not yet received sufficient attention 
in modern publications: 

In order to understand better the old musicians and their rules, one should 
notice that a double or triple mensuration of the longa, brevis and semibrevis 
exists — that is, a quick ('cita'), a slow ('morosa') and a medium ('media'). 
This is pointed out also by the moderns. One of them says this: one can 
sing in three different ways — 'tractim,' 'velociter,' and 'medie'; however, 

1 Vitry's reason for distinguishing these five types of tempus shows that even this progressive 
thinker occasionally inclined toward mediaeval scholasticism (CS in, 22, 'Et sic apparet . .'): 'And 
thus it appears that the perfect [tempus] is divided into three kinds of prolation just as the perfect 
[brevis] consists of three semibreves; and that the imperfect [tempus] is of two kinds, corresponding 
to the fact that the imperfect [brevis] contains only two semibreves.' 

1 'Tunc pronunciabantur longa et brevis ita velociter ut nunc tempus imperfectum' (CS in, 362). 
J. Wolf (GdM 1, 67) maintains, probably rightly, that it should read tempus perfectum instead of 
tempus imperfectum. No less definite and conclusive is the statement by Hieronymus de Moravia 
(CS 1, 90): 'Nota longa, in cantu ecclesiastico sumpta, habet et habere debet duo tempora moderno- 
rum. resolvendo vero sex tempora antiquorum.' Later on he speaks of 'unius temporis modernorum, 
sed trium temporum antiquorum.' 



342 French Notation 

the notation remains the same in each case. Another, in limiting himself 
to tempus perfectum^ says: tempus perfectum may be of three kinds, namely, 
'minimum,' 'medium' and 'maius.' 

Here one must know that when the ancients say that tempus perfectum 
cannot be divided into more than three semibreves, they presuppose the 
quick mensuration ('cita mensuratio'), as is confirmed by a contemporary 
scholar with reference to Franco. ... In reality, the semibrevis is to Franco 
the same as the minima or 'athoma' is to the moderns, being the ninth part 
of the brevis and in general considered indivisible. 

When the ancients said that the perfect brevis can be divided into three 
semibreves and not into more, they referred to the customary practice [in 
performance] of their time, particularly in the motets. ... I say particu- 
larly in the motets; for if we speak of the hocket . . . the perfect brevis 
had here such a quick mensuration that one could hardly place three semi- 
breves in place of it. Here . . . one can really speak not of a quick men- 
suration but rather of a very quick one ('citissima'), since there the perfect 
brevis does not last any longer than the semibrevis minima [i.e., the minima] 
does today. 

Modern musicians on the contrary frequently employ a slow mensura- 
tion. In reality, in modern writing the third part of the brevis perfecta 
lasts as long as the brevis perfecta was formerly . . . and the brevis per- 
fecta is worth as much as the longa was formerly. . . . 

Thus it is that they [the moderns] attribute to the semibrevis . . . 
exactly that which is the property of the brevis — namely, to be divisible — 
and also many other properties which do not belong to it. In this way 
they follow certain [musicians] who attribute to themselves the honor of 
inventing [the small note values] although the ancients had already used 
the quick mensuration in motets and also the very quick one in the double 
hocket. However, they too have made use occasionally of the slow or 
moderate manner ('morosam et mediam'), in which more than three semi- 
breves are used in place of the perfect tempus. That eminent composer 
Petrus de Cruce . . . made the beginning when he set four semibreves for 
the perfect tempus. 

By these remarks the conservative author seeks to defend the doctrine 
of Franco, according to which the S is the smallest note value ('indivisi- 
bilis') against the modern champions of the M. He shows that the M 
really represents nothing new; its smaller value is only an illusion since 
it is compensated in practice by a general tempo three times as slow as 
formerly. Expressed in modern terms the whole change simply amounts 
to this: the same tempo is no longer expressed as allegro in half-notes but 
as andante in quarter-notes. 

A study of the organa and motets from 1200 to 1350 shows that there 
occurred four definite changes in the duration of the note values, changes 



The Notation of Machaut 343 

which, however, entail only two really different tempi, as appears from 
the following table: 

/ 

Perotinus: D =40 L = 80 B = 240 

Franco: L =40 B = 120 S = 360 

Petrus de Cruce: L = 27 B = 80 *9 = 240 

Vitry: 5 (pf.) =40 S = 120 M = 360 

Machaut: 5 (pf.) =27 £ = 80 M = 240 

The column marked / represents the /«f/«j (beat). 1 

It follows that there occurred twice an almost exact triplication of the 
note values, without a real change of tempo, the temporal value M.M. 80 
being represented by the L y B, and £ around 1225, 1275, and 1350 respec- 
tively. A really different tempo, however, is found in the Franconian 
motets, and recurs in the early Ars Nova (Vitry). It appears that the 
terms Velociter,' 'medie,' and tractim' can be interpreted as indicating 
the values M.M. 120, 80, and 40 for the B. The former duration is the 
'minimum in plenitudine vocis' of Joh. de Garlandia (CS 1, 97). 

From the point of view of our present study the important conclusion 
is that the actual tempo of an Ars Nova motet was the same as that of a 
Franconian motet; the notation was simply made in smaller values, the 
speed of S MMM S S now being the same as that of the former B SSS 
B B. This means that, once more, we have to change our scale of reduc- 
tion, rendering the S by the quarter-notes of modern notation. This 
leads to a transcription in semibrevis -beat which, as we know, persisted 
throughout the fifteenth century. 

B. The Notation in the Works of Machaut 

The establishment of perfect and imperfect mensuration in the three 
degrees of modus •, tempus and prolatio, together with the application of the 
Franconian principles of perfection, imperfection and alteration to each 
of these degrees, led to a notational system which is essentially identical 
with that known to us from our study of white notation. In fact, white 

1 This table may be compared with that given by H. Besseler in AJMW vm, 212 and reproduced in 
G. Reese, Music in the Middle Ages, p. 233- It will be seen that our tempi differ from his indication 
chiefly in the case of the motets of Petrus de Cruce for which Besseler suggests a considerably slower 
tempo (M.M. 54). It goes without saying that our above metronome marks are deliberately 
'standardized' and, therefore, should not be taken too literally. They are intended to show not 
only that there existed only two different tempi in the period under consideration but, in addition, 
that these two tempi are related to each other. As a matter of fact, three quarter notes in M.M. 120 
are equal in duration to two quarter notes in M.M. 80. It appears that, for instance, Franco's 
tempo results by dividing the D of the Perotinus tempo in three, instead of two, parts. 



344 French Notation 

notation is, in principle as well as in most details, nothing but a graph- 
ological modification of the fourteenth century French notation, with 
white shapes used instead of the black ones. Therefore few explanations 
are necessary in addition to those given previously. 

The earliest source of fourteenth century French notation is the MS 
Ivrea. 1 Its notational features are practically the same as those of the 
various MSS containing the works of Machaut (1300-1377), to which the 
subsequent explanations chiefly refer. 

Imperfection and Alteration. Whereas in the thirteenth century these 
devices were limited to the L and B> they can now be applied in any per- 
fect degree. In addition to the imperfectio ad totum (L - B; B - S; 
S - M), the imperfectio ad partem is used (L - S; B - M), and theorists 
hastened to expand this scheme by the addition of imperfectio ad partem 
remotam and partes remotas {Mx - S; L - M), as well as of imperfectio ad 
partem remotissimam and partes remotissimas {Mx - M). 2 They take a 
particular delight in constructing tricky examples showing the combina- 
tion of imperfection and alteration. 3 As a curiosity the following exam- 
ple from Tunstede {CS iv, 270; see also GdM 1, 129) may be cited: 

■ ■♦!■■ ♦ i ■ ♦ i ■ 

Here the mensuration is [III, 3, 3]. The punctus indicates the end of 
a group of notes equal to a perfect L. The L itself is imperfected by a 
B which in turn is imperfected by a S which again is imperfected by a M. 
A second group of the same value is contained between the punctus and 
the final L. In order to reach the value of three B or nine S y one must 
double the value of the second B (alteration). However, both the B 
recta and the B altera are imperfected by the group S - M which follows 
each of them. Here is the transcription: 

SirTr ■ if r p irr p irTrr p irTrTri 

Needless to say, no such tricks occur in the musical sources. Their 
difficulty lies in clerical errors or inaccuracies rather than in deliberate 
intricacies of notation. Most frequently the complications are caused by 
the lack of a punctus divisionis which would be necessary or at least help- 
ful in clarifying the situation. Below are two examples from Machaut's 
Mass. In (a) the normal grouping of the four B between the two L 

1 See the description by H. Besseler in AjMlV vu, 174. 

2 See p. 112. 

3 See p. 122. 



The Notation of Machaut 



345 



would be i +3; however, the context shows that they have to be divided 
as follows: 3 + 1 (imperfection of the following, instead of the preceding 
L), Example (b) shows a similar case of seven B which, according to the 
context, must be grouped 3+3 + 1, instead of 1 + 3 + 3. In both 
cases, a punctus divisionis after the first L would have been sufficient 
fully to clarify the rhythm: 1 




(a) cf. GdM 11, 29, staff 5; (b) cf. GdM 11, 35, staff 8. 

An interesting license of Machaut is illustrated by the following ex- 
amples of imperfectio ad partem: 



[III, 2] 



b,*]: .i4U.ni 



r -!loJJI 

Such use of imperfection does not correspond to strict theory, accord- 
ing to which imperfection may be caused only by a note which belongs 
to a perfect mensuration or, in modern terms, which is one-third of the 
next higher value. In the above examples, however, the 'imperfecting' 
note is one-half of the next higher degree. As a matter of fact, an exam- 
ple like the above is extremely rare in the sources of mensural notation. 
It seems that Machaut alone was open-minded enough to transgress the 
theoretical limitations and to admit a freer, yet perfectly logical and sim- 
ple use of imperfection. 2 Two examples from the ballade De petit po are 
quoted by Wolf in GdM 1, 171 (without indication of the MS source): 





1 In these two examples our thirteenth century scheme of transcription (B = quarter-note) is 
used because the entire mass is evidently written in irevis-beat. This fact is one of the various fea- 
tures proving that Machaut's mass is one of his earliest works, possibly written under the immedi- 
ate influence of the mass of Tournay (see G. Reese, Music in the Middle Ages, p. 356). There should 
be an end to the story, inaugurated by Kiesewetter one hundred years ago and still repeated in mod- 
ern books, that Machaut's mass was written for the coronation of Charles V in 1364. 

2 Machaut was known among his contemporaries for his freedom in the treatment of established 
principles of notation, as we know from his contemporary Johannes de Muris (see GdM 1, 170). It 
is interesting to recall in this connection Glarean's similar remark about Josquin de Pres, two hundred 
years later (see p. 108, footnote 2). 



34^ 



French Notation 



The following passage from the ballade Plourez dames (beginning of 
the contra) illustrates the use of imperfection in [3, j]: 



The first three puncti mark off groups totalling the value of a perfect 
B. The second and the third B are reduced by imperfectio ad partes from 
nine S to the minimum number of four S. The next perfection would 
seem to include the group MBM, after which there is another punctus. 
Actually, however, this group has the total value, not of nine S, but only 
of six, the three missing S being supplied by the two following M (with 
alteration). A similar group occurs at the end of the passage (for the 
complete piece, see GdM 11, no. xxv) : 



u~~i ? 



Determination of the Mensuration. In the sources of the French Ars Nova 
the note values Mx, L, B, S, and M are used in the various combinations 
of modus, lempuSy and prolatio. However, the mensuration is almost 
never indicated by signs but must be derived from the context. 1 Herein 
lies the chief difficulty presented to the novice by the works of Machaut. 

In his Geschichte der Mensuralnotaiion J. Wolf has treated the subject 
of the determination of the mensuration in a special chapter {GdM 1, 
150), containing 34 rules by means of which this problem is to be solved. 
F. Ludwig (SIMG vi, 607) criticises this procedure as unnecessarily com- 
plicated and recommends that one rely chiefly on the musical sense of 
the composition or the part — that is, he should recognize the mensura- 
tion from the rhythmical nature of the entire melody rather than from 
single details. In particular, he points out that in many cases the men- 
suration is indicated in the original MSS by the writing of notes in 
groups (e.g., groups of three S written close together would indicate 
tempus perfectum, etc.) and regrets that this important detail of notation 
is obscured in Wolf's reproductions {GdM 11). 

Ludwig's advice is thoroughly justified and we repeat here the sugges- 

1 Such time signatures are mentioned by nearly all the theorists of the fourteenth century; see the 
comprehensive table in GdM i ic. The absence of such signs in most of the compositions is all the 
more striking when one considers that Jacobus, the champion of the Ars Antiqua, bitterly complains 
about their use (CS 11 431: 'Haec et multa alia ponunt moderni. . . .'). 



Determination of the Mensuration 347 

tion given previously that one try to sing short sections of each voice be- 
fore attempting to transcribe it. On the other hand, however, some of 
the rules given by Wolf prove to be useful and indeed necessary. Below 
is a presentation of these rules condensed and put into different order: 
/. Rests. The rests are the surest and most valuable aid in recognizing 

the mensuration. The rest of three tempora EJE unequivocally indi- 
cates modus perfectus (III), while the combination =p= invariably in- 
dicates modus imperfectus (II). A single rest of two tempora may occur 
in both modi; obviously however in III it must always be accompanied 

by a preceding or following B: ■ \ =F J:I . If it should appear be- 
tween two L, the modus is imperfect: g 1 ■ . Also two successive 
binary rests indicate II: EHE , since in III the same duration would be 
expressed by — {-*- . 

As regards the tempus (or prolatid) , a clue is frequently found in the writ- 
ing of two successive S (or M) rests. Such rests occur either on the 
same line of the staff, =^= , or on two different lines, =^= , according 
to whether they belong to the same or two different groups of two or 
three S (or M). Whereas the latter way of writing can be used in either 
perfect or imperfect mensuration, the former will be found only if the 
tempus (or prolatio) is perfect. As a matter of fact, in imperfect men- 
suration two such rests would occupy a full group of two S (or M) and, 
therefore, will have to be replaced by a B (or S) rest. It follows, that 
two S (or M) rests written on the same line indicate tempus perjectum (or 
prolatio perfecta) . 

2. Notes. A generally trustworthy indication of perfect mensuration 
is found in the occurrence of groups of three notes of the same kind be- 
tween two of the next higher value, e.g.: 

Ill: q---^ ; 3: ■♦♦♦■; J: ♦!!!♦. 

Of course, such a combination may occur in imperfect mensuration as 
well, namely, as a syncopated rhythm: *♦» ♦• ,|J|J J! JJJJ . However, in 
this case a fourth note of the same value will always be found in close 
proximity which will complete the gap left by the syncopation. Synco- 
pation is very frequent in the French Ars Nova and may easily obscure 
the mensuration. The more frequently combinations such as B SSS B 
(S MMM S) appear, the more likely they are to indicate perfect men- 
suration. Similar deductions may be made from the appearance of an 



348 French Notation 

isolated note between two others of the next higher value. Persistent 
alternation of B and S (or S and M) generally indicates that the lempus 
(or prolatio) is perfect: ■♦■♦■♦ (3); ♦!♦!♦! (3). Again, however, the 
possibility of syncopation has to be taken into account: 

♦ l*i*UI-*IJJ3LJWJJ|j. 

Frequent groups of two point to imperfect mensuration, although they 
may also occur in perfect mensuration, with alteration of the second note. 
The conclusion in favor of imperfect mensuration becomes more binding 
if the last note of such a group is replaced by its 'valor,' i.e., by smaller 
notes of the same value, since in such a case alteration is impossible. 
However, a combination such as B S MM B is also possible in tempus 
perfeclum if both imperjectio a parte post and imperfectio a parte ante are 

applied:. ♦U..i|JJ|/3J|. 

J. Dots. Here we must recall the statement previously made (p. 116 f) 
that there are in reality only two kinds of puncti — the punctus divisionis 
in perfect mensuration, and the punctus additionis in imperfect mensura- 
tion. The latter demands the presence of a note of the next smaller 
value to supply the missing part of the beat. Therefore, if such a note 
is not present (either following immediately or in close proximity) the 
dot must be a. punctus divisionis and therefore points to perfect mensura- 
tion. 

4. Red notes. In this period, red notes (which, by the way, appear only 
in tenors) have the same significance as blackened notes have in white 
notation: three red notes are equal to two black ones (proportio sesquial- 
tera^ or hemiolia). Although in white notation blackening (coloration) is 
used in both perfect and imperfect mensuration, in early fourteenth cen- 
tury music the use of red notes occurs chiefly, if not exclusively, in per- 
fect mensuration, which is thus temporarily changed into imperfect 
mensuration. As we have seen previously (p. 131), coloration of breves 
(for instance) causes a change not only in the tempus but also in the 
modus. The appearance of red B points therefore not only to lempus 
perfection but also to modus imperfectus in the black notes. The passages 
notated in red (reproduced below as white notes) are then in tempus 
imperfectum and modus perfectus: ■♦♦♦naa=i| c J.|JJJ|iJ 6 JJ| . 

It is scarcely possible to give more detailed information on this subject, 
since everything depends upon the context. In this connection it should 
be noted that many of the rules given by Wolf are by no means as in- 
fallible as he suggests. As an example we may take the rule I, 7 of his 
list, according to which modus perfectus is understood 'wenn hinter drei 
breves sich ein Punkt befindet': ■ ■ ■• . This conclusion is by no means 
certain. If a S were to follow the dot, the dot might then be a punctus 



Ouverl and Clos 



349 



additionis and the modus might be imperfect: ■■■-♦=U|J|JJJ J| . Also 
rule 8 of the same group ('wenn die einer longa folgende longa einen 
Punkt hat') is incorrect; ^y may mean l<H©-| as well as|o|o|_«j (with 
a following B). 

It should be noticed that several compositions of Machaut display a 
mixture of mensurations, another feature illustrating his free treatment 
of the theoretical rules. For instance, in his rondeau Rose lis , passages 
such as those given under (a) clearly point to [3, 2], while others such as 
under (b) no less definitely suggest [2, j]: 

Obviously, the rhythm changes here from one mensuration to the other, 
e.g.: 



For more details, see GdMi> 168, and F. Ludwig, Guillaume de Machaut, 
Musikalische tVerke (Leipzig, 1926), 1, 00. 

Ouvert and Clos. Finally, the problem presented by the repetition of 
sections in the secular forms of the fourteenth century (ballade, rondeau, 
virelai) must be briefly considered. The ballade, for instance, consists 
of two sections, the first of which is provided with two lines of text and 
must be repeated, so that the form A A B results. The repeated section 
usually has two different endings which are sometimes designated ouvert 
and clos and which correspond to our prima volta and seconda volta. 
However, these cadential passages are not as clearly marked off as they 
are in modern music and, therefore, demand special attention. 

The ballade De petit po may be considered as a first example. Follow- 
ing is a reproduction (from MS Paris, B.N./rf. 9221) of the passage near 
the end of section A, beginning with simultaneous notes (the mensura- 
tion is [3,^]): 




wa SBj 



\ 



In each voice, the end of A {prima volta) is indicated by a single long 
stroke, whereas the seconda volta group extends from this stroke to the 
double stroke, after which the second section B begins. This clos group, 



35° 



French Notation 



of course, is not meant to follow after the last note of the ouvert group, 
but to be sung in place of a corresponding part of the prima volta. The 
main question, then, is to decide at which point to leave the ouvert and 
substitute the clos group. It is in their failure to indicate this point that 
the manuscripts of this period differ from modern practice. The situa- 
tion is usually made clear to some extent by the fact that the clos group 
at its beginning repeats one or several notes of the ouvert group; there- 
fore, the initial notes of the clos group serve as a clue as to where the 
ouvert group starts. 1 Here follows the transcription of the passage: 




It must be noticed, however, that this is an exceptionally simple exam- 
ple for two reasons: first, because, in each single voice, the clos group has 
the same length as the corresponding ouvert group; second, because the 
length of these groups is the same in all three voices. Neither regularity 
is requisite or even usual. The following passage from the ballade 
S' amours ne fait (see GdM n, no. XXIII) may serve as an illustration: 



x=x 



■ UU'W 



* 



WE= 



In the discant, the lines of demarcation appear as short strokes which, 
having the shape of B rests, may easily mislead the novice. The clos 
group of the discant includes three B and the final L (the mensuration is 
[2, j]), while the ouvert group, beginning with the same two notes as the 
clos group, includes only two B and the final L. Similarly, the tenor has 
five notes (four B and one L) in the clos group, but only four (three B 
and one L) in the ouvert group which, of course, opens with the second 
note of the ligature. It appears not only that within each part are the 



1 Another clue is provided by the distribution of the second line of text. However, owing to the 
habitual carelessness of the scribes in the underlaying of the text, these indications cannot always 
be relied upon. 



Ouvert and Clos 



35i 



two groups unequal in length, but also that there is a Vertical' variation 
from one part to the other: 



Ouvert 



Clos 



Cantus: 2B+L 3B + L 

Tenor: 3B + L 4B + L 

It is particularly this vertical variation which calls for attention. 
It implies that the performers of the two parts must change from their 
ouvert group to their clos group at different times. Although, from the 
point of view of part-performance, this is a perfectly legitimate proce- 
dure (it is obviously dictated by the desire to make the endings as short 
as possible), it causes some inconvenience if a transcription in score is to 
be made. Here the clos group must be filled out with certain notes which 
do not appear in the original. These are indicated in brackets in the 
subsequent transcriptions. Asterisks are added to show the places in the 
original notation where the singer must leap to the clos group. 




Naturally, the first measure of the seconda volta may be omitted in the 
final draft, as it happens to be identical with the corresponding measure 
of the prima volta. In this case, the signs 1 and 2 must be shifted for- 
ward by one measure. 

An example showing a different 'jumping-off place' in each of its three 
parts is furnished by the ballade Ploures dames. Below is a reproduc- 
tion of the passage in question: 

D- 1 1 I 1 , , a b 




In the discant and contra, the end of the prima volta is indicated by a 
small stroke in the shape of a B rest, while a sign x indicates the cor- 
responding place of the tenor. It appears that in this example the strokes 



35* 



French Notation* 



have the meaning of real rests; they are the equivalent of the group of 
the tenor between the L and the asterisk. 1 The only clue for the 
'jumping-off place' in each part is found in the fact that the initial note 
(or notes) of the seconda volta reiterate the corresponding notes of the 
■prima volta. Thus, the S on e' in the discant refers back to the final L 
on e', while in the lower parts the indication is a good deal clearer on 
account of the fact that a small group of notes, identical in pitches as 

well as in values, is reiterated. In the above example these points of 
reference are marked by the letters a and b. It is important to notice 
that in the score the relative position of the signs b for the seconda volta 
always conforms to that of the signs a for the prima volta. This observa- 
tion provides a helpful cue as to where to start with the f/oj-endings of 
the different voice parts. In the present example the clos-ending of the 
contra starts one measure, that of the discant two measures after that of 
the tenor. The empty measures (two in the superius, one in the contra) 
must be filled in with the notes found in the corresponding measures of 
the prima volta. 




Examples. We turn now to the consideration of several compositions by 
Machaut. Facsimile 68 shows a two-part ballade Ne pensez pas. The 
frequent groups S - M indicate prolatio perfecta, as do still more clearly 
the two M rests followed by a third M near the beginning of the second 
staff. As to the tempus, the two S rests in the first staff (second half) 
following the S over the syllable '-e' point to tempus perjectum. The 
mensuration [3, 3] is also implied by the group of notes found between 
the first L of the cantus (syllable 'pas') and the next B. 

This piece illustrates the difficulties brought about by the too sparing 
use of the punctus divisionis in Machaut's works. Actually, this sign is 
all the more necessary here, since in the present mensuration the B can 
be reduced by various degrees of imperfection from its normal value of 
nine M to as little as four M (see p. 122). However, the correct group- 

1 The transcription of this passage in GdM III, 69 is not quite correct. 



Examples 
Facsimile 68 



353 




lilliiillfe 



& ptiteP&mwmm «• te Dot* * m*> 

-«» , Viiilcittcttt tag gejeggM c mntnota ^ "y 



itr ratre 

i=i3ti 



i rr»w*te ; 



fc (cm /icwr nc Doufl Mop .^ Of 
- n ton nc . , , T* * Un 



gg§ 




en Twin awM^^Wewri^.wnc itfqiufin; ae mt 



^^"'^^^jggtt^ 



Sefour m •Ann'touSnepttt 




ft ou que « 




MS Paris, Bibliotheque Nationale/rf. 7J<S^ (<ra. 1375) 
From page 459' 



354 



French Notation 



ing is rarely indicated by a punctus divisionis, but must be determined 
by other considerations. For instance, in the group to the value of six 
(perfect) S right after the first B of the discant, the 'Franconian' group- 
ing 6 = 1 +3+2 (involving imperfection and alteration) is impossible 
because the last S is replaced by the combination £ + M which, of 
course, cannot undergo alteration. The proper grouping therefore is 
6 = 3 + 3, so that the initial B remains perfect. In the group of nine 
S to the text: Vous ne pen-' (fourth staff) the desired grouping 9=3 + 
3 + 3 is suggested by the writing of the notes in close groups, a feature 
which frequently provides a helpful clue. However, the second B on 
staff 3 remains perfect although it is written close to a S and M. In all 
cases of doubt, the correct values must be derived from the context. 

The c/os group of the discant (syllable 'foy') includes only one L, that 
of the tenor a S and B in addition to a L, so that some notes must be in- 
serted in the discant. Unfortunately, the writing gives no clear indica- 
tion as to the place where one has to make the jump to the c/os group or, 
in other words, where the ouvert group begins. Below are two transcrip- 
tions which illustrate the situation. The second is that given by F. Lud- 
wig (Machauty 1, 9). The first seems preferable not only from the mus- 
ical point of view, but particularly with regard to the underlaying of the 
text. In fact, in Ludwig's transcription the place of the syllable 'foy' is 
willfully changed. 1 





^ 




^ ♦_. 


Tr ~ .♦/* 


nfrn ' 1 p r Pr frft Pr v r ff r r*r i r r ff r ir mt •» r r i p* \ 


8 


sou - 
cuer 


- vent 
en 


ne vous voy. 
♦ 


bonne foy. 


■wit f 4 ' 1 >. r r~ \f nr r irr r rip* rr j: til tt^ 






The two sharps on the fourth staff refer to the note f, not g. The form of the piece 
is that of a ballade, i.e., A A B, the first section being repeated. The beginning is 
transcribed in the appendix, No. 47. 

1 It may be remarked here that F. Ludwig, in his edition of Machaut, practically always inter- 
prets adjacent notes of equal pitch as tied notes, by connecting them with a dotted tie. We cannot 
see any justification for this procedure. 



Examples 



355 



The two-part ballade Do/is amis of Facsimile 69 has the less usual form 
A A B B, both sections being repeated. Since it includes several L (see 
also the first two ligatures of the tenor) the mensuration involves not 
only tempus and prolatio, but also modus. The combination B L B L B 
at the beginning of the tenor strongly suggests modus perjeclus, as does 
also the corresponding passage of the discant. The groups of smaller 
notes, such as S M M, or M M M M, clearly point to imperfect tempus 
and prolatio. The mensuration is, therefore, [III, 2, 2]. However, the 
modus is not always strictly observed. For instance, the tenor for sec- 
tion A includes 31 B prior to the final note of the ouvert group, that is, 
prior to the last note of staff 4 — which by the way, should properly be 
written as a L (see the last note of the clos group). This number is one 
too many to fill in perfections of three B each, so that one measure must 
be expanded to include four half-notes, as indicated below. It may be 
noticed that this change of meter would be unnecessary if the punctus 
divisionis after the first ternaria of the tenor were considered as a clerical 
error; in fact, the corresponding note of the cantus {L over '-plaint'; this 
L is written with an upward stem which, however, does not have the 
meaning of a plica) has no dot. If this conjecture is adopted, the two L 
would be imperfected by the following B, a procedure which would re- 
duce the number of B to 30 (see below, version (a)). 

j, n JiJJ J J ^\HJ j j 




A similar case of irregular measures occurs in the second section which 
contains 28 B before the final note. As before, this number can be re- 
duced to 27 if the punctus divisionis after the third L of the tenor is dis- 
regarded (once more, the corresponding L of the discant — end of the 
second staff — has no punctus). The student is advised to make two 
transcriptions and to compare them, not only from the notational point 
of view, but also from that of the musical phrase. 1 

In both sections A and B the clos groups of the tenor (beginning of 
staff 5 and end of staff 6) include 3 B before the final note, while the cor- 
responding groups of the discant (second staff, middle, between the two 

1 F. Ludwig's transcription (Machaut i, 5) introduces numerous changes of meter (|, |, f) which 
are not indicated in the original notation and which, from the point of view of the musical phrase, 
are frequently not convincing. The same remark applies to many of his transcriptions. 



35& 



French Notation 



pseudo 5-rests, 1 and a similar group at the end of staff 3) include notes 
of the value of only one B before the final note. Hence, notes to the 
value of two B must be supplied in the transcription of the discant. It 
may be noted that the final notes of the various sections are written al- 
ways as B in the discant, whereas in the tenor they are written partly as 
B, partly as L. In any case, their duration is not exactly determined, 
so that a fermata sign would properly indicate their character. 

The sign before the B in the middle of the first staff is a \>. At the end of the second 
staff one finds a sharp for the L on g, a sign which probably is not valid for the following 
M on the same pitch, since otherwise a chromatic progression g#, a, b|? would result. 

Finally, a three-part ballade Biaute qui toutes autres (Facsimile 70) 
may be studied, which is particularly interesting because it is one of the 
earliest compositions to show the use of Vitry's signs OC (see the 
tenor). The tenor starts out in [3, 2] which is the normal mensuration 
of the whole piece, but changes three times to [2, 2]. The first and the 
third sections in [2, 2] are lengthy examples of syncopation, in the scheme 
S B B B . . .BBS. The sign C makes all these B binary whereas 
under the sign O they would be ternary. Other manuscripts indicate 
the binary value of these B by the use of red notes (e.g., Paris, B.N. frc. 
J 586) or white notes (Paris, B.N./rf. 1585): ObObbbbbIIOb = 

O-oaaoU. - JlJ.liUJjJJJUJJlllJ.I 

Below is a transcription of the beginning of the tenor: 




The transcription of the other parts presents no difficulties. The sec- 
ond B of the contratenor is perfect, as is suggested, in a vague manner, 
by the arrangement of the subsequent S in ligatures c.o.p. In fact, it is 
more natural for such a ligature to be placed within one perfection; how- 
ever, this is by no means a universal usage. 



In Machaut's motets it is principally the tenors which show notational 
features of interest. Many of them are 'isorhythmic,' that is, they re- 
peat several times a long and elaborate rhythmic pattern called talea. 
This principle of rhythmic reiteration is evidently a continuation and 

1 I.e., the two dashes which lock exactly like 5-rests, but actually are lines of demarcation. 



Examples 
Facsimile 69 



357 




nd fltine o?mon compWnt » a top fc plamt" ot m»» 
ncrs qitaiirftfticpn , 1mint,quctienetX!in#]. 





titomt , parjcfimr uctce fc corns . <£?i nice Ian 



tttmnt • a# tBtmnunt ft f , , conn? . fc cmitt mca , woW 

^y- tnr fcflillom*« neftncns 9111 confix mamait. 

v/^ tons Ice lonnQ.onftttttce Writers cnmofnc mair 



T i. r , 1 i,,, T .,^>wrT> j V^ 



&%. 



OJ- 



01 



d|n.frl ♦s* 1 



n 



0*- 



MS Paris, Bibliotheque Nationale/rf . 7jvfy (*yz. 1375) 
From page 456' 



358 



French Notation 



development of the modal patterns of the thirteenth century. Just as 
in the Franconian motets the liturgical tenor was forced to conform, for 
example, to the rhythmic scheme of the first ordo of the third mode 
I J- 1 J J I J-I--I, so we find here schemes of longer extension and of freer 
design, as for example in the motet He mors-tyuare non sum in which 
each talea comprises eleven L (see below, A, B, C). Another principle 
of construction to be found in nearly all the motets of Machaut is the 
writing in two sections (I, II), the second of which repeats the tenor of 
the first in diminution. 1 Thus, our tenor continues (after a fourth in- 
complete talea D) with three groups a, b, c, each of which includes eleven 
B, replacing each note of the first section by its half: 




As appears from the rests, the tenor is in modus imperfeclus, i.e., with the 
L equal to two B. The tempus and prolatio which, of course, must be 
determined from the upper parts, is [2, j], so that each B occupies one 
^-measure, each L two, each Mx four: 



In section II the grouping of notes and rests suggests phrases of three 

* measures each or, in other words, modus perfect us (see GdM II, no. xiv). 

A more complicated structure is found in the four-voiced motet Felix 

virgo — Inviolata — Ad te suspiramus — (contratenor), the tenor and contra 

of which are reproduced on page 360. 

The motet begins with a long 'Introitus' which, in the two lower parts, 
includes eight rests each of the value of a perfect L and notes to the value 
of six perfect L. The double bar after this indicates the beginning of the 
main portion which shows alternation of groups of black and red notes 
in both parts. As is indicated by the inscription 'Nigre sunt pertecte, 
et rubee imperfecte,' the black notes are in perfect mensuration, i.e., per- 
fect modus, the red ones in imperfect. Each black L, therefore, equals 
three B, each red L two. Of particular interest is the fact that the black 
and red notes do not appear simultaneously in both parts, but in alterna- 
tion. As a matter of fact, the initial group of the tenor (after the Introi- 

1 The cantus firmus melody itself is called color. See C>. Reese, Music in the Middle .iges, 339. 



Examples 
Facsimile 70 



359 




J « 

^ Oh 

<" - 

cr o 



j6o 



French Notation 



Jll H Tj p l | l J'h li11iA l | bl CLJ >il'fl1| ^ 
flnomifl. Ccno? . ao tc ftjftmntmtg ymcmre ft watt -if.' vlifx funr 



crftor • «r Rutec iiiqierfrnr Xnuu a « 



jimvcrc . tt Bigg intjicrfrftt 




fll i I «. 01 m_ ' 



tus) includes six perfect Z,, equal to eighteen B i while the initial group of 
the contra includes nine imperfect L which also equal eighteen B. This 
scheme of alternation continues throughout the entire motet. As usual 
with Machaut, the tenor and contra are repeated in the diminution. 
The beginning of this final section is indicated in the contra by three long 
'bar-lines' (not rests) although a similar sign is missing in the tenor. As 
can be seen from the identical succession of pitches, as well as from the use 
of smaller values («?), the diminution section begins after the first quater- 
naria of staff 2. Here the black and red notes indicate perfect or imper- 
fect tempus, so that six black B or nine red B are equal to eighteen S. 

The upper parts (not reproduced here, but to be found in GdM n, 24- 
27) are in [2, j>], that is, in g-meter with imperfect modus (binary L) 
throughout. For simplicity's sake this meter has been disregarded in 
the subsequent transcription (see p. 361) in which the B are rendered 
as plain half-notes (instead of dotted half-notes), each of which equals a 
s-measure of the upper parts. They are grouped in %- or 2-measures, 
according to the mensuration indicated by the black or red notes. The 
small notes on top of the staff indicate the rhythm of the discant (D). 

C. The Notation of the Later Sources 

The French notation just described, which on account of its clarity 
and simplicity may be regarded as the classical notation of the Middle 
Ages, persisted with but slight modification through the first half of the 
fifteenth century. Indeed, in a sense it continued to exist much longer, 
since the white mensural notation is its direct continuation, with the 
black notes supplanted by white ones. Aside from the manuscripts 



The Notation of the Later Sources 

J. UJ>JJU 



361 





I *JV JhfJ>*'J>iJ.*J>i 




containing the works of Machaut, the preserved repertory of fourteenth 
century pieces written in French notation is rather limited, as appears 
from the list given on p. 202. Additional material for the study of this 
period is available in the reproductions, contained in SchT, p. 80-82, of 
the fragment Bern, Bibl. Bongarsiana Ms. A 421. The study of these 
facsimiles is strongly recommended. The beginning of the cantus of 
the ballade II nest si grand possession (p. 82) illustrates a very free 
application of the principle of imperfection: 



M 



ggggg 



The initial L is reduced here by the following M, although the men- 
suration of the piece is imperfect in all degrees ([II, 2, 2]): 




Similar cases are cited in GdM 1, 183 and 323. 



362 French Notation 

The fifteenth century sources of French notation (see the list, p. 202) 
show an increased use of red notes which now appear in all the parts. 
They usually occur in groups of three B or three S, that is, in the familiar 
combinations of coloration (three red notes equal to two black ones). 
Aside from these groups one finds single red M which have the meaning 
of an Sm. A three-voiced Kyrie and Christe from Cambrai Ms. 6 may 
serve as an illustration (Facsimile 71 ; in the original the discant is written 
on p. 4', the tenor and contra on p. 5; the red notes are reproduced here 
as white shapes). The discant of the Kyrie contains several red Sm, the 
contra red Sm as well as coloration-groups. The second red ligature of 
the contra (L-B) appears in syncopated position, being inserted between 
the second and third of a group of six M. Similar examples have been 
encountered in our study of pieces from the MS Canonici (p. 133, 134) 
which is only slightly later than the MS Cambrai. As will be seen later, 
this use of syncopation is only a modest reminiscence of those rhythmic 
complexities of the late fourteenth century which will be treated in our 
last chapter (Mannered Notation). Here follows the beginning of the 
contra in transcription: 

orf j.ijj 1 j j 1 n JjJ JjJ y *n I J J J I 



The Christe is written in tempus imperjectum diminutum, that is, in 
about twice its apparent speed. The beat falls here on the B which, 
therefore, must be transcribed as a quarter note. It should be noted 
that this section contains no Sm which here would be too rapid to be 
performed. 1 

The same notational methods occur in other manuscripts of the period, 
such as Rome, Vat. urb. /at. 1411 (see the examples in GdM 1, 193); 
Munich, mus. ms. 3/92 (GdM 1, 194, 195); Bologna, Lie. mus. cod. 37 
H. E. Wooldridge, Early English Harmony, pi. 4.9-60; GdM i, 198); 
Bologna, Bibl. Univ. 22/6 (GdM 1, 199 ff); Oxford, Selden B 26 (facsimile 
reproduction in J. Stainer, Early Bodleian Music, 1, pi. 37-97 and 109; 
see GdM 1, 368 ff); and the Old Hall Manuscript (ed. by A. Ramsbotham 
and H. B. Collins, 3 vis., Westminster, 1935-38; see GdM 1, 373 ff),— the 
last two of English origin. The reproductions given in GdM 11, nos. 
XXX — XXXVII provide additional material for the study of the nota- 
tion of the Dufay period. Regarding no. XXXVI (Dufay) it may be 
mentioned that the section 'Qui ipsa . . . dubitationem' (p. 57), 
marked 'faulx bourdon,' calls for the addition of a third part which is a 

1 See footnote of p. 193. 



The Notation of the Later Sources 
Facsimile 71 



363 




r^^r^ 



umM 



llfl'.tortiii ,. 



lfpflm. 



g ^l.- i ^i ||, S 



ttnm. 'tj»i 






vcmmtn 



VOntmniu».ijttif. 



l ' won. 



I fpfon Ipjiflr I I 



ifpfon 

E55 



lepfai. 



MS Cambrai, Bibliotheque Communale Ms. 6 {ca. 1425) 
From pages 4', 5 



364 French Notation 

fourth below the written discant throughout (J. Wolfs transcription, vol. 
iii, p. 87-88 gives only the two notated parts). 1 The section 'Quamvis 
benedixeris' (p. 59) is- also in "faulx bourdon," with two notated parts. 
Unfortunately, the lower part is missing in the source used by Wolf. It 
may be noticed that the transcriptions of pieces from Bologna, cod. 37, 
which are given in vol. 11 of Early English Harmony, contain numerous 
errors. These are due chiefly to a failure to realize the correct meaning 
of alteration and of the red notes (compare, e.g., the facsimiles pi. 51, 52 
of vol. 1 with the transcription in vol. 11, p. 120). 

Owing to its notational peculiarities, the Old Hall MS, which was 
written in the first half of the fifteenth century, deserves a few explana- 
tory remarks. The most striking feature is the extensive use of score 
arrangement, a method of writing which, as has been stated previously 
(see p. 271) was generally abandoned after the school of Notre Dame and 
which was not readmitted for the writing down of ensemble music until 
the early seventeenth century. Its use in the Old Hall MS is, no doubt, 
a feature of typically English conservatism, similar in nature to those 
which have been observed in our study of English keyboard music of the 
sixteenth century (see p. 8 ff). The score arrangement is used for all the 
pieces which are written in the conductus style of the thirteenth century, 
i.e., with similar rhythm in all the parts. For an example see the fron- 
tispiece of vol. in of Ramsbotham's publication. On staves 8, 10, and 
11 of this facsimile there occur examples of a rare ligature to which ref- 
erence has been made in footnote 1 of p. 90. 

Facsimile 72 shows a page from the Old Hall MS containing a Et in 
terra by J. Tyes. The notation is without problems, except for the ques- 
tion of the temporal relationship between the sections in G and in C 
which alternate several times. This question, however, is clearly an- 
swered by the tenor which shows black notes for the former sections, red 
notes for the latter. It follows that the B of C is two-thirds of the B 
under G , or in other words, that the M have equal duration throughout 
the piece. Therefore, a transcription in g-meter alternating with g-( 4 ) 
* meter results, with the eighth-note unchanged. 

An understanding of the examples in GdM 1, 374 fF., illustrating the use 
of red and white notes in the Old Hall MS will be facilitated by the re- 
mark that in the examples la) and lb) we have color prolationis, in those 
under 2a) and 2b), color temporis. The former indicates the change from 
l 2 > 3\ to [3, >], the latter from [II, 3] to [III, 2]. The examples 3a), 3b), 
4a) show the use of white or red M in the meaning of a Sm, a practice 

1 See the explanations on improvised fauxbourdon (supra librtim) in H. Riemann, Geschichte der 
Musikthcorie, Leipzig, 1898, p. 142 ff. Also M. Bukofeer, Geschichte des Eng/ischen Diskartts, 1936. 



The Notation of the Later Sources 
Facsimile 72 



3(>5 



^Effl^uS* 



V innrrO|WH^h«f tfifiKHiitttwu. 9MJP 

t i ll i l ln. j B ^"'jp.r E , U ' I i l ■ 53 S& 



*n in^pm- magiM gtanrnn ma 



'■"V 1 * "".<* 



*mw*ft|i 



iiin|ftffiHnniftr.| 7 , *o«>ranmilOinnfemrnrtH*. . ,. 




^fe^ ^^^^fe 1 . /) 1 1 fey 



fc3 



> at ami 1 nuus ^ nw 4111 »iu« rro.tt 



mufti intejrttpci 



ion 



id n onfnoftp. *inniftUw fan** moiu.* 

rri l i. lT 'lli:,ilHI.-vA„|, u ,l-l,l i r 



tonus' 



t'lifnnno Qmm item mjwrtf. 




^ 



j^lpjwi^vyi.^M^u nig 



Old Hall MS 

Old Hall, Catholic College of St. Edmund {ca. 1425) 

Page 15 



366 



French Notation 



which was already observed in our previous facsimile. The MS contains 
several pieces in which this meaning of coloration, that is, halving of the 
normal value, is applied to whole passages written in 5, S, and M. The 
following reproduction (beginning of an El in terra by Pycard, p. 21' of 
the MS) illustrates this usage: 




t' l '^M"iii i .jli4yjlkt ^ 



tmitiw 



I ni iot.1 p»rliwiniotin»rituiHiMiuni< tenmiiiVinirom iu|«trMD.>nm 4 



S^E 



l.j.l III.' I'l |j ^ fe 



irglOuAaiiiiuitr.fMiuuiagiwiijtito ,|prrr tnr^uim jrttotflm tuatn 



Here the white Z?, S, and M are identical in value with the black S s M y 
and Sm respectively. 1 

Although the majority of the pieces in the Old Hall MS are written in 
the simple French notation, there are a number which present consider- 
able problems, some of which are mentioned in the introductory notes to 
vol. in (pp. xxi ff and xxvi ff) of the modern publication. Here we must 
confine ourselves to an example illustrating the canon-technique of the 
tenors. Below is the tenor of a motet by Sturgeon Salve mater Domini 
— Salve templum gratiae — In nomine Domini (p. 92 of the MS), which in the 
modern publication (vol. in, xxviii) is described as 'particularly puzzling': 



^mm.^rmuimtmrtonran. ^emo&jfto. 

This, indeed, it is, and it goes without saying that with a tenor like this 
all hopes to arrive at a solution by deduction exclusively must be aban- 
doned. Only through an experimental procedure, following the comple- 
tion of the upper parts which are free from notational problems, will the 
puzzle presented by the tenor be solved. While this practical goal has 
been fully achieved by the editor of the Old Hall MS (see vol. in, 51), his 
explanation of the enigma is not satisfactory. First of all, it must be men- 
tioned that the original contains a clerical error: the last two of the men- 
suration signs should appear in the reverse order. Only by this assump- 
tion does the table of values, given by Collins, become understandable. 
In order to obtain an insight into the construction of this tenor it is best 
to begin with the sign o , indicating tempus perjectum. Here it must 

1 See the complete transcription in vol. 1, p. 76 ffof the publication. 



The Notation of the Later Sources 367 

be noticed, that in this tenor, as in many others of the Old Hall MS and 
of other English sources of the fifteenth and sixteenth century, the 
modus is usually understood to be perfect. 1 Thus, the actual mensura- 
tion is [III, 3], leading to groups of three 4-measures in the transcription. 
Considering now the first group of black values: (S).(S) (B) B L (S) (S) y 
it appears that the whole group contains notes to the equivalent of two 
perfect L, the first of which is replaced by a group of two 5, with altera- 
tion of the second B. The resulting larger values, however, are imper- 
fected by the £-rests through a very peculiar process which can only 
be understood if the functus at the beginning is interpreted as a functus 
syncopationis, calling for an imaginary bar-line after the first quarter- 
rest. 2 To explain the situation from the point of view of the singer, the 
punctus directs to count, not 123,456,789,12 . . 9 (two L of 
nine S each), but: 1 ; 1 2 3, . . . 9, 1 2 3, . . 8. Once this meaning of 
the dot is understood, the rest is relatively simple. In the first of the 
two groups: (S) (B) B, the second B must altered, but also imperfected 
by the (S), since the B-rest cannot be imperfected. Therefore, the signs 
have the values of 1, 3, and 5 S respectively. The total value of the sec- 
ond group, L (S) (S), is reduced from nine to eight by the syncopation. 
The two final ^-rests reduce the L from eight to six S. Following is the 
transcription of the black notes: 



Ui* * 




The red notes indicate change from perfect to imperfect tempus. Since 
the modus remains perfect, the B must be altered, leading to the values 
of 2, 4, and 6 S for (B) B L. There follows a second talea in the same 
notation and rhythm. 

The first presentation of the tenor, in © , is, of course, the exact tripli- 
cation of the above values, owing to the augmenting character of the 
prolatio perfecta. Each S of the integer valor becomes a perfect B. A 
correct evaluation of the second representation, in c , is obtained if 
each S of the integer valor is read as an imperfect B; thus all the values 
of the above transcription are to be doubled. This, of course, is not the 
correct meaning of this mensuration in which, properly speaking, no im- 
perfection of a B by a S would be possible. It is only here, then, that we 
must admit a fault in what otherwise may be termed a perfect example 
of fifteenth century notational arithmetic, — higher arithmetic, to be sure. * 

1 In the example under consideration this is expressly indicated by the remark 'De modo perfecto.' 

2 See the detailed explanation of syncopation, p. 395 ff. 



VII. ITALIAN NOTATION 

A. The Origin of Italian Notation 

WHILE the French music of the fourteenth century represents for 
us the result of a long development, the characteristics of which 
we can recognize in all their essential points, the evolution leading to the 
Italian Ars Nova is veiled in obscurity. That there was in Italy an ac- 
tivity in the field of part music as early as the thirteenth century can 
scarcely be doubted for several reasons. First, the earliest preserved 
Italian compositions, dating from the mid-fourteenth century (Jacopo 
da Bologna, Giovanni da Cascia) by no means bear the stamp of a first 
attempt, but rather exhibit remarkable traits of individuality and per- 
fection. To be sure, the term individuality should not be construed to 
suggest complete freedom from outside influence. Such influence can 
clearly be seen in the fact that the style of early Italian polyphony is 
obviously derived from the conductus style of the French Ars Antiqua^ and 
that there exist French models for the caccia which, for a long time, has 
been considered a purely native type of Italian music. 1 However, these 
facts do not invalidate the above statement, but only show that Italian 
music must have had sufficient time to develop those indigenous traits 
which distinguish the earliest preserved examples from those of contem- 
porary French music. 

More definite evidence of the origins of Italian polyphonic music is to 
be found in the field of musical theory, that is, in the Pomerium musicae 
mensuratae of Marchettus de Padua. This important treatise, which 
was written nearly simultaneously with Vitry's Ars nova {ca. 1325), 2 

1 See the French chace from the MS Paris, B. N. Coll. de Pic. 67 which has been reproduced by 
H. Besseler in AjMW vn 251 f. 

* Marchettus de Padua is also the author of a treatise Lucidarium musicae planae (GS m 64-121) 
which deals in a well-known manner with the intervals, ecclesiastical modes, etc. The dates of these 
two MSS have been the subject of extended controversies, chiefly between J. Wolf and F. Ludwig. 
Regarding the date of the Lucidarium, see p. 320, footnote 2. The Pomerium was written after 1309, 
since it is dedicated to king Robert of Sicily who ascended to the throne in this year. J. Wolf gives 
1309 as the exact date of the treatise (GdM 1 26; HdN 1 277). Again this date is perhaps a decade 
or two too early. In fact, in the above mentioned comparison ('De distantia et differentia cantandi 
de tempore imperfecto inter Gallicos et Italicos, et qui rationalibilius cantant') Marchettus refers to 
the tempus imperfectum, the semibrevis maior, minor, and minima, to the use of semibreves caudatae 
to a 'lertia divisio temporis' (i.e., to notes equivalent to a semiminima), and to other devices of four- 
teenth century French notation which are not likely to have been fully developed, much less to have 
become known outside of France before 1320 at the earliest. 

368 



The Origin of Italian Notation 369 

contains a detailed description of the principles of Italian notation and, 
in addition, an interesting comparison between this system and the 
French one, the latter being recognized as superior (GS in, 175). Evi- 
dently, at this time Italian notation was already sufficiently developed 
to be codified and discussed. 

Finally, notational as well as stylistic features of Italian music rather 
definitely point to the late thirteenth century as the period when the 
Italian tradition branched off from the French. The Italian system of 
notation obviously rests upon the basis created by Petrus de Cruce. In- 
deed, while his fundamental principles of notation, the grouping of sev- 
eral S to the value of a 5, and the consistent use of the punctus divisionis 
for the marking off of these groups, were soon abandoned in France in 
favor of principles derived from the Franconian theory {tempus, prolatio y 
imperfection, alteration, etc.), they were kept up and developed in Italy. 
Actually, the Italian notation is but a modification of the Petronian sys- 
tem, a modification characterized by the introduction of numerous spe- 
cial shapes of semibreves {semibreves signatae y caudatae) against which 
French and English theorists of the time frequently raised their voices in 
protest. 

Needless to say, the close alliance of the notational systems is paralleled 
by one of the musical styles. The rapid parlando declamation of the 
Petronian school was adopted by the Italians and was developed into a 
highly decorated style which frequently reminds one of the coloraturas of 
seventeenth century Italian arias. In fact, if viewed in the light of gen- 
eral music history, the Petronian parlando appears to be so much closer 
to the Italian than to the French idiom that one is almost tempted to re- 
verse the usual assumption, by venturing the conjecture that Petrus was 
not a Frenchman 1 whose ideas spread to Italy, but an Italian who came 
to Paris and introduced into the French motet certain features of a na- 
tive thirteenth century Italian music all other traces of which are lost. 

B. The Principles of Italian Notation 

The explanation of the Italian notation by Marchettus is scarcely suit- 
able to serve as the starting point for our study. His thought processes 
are overladen with scholastic arguments and lengthy elaborations which 
are not conducive to an understanding of the essential points. His 
factual information corresponds only in a general way to the notation 

1 The much-used version Pierre de la Croix is, of course, an arbitrary Frenchifkation introduced 
probably by Coussemaker but still retained in recent publications. Perhaps we may have the 
pleasure, before long, of reading in German books about an illustrous predecessor of 'Peter vom 
Kreuz,' named 'Franz von Koln.' 



370 Italian Notation 

used in the documents and is in many particulars more complicated and 
less definite than actual practice. Since, moreover, his teachings have 
already been given in detail by J. Wolf (GdM i, 28), we shall resort to 
Marchettus only for the rudiments and the terminology, drawing our 
presentation chiefly from the actual documents. 

Divisiones. The Italian system of notation rests entirely upon the 
Petronian idea of the B as the fundamental unit. Whereas, in French 
notation, the B may be shortened or lengthened by imperfection and 
alteration, in the Italian system it is an unalterable value. The smaller 
notes always appear in groups each of which takes the place of a B. The 
marking off of such groups is effected in exactly the same way as in the 
system of Petrus de Cruce, namely, either by a B or L, or by a i?-or Lr 
rest, by a ligature (generally a binaria c. 0. p.), or in the majority of cases 
by the puncl us divisionis. An example follows: 

Here nine groups (measures), each having the value of a B, are easily 
recognizable. The only remaining problem, then, is the determination 
of the rhythm within such groups. For this purpose a great variety of 
signs, so-called semibreves signatae or caudatae, were introduced, some of 
which are shown in the above example. 

The division of the B into smaller values does not depend, as with the 
French, upon tempus and prolatio but upon the so-called divisiones which, 
to a certain extent, can be considered ready-made combinations of tempus 
and prolatio. These divisiones are distinguished according to the num- 
ber of parts into which the B is broken, and appear in three different de- 
grees, namely, as prima, secunda and tertia divisio. In each degree, two 
or three notes can appear in the place of one of the preceding degree: 



divisio prima: 


binaria 

2 


ternaria 
3 


divisio secunda: 


quaternaria senaria imp. 
4 6 


senaria perf. novenaria 
6 9 


divisio tertia: 


octonaria 

8 


duodenaria 
12 



The two divisiones primae are of only theoretical importance. The 
others are indicated by letters as follows: 



The Note Forms 371 

.q.: quaternaria; J.: senaria imperfecta; .p.: senariaperfecta; .n.: novenaria; 
.0.: octonaria; ,d.: duodenaria. 

By representing the B as a half-note, or a dotted half-note, we arrive at 
the following schemes of transcription: 

.q. .i. .p. .n. .0. .d. 

J J. J. J: J J. 

nn mm nnn mmm jmim miimsm 

Apparently, the four divisiones secundae are equivalent to the four 
combinations of tempus and prolatio (Vitry's 'quatre prolacions'). 

Note Forms. Within this general frame the notational fixation of 
rhythm is governed by the following principles: 

1. If in a 5-group the full number of notes demanded by the divisio is 
present (i.e., four notes in .q., six notes in ./. or .p., etc.), each of them is 
represented by a semibrevis with an upward stem or, as we might call it, 
by a M. This means, therefore, that the value of an M fluctuates be- 
tween \ B and -h B, according to the prevailing divisio. However, it must 
be noted that within a given divisio the value of the M is constant, that 
is, it is always worth that part of the B which is demanded by the divisio. 
1. If in any {secunda or tertid) divisio the slower rhythm of any preced- 
ing divisio {prima or secunda) is to be expressed, the plain S is used. In 
the four divisiones secundae^ in which there is only one preceding divisio^ 
this principle leads to the same manner of writing as is used in French 
notation: 

.q. .p. .i. .n. 

iiii iillil iiiiii UiUUU 



However, something essentially different results in the case of the two 
divisiones tertiae, in which there are two degrees of slower rhythm, both 
of which are represented by S: 

.0. .d. 

♦ ♦ ♦ ♦ = n n ♦♦■♦♦♦♦-- «ra n n 
♦ ♦ = j j ♦ ♦ ♦ = j j j 



372 Italian Notation 

3. If in any divisio S are used in smaller number than that of the normal 
groupings indicated under (2), the last of these £ will be lengthened. 
This principle, which obviously is rooted in the alteration of French no- 
tation, leads to the following combinations: 

.p. .n. .0. .d. .d. 

♦ ♦-JJ ♦♦-J.J. ♦♦♦-J3J ♦♦♦♦♦-J3J3J,#*^-J3JJ 

♦♦-JJ 

The resulting rhythm is a rhythm in which the longer notes appear at the 
end of the group, and is called via naturae (in the natural way). 

4. If a rhythm is to be expressed in which the larger values are found 
at the beginning or in the middle of the group, this must be represented 
by the S major: f . These rhythmic formations are called via artis (in 
the artificial way). Here are some typical examples: 



.p. .n. .0. 

I*»JJ f*-J.J. f**.-JJ3 
♦ f = JJJ 


.d. 

r -JJ 
......JJ1I2 

......nJJl 


5. In the divisiones .q. y .p. y .0., and .d. each S can be replaced by two 
M. Examples: 

.q. .p. .0. .d. 

• U-J.J3 I'U-JJJ jUU.JJOT ♦ii t ii-J73J/31 



6. In the divisiones .i. and .n. each £ can be replaced by three M or by 
the group S-M. Examples: 

.i. .n. 

♦ 411-J-J33 t iii-J.J33 

♦n.jij. ♦uu.jaiai: 

7. In each divisio two ^w may occur in place of one M. Examples: 

.q. .p. .0. .d. 

mi T m .mm . mm . 



The Divisiones 373 

8. In .q., .p., .0. and .d. (cf. no. 5) triplets are often found in the place 
of two M. These are indicated by the form: \ . Examples: 



.q. 


.p. 


.0. 


.d. 


inn 


Allili 


aiu 


♦UUIIU 


* 


j.m/73 

1 


JT^J 


ST73J7T1J 



It must be noted that the flagged notes of nos. 7 and 8 are often used 
with the meaning exchanged, that of no. 7 for triplets, and that of no. 8 
for the Sm. There even are pieces in which one and the same shape 
serves both purposes, the proper interpretation for a particular passage 
being easily recognizable from the number (two or three) in which they 
occur. 

9. In the same divisiones, the value of three M is represented by the 
sign /* . This is equivalent to the dotted S {punclus additionis) of 
French notation. Examples: 

.q. .p. .0. .d. 

A 1 ♦'/♦ ♦ 1 /♦♦♦! /♦.! ♦/♦ 111 

j. j> j j. j=3 rm j-3 rum 

This form is found also in .«., especially in syncopated rhythm, for the 
sake of clarity. The normal S will then have the value of two M. Ex- 
ample: /♦♦♦!! = J-JJLJTJ . 

10. The value of three Sm or, in other words, of a dotted M, is indicated 
by the sign yi . Examples: 

Mil ;ui;ui iuifUiu 

J1J1 JTT3 J7T3 /JT3 J J J J J J 

3 

From these explanations it is apparent that the signs in Italian nota- 
tion are of two types, those which have an unalterable value within a 
given division and those whose value is variable within a given divisio> 
depending upon the other notes found in the group. The signs of the 
first type are l ; i=U: ^=zl;/* =3i ;y l=!l , whereas the S and the S major 
are the signs of the second type. The following example shows that, in 
J. y the value of the S may vary from an eighth-note to a half-note: 
♦ ♦♦♦♦♦•♦♦♦t*.=|«T3 X3 «Q|JJJ|JJ|J.|. Usually, the determination of 



374 Italian Notation 

the value of these variable signs is without difficulty. In the case of 
complicated combinations, especially in the J. y the advice given by J. 
Wolf {GdM I, 284) is useful: first of all subtract from the B the fixed 
values, and then determine the alterable notes from what is left. For 
example, in the following group, .d. /♦ i 1 1 X ♦ ♦ , the two first notes require 
four My the next three two M. In order to complete the duodenaria> the 
remaining two S must comprise the value of six M. Since they would 
normally yield only four M the value of the last S must be doubled via 
naturae: JT3 J J J J J . 

*C. , Examples of Italian Notation 

The sources which are available for the study of Italian notation are 
indicated in the general list of manuscripts, p. 203. x Except for the MS 
Rossi, which is of a slightly earlier date and which will be considered 
separately (p. 382), these sources form a unit, musically as well as nota- 
tionally. As a matter of fact, they have many pieces in common, 2 and 
the same notational methods are found in each of these five codices. This 
is not to say that all the pieces are written in one and the same system of 
notation. On the contrary, the large repertory contained in these books 
falls into three distinct classes: French notation, Italian notation, and a 
mixed type. The first class comprises chiefly the pieces with French 
text. The second group generally coincides with the repertory of the 
representatives of the early Italian school, such as Giovanni da Cascia, 
* Jacopo da Bologna, and Giovanni da Florentia (active ca. 1350). The 
number of the pieces in this group is relatively small. The majority of 
the Italian pieces are compositions of the later Italian school (second half 
of the fourteenth century) of which Francesco Landini (1325-1397), 
Laurentius de Florentia, Bartolinus de Padua, Paolo tenorista are mem- 
bers. These pieces are generally written in a notational system combin- 
ing French and Italian elements ('mixed notation'). Finally, about a 
dozen of pieces in // and Rei belong to a notational type of considerable 
complexity which is called in this book 'mannered notation.' 

Facsimile 73 contains a three-voiced piece by Jacopo da Bologna which 
may serve as a first illustration of Italian notation. The simultaneous 
use of different texts (Aquil' al tera ferma — Ucel' di dio — Creatura 
gen til) probably points to an influence of the French motet. The com- 

1 In the subsequent explanations the abbreviations: Pane, Brit, It, Sq, and Rei are used for the 
MSS 2-5 listed on p. 203 under Italian Notation. 

1 See the lists of contents in GdM 1 pp. 233 ff, 245 ff, 252 ff, 261 ff, and 269 ff. Corrections of 
these lists have been given by F. Ludwig in SIMG vi, 613-616. 



Examples 
Facsimile 73 



375 




''■#0 


: 'i-^r 


— - ■ 




— 3 p 


■ — 1»£ 


*T 


n " 




<& ft -- 


e _:" 


r^dir 


r -u 






1 _ -- s 1 _ 


fe . 


: e- -=. 


1 


• |4:: 


. j£-* 


■= z ; 




-=g • 


i= -- - 


i - 




-5 

* 






""/§ -In 




Af*S « 






bfl 



3 

a* 

■M 

.2 

S 



376 Italian Notation 

position falls into two sections the first of which is obviously in octonaria. 
Typical combinations are: 

♦ r u.iwjji;U~.jiJJ3Ji«fiU.iwni 

In the second section (La el parere — La vidi — La el imagin) the 
divisio changes to senaria perfecta. This change of rhythm, which is a 
typical feature of the fourteenth century madrigal, raises the question as 
to the time relationship between the two sections. Considering the 
fundamental role which the B plays in Italian notation, one is naturally 
inclined to consider this note as the common unit of time and, therefore, 
to attribute to a group of six M in senaria the same duration as to a group 
of eight M in octonaria. This theory, however, does not agree with the 
explanation of Marchettus who in his Pomerium repeatedly maintains 
that the B perfecta has a longer duration than the B imperfecta (GS in, 
172). If he is to be trusted, the 6 1 , rather than the B> must be considered 
the unchangeable unit of time measurement. In the present case this 
would mean that the temporal relationship between the two sections is 

as follows: II-T3J3HI J^ -Q Jll ; not: 111113 l! 1212!} I 
Although this result would seem to be acceptable from the musical point 
of view, the general principle expressed by Marchettus is clearly contra- 
dicted by a composition to be considered later (Facsimile 75) in which 
the B has the same value in four different divisiones . 

The beginnings of the two sections are transcribed in the appendix, 
No. 48. A reproduction of the same composition from Sq is given in 
SchT, p. 79. The other composition of our facsimile (p. 3, Fortune) will 
be studied later (see p. 400). 

Facsimile 74, containing a two-voiced \P\erche cancato eU mondo by 
Bartolinus de Padua is a slightly more complicated example of Italian 
notation. The divisio is not indicated at the beginning, but can easily 
be derived from a group such as the one beginning over the syllable '-che,' 
which consists of nine M, one of which is replaced by two Sm. With the 
syllable 'Non' near the beginning of the second line the meter changes to 
duodenaria (.d.) and returns later to novenaria (.«.), on the syllable '-mi-.' 
The latter divisio persists throughout the second section of the piece 
('Che . . . amara'). 

This piece, which no doubt belongs to a later period, is remarkable for 
its unusual display of syncopated rhythms. In order to express them 



Examples 
Facsimile 74 



377 



I fee z 



l 



:\Wli/flir\;i lb."! 'fill Mill 



IF 



cfc ouzUD AnSm Tahiti ' 




MS Paris, Bibliotheque Nationale «owt>. acq.jr$. 6771 {ca. 1400) 
Page 117 



378 Italian Notation 

clearly, a distinction is made between a binary S y ♦ , and a ternary S, 
/♦ (see p. 373, rule 9), for instance (first line, after 'mondo'): 




However in groups with plain unsyncopated rhythm this distinction is 
not observed, e.g., in the initial group, the first two S of which are ternary 
whereas the third, written in the same shape, is binary. 

In contrast to the distinction between two types of S, one and the 
same sign is used for the binary and for the ternary S rest. For instance, 
the rest in the last group of the first line equals two M, whereas those 
placed at the end of the first and the second section have the value of 
three M, which, of course, is the normal one in .n.. The sign after the 
first note of the fourth group is a Sm rest. 

The piece is written with a B-flat in the upper part and an E-flat in the lower part, 
probably in conformity with the average range of the two voices. It goes without saying 
that the E-flat of the tenor entails the use of a B-flat wherever this degree occurs. In 
the discant the E is normally natural, as appears particularly from the beginning of the 
second section (third staff). However, for the conclusion of the piece, a flatted E is 
required from both the harmonic and melodic point of view. This change of tonality 
is probably indicated by the (misplaced) flat on the third staff, over 'dolce' (the same 
shape for the flat is used in the signature of the last staff). The penultimate note of the 
first staff is A, not G. In the second group of the novenaria passage near the end of the 
first section ('- mi - cho') a binary S, on D, is missing after the first M, as appears from a 
comparison with the notation in Sq. See the appendix, No. 49. 

The three-voiced Benedicamus Domino of Facsimile 75 is interesting 
not only because it uses four divisiones (.0., .s /., .p., and .5-.), but also be- 
cause of the notation of the tenor. This part contains, in addition to 
ordinary ligatures and single L, certain conjunct ura-Yike characters which 
are very unusual in the polyphonic music of the fourteenth century, and 
which actually have no place in the Franconian system of ligatures. The 
explanation lies in the fact that the entire tenor is not written in men- 
sural signs but in the characters of plainsong notation, which, although 
similar in appearance, have an entirely different significance. In their 
original form as neumes they indicated, of course, the unmeasured rhythm 
of Gregorian Chant. However, in the thirteenth century, the Gregorian 
tradition was lost, and plainsong was interpreted as consisting of notes of 
equal duration (hence the name 'cantus planus,' in contradistinction 
to 'cantus mensuratus'). It is in this meaning that the 'Roman cho- 
rale notes' (i.e., the Roman, not the Gothic, thirteenth century modi- 
fication of the neumes) were occasionally adopted for the writing down 
of liturgical tenors of polyphonic compositions. In such tenors, which, 



Examples 
Facsimile 75 



m 



1 | M H iii|in m m 



U>«iMK 



* ! I Tl^f T T IT ! HI 



■ nr ri i i 1 fa t 



i n [ || |[ | ||[ ih , 1,'" 



llVTlUZH'lVUII 



,liin^i,ilikpiigpi 



no 








* ** ■ iff I I / 



379 







MS Paris, Bibliotheque Nationale ital. 568 (ca. 1400) 
Page 138 



3 8o 



Italian Notation 



by the way, are encountered also in manuscripts of the fifteenth and six- 
teenth century (for an example see HdN i> 404), each note always has the 
value of a B, regardless of its shape. The unalterable value of the notes 
of the tenor entails, of course, equal duration of the B in the different 
divisiones of the discant and contra, a fact which is in opposition to 
* Marchettus' statement regarding the duration of the B (see p. 376). 
The piece presents no difficulties except for the end of the last section 
which is in quaternaria. The last group of the discant includes four Sin 
and two S\ instead of four Sm and two M. This manner of writing is all 
the more irregular since the two S are written in ligature which, accord- 
ing to a fundamental principle of Italian notation, always occupies for 
itself the place of a B. Still more corrupt is the notation of the contra. 
The letter .p., given at the beginning of the section 'mi-no' is a clerical 
error since the grouping clearly indicates quaternaria. Beginning with 
the third ligature (c.o.p.), some sort of diminulio dupla (halving of the 
values) must be conjectured, in order to arrive at a satisfactory result: 1 




Although the above reference to diminutio dupla is merely conjectural, 
there is sufficient evidence to show that Italians as a matter of fact were 
quite familiar with the idea of halved values or of doubled speed. Fol- 
lowing is the beginning of Jacopo da Bononia's madrigal Un bel sparver 
in two versions, (a) from Rei, p. 4, and (b) from Sq, p. 91: 



(a) 




kl fjMwc fmlKefftta bum 



1 For another emendation see GdM m. 118. 



Examples 



38i 



(b) 



siriBfeislpa 



n 



TL 



Apparently (a) is written in quaternaria, whereas for (b) octonaria is 
indicated at the beginning and clearly expressed in the notation. By 
adhering strictly to the general principles of Italian notation the follow- 
ing two transcriptions would result: 

(a) 

■ Mi I 1 in u i| j iqj run niii! 1 jij 1 




Which of these two versions requires modification in order to make it 
conform with the other is easy to decide if our general principles of tempo 
transcription are born in mind. If, as always, the quarter-note is taken 
to represent the beat, it appears that only version (b) leads to a musically 
sound result. In other words, version (b) conforms with the general 
fourteenth century practice of having the beat represented by the S> 
whereas (a) uses the B for the beat and hence must be considered as 
written in diminution. 



These explanations will suffice to demonstrate the character of the 
Italian notation and to show that, in spite of a somewhat confusing 
variety of notational symbols, it surpasses all the other systems in sim- 
plicity, chiefly on account of the persistent use of what are the equiva- 
lents of bar-lines. This feature and the rhythmic regularity of Italian 
fourteenth century music make it easy to clarify notational details of 
minor importance which are occasionally encountered, such as special 
signs of rare occurrence, or minor deviations from the general principles. 
We refrain from further discussion of these details, since additional 
information as well as numerous examples are available in HdN 1, 
293 ff., GdM 1, 274 ff., CdM 11, nos. 38-51, 53-58, 60-62, and SchT, pp. 
77-79- 



382 Italian Notation 

D. The Early Stage of Italian Notation 

In conclusion, we may add a few remarks regarding the early history 
of Italian notation, or, in other words, regarding the transition from the 
Petronian notation of the late thirteenth century to the Italian notation 
of the mid-fourteenth century. Obviously, the most striking difference 
is the use of the semibreves caudatae in the latter, instead of the plain S 
in the former. Although such a development is quite natural, it is some- 
what surprising to see that it went as far as the expulsion of the plain S 
from its dominant position and its replacement by the semibrevis minima 
or, in other words, by the M. In fact, the fundamental rhythm of the 
divisiones quaternaria y senaria, novenaria, etc. is expressed in Italian no- 
tation by four, six, nine, etc. M, whereas, in the Petronian system, the 
corresponding signs have the form of simple S (see the reference to semi- 
breves quartae, quintae, sextae, etc., p. 323). It is natural therefore to 
suppose that there was an early stage of Italian notation in which the 
plain S still held its former place of importance. 

There exists, in fact, a manuscript which illustrates such a usage, 
namely the MS Rome, Vat. Rossi 2/j. 1 This interesting source, which 
probably enables us to trace back the documented history of Italian poly- 
phonic music to the first quarter of the fourteenth century, is written in 
a notation which actually forms a link between the Petronian system 
and the fully developed Italian notation. Our Facsimile 76 shows a 
three- voiced caccia Or qua conpagni, 2 in two canonic parts (for the imi- 
tating voice, only the beginning and the end are notated, top of the right- 
hand page) and an accompanying tenor. The divisio is indicated by the 
* letters .sg. which evidently signify senaria (the literal meaning of the let- 
ter g is unknown to this writer). In fact, groups of six notes can be 
seen at the beginning of the discant, on the seventh staff of this part, and 
in the final passage of the canonic voice. Downward tails and upward 
tails are sparingly added to the notes, indicating larger or smaller values, 
according to the principles expounded in connection with the Roman de 
Fauvel. That the senaria is imperfect may be concluded from the fre- 
quent occurrence of groups of two S (particularly in the tenor) and of 
four S. A rhythmic evaluation of the various combinations is not with- 
out its difficulties. Without attempting to prove our conclusions we 
submit them in a table reproduced on page 384. 

It is interesting to note that the rhythms via naturae absolutely con- 

1 See the study by J. Wolf in Jahrbuch der Musikbibliothek Peters 45, 1938. 

2 I am indebted for this photography to Mr W. Th. Marrocco, whose Fourteenth-Century Italian 
Cacce (1942) contains transcriptions of all the Italian caccias. 



The Early Stage 
Facsimile 76 



383 




o 



C « 
u ^ 



CQ 



384 Italian Notation 



Via naturae 


Via artis 


.j.j. 


♦;• -JJJ.ajj?) 


♦ .-J.JJ 


♦♦ =jjjj 


uu -JJJJ 



♦♦♦♦♦♦ 



JJ3J73 ♦♦♦1-JJ3JJ 



tradict the teaching of Marchettus and other fourteenth century theo- 
rists, according to which the longer values appear at the end of the group. 
For instance, in a group of three S the values would follow exactly in the 
reverse order of those indicated above (see GdM 1, 30, or HdN 1, 288, un- 
der divisio senaria imperfecta). This is but another evidence of the un- 
certainty in the evaluation of the small notes which prevailed around 
1300 (see p. 339). In fairness to the theorists it should be mentioned 
that they were by no means unaware of this situation, as appears from 
various remarks in which the singer is given a choice between the tro- 
chaic and the iambic rhythm (Theodoricus de Campo, CS in, 185). 

The initial character of the canonic parts and the tenor is a B plicata. The rest near 
the middle of the eighth staff should be a B rest. The second note of the ternaria near 
the end of staff 6 (syllable M'u-') is probably a clerical error and should read c, instead 
of d. The concluding passage for the imitating voice is to be used instead of the passage 
of the dux beginning with the ternaria to the syllable 'stan-'. A transcription of the 
beginning of the caccia is given in the appendix, No. 50. 

We may now refer the reader back to a piece which has been briefly 
discussed near the beginning of this book, that is, the example of the 
earliest organ tablature to be found in the Robertsbridge Codex (repro- 
duction p. 38). Indeed the upper part of this piece is written in exactly 
the same type of 'primitive' Italian notation — a fact which would seem 
to allow for some doubt regarding the supposedly English origin of this 
manuscript and its contents (another suspicious detail is the rather un- 
* English name Petrone to be found at the beginning of the piece). The 
divisio is, as can easily be seen, quaternaria. Musical considerations 
show that this quaternaria is in diminution, similar to what we found in 
the Reina version of Un bel sparver (p. 380). In other words the B rep- 
resents not the measure, but the beat. As a rule, three B form a rhyth- 
mic group (modus perfectus), so that a transcription in 4-meter results. 



VIII. MIXED NOTATION 

A. General Characterization 

THE most characteristic feature of the Italian notation is the consist- 
ent use of the punctus divisionis with the same meaning as the mod- 
ern bar-line. Considering the progressive character of this principle one 
is rather surprised to see it disappear after a short period without leaving 
any traces in the notation of the ensuing centuries. The reason for this 
disappearance, however, is not difficult to find. The bar-line means a 
great simplification but also a decided limitation of rhythm, unless it is 
accompanied by the use of the tie for syncopated effects. As a matter 
of fact, there was no place in Italian notation, and consequently in Italian 
music of the fourteenth century, for syncopation from one measure to 
another; the entire display of rhythmic imagination is an unfolding of 
the possibilities within a measure and nothing more. In other words, 
the rhythm of the early Italian school is merely a more decorated variety 
of the rhythmic structure of the compositions of the Ars Antiqua, partic- 
ularly of the conductus. When, after 1350, Italian composers came into 
contact with contemporary French music, they soon became aware of 
the limitations of their style and hastened to introduce into their music 
the newly won achievements of the French Ars Nova. The adoption of 
the rhythmic innovations of Philippe de Vitry and Guillaume de Machaut 
made it necessary to give up the principles of Italian notation. A new 
notational system evolved which was essentially French in character, but 
which retained certain features of the earlier Italian system. This nota- 
tion which, for want of a better name, is called here 'mixed notation,' 
differs from the pure Italian notation chiefly in the abandonment of the 
punctus divisionis as a regular device of barring, and differs from the pure 
French notation by the continued use of some of the Italian shapes of 
notes. 

It goes without saying that this characterization should not be inter- 
preted too rigidly. The term mixed notation is introduced here chiefly 
for purposes of general classification, without making special claim to 
historic significance. This writer is fully aware of the fact that what he 
calls mixed notation is a rather loose aggregate of various notational ele- 
ments differing from each other as to localities and periods. However, 

3*5 



3 86 



Mixed Notation 



our very incomplete knowledge of the state of affairs in the late four- 
teenth century renders futile all attempts towards a more thorough 
classification of the subject. 

The sources for the study of mixed notation are the same which served 
as a basis of our discussions of the Italian notation. By far the greater 
part of the Italian music of the fourteenth century is written in this sys- 
tem, particularly the compositions of the later school, including practi- 
cally all those of Francesco Landini. 



B. Examples of Mixed Notation 

As a first example we choose a composition of the earlier school, Gio- 
vanni de Florentia's madrigal Naschoso el viso (Facsimile 77), which illus- 
trates the transition from the pure Italian notation to the system under 
consideration. The Italian divisiones are still indicated by the letters 
.7?., .q. y ./., ./>., but the punctus divisionis is never used. Instead, the dot 
appears as a punctus additionis, a practice to which the pure Italian sys- 
tem had been thoroughly opposed. No less 'un-Italian' is the use of a 
dotted L in the tenor (first note of the initial ligature, and various single 
L) which, as can easily be seen, are perfect L in modus perfectus. Simi- 
larly, a passage like that which follows the first ligature of the tenor (sin- 
gle S and syncopated B) is impossible in Italian notation. As a matter 
of fact, the beginning of the piece may be transcribed with the least diffi- 
culty as an example of French notation, in [III, 2, 2]: 



1 l| 11 ll him nD|| I , 1 II l 



It may also, however, be considered as being written in a free, 'Frenchi- 
fied' qualernaria, in which the puncti divisionis are missing and the B 
occasionally occur in syncopation: 




Italian notation is more clearly suggested by the passage 'me guardava' 
(end of the second staff) where the letter .n. calls for novenaria, i.e., for 
nine M to be placed against a B of the tenor. Unfortunately this obvi- 



Examples 
Facsimile 77 



387 




d 



Lt 



x 




-- 




is--*— 








ii — 




^ 3 






i 


-=5 




!" • 


r ? '< 


-s? 




*" * 


-kr 


= 2 












j'S " : 




I 


■ $1* 










e fe 






Si 

1 ■ 


r: 


- 






r « a 












1 


j- -V. 


-Z 


F 


"5 


■ «H - 3 i 


!• 1 


-5 




" 3 . 


;=' 3 ^= 






n. --: 








.5^ 








=:r - = ? 


§v| = 








'- vP"i - 












*- i 






3^ 



" ' if fB> 

- ::i 



111 



m 




s 



388 



Mixed Notation 



cms interpretation turns out to be incorrect, as appears from the follow- 
ing transcription: 
•n« 




A correct transcription is obtained if each group of nine notes is spread 
over three B, in some sort of threefold augmentation, as follows: 

^~s^ ""T*^ ^T^ "T^ 




Obviously, this means that the nine notes of the .n. are equal, not to a 
B, but to a (perfect) L. In other words, the novenaria is not, as is the 
normal case, a divisio of the B, but a divisio of the L. From a study of 
the whole piece it appears that .n. and ./. are treated as divisiones of the 
L, whereas .q. and .p. are divisiones of the B as usual. In GdM i, 315 ff., 
J. Wolf has mentioned various examples of the same kind. 

A truer understanding of this practice will be obtained if our previous 
remarks regarding the use of diminution in Italian notation are recalled. 
Once more it appears that a clear insight into such problems cannot be 
gained without the question of tempo being taken into consideration. 
Obviously, the above interpretation, although it leads to a correct align- 
ment of the parts, suggests a tempo which is much too slow. The fault 
of our transcription lies in the fact that the quaternaria of the beginning 
has been taken to indicate normal tempo {integer valor, in the language 
of the fifteenth century) and that, as a consequence, the novenaria has 
been interpreted as augmentation. Actually, the reverse interpretation 
is correct. The .n. is in integer valor, and the .q. in diminution, so that 
the transcription given on page 389 results. 

The correctness of this rendition is confirmed by a comparison of our 
facsimile with the version of Sq which follows the familiar principles of 

Italian notation (see GdMu, no. xxxix) : 

The reason why another method of writing is chosen in our manuscript 



Examples 



389 




is not difficult to find. Obviously, the idea was to avoid the duodenaria, 
the most complex of all the divisiones, and to express its rhythm and 
tempo by the quaternaria, performed in three-times the normal speed: 

(a) .q. in normal tempo (b) .q. three times as quick 



B B 



B 



II JTflfiTHffl 



B 



Evidently, (b) is identical with duodenaria. 

The principles to be observed in the transcription of this piece and of 
others written in a similar way may be summarized as follows: The divi- 
siones with 'prolatio perfecta,' that is, .n. and ./., are in integer va/or, 
those with 'prolatio imperfecta,' that is, .q. and ./>., in diminution. Their 
exact metrical relationship appears from the following table in which a 
horizontal bracket is used to indicate the laclus, i.e., the common unit of 
time: 



%\{nsnm\ %\mm\ njsai \\smn\ 
l\JT2iJim\ iijejjj 



IIJ333 



| X J v£^ £, 



^8,. 3 



It will be noticed that the B (represented in each case by a whole 
measure), has the duration of a quarter-note in .7., a dotted quarter-note 
in ./>., a half-note in ./., and a dotted half-note in .«. . 

A sign indicating quaternaria is missing at the beginning of the third 
staff, syllable 'So-'. The second section of the piece, from 'Qual'era' is 
transcribed in the appendix, No. 51. It may be noticed that in Sq this 
entire section is a tone higher (see GdM 11, no. xxxix). 



390 Mixed Notation 

The musical form of the piece is that of the fourteenth century madrigal which usually 
agrees with that of the French ballade: A A B. Section A includes three lines of the 
poem : 

Naschoso el viso stavam fralle fronde 
D'un bel giardino appresso a me guardava 
Sopr' una fonte dove si pescava, 

section B, the so-called ritornelh (indicated in the original by the letter R) y the two con- 
cluding lines: 

Qual era scalza e qual com'ella nacque 
Piu non vo' dir quanto quel di mi piacque. 

The text for the repetition of A, before the ritornello, is given at the end of the music: 

E vidi donne vermigliette e bionde 
Leggiadre al modo che solean leguane 
Trovarsi al boscio e quando alle fontane 
(Qual era. . . ) 

The second piece of the same facsimile, Francesco Landini's ballata 
Choi gli ochi y is a more typical example of mixed notation. The basic 
mensuration is the French [3, <?], as appears clearly from the tenor (bot- 
tom of left-hand page). Aside from the occurrence of the Italian triplet- 
minima (see discant, third staff), the most striking feature is the ample 
use of white notes as well, with exactly the same meaning: ♦iiiili- 

tl J JT3 JT3I • The transcription presents no difficulties. 
3 3 
For the correct underlaying of the text it is important to know that the ballata, which 
is the Italian counterpart of the French virelai (not of the ballade!) consists of two 
sections of music, A and B, which are repeated as follows: Abba A. 1 The general 
disposition of the text is indicated below: 



Choi gli occhi . . . sospiro 
Questo fo . . . sentir mi fay 
[E tu sempre . . . cio fu may] 
[Dunque singnor ... in martiro] 
Choi gli occhi . . . sospiro 



The text of the lines in brackets is given at the end of the music in the 
original. 

Facsimile 78 contains a ballata Se pronto by 'Magister Franciscus 
Caecus Horghanista de Florentia' (the first three words are found on the 
opposite page of the MS), i.e., by Francesco Landini. The mensuration 
is [2, 2] (.q.)> as appears, e.g., from the beginning of the tenor. The 
white notes appear in different degrees and relationships. A single group 
of three white M stands in the place of two black M and thus occupies 
half of a 4-measure. A group of three white S or their equivalent in 
other values (e.g., B MM), on the other hand, comprises a whole measure 

*See p. 151 f. 



Examples 
Facsimile 78 



39i 



9 






1? p*ntot*wfr 19 Iwcmafcjiifi 



■f& 



if 



3zn: 



K 



a4«ffin<it; 



Hfl^'iUil,,ll 



mt 



re fc»u»t nt m»« 1 ill,, , **'• \ & 



j_ji 



cix 



HB 



1 1 a wilt 



•a 



A 



u«. Tt<r (unrthhc tatsatelfvoa u&< 



/ 



i ■■a- ii 7.»i:iT7 v *n unp n tKi n a 5s: > ' ■ : ■ v: 1 g w mm pgn r«H.i? 



,/ 



5 pnnss > r? n ( j :: t ri7 ">'"F 



WtttH* U-ife fe fe 



ass 



ytento Tionfara liitfwj ie»l fa 



^tt 



frpfTnhen pe. 



US ♦ 



l ^^ g 



s 



buHtfo manca 



H& 



43 



£ 



*+4 



'■Sr>tf«» i 



fe 



I 



*eTp^t ^' lofpT^r^ ntfty m w &c 



■rur 



^ * u-4 



u<> 



(n lEgkWta* fcft ^elfrW 



i* 



Codex Squarcialupi 

Florence, Biblioteca Medicea-Laurenziana Pal. Sj (ca. 1400) 

Page 170 



392 Mixed Notation 

and brings about a temporary change from quaternaria to senaria per- 
fecta, which may be most clearly indicated by triplets of quarter-notes. 
In the middle of staff 5 we find a group of three white B which naturally 
occupy two 4- or one 4-measure (half-note triplets). The following 
schematic example clarifies the meaning of the three varieties of col- 
oration : 

fu jpiflj iJjjiu u n\% j^jjii J 1 

The beginning of the ballata is transcribed in the appendix, No. 52. 1 

A more complicated specimen of mixed notation is Landini's three- 
voiced ballata Nessun ponga speranza, which is preserved in four manu- 
scripts. 2 Our facsimile (no. 79) is from the Codex Squarcialupi. 

The beginning clearly shows senaria rhythm (cf. the group between 
the first and the second B). That one is here dealing with senaria im- 
perfecta^ [2, j>], is apparent in the writing of the next group (after the sec- 
ond B) in which two groups to the value of three M each are clearly dis- 
cernable. The white B and S which follow indicate, according to the 
principles of coloration, the transition to senaria perfecta^ [3, 2]. Toward 
the end of the staff two white B appear in succession, followed by two 
groups of four black M each. Evidently, the divisio changes here from 
senaria to quaternaria^ a change which, in the transcription, is expressed 
by a transition from \ (or J) to 4, with the quarter note unchanged in 
duration. Similar passages in quaternaria are found later (end of the first 
section), and it is for these that the punctus divisionis is reserved. 

Later in the course of this piece there frequently occurs a double- 
stemmed note form (beginning of the third staff) which such theorists as 
Anon. Ill {CS in, 373) and Theodoricus de Campo (CS in, 186) call a 
dragma. It is used in various connotations by theorists as well as com- 
posers. 3 In the present case it has the value of two M, and is thus equal 
in duration to the white S. In fact, either the white form or the dragma 
occurs here to represent the same rhythmic relationships, in the quater-, 
naria as well as in the senaria: 

Quaternaria: □ ul-il Jl?v Jl Senaria perfecta: a*ill- 3UJIJJJI 

For the transcription of the beginning (discant), see the appendix, No. ^ 

1 In L. Ellinwood, The Works oj Francesco Landini (Cambridge 1939), P- 1 57, a rather arbitrary- 
rendition in senaria imperfecta (^-meter), is given, the white notes being considered as indicating the 
normal mensuration, and the black notes as being equal to dotted white notes. 

2 Sq, 162'; Pane, 40; //, 11; Brit, 75.' 

3 See the table on p. 405. 



Examples 
Facsimile 79 



393 



jip3Tpn^ 




1 i 



n 



>p|" (un pMi^ifjn.iiioJulljf'io^i.nii iw c.i.Jlvk Ijjfc .iij^x <4.u« teu, 




Codex Squarcialupi 

Florence, Biblioteca Medicea-Laurenziana Pal. 87 (ca. 140x3) 

Page 162' 



394 



Mixed Notation 



Occasionally, one encounters still other notational characters in the 
pieces of the Italian composers of the late fourteenth century, particu- 
larly in those of Paolo tenorista. Following is the beginning of his 
three- voiced ballata Amor da po che lu ti maravig/i (It, p. 79780): 



D. 



XlfV w*»fwte t»ti -mAWui ^v"3^mi^m^ 




^mte 




JHffl(l>i$ fWfc«|U<>T»wn»>u^}- 



Hrr-T 

t. *&£ 



VHt+ 



Pe 



'MM 



^ 



tZE3t 



The tenor clearly indicates tempus perjectum. In the contra, the shape 

i occurs repeatedly in groups of four. Apparently it is used here in 

the meaning of a Sm> not of a triplet-note (see the remark p. 373, under 

no. 8). The note I has the value of three Sm, that is, of a dotted M. 

The three white notes with the flag to the right side are, of course, trip- 
lets. As can easily be seen, they take the place of one M: £££ = 1 . In 
turning to the discant we find a double-stemmed white note which always 
appears together with one of the white triplet-notes and which, therefore, 

evidently equals two of these: J Jf = A £ = 1 . Following is the transcrip- 
tion of the beginning of this part: 



Syncopation 395 

The pieces to the study of which we shall turn presently are still more 
'French' in their notation, particularly by reason of the extended use of 
syncopation to be found in them. Since this device, which plays a still 
greater part in mannered notation, presents considerable difficulty to 
the modern reader, a detailed study is given below. 

C. Syncopation 

The earliest mention of syncopation occurs in the writings of Philippe 
de Vitry {Ars perfecta in musica Magistri Phillipoti de Vilriaco, CS in, 
28) and of Johannes de Muris {Libellus cantus mensurabilis secundum 
Johannem de Muris, CS in, 46). Their explanations are almost identi- 
cal, namely (see CS in, 34 and 56) : 

Sincopa est divisio cujuscumque figure ad partes separatas que ad invicem 
reducuntur perfectiones numerando. 

Syncopation is the division of a note into separate parts which are con- 
nected with each other by counting perfections. 

This means that the parts of a given note (for example, the three M con- 
tained in a perfect S) do not appear in immediate succession, but are 
separated from each other by larger values, such as a perfect S or B. In- 
deed, if in the combination \JT2 J. I the dotted quarter-note is placed 
after either the first or the second of the eighth-notes, syncopation re- 
sults: |J > JJ > J^|;|J3J ) Ji| . Naturally, the eighth-notes may be separated 
also by longer groups of inserted values, e.g.: 

umu.iJ.j.i-^iJijj. j. j. j. iJH 

ot-.\ JT3J J)LU J>U JU a 

As appears from the above-cited explanation of Vitry and Muris, synco- 
pation was originally limited to perfect mensuration. However, Muris 
mentions the possibility of using it also in imperfect mensuration, for 
instance: 

I/1J IJ I -^ 1-hJ J JW=lJ>J MJ.J)\ 

In turning to a consideration of how syncopation was expressed in 
mensural notation, it may first be noticed that there is no difficulty at all 
if the mensuration (more properly the prolalio) is imperfect. One simply 
has to write the shorter and longer values in their desired order, e.g.: 

c.ul. IIJUJU J3LTJJUI 
o.u...i. IIJJ JJ|J)J J J)|J.| 



396 Mixed Not alio n 

The student will recall that this kind of syncopation is very frequent in 
the compositions of the Flemish masters, from Ockeghem to Lassus. 

The setting down of syncopation becomes considerably more compli- 
cated in prolatio perfecta, which prevails in almost all the pieces of the 
late fourteenth century. The following example, showing the same 
values in normal (a) and in syncopated (b) position, will illustrate the 
difficulty: 

(a) eUU** (b) gU*~I 

It appears that, according to the fundamental principles of mensural 
notation, the writing (b) by no means indicates the intended rhythm, but 
has to be read by applying alteration and imperfection, as follows: 
I .N J-IJ-JJ1 In order to guarantee a syncopated execution dots pre- 
venting alteration and imperfection must be added, as follows:!. !♦♦♦•! = 
IJUJ-JJ.J1 • I n reality, these dots are nothing but the ordinary puncti 
divisionis. However, because of their special function and their appear- 
ance at other points than the beginning or exact middle of a measure they 
are usually called punctus syncopationis, demonstrationist or reductionis. 
The number of the dots required to guarantee syncopation varies. In 
most instances two are sufficient to bring about the intended effect, as 
appears from the following example (all the examples considered here 
are in [2, j]) : 

(a) (b) (c) 

-UIU U-U* -i-IU 
LWJLNJJ IJJJJJJJ.I IJ.iJJ^J-1 

Only the version (c) is in syncopation. Here the first dot prevents the 
initial S from being imperfected, and the second has a similar effect upon 
the second S. 

The following example shows another combination: 

(a) (b) (c) 

-iUU ♦l.Ui* -w-u 
ij.jgijjj.i ijj-iJiu u.JT3Lrn 

Again, the first dot in (c) prevents imperfection of the initial S, while the 
second prohibits the use of alteration for the pair of M. In a case like 
this, where there happens to be only one note between the two dots, these 
are frequently written so close to each other that they look like a pecul- 



Syncopation 



397 



iar sign of syncopation, in the shape of a 'pair of dots': i . J. Wolf in 
his explanations on this matter (HdN I, 343) repeatedly speaks of the 
'Punktpaar' as a somewhat mysterious sign of syncopation. Although 
the Punktpaar does indicate syncopation, a clear understanding of its 
meaning and function can only be gained if it is understood as consisting 
of two different puncti divisionis each of which serves its own purpose. 
Generally speaking, the function of the dots is negative, namely, to 
obviate the application of imperfection and of alteration. 

As a further illustration of the principles of syncopation there follow a 
number of examples, all in [3, j], found in fourteenth century treatises. 1 
In the study of such examples, it is frequently helpful to identify the 
'partes separatas' which must be referred to each other 'perfectiones 
numerando' (see the definition of syncopation, p. 395) : 

1. Ars perfecta in musica (CS hi, 31) 



As none of the B may be imperfected, we have to look for values which 
complete the isolated £ into a perfection. These values are the S rest 

and the group of three M: 

1. Philippi de Vitriaco Liber musicalium (CS m, 44) : 



The two dots, one on each side of the M, prevent this note from being 
connected through imperfection to either the preceding B or the follow- 
ing S. Here again, two other values must be found which will complete 
a perfect group. Evidently, these are the second and the last M of the 



example: 

It must be noted that in syncopation the general rules of perfection and 
imperfection are valid, particularly the rule 'similis ante similem per- 
fecta.' In the present case, the first three of the four S in ligature c.o.p. 
are necessarily perfect, and only the last <? could be imperfected by the 
following M. Since this is not intended, a dot should appear after this S, 
rather than after the M. However, the latter manner of writing is suffi- 
ciently clear; the dot, then, indicates the end of a measure or, in other 
words, the return to normal meter and accent. 

1 For a detailed discussion of the syncopation as explained in the theoretical sources, see GdM I, 



398 



Mixed Notation 



3. Johannes Verulus, Liber de musica (CS ill, 161, 165, 161, 159): 




In (a) the M must be connected with the last S, as the two preceding S 
are both perfect. In this example the dots are not necessary, since the 
first and the second S are already perfect. In (b) the second M makes 
a perfection with the last S, as the penultimate S is necessarily perfect. 
In (c) both S are perfect; since there are only two M in the group, the 
second must be altered. In (d) the perfect S and the M take the place 
of four M; thus, only five M are left (by imperfection) for the B. 

We now turn to the study of compositions involving syncopation. 
Facsimile 80 shows a three-voiced Benche partito by Dom. Paolo [ten- 
orista]. The mensuration is obviously [2, j]. The tenor presents no 
difficulty and may be transcribed first. Near the beginning of the dis- 
cant, four dots appear in close succession, all of which serve to clarify the 
syncopated rhythm of the passage beginning with the syllable 'par(ti'): 
S M.M.M S M.M.M (M) (M). The first of these dots is a normal punc- 
tus divisionis, since it occurs exactly in the middle of a (§-) measure. The 
second is a punctus divisionis in irregular position or, in other words, a 
punctus syncopationis; it prohibits the alteration of the third M and, at 
the same time, indicates imperfection a.p.a. for the subsequent S. The 
other two dots would not seem to be absolutely necessary. They are 
added merely for the sake of clarity, the third obviating alteration for 
the subsequent M and the fourth indicating return to the normal beat 
{punctus divisionis): 



It may be noticed that the next passage in syncopation (shortly before 
the syllable '-a') uses only three dots for the same rhythm. 

Another example of syncopated notation is found in the final passages 
of the first and second section of the contra: S.{M) (M) S S.M.L . Here, 
the two M-rests together with the penultimate M form a perfection which 
is interrupted by two perfect S. In the corresponding passage of the 
second section there is only one dot, instead of three. As a matter of 
fact, only this second dot is indispensable; the first is desirable for the 



Syncopation 
Facsimile 80 



399 



>so-Y)*olo 



MH.Lt#»U il 



325 



¥ 






bcmnoctc^t 



Hy 



*«a 



t 11 *** 




ft 



1 



av i e wo 



p^^M«| l ffP% 



n mi t» crfUmctaku t*i-£J*i»4Wr»c<» JiwolnU(i*c 




^^ 



MS Paris, Bibliotheque Nationale zta/. 5&? (ca. 1400) 
Page 84 



400 Mixed Notation 

sake of clarity (preventing imperfection of the preceding S) y and the last 
is superfluous. 

The dragma which occurs in the discant and in the tenor is the equiva- 
lent of an imperfect S (two M). When this shape occurs in groups of 
three (e.g., beginning of the last staff), it temporarily introduces [3, 2], 
while single dragmas usually serve to express syncopation. Particularly 
informative is the combination Dr S.M near the middle of the seventh 
staff, in which a binary S is followed by a ternary S y the measure being 
completed by a M. 

The sharp immediately after the initial B of the contra probably refers to c' rather 
than to b. The signatures (B-flat for the entire discant and for sections of the tenor 
and contra) as well as the accidentals (C-sharp at the beginning of the contra, B-natural 
at the beginning of its second section, E-flat in the closing passages of the tenor) are 
a reliable indication of the tonality of the piece. Only in two places of the contra is a 
conjecture necessary, namely for the two dragmas on B, which must be read as B-flats, 
and for the end of staff 7 where the previous B-flat must be suspended for the last three 
notes on B. The fact that a seconda volta (chiuso) is provided for the Secunda Pars 
shows that this composition is a ballata. The first section is transcribed in the ap- 
pendix, No. 54. 

The two-voice Fortune of Facsimile 73 serves as another example of 
syncopation. This is one of the few pieces in the sources under consid- 
eration to show the familiar signs of mensuration, the whole and the 
semicircle. However, in the fourteenth century, the meaning of these 
signs frequently differs from the established practice of the fifteenth and 
sixteenth centuries and, therefore, must be verified in each case. In the 
present piece the full circle denotes [3, 2], as is easily seen from the tenor. 
The reversed semicircle, however, signifies, not diminution, but [2, j], a 
meaning which is most clearly indicated in the Secunda Pars of the tenor. 

The upper part is conspicuous for the frequent use of single white notes. 
The value of these notes is the same which they possess in ordinary 
coloration-groups, i.e., two-thirds of that of the black shapes. Thus, the 
white B equals four M, the white S two. The first section of the discant 
is interesting because it includes examples of syncopation in [3, 2], which 
are much rarer than those in [2, 3]. The initial passage shows a perfec- 
tion consisting of a black S and a white B inserted between the third and 
the fourth of four M: |J J3 J^jJolJI J.| • Actually, the white form of the 
B is not really necessary here; if the note were black, it would be reduced 
to its imperfect value by the preceding S. Towards the middle of the 
line, one finds two M rests in succession which normally ought to be 
written as one S rest. The idea may have been to facilitate the reading 
of the syncopation, by suggesting counting M, rather than S. The 



Syncopation 



401 



various dots placed after a S are, of course, puncti additionis. The 
fourth note from the end of the first staff is a M (not a S) which com- 
pletes the syncopation inaugurated by the dotted S of the first ligature 
c.o.p. 

In the Secunda Pars, there follows after the initial B a passage in which 
white and black S alternate, so that groups equalling five M, or in mod- 
ern notes, g-measures, result. We see no reason why this clear and defi- 
nite rhythm should be obscured by forcing it into the scheme of g-meter, 
a procedure which would result in a complicated succession of tied notes. 
Of course, the use of g-meter in the upper part against g-meter in the tenor 
is likely to cause grave disturbance to the eye of the modern reader. 
However, it must be remembered that we are concerned here with cham- 
ber music of a truly polyphonic nature, a type of music which allows for 
a much greater rhythmic independence of the parts than piano music or 
orchestral music. As a matter of fact, nothing is more obstructive to an 
understanding of fourteenth and fifteenth century polyphony (or, by the 
way, to the introduction of true polyphony into modern music) than that 
concept of rhythm which is embodied in the person of the orchestral con- 
ductor who directs all the players with one unifying beat. Of course, 
early polyphonic music is also based upon a common unit of time, with- 
out which, needless to say, ensemble performance is impossible; however, 
this unit is not necessarily the beat (quarter-note), but frequently a 
smaller value (eighth-note, M), which may be grouped in different num- 
bers in the different parts. Following is a 'polyrhythmic' transcription 
of the beginning of the Secunda Pars. 



Secunda pars 



402 Mixed Notation 

This passage shows that in fourteenth century notation syncopation 
could be expressed, not only by means of the punctus syncopationis^ but 
also by the intercalation of notational characters denoting irregular 
values, such as the white S in the above example. More complicated 
examples of both methods will be encountered in our study of mannered 
notation. 



IX. MANNERED NOTATION 

A. General Characterization 

TOWARD the end of the fourteenth century the evolution of nota- 
tion led to a phase of unparalleled complication and intricacy. 
Musicians, no longer satisfied with the rhythmic subtleties of the Ars 
Nova, began to indulge in complicated rhythmic tricks and in the inven- 
tion of highly involved methods of notating them. It is in this period that 
musical notation far exceeds its natural limitations as a servant to music, 
but rather becomes its master, a goal in itself and an arena for intellec- 
tual sophistries. In this period, we find not only black, white and (filled) 
red notes, but also hollow red notes, as well as notes which are half red 
and half white, or half red and half black, and many special forms de- 
rived from or similar to those of Italian notation. Here for the first time 
we find use made of canons, i.e., written prescriptions which explain the 
meaning of the notes 'sub obscuritate quadam.' Here we find composi- 
tions written in the form of a circle or a heart, again an indication of the 
strong hold upon the imagination of the composer that the purely man- 
ual business of writing exercised in those days. Frequently these elab- 
orations of notation are mere tricks of affected erudition, since the effects 
desired could be represented in much simpler ways. In other cases they 
are indispensable, leading then to a product of such rhythmical complex- 
ity that the modern reader may doubt whether an actual performance 
was ever possible or intended. Regardless of their artistic value, these 
'pathological cases' are of particular interest to the student of notation. 
Each of them calls for separate examination and presents problems which 
are not easily solved. Thus they form a fitting conclusion of our study, 
as the 'gradus ad Parnassum,' the 'etudes transcendentales' of notation. 
Once more, as in the introduction to the previous chapter, we wish to 
point out that our classification and terminology are based primarily on 
principles of methodical study and of instruction. Terms such as 'mixed 
notation' and 'mannered notation' are introduced here chiefly because 
they permit us to arrange conveniently and appropriately the material 
which we have to present. Whether, in addition, they have a historical 
significance is quite a different question and one which, as has been re- 
marked already, we are not in the position to answer definitely, owing to 

403 



404 Mannered Notation 

the very rudimentary state of our knowledge of music history between 
Machaut and Dufay. There can be little doubt that the systems de- 
scribed in this book as French notation, mixed notation, and mannered 
notation were in use simultaneously around 1400. The problem pre- 
sented by the most striking contrast between the classical simplicity of 
French notation, the motley appearance of mixed notation, and the highly 
involved character of mannered notation may perhaps be accounted for 
by differences of localities or schools. Tentatively, one is tempted to lo- 
cate the first in northern France (Cambrai, Paris), the third in 
southern France (Dijon, the capital of Burgundy), and the second in 
northern Italy and the bordering provinces of the two countries. How- 
ever, as far as the two latter systems are concerned, no clear line of de- 
marcation is possible, either geographically or notationally. Regarding 
the geographical (or national) point of view, it may be noticed that of 
the two main sources of mannered notation, one, the Codex Chantilly, is 
entirely French, while the other, the Codex Modena, includes chiefly 
pieces by Italian composers, many of which, however, have French texts. 1 
As regards the notational characteristics, the border lines are even more 
blurred. For instance, to classify the piece Fortune of the previous chap- 
ter as an example of mixed notation, rather than of mannered notation, 
is rather arbitrary. 

Our statements regarding the highly involved and affected character 
of the notation under discussion should not lead the reader to conclude 
that the music itself is just as artificial. As a matter of fact, although 
our incomplete knowledge of the musical situation around 1400 makes it 
difficult to generalize, there are a number of pieces which are quite re- 
markable for their musical qualities and charm. 

The most extensive sources for mannered notation are the Chantilly 
and Modena MSS just mentioned. However, pieces of this type also 
occur in MS Florence, Pane. 26 (here only two, on p. i6',i7, evidently 
written in a later hand), in MSS Paris, B.N. ital. 568, andf.fr. 677/ , and 
in MS Torino, Bibl. Naz. J. II. 9 (see HdN 1, 368). Although, as has 
been previously remarked, each example of mannered notation presents 
its own and individual problems, it will be useful to discuss briefly a few 
general points. 

B. Principal Features 

Signs of Mensuration. Signs of mensuration are still of rare occurrence. 
Their absence presents, in many cases, considerable difficulties which are 

1 See the lists of contents in GdM i, 328 ff., and 336 ff. Corrections of these lists have been given 
by F. Ludwig in SIMG vi, pp. 611, 616. 



Principal Features 



405 



increased by the frequent use of syncopation and other irregular group- 
ings. But even if signs of mensuration are given, they cannot always be 
relied upon to have their familiar significance. As far as the present 
author's experience goes, the signs o G © always have their usual 
meaning. However, the semicircle and the reversed semicircle, CD , * 
are very inconsistently used. The former may indicate [2, 2], but is also 
found to indicate [2, j>], and [2, 2] in diminutio simplex. Exactly the 
same three meanings occur with the reversed semicircle, which frequently 
signifies tempus imperjectum diminutum i but is also used as a sign for 
[2, 2] or for [2, 3}. 

Special Notes. A great variety of semibreves caudatae occur in the sources 
under consideration. Some of the more common ones are shown in the 
table below, the data of which cannot, of course, be applied indiscrimi- 
nately. As will be seen, some of these shapes are used with different 
meanings even in one and the same composition. 



\ 



1 M (79, 80) 
\ M (82, 83, 86) 
i M (83) 
1 M (WO 

i M (GdM, no. 66) 



T 



3 M (82) 
2M(F) 
4 9 M (R) 



m 



\M 

'(A, L) 



t 



M 
(W 4 ) 



M 


t 


I 


I 


M 


\M 


§M 


\M 


(87, wo 


(WO 


(L) 


(L) 



The numbers 79, etc. refer to the Facsimiles; W,, etc., to the pieces from Wolf's GdM 
discussed on p. 426ff. A = Amor da po, p. 394. F = A qui fortune (Mod, 19'). H = 77 
n'est nul horn (Ch, 38')- L = Le grant desir [Mod, 46; see W. Apel, French Secular Music 
of the Late Fourteenth Century [FSM], No. 2). R = En remirant (Mod. 34'; see FSM, 
No. 59). See also the tables in GdM i, 302, and in FSM, 'The Notation'. 

Coloration. The ample use of red notes in the codices Modena, Chan- 
tilly and Torino bestows upon these a special character of decorativeness 
and complexity. There is, of course, no essential difference between the 
red notes encountered in these sources and the white ones used in others. 
For instance, Anthonello de Caserta's Biaute parfaite (Facsimile 86) 
occurs in the Codex Modena (La beaute parfaite, p. 14) with red notes 
instead of the white ones used in the Codex Reina. The following ex- 
planations, therefore, apply equally to red and to white notes, unless 
there is a remark to the contrary 

1. Normal coloration, i.e., groups of three red notes (or their equiva- 
lent) equalling two black ones. This device, being identical with the 
coloration of white notation, does not need further explanation. It 
occurs in [3, 2] (three red B) and, most frequently, in [2, j] (three red S); 



406 Mannered Notation 

also, occasionally, with triplet-effect, in [2, 2] (three red S, see GdM 1, 
345, d; or, three red M, see GdM 1, 345, e). 

1. Syncopated and incomplete coloration. By these terms, we refer to 
a variety, frequently encountered in the manuscripts under considera- 
tion, of the normal type in which the red notes essentially retain their 
normal meaning, but appear in groups of less than three. In many 
cases, complementary notes will be found shortly after, in the typical 
manner of fourteenth century syncopation, e.g.: 



1. gu.ijju j>j ;>j 1 



There are also examples showing a dovetailed arrangement of incomplete 
groups of black and red notes, e.g.: 

i ..liu ♦♦ §l J> JJ MJTiJTi I J> J J.I 

In cases in which there are not sufficient red notes to complete a full 
group of coloration one has to consider these notes separately. In [2, j], 
the only mensuration which concerns us here, we have the following 
values : 







■ = \M 


♦ 


= 2M 


I =M 


as 


against: 


■ = 6M 


♦ 


= 3 M 


| = M 


Examples: | ■■+ 


=ij>jjj>ij.j.i; ♦♦♦;.;. 


♦ i-IJWJIJ73JJ1 



3. Red notes indicating dotted values. Although coloration usually 
diminishes the value of a note (by one third), it is occasionally used in an 
opposite meaning, signifying an increase by one half, that is, synonymous 
with a dotted note. Naturally, this type of coloration can only be ap- 
plied to imperfect notes. For instance, in [2, 2] a single red B is likely 
to represent a dotted B, and a red S in the meaning of a dotted S may 
occur in [2, 2] or in [3, 2]. The following examples will help to clarify 
the meaning of 'reversed coloration,' as we may call it: 

(a) [2,2b ... - 2| J IJ^JJ J I 

(b) [3,2]: .♦.♦ =|| J j I J. j I 

(c) [2, S ] : ♦♦uu=g|j. j Mm. J. 1 

4. Red notes indicating halved values. This meaning of coloration 
occurs only with the M, the red M thus being used instead of the Sm. 



Examples 407 

These red (or white) Sm are very frequent in the early fifteenth century 
sources of French notation, as has already been observed (p. 362). 
5. Hollow red notes. These characters — for which there is obviously 
no equivalent in white shapes — usually serve to introduce binary groups 
instead of the ternary groups of prolatio perfecta. Depending upon 
whether the S or the M is considered, the relationship to the normal. 
characters is either 2:1, or 4:3 : 

♦ uioouu jij. /ni/3JTOi 

C. Examples 

We turn now to the consideration of a number of examples of man- 
nered notation. 

1. Pa[olo tenorista], Amor tu solo 7 sat (Facsimile 81). The most 
striking feature of this three- voice ballata (discant on left-hand page; 
texted tenor and untexted contra on right-hand page) is the use of red 
notes, B and S, which appear either singly or in groups of two, never in 
the normal grouping of three notes. Their meaning depends upon the 
mensuration, the determination of which, in turn, is not without difficul- 
ty. Only with the contra is a sign of mensuration given, calling for 
[3, 2]. Here the red B indicate the imperfect, instead of the perfect 
value and therefore equal four M instead of six. With the red S the 
situation is different, since the black S is already imperfect. The red S, 
therefore, indicate 'reversed coloration' or, in other words, dotted values. 

The application of the same methods to the discant fails to lead to a 
satisfactory result. Actually, this part is in [2, 2], as appears most clearly 
from the group of eight M on the first staff (syllable 'sa — [y]'), a combina- 
tion which virtually excludes the possibility of perfect mensuration in 
tempus as well as in prolatio. Here, then, the red B as well as the red S 
signify dotted values. The notation of the tenor gives hardly any clue 
regarding its mensuration. One must, therefore, resort to experimenta- 
tion. Such a procedure, however, will not result satisfactorily, unless it is 
realized that the two texted parts must be read in diminutio dupla. In- 
deed the direction is found written with the contra 'ut jacet et aliud per 
medium,' i.e., '[contra tenor] as it stands, but the other parts in halved 
values.' According to this canon each B of the texted parts equals one 
S of the contra. On the basis of this direction the tenor will be found to 
be in [2, 2]. 

Although tempus perjectum is expressly indicated for the contra, its 
rhytnmic design as such shows but little evidence of ternary meter. In 



408 Mannered Notation 

fact, the principles of alteration, perfection, and imperfection cannot be 
applied without taking regard of the free metrical structure. To a certain 
extent this is indicated by puncti divisionis in displaced positions (puncti 
syncopationis). For instance, the first punctus appears after 19 S (the 
half-red ligature is a binarid). Therefore one extra beat (19 =6 X 3 -+- 1) 
must be interpolated in order to get the two ensuing S into the proper 
position as a group of alteration, 

A similar situation occurs in the middle of staff 6, where the consistent use of 1-meter 
would cause the S-rest (after the single red S) to fall on the first beat, thus leading to 
alteration for the ensuing S. Actually this S is not altered. In order to guarantee correct 
reading, a punctus syncopationis should appear before the red S (or, at least, before the 
first black S thereafter). The following figure shows the rhythmic structure of the pas- 
sage, starting with the first single B of the staff: 

IJJUJiJJlJ J3|J.J>;3iJ*Ji* I JlJJ>J3U J3JjJ3J3Jl*J 

The S on c' appearing above the word *Ut' should probably be on d', and the black B on 
c' appearing below this word may be read as a. See the appendix, No. 55. 

1. Je la remire sans mensure (Facsimile 82). The basic mensuration 
* of this textless (instrumental ?) piece is [3, 2], as appears from the use of 
two S rests in succession, at the beginning of the discant as well as 
throughout the tenor. However, [2, 2] is introduced frequently by the 
semicircle. Several times the latter sign is followed by a group of three 
B, which evidently take the place of two perfect B. The resulting 
rhythm is the same as that usually indicated by coloration. In the 
transcription three 4-measures may be combined into one J-measure. Of 
special interest are the passages in which the mensuration changes with 
each single note, as in the middle of the second staff. This passage falls 
into three groups, each of which consists of an imperfect L, a perfect B, 
and an imperfect B, in the value respectively of 4, 3, and 2 S. Together, 
they fill in three 4-measures in syncopation : 3 | J. | J J | J J | • 

Finally, the semicircle is also used in connectiorTwith two special signs, 
the semibrevis with a downward stem (S maior, see p. 332), and the 
double-stemmed semibrevis (dragma, see p. 392), both of which have 
occurred already in our previous studies. However, they have a differ- 
ent meaning here. The former character has the value of a dotted S, 
(3 M, dotted quarter-note), and the latter is half of the former (f M, 
dotted eighth-note). A rendering of these values in J-meter is somewhat 
awkward. Their significance is more easily grasped if they are inter- 
preted as duplet formations in 4-meter (see p. 410). It follows, then, 
that, in spite of the changes in mensuration, triple meter can be main- 
tained throughout the piece (a full circle is missing after the ternaria on 
the first staff). 



Examples 
Facsimile 8i 



409 










bO 



4io Mannered Notation 



mtt iijj u .n 



hffi 






The beginning of the discant contains an example of syncopation in 
[3, 2]. Another example, including the Punktpaar, occurs near the be- 
ginning of the second staff. As always each dot has its own significance: 
the first prevents the preceding B from being imperfected, whereas the 
second prohibits the use of alteration. Each of the following B is per- 
fect, since another B follows immediately, while the last B is rendered 
perfect by the third dot. 

The fourth S maior of the group in staff 4, over 'Je la remire,' should be c', not a. 
The correct reading is found in both other sources, ital. 568 (p. 126'/ 127) and/./r. 6yyi 
(p. 80), which, however, contain several other errors. For the three main cadences of the 
discant sharps are given which, although evidently not a part ot the original writing, 
probably are of sufficiently early date to be considered as authentic. No editorial acci- 
dentals are needed, not even for the last f (S maior) on staff 5, although it occurs almost 
simultaneously with a c-sharp in the discant. The beginning of the first and second 
section is transcribed in the appendix, No. 56. Our transcriptions are designed to clarify 
the notational peculiarities of the compositions. For a final rendition it may be prefer- 
able to make a homorhythmic score, in equal measures, indicating the original rhythm 
in small notes on top of the staves. 

On the bottom of the page one finds a two-voice rondeau Se vous n'estes which is a 
composition by Machaut (see F. Ludwig, Machaut, Werke, 1, 56). This is one of the few 
compositions contained in the Machaut MS of the Pierpont Morgan Library, New York 
{MS no.jp6, f. 214V). 

3. Je ne puis avoir (Facsimile 83). The notational methods used in 
this piece are nearly the same as those encountered in the previous ex- 
ample. 1 The chief difference is the use of the reversed semicircle for the 
passages written with the semibreves signatae (S maior and dragma), for 
instance, those above 'puis avoir.' Actually, there is no diminution to 
be applied to these passages, the notes having exactly the same value as 
they had in Je la remire under the simple semicircle. The notation used 
in the present case is apparently a confusion of two different methods to 
bring about the same rhythm, one by the S maior in tempus imperjectum y 
the other by the B in tempus imperfectum diminutum.-OmC j ♦ = 0« 3«« = 

IIJ-IJJI • Occasionally, there occur groups of three red dragmas which, 

1 In the original nearly all the signs of mensuration are written in red. It has not been deemed 
necessary to preserve this peculiarity in our facsimile. 



Examples 
Facsimile 82 



411 



jG 



a<A.1..l ."V.I i =F^ 



tv... ^y/Pfiy ■ '■> , 




:V" » a... j 



■*J 



-C" L» rcmirc din* »«<nlii 



^^N w ,,., 1,; >^^^i^N«. i , 1 ^ 






£ tfn 



# 



4 



^■f^ryfi 



jgggg 



J I j jmcljhO ntea «mcnr~"fclrtwc»im\«-(«ni»'m«fiiie> 



b • -y > g 



* J ^f ' 



W 



tf 



eg • , HA4i^ u >]h^r4 




MS Modena, Biblioteca Estense L. 368 {ca. 1400) 
Page 34 



412 Mannered Notation 

as can easily be seen, take the place of two black ones, thus introducing 
triplet groups among the duplets (see the transcription below). 

Only once is the reversed semicircle used in its proper meaning, that is, 
in the group after the binaria near the beginning of the third staff. This 
group consists of two plain S preceded by three dragmas which take the 
place of another pair of S. Thus, the whole group comprises notes to 
the value of two B (four S) in tempus dtminutum, or of one B of the in- 
teger valor. The rhythm of this group is identical with that expressed 
elsewhere (near the end of the second staff) by three red and two black 
dragmas: ^_^ 

3 m«-tfHt- wrnn\ 

It appears that in this piece one and the same note, the dragma, is used 
in two different meanings, either in the value of 1 M or of i M. 

The red S (in ligature c.o.p.) near the beginning of the second staff 
are 'reversed coloration'; each of them equals a dotted S or in other 
words, a S maior. In the middle of the third staff, the first note after 
the punctus above the syllable 'sou'- is a S, not a M (correct in Modena). 
On the last staff, the third L from the end is imperfected by both S. 
The dot does not indicate the end of a perfection, but serves to prevent 
alteration of the two S. The end of the second section affords another 
example of a clos (and, consequently, an ouvert), the length of which is 
different in each part. As a matter of fact, the clos group comprises five, 
six and eight B (J-measures) in the discant, contra, and tenor respec- 
tively. This passage is also remarkable for the bold treatment of 
dissonances. 

Special mention must be made of two ligatures in the tenor (fifth and 
thirteenth ligature on the fifth staff) which show the extremely rare use 
of oblique writing for an ascending ligature. 1 In the late fifteenth cen- 
tury these shapes became the issue of a heated controversy between 
theorists (see p. 90, footnote). In the present piece, the ascending 
binaria with a downward tail has the value B B (not L B) } in conformity 
with the view held by Tinctoris. 

The piece has a rather unusual signature, a B-flat in the discant, and an E-flat in each 
of the lower parts. Properly, the lower parts should have a B-flat in addition to the 
E-flat. The reason for the omission probably lies in the fact that the lower parts reach 
the B only a few times, whereas the E lies within their normal compass. The form of 
the composition is that of the virelai, as can readily be seen from the fact that the second 
section is underlaid with two lines of text, whereas in a ballade the first section has two 
lines of text (see, e.g., Facsimiles 68, 70). The structure of the virelai (and of the 

1 Disregarding, of course, ligatures c.o.p. 



Examples 
Facsimile 83 



413 




^gpi! 



^T^LWpUfe^tt p fa* * bt ftrg«r «m«n»*v™^ 




fills |A I, Ji , U , wl W L ^L i- ^ M t i i.j J Ji 

fflonourqwcftUnncf ft *V t> \ 



wortourqmwUnwi ft no/ 




*2Elto»3 



^A^tp^cpy^^ryr^^^ l ^ 



|lH>^^,.,"-, t >>, ro! v^v t - t ^ f | f | t f, ) ,'( ! )( ) ()p 



f t >llttllt t ll^ , >FA^>^-li f ^W B 



j^.l|^l,»-1 r T|lllj g !^j^ 



m w**'* 



MS Chantilly, Musee Conde /<V7 («• '4°°) 
Page 24 



414 Ma n n ered Notatio n 

Italian ballata) is A b b a A. The second line of text for the section a is given after the 
music. The following scheme clarifies the underlaying of the complete text: 
A b b a A 

Je ne . . Car son . . Et quant . . Pour quoy . . Je ne 

The beginning and the end of the discant are transcribed in the appendix, No. 57. 

4. Anthonellus, Dame gentil (Facsimile 84). This piece shows inter- 
esting examples of syncopation, particularly in the discant. The men- 
suration is [1, j], as appears from a glance at the lower parts; in fact, as 
has already been remarked, the great majority of the compositions of the 
late fourteenth century are written in this mensuration. The dot after 
the initial B is both a punctus divisionis and a functus additionis; not 
only does it prevent the B from being imperfected by the following M, 
but it actually increases its value from six M to nine M. The subse- 
quent passage in syncopation begins with two M, between which there 
is a dot preventing the application of alteration. Thus, each M equals 
one eighth-note of the transcription. The first of the two £ in ligature 
c.o.p. is, of course, perfect (three eighth-notes) because it is followed by 
another S. The second S, however, is imperfected a parte post, and so 
are the two following B, each of which is reduced to five eighth-notes by 
the following M. The third S (on d) is perfect by virtue of the punctus 
following it: 



Although this transcription gives the correct rhythm, yet it obscures 
to a certain extent the real nature of fourteenth century syncopation 
which is quite different in character and meaning from that of more re- 
cent periods. It suggests that type of syncopation which is most clearly 
expressed in jazz music, and which may be explained as an omission of 
the strong beat within an unchanged meter. The aesthetic significance 
of this rhythmic peculiarity is that of an unexpected loss of balance, of a 
sudden shock, which momentarily upsets our rhythmic security. Four- 
teenth century syncopation, needless to say, is far from having this char- 
acter. It can be most properly described as a temporary displacement, 
rather than an omission, of the strong beat. Thus, it is much closer in 
nature to that more recent type of syncopation which is frequently en- 
countered in the works of contemporary composers, such as Hindemith 
or Stravinsky. The difference between the two interpretations appears 
from the following example in which one and the same rhythm is notated 
in two ways, one indicating 'elision,' the other 'displacement': 



Examples 
Facsimile 84 



415 



^nt^rwl\wf- 



Uiu Mp'km^mm d 



ES 



d tut Qen hi 



^m4Vma. 



i.-..i[„>ti ll i,i l .ii| i i i 1 HHa ^ 



ffsfrrttltf*- "Vtft** 



4AJ-4 



to 



/ r 



Mv^ 



rfto* fpiir m«*n 



I'icn cr im"i cpnfeii 



il 



«i^ 



It 



I A 



..Y*>Vu , F» i * TW 



nrr 



C"TICII\' r.lUK 



VntiL- 



1 , vt* c,rt * 



E , > 



^^^fe 



» «' *t< t > 



Ip.h 1 ' If 



^iHr«l rtitdrr^inttf^cnKl- 



m m .in lui 



S gigg 



H 1 V ZQT Z1 



♦ — ^4 



^)OM* «I>C*- 



a mv\ 1 H I ' I """ rt r ' cw * n '* v ""* nr P |rtl ^ lntT - T>fln " : JcanEaS £rpm- 

11 ! li 4 A . -I tULH£Jnil& bU3l£ .ifc>iint*i«fg. dminr iflntrt iu^u- no fi-cf. ovt 



IT'VHi 



fr p>:;<-fTnnit;cnnt- 



MS Modena, Biblioteca Estense L. 568 (ca. 1400) 
From page 38' 



416 



Mannered Notation 



§iJ. j h rriTn\rril j>i j. i 



giJ- j j>if jiijj j> j jit j. j>i§ j.i 

The initial passage from Dame gentil'is a typical example of fourteenth 
century 'displacement of bar-lines.' Indeed, if an imaginary bar-line is 
drawn after the second M, there results a series of normal perfections to 
the value of three B. Below is a 'displacement' rendition of the passage, 
together with still another method of writing which, although quite un- 
familiar in appearance, actually is particularly well suited for our pur- 
pose, because it makes clear not only the displacement of the bar-lines 
but also the 'insertion' character of fourteenth century syncopation 
which causes the accent to return to its normal position after a shorter 
or longer stretch of syncopation: 




Another interesting passage in syncopation starts with the M-rest 
after the four M: (M) B B S.M S S.M. All the B and S are perfect, 
either because they are followed by another perfect note or by a punctus 
perfectionis (in correct writing, there probably should also be a punctus 
perfectionis after the second B). Another perfection is formed by the 
three M which, however, are separated from each other by the insertion 
of longer values (see Philippe de Vitry's explanation of syncopation, p. 
395). The following rendering clarifies the rhythmic construction of the 
passage: 

| 7SJ.;J.;J. 5f! J.J.; r | = ||rJJ|J>^J^JJ71|J J>J J>| 

An unusually long passage in syncopation starts with the first S on the 
second staff. This S is preceded by a M-rest which falls on the first beat 
of the measure. However, the dot after the S prevents it from being im- 
perfected by the preceding rest. Then begins a long passage in the normal 
rhythm of [2, 3] (f), in which the principles of perfection, imperfection, 



Examples 417 

and alteration apply as usual; however, the whole passage is removed by 
one eighth-note from the normal accent and barring. After six and a 
half measures, the barring is brought back to normal by the two M which 
are separated by a dot (in order to prevent alteration). 

Various other instances of this method occur in the piece, for example, 
at the very beginning of the contra. Aside from this passage, the two 
lower parts present no difficulty, the red notes of the tenor being normal 
coloration. As a matter of fact, there is such a striking difference of 
rhythmic and notational complexity between the discant and the lower 
parts, particularly the tenor, that one gets the impression of a composi- 
tion written for a 'syncopation virtuoso' and two accompanists of average 
musical intelligence. There exist a great number of pieces of this type 
in the sources under consideration. 

A correct transcription of the discant will be facilitated by the remark that the two 
closely grouped A/-rests that appear twice on the first and three times on the second 
staff each time stand at the beginning of a perfection (that is, of a full or of a half measure), 
thus causing the ensuing note to appear in displaced position. 

The form of Dame gen til 'is that of the rondeau: ABaAabAB (see p. 140;, as appears 
from the reiteration of the refrain 'Dame gentiP in the text given at the end of the music. 
The complete underlaying of the words is as follows: 

A B 

1.4.7. Dame gen til . . . sperance 2.8. Vous estes . . . confort 

3. Ny d'autre . . . playsance 6. Quant ie puis . . . port 

5. Et pour vous . . . aboundance 
The first section is transcribed in the appendix, No. 58. 

5. Tout houme veut (Facsimile 85). This is a three-voice ballade, the 
Abgesang 1 of which falls into two sections, one to the text 'Car celui — 
oublier' (second staff), the other to the text 'Sans — entreprendie' (third 
staff). The tenor, written in plain [2, 3] with normal groups of colora- 
tion presents no difficulty, aside from the careless writing. 2 The contra 
shows similar features of notation and, in addition, a few relatively simple 
and short passages in syncopation, e.g., immediately after the first 
group in coloration. Both parts contain many instructive examples of 
alteration. 

As in the previous piece, the discant is a part for the 'syncopation (or 
notation) virtuoso.' It contains two particularly interesting passages in 

1 We borrow the terms Stollen and Abgesang for the first and second section of the ballade from the 
German counterpart of this form, the Bar of the Minnesinger and Meistersinger. See the descrip- 
tion in R. Wagner's Meistersinger, act I, 3 (Kothner: 'Ein jedes Me< c tergesanges Bar . . .'). 

2 In the photographic reproductions of the Codex Torino which have been available for the pres- 
ent study, the indication of the red notes is frequently very poor, so that in some places conjectures 
have been necessary. 



4 1 8 Mannered Notation 

syncopation, the first beginning immediately after the initial B (here, the 
M-rest, the subsequent M, and the final M on c form the perfection which 
is interrupted by five *?), the other starting with the M on g after the S- 
rest in the middle of the first staff (here the perfection is formed by the 
initial M, the second M on e after the red ligature, and the Monc). The 
reversed semicircle indicates that type of proportio dupla which also pre- 
vails in the earliest sources of white notation (see p. 151), and which 
serves to introduce duplets, two S of the proportion being equal to one 
(ternary) S of the integer valor. In the passage marked I, three S are 
equal to two normal S. The prolatio is here perfect, so that groups of 
nine M result, each of which takes the place of a group of six M in the 
integer valor. The passage at the end of the third staff (after the binarid) 
reads ge fdgbd'c'a (the final character of the staff is the custos which 
merely anticipates the first note of the next staff). 

The section A {Stollen) of the discant is transcribed in the appendix, 
No. 59. 

6. [B]iaute parfaite (Facsimile 86). The entire tenor is in [2, j], as 
appears from the frequent groups of two M-rests followed by a single M. 
In the contra, however, the prolatio is normally imperfect, as is suggested 
by the occurrence of dotted S in succession, since otherwise the dots would 
be unnecessary. As for the tempus y the music itself fails to lead to a 
decision between tempus imperjectum and tempus perjectum. Nota- 
tional considerations suggest [2, 2] as the intended mensuration, the main 
point in evidence being the 5-rest near the beginning of staff 6, which 
must be binary, not ternary. For the first section of the Secunda Pars 
{Abgesang), [3, 2] is introduced by the full circle, while for its second sec- 
tion the mensuration changes back to [2, 2]. It must be noticed, how- 
ever, that throughout the contra the mensurations have a notational 
rather than a musical significance. Although they correctly indicate the 
values of the notes and rests {B and S), they fail to express the prevailing 
rhythm. This is particularly true for the sections notated in [2, 2] 
which, from the musical point of view, suggest a free alternation of 
* measures or passages in 4, 4, and 8 . 

In the discant, the normal mensuration is [2, j], on the basis of the 
same evidence as in the tenor. The initial passage is in syncopation; in 
fact, the first dot is not, as one might believe at first sight, meant to mark 
off a perfection (which would lead to alteration of the second M), but is 
a punctus syncopationis which indicates the beginning of displaced bar- 
ring. The B, being followed by an S, retains its full value of six M, 
while the S itself is imperfected by the following M. The two M placed 
between the second dot and the B do not undergo alteration, any more 



Examples 
Facsimile 85 



419 




k jj k '%V'iL k - litis 




k 



m 



MS Torino, Biblioteca Nazionale J. II. 9 (ca. 1400) 
From pages 134', 135 



4^o Mannered Notation 

than those at the beginning of the piece. The fourth dot is similar in 
function to the second, while the fifth, as usual, prohibits the use of alter- 
ation for the last two M. A transcription according to the idea of broken- 
up perfections and displaced bar-lines readily clarifies the rhythmic 
structure : 



rrl j.jj> trr ,rn rr 



In the first section of the Abgesang ('Je ne puis — endurer') syncopation is 
effected by the use of special note values, the white S and the dragma. 
The former sign equals i M, the latter i^ M. At the beginning of the 
second section ('Puis') a sign indicating [2, 2] is missing. As in the corres 
ponding section of the contra, this sign has only notational significance, a 
rendering in \ and 4 being musically appropriate. 

The use of the white notes in the discant is very peculiar. According 
to the normal mensuration [2, j] one might expect to find three white S 
taking the place of two black ones. Actually, however, the S remains 
unchanged; the coloration applies to the M, with which it indicates the 
transition from groups of three to groups of two, i.e., to dotted M or dup- 
lets. Therefore, this is a case of 'reversed coloration' of the type illus- 
trated by the example (c) given under no. 3 (p. 406). In order to clarify 
the difference between the two interpretations, it may be observed that 
both lead to the same mensuration [3, 2] for the group of white notes, in 
conformity with what is indicated in the original. However, although 
in normal coloration this group, which comprises 6 white S> would be 
equal to 4 black S and, therefore, would fill in two ^-measures, it actually 
is equal to 6 black S and, consequently, takes the place of three such 
measures. 1 

The interpretation of 'reversed coloration of the M' applies to the first 
and to the second passage of white notes. However, the next passage of 
white notes is in 'normal coloration of the 6 1 ,' with triplets introduced by 
the prolatio perfecta. With the subsequent groups and with the single 
white notes the situation is much simpler, because they include only S> 
no M. Here the prevailing mensuration unequivocally indicates which 
type of coloration is meant in each case. 

1 See the erroneous transcription in GdM i, 344, where the group of red notes (the passage is copied 
from the MS Modena) occupies two, instead of three, normal measures. 



Examples 
Facsimile 86 



421 



■%f M ili ll E ldE S 



i/.m s Aifiiiinii3«i. , inMnw!Mfiir 



i 



gi j P }p 



5C 






» W y v n ''# 




" JaS irjgtgt 



M 




s 



j 



JrVi, J« ' # i 



f My* 






nfi^SUe<f<MSe« B^Sr 



swam a 



iff 



II J- 






lAWkllt|HVW Si 






JjJiiaMI 



MS Paris, Bibliotheque Nationale wo«&. acq.frg. 6jji (ca. 1400) 
Page 46 



422 Mannered Notation 

The following errors or inaccuracies of writing may be noticed. Discant: A semicircle 
is missing at the beginning of staff 3. Contra: (1) After the 13th note (dotted S on d') 
three notes M M M on d', g, d' are missing (correct in Codex Modena); (2) in the last 
binaria of staff 5, only the finalis is dotted, not the initialis; (3) the last M on this staff 
is g, not a; (4) in the final section (staff 7) the 14th note {S on g) should be dotted; the 
21st note (Mon d') should be c'; the 25th note (Mon g') should be a'. 

The first section of the piece is transcribed in the appendix, No. 66 

7. Jacopinus Selesses, En attendant esperance (Facsimile 87). The 
basic mensuration of this three-voice ballade 1 is [2, 3] in all the parts. 
The tenor is free from rhythmic complications and, therefore, provides a 
basis (a very desirable one, indeed) for the interpretation of the other 
parts. In the contra we find filled red notes which have the usual mean- 
ing of coloration (red B = 4 M, red S = 2 M; red M = 1 M). The 
value of the hollow red M can easily be derived from the fact that they 
appear in groups of eight (or sixteen, see the group beginning at the end 
of staff 8). Four of these notes are equal to a S y thus introducing quad- 
ruplets instead of the ternary groups of the prolatio perfecta. In the dis- 
cant, we find three new forms in addition to those encountered in the 

contra: <> ( a )» ; (b)> an d r (c) 2 - These shapes are used in a very 

inconsistent and confusing manner. In a way, they all indicate one and 
the same rhythm, that is, triplets instead of two notes of the quadruplets 
indicated by the hollow red notes. On the other hand, however, the 
form (b) is also used with a totally different meaning, that is, equal itself 
to two of these quadruplet-jiotes. The only clue as to which interpreta- 
tion applies in a given case is found in the grouping of these notes. The 
passage towards the end of the first staff, after the syllable 'a — (voir)' 
serves as an illustration; it shows the identity in meaning of the forms (a) 
and (b), as well as the two different meanings of (b) : 



uiu %\m}nm 



In the middle of the staff three, we find exactly the same rhythm, with 
the form (c) used for the triplets. 3 

The discant contains several interesting and complicated examples of 
syncopation. Instead of dots (punctus syncopationis), red notes are used 

1 The figure 4 given in GdM 1, 337 for the number of parts of this piece is erroneous. 

2 The form (a) is hollow black, the other two (characterized here by a dot) are hollow red in the 
original 

1 The present writer has made numerous, but futile, efforts to arrive at an interpretation wfticn 
would make the meaning of these characters less equivocal. A comparison with the version in the 
Chantilly Codex has proved of no help since the writing there differs in many particulars. 



Examples 
Facsimile 87 



423 



InfPpin ■f*V<Tc* 




^^^^^^^ 



MQfcf 



w 



im\^^M\M 



§P 



S a Try 



C4; qui mcfef unw»V 



ill tfW-U 



pp^ 



MS Modena, Biblioteca Estense L. 5<5£ (r<z. 1400) 
Page 39' and part of page 40. 



424 Mannered Notation 

to introduce and to indicate irregular grouping. For instance, in the in- 
itial passage, the black 5, S, and M always designate full perfections, 
while the red S and M occur in groups of the value of 4 M , 2 M, 4 M, and / 
M which, together with a M-rest, add up to 12 M, that is, to two complete 
^-measures. There is no mensural interdependence between the black 
and the red notes; that is, in spite of subsequent or preceding red notes, 
the initial B remains perfect and the two black M form a group of altera- 
tion, as if they were separated from the red notes by a dot. With an ex- 
ample of this type our method of transcribing syncopation proves partic- 
ularly suitable and natural: one simply has to write the black notes with 
an upward stem, the red notes with a downward stem, as follows (the 
group with the semibreves caudatae is treated as a 'black* group, because 
it fills in a full perfection of g): 

llJ-l C/r .lJ ) J.l r IJ^Ir rr U..J.^|J.M 

In the next group, to the words 'esperance con forte,' the red notes from 
two complete 4-groups, S S MM S S S. The second of these, however, is 
broken up by the insertion of a black M which imperfects (by remote 
control) the black i?, reducing this to five M. 

The subsequent passage, Thoume qui vuet,' shows a group of three 
black S interspersed between a group of hollow red M, four of which 
equal in value three black M. Since the inserted groups appear after two 
of these red notes, a shift to the value of 1 J M results: 

l PP !Jjj! PP | s wiJ-j'jiJ3.u« mn\nrn\ 

The contra of this composition is almost as full of intricate rhythms as 
is the discant. Right at the beginning we find a passage consisting of 
split groups of black as well as red notes: 

j.j.j Pr jjuj. ! r |J)Ji P/ l=ljJ4,jj^jjj|j.jjjOT ? mi 

A different example of syncopation occurs immediately after the first 
group of hollow red notes (middle of staff 7). Here a single M-rest (which 
falls on the first beat of a measure) is followed by the combination 
S S S S B. Syncopated rhythm results here from the fact that the rule 
'similis ante similem perfecta' prevents imperfection of the first three «S\ 
With the next M-rest of the contra another passage of syncopation starts 
in a similar way. Here the question of when and how to return to normal 



Examples 425 

barring is more difficult. The simplest solution would be to use the first 
black S after the red notes for this purpose. The M-rest at the end of 
staff 2 presents quite a problem. It can only be retained if its value is sub- 
tracted from the two subsequent hollow red B, making each of these f M. 
In the appendix, No. 61, a transcription of the first section of the discant is given. In 
order to facilitate orientation, the normal bar-lines as they occur throughout the tenor, 
have been indicated above the staff - . The entire composition is transcribed (from Modena) 
in W. Apel, French Secular Music of the Late Fourteenth Century \ No. 23. 

8. Baude Cordier, Belle bonne (Facsimile 88). After the intellectual 
labour and the rhythmic intricacies of the foregoing examples, our last 
facsimile, the 'Musical Heart' from the Codex Chantilly will be greeted 
with relief. Its relatively simple notation and rhythm characterize it as 
an example of a slightly later period than that to which the previous 
pieces belong. This assumption is corroborated by the mensuration * 
[3, 2], the typical meter of the Dufay period, as well as by the fact that 
the prolatio perfecta, which is repeatedly introduced in the discant and 
tenor, has the same meaning it normally has in white notation, namely, 
three-fold augmentation, with the M equalling the S of the integer valor. 
This fact is all the more remarkable since this interpretation was not 
unanimously adopted until the later part of the fifteenth century (see 
p.i6 4 ff). 

Coloration is used in three different degrees: in the discant we find 
groups of three red M in the place of two black M (triplet coloration) as 
well as three red B in the place of two black B (courante coloration, ow- 
ing to the perfect value of the black B); the contra shows groups of three 
red S in the place of two black (perfect) S, values which, owing to the 
augmenting character of [2, 3] are identical with those of the red B in 
Lj> 2 \ ( or J more properly speaking, in [II, 3]). 

The white notes in the middle of the first staff indicate diminutio dupla 
within the augmentation of the prolatio perfecla. Therefore, two white 
S equal one black S of the augmentation or, one B of the integer valor. 
The figure 3 to be found near the end of this staff indicates proportio trip/a 
within the augmentation: three M equal one M of the augmentation or, 
one £ of the integer valor. The rhythm of this group is actually the same 
as that indicated previously by the red notes. In a way the proportio 
tripla cancels the augmentation of the prolatio perfecta, since the three 
(perfect) S of this group consume the same time as three (imperfect) S of 
the integer valor. As a matter of fact, the subsequent group of white 
notes is in integer valor, two white S being equal to a normal black S. 
The sign e at the end of this staff indicates (or confirms) the return to 
normal tempus perjectum. In spite of the dash the sign has no propor- 



426 Mannered Notation 

tional meaning. The explanation of this uncommon usage probably lies 
in the fact that this sign serves here merely as a time-signature which is 
understood at the beginning of all the parts. It would then merely indi- 
cate an increased speed (S = M.M. 96) which is actually necessary for 
the performance (see p. 193). At the end of the second staff we find a 
rare instance of augmenting proportion: the sign J indicates that the sub- 
sequent eight notes are equal to the nine notes of the preceding passage 
marked 3. 

H. Riemann, in RHdM 1. ii, 354, has given a transcription of this piece 
with a D-major signature and with an occasional introduction of G-sharp, 
a procedure which he considers justified by the fact that in a few places a 
(non-cadential) C-sharp and F-sharp are indicated in the original. Need- 
less to say, this theory is wholly without foundation. In reality no edi- 
torial accidentals are required, if the C-sharp near the end of the first 
staff of the contra is considered to have prolonged validity until the end 
of the staff. Only in the cadences is the use of leading-tones (sub- 
semilonium for the octave as well as for the fifth) admissible (see the ex- 
planations on this question, p. 106). The beginning of the piece, which 
is interesting on account of the initial imitation, is transcribed in the 
appendix, No. 62). 

D. Discussion of Examples from Other Publications 

We close our study of mannered notation with a consideration of some 
pieces which have been given in other books (chiefly in J. Wolf's Geschichte 
der Mensuralnotatiori) , to which the reader is referred for the reproduc- 
tions as well as for the complete transcriptions. It is hoped that our ex- 
planations will help the reader to understand more clearly the problems 
presented by these pieces. 

1. Guido, Dieux gart {GdM 11, no. LXIV). In this piece, as in many 
compositions of the late fourteenth and early fifteenth centuries, the 
determination of the mensuration is difficult because the basic meter is 
obscured by the frequent use of syncopation (most of the puncti are 
punch divisionis in displaced position, i.e., puncti syncopationis). None- 
theless, upon closer examination one finds various features indicating 
t 2 > jL f° r instance, groups of two S {tempus imperjectum) in the tenor, 
and numerous groups S — M (pro/atio perfecta) in the discant. 

The red notes indicate normal coloration or, if they appear singly, a 

loss of one-third {S — 2 M, B = 4 M). Two forms, namely ( and f 
are used indiscriminately for the value of half an M (Sm; cf. the begin- 



Examples 
Facsimile £ 



427 




ll a\- Ja»S55u£5miL55i85uia iwiy man <m«<miA 
- -^~41 t^2 OO ' J7> . r» J> ^ IT) r> _ 



l.v. 



d&iL., 



MS Chantilly, Musee Conde /o^/ (ca. 1400) 
Page 11' 



428 



Mannered Notation 



ningof staff i with that of staff 4). On page 11 4, the combination \i\t 

appears several times. The value of this whole group is a perfect 

S, as can easily be seen. Obviously, the note i is worth two I , so 

that the following rhythm results: J JJ 3(= J.) . Thus, the form 1 has 

the same value as the simple M 1 . Probably the use of the above man- 
ner of writing, instead of 1£1£ , is meant to indicate the change of the 
ternary S (prolatio perfect a) into a binary S } or, in other words, the in- 
troduction of two groups of triplets: J J JJ instead of syncopation: 

In this ballade there are various interesting examples of syncopation. 
As explained above, the meaning of the punctus syncopationts is to indi- 
cate an imaginary displacement of bar lines and, consequently, to prevent 
the use of alteration and imperfection, such as would normally apply. 
For instance, disregarding the punctus^ the beginning of the discant 
would have to be read as follows: 



However, the punctus {syncopationis) after the fifth note indicates the 
beginning of an imaginary g-measure immediately after the first note (M) 
of a normal measure. Thus, instead of a group of five M, which would 
call for alteration of the last M, we have a group of four M which calls 
for imperfection (a.p.a.) of the S. At the end of the passage there ap- 
pears a group of four Sm (equalling two M), complementing the single 
M which served to introduce the syncopation: 




1. Jo. Cunelier, Se Galaas {GdM 1, no. LXV). The mensuration is 
[2, j], as is readily apparent from an examination of the contratenor. 
The filled red notes have the normal meaning. In fact, the whole sec- 
ond part of the composition ('Dont doit . . . devise') is written in red 
notes throughout and, therefore, is in [3, 2]. The hollow red notes indi- 



Examples from Other Publications 



429 



cate, as usually, diminutio dupla, two of these S being equal to one nor- 
mal S. 

The bow-like signs above the first notes of the third part ('febus . . .') 
are fermatas, such as appear very frequently in the documents of the fif- 
teenth century (Dufay etc.), under various forms, for instance: v.'- (cf. 
GdM 11, 132, 133; also HdN 1, 385). Immediately after these fermatas 
we find groups of white notes (S and M) in the contra against black S 
and M in the other voices. They are used here with a special meaning, 
namely, to indicate diminutio dupla in prolatio perfecta. Thus two 
groups, o i ♦ I , are equal in value to one group ^ j : 




UWt 



3. Conraaus de Pistoria, Vert almi pastoru {GdM ii, No. LXVII; 
The tenor and contra clearly indicate [2, 3] and, indeed, fit together sat- 
isfactorily. However, if one tries to apply the same mensuration to the 
discant, impossible results are obtained, as appears from the following 
tentative sketch: 




In reality, this composition is one of those examples in which differ- 
ent mensurations are called for in the different voices without signs to 
indicate the fact. The mensuration of the discant is [2, 2], with the M 
as the common duration-value in all the voices. The single red notes, 
then, do not indicate a decrease, but rather an increase in value, namely, 
dotted notes (reversed coloration). The beginning of the transcription 
is given on page 430. 

It is, of course, possible, to write the top voice in f-meter also (see GdM 
in, p. 161); however, it seems to us that in so doing a particular charac- 
teristic of rhythm and phrasing is lost, to say nothing of the complete 
obscuring of the notation which results from such a method. 

4. Bartholomeus de Bononia, Que pena {GdM 11, no. LXVIII). In 



43Q 



Mannered Notation 




this composition all the parts are in [3, 2]. In the tenor we find single 
red S as well as groups of three white S with a downward stem. The 
former indicate reversed coloration (dotted values), the latter normal 
coloration, that is, three *S" in the place of two normal S. Since the mensu- 
ration is tempus perjectum^ there results an unusual rhythmic pattern 
involving triplets in the place of two notes of a 4-measure. In an earlier 
discussion (p. 158, below middle) this rhythm has been characterized as 
being 'of purely hypothetical significance,' a characterization which is 
correct for the period to which these explanations referred. In the late 
fourteenth century, however, such a rhythm appears as a relatively mild 
manifestation of the prevailing tendencies. 

If several such groups of three white S caudatae appear in succession, 
as for instance in the discant, p. 123, st. 7, it is advisable temporarily 
to change from 4-measures to 4-measures, in order to avoid artificial 
syncopation : 

' m i||jjjjj»|jijjjjuiijjj|jjj|jjji 



Coincident with this passage is one of similar design in the contra (p. 
125, st. 5). This starts with a dotted S caudata, a form which, as a simple 
calculation shows, has the same value as a normal black S (-§ + j; = 1). 
Therefore the triplets of the contra appear in syncopated shifting against 
those of the discant. Toward the end of this passage we find the very 
unusual form of a B caudata, to the value of two of the S caudatae. Here 
follows a transcription of this interesting passage (p. 431, .top). 

The white B which appear twice in the discant (staff 5, 6) have the 
usual meaning. Each of them has the value of two S. Finally, in the con- 
tra there is peculiar form, { ( { in Wolfs reproduction), which equals 
a dotted M. 

Aside from these special signs frequent use is made of proportions which 
are indicated by the figures 2 and 3. Their meaning is explained at the end 
of the music by a 'Canon virilarie' (canon of the virelai), according to 
which 2 calls for proportio dupla and 3 for proportio hemiolia {sesqui- 



Examples from Other Publications 



43* 




altera). Under the former proportion 1 M take the place of one normal M 
(or 6 S the place of three normal S), while under the latter three M (or 
S -|- M) are worth two M of the integer valor > so that triplets of eighth- 
notes result (middle of staff 4) : 



In two places of the discant, on staff 1 and staff 6, the combination 
B S appears as a part of a sesquialtera group. This hemiolia temporis, as 
it may be called in distinction from the hemiolia prolationis y S M, intro- 
duces the same rhythmic patterns which is expressed by the groups of 
three white S caudatae, that is, triplets for two quarter-notes of the 
4-measure. Here is a transcription of the passage on staff 1 : 



~T 3 *~' 3- 3 

In the sesquialtera passage of the contra, p. 125, st. 5/6, a S (possibly on c') seems to 
be missing between the ligature and the final M. This conjecture would make it possible 
to read the end of this passage in conformity with all the other passages of this type, that 
is, in binary values (such as are customary for passages in coloration). Otherwise the 
ending of this passage (starting with the fifth note before the circle) would have to be 
read in perfect mensuration, applying alteration and imperfection (see the rendition in 
GdM iii, p. 1 66, syst. 4, meas. 3). 

5. Magister Zacharias, Sumite karissimi (GdM'i, no. LXX). This 



432 Mannered Notation 

piece may be said to represent the acme of rhythmic intricacy in the en- 
tire history of music. Not unreasonably F. Ludwig disposes of it as a 
'Schulbeispiel ohne Bedeutung' (SIMG vi). Nonetheless, it is interest- 
ing from the notational point of view, and its rhythmic oddities, at least, 
throw an interesting light upon the mentality of the period. 

The notes appearing in this piece, as well as the mensuration, are the 
same as in the preceding example. The eccentric feature of the present 
selection, however, is the excessive use of 'displaced barring.' Time and 
again an existing mensuration is not carried on to the end of the normal 
measure, but stops somewhere in the middle of the measure and is fol- 
lowed by a long passage in a different meter, at the end of which the in- 
terrupted measure is completed. We have repeatedly illustrated this 
principle of fourteenth century syncopation in the previous discussions. 
However, in the present case, it leads to formations far more complicated 
than usual. As a matter of fact, the rhythmic intricacies of this piece 
are so involved that a satisfactory rendition in the normal notation of the 
present day is not possible. J. Wolf, in his transcription (GdM m, 168), 
resorts to a method which is arithmetically correct, but which does not 
reveal an insight into the rhythmic construction. It seems to us that 
only our method of 'displaced bar-lines' leads to a result which is, if not 
wholly satisfactory, at least clarifying and instructive. The first section 
is transcribed in the appendix, No. 63. Of particular interest is the pas- 
sage at the end of the first staff, beginning with the red B on 'de re- 
(mulo),' in which two syncopations of the above-described type overlap. 

6. Patrem omnipotentem (Old Hall MS). This interesting specimen, 
which illustrates the spread of mannered notation to England, has been 
reproduced in facsimile in A. Ramsbotham, The Old Hall Manuscript, vol. 
in, after p. xxiv, and has been transcribed in vol. 11, p. 101-1 13 of the same 
publication. 1 Although the transcription is essentially correct, it fre- 
quently obscures the notational features of the original, particularly by 
the choice of the same meter and the same barring for all the parts, a 
procedure which may find some justification in the primarily prac- 
tical purpose of the publication. Since, moreover, the explanations 
given in vol. 11, p. ix-xii, do not cover all the points of interest, there fol- 
lows a concise study of the piece which, it is hoped, will enable the reader 
to make a transcription of his own, according to the principles set forth 
in the present book. 

The piece is written in three parts, discant, contra and tenor. How- 
ever, the discant itself is a three- voice canon, so that the number of parts 

1 The transcription of this piece is chiefly the work of H. B. Collins who has been particularly 
ingenious in the emendations of the missing notes of the discant. 



Examples from Other Publications 433 

actually is five. The notation is in black, red, and blue notes. Their 
meaning as well as that of the various signs of mensuration is explained 
in a canon (see the reproduction, p. 101 of vol. 11). Instead of a literal 
translation, there follows below a summary of its main contents in a differ- 
ent order, corresponding to that of the subsequent explanations: 

The tenor and the contra are in [2, j] (de tempore imperfecto perfecti) 
with the red notes indicating [j, 2] {proportio sesquialtera, that means: 
three red [imperfect] S equal to two black [perfect] S). 

The discant yields three parts, I, II, III. They are in different men- 
surations which also vary from one section to another, as follows: 



'Before 


the figurd* 




'After th( 


ifigurd 


Black 


Red Blue 


Black 


Red 


Hollow red 


I- [U,2 3 2] 


[3>j] b b, 2} dim* 


[2,3] 


[3, 2]* 


3 B = iB 


II. [111,3,*] 


[2, 3] [3, 2 \ dim* 


[2,3] 


[3, 2]° 


iB = iB 


HI. [HI, 3, J] 


[2, ^] c [3, 2} dim* 


[2,3] 


[3> 2] e 


3 B = iB 



Annotations: (a) The figura mentioned in the canon is the sign of prolatio 
perfecta in the middle of the eighth staff, (b) In the canon, this mensura- 
tion is explained as proportio dupla sesquiquarta, that is, proportion in 
the ratio of nine to four. Actually, no proportional reduction in this 
ratio or in any other takes place; the term merely refers to the fact there 
are now groups of nine M ([3, 3]) instead of the previous groups of four 
M ([2, 2]), with the M unaltered in value, (c) This mensuration is de- 
scribed in the canon as proportio dupla sesquinona. This designation is a 
blunder from the point of view of terminology as well as of notation. It 
should read proportio subdupla sesquiquarta, i.e., the ratio of four to nine 
(the version sesquinona has probably been caused by the fact that here 
the figure nine appears in the denominator) ; regarding its notational mean- 
ing, the explanation given under (b) applies in the reverse, (d) The 
diminutio of the blue notes is properly referred to in the canon as propor- 
tio dupla. (e) This mensuration is explained as proportio sesquialtera, a 
designation which correctly, though not very clearly, indicates the fact 
that in [3, 2] three (imperfect) S are equal to two (perfect) S in the men- 
suration [2, 3] of the black notes. 

On the basis of these explanations, the actual transcription may pro- 
gress as follows: 

a. The tenor is in [2, 3] throughout with normal groups of coloration. 
Its transcription in § with interspersed measures of 4 and I presents no 
difficulties. 



434 Mannered Notation 

b. The contra is in the same basic meter, but involves much greater 
problems. In a way, it is the most difficult of all the parts. In addition 
to normal groups of coloration, red notes are used singly or in groups of 
other than three notes. In the sections in [2, j] they represent the fol- 
lowing values: 

A O a Ki Cj "j 

1 M 1 M 4 M 5 M 8 M 10 M 

(Here, as in all subsequent explanations, M is the black M as it prevails 
throughout the tenor). The black-red oblique ligature on staff 3 equals 
two black-red B of the value of 5 M each, like the preceding ligature in 
square shape. The red B rest on the same staff has the value of 4 M. 
The red L after the black-red ligatures is reduced to 7 M by the subse- 
quent M. The meaning of the blue S rests on staff 2 is obscure. As is 
suggested by the sign © , the total value of a black-red B and the sub- 
sequent blue rest is nine M. If, as may reasonably be assumed, the note 
retains its value of 5 M, the rest would equal 4 M (in Collins' transcrip- 
tion, p. 105, the distribution 6+3 has been adopted). 

In the section marked © which begins at the end of the third staff, 
the red B equals in value, of course, 6 M, since the value of the black is 
here 9 M. The correct rendering of this section is made difficult not 
only by a clerical error (the first note of staff 4 is a red S, not a B), but 
also by a very tricky meaning which attaches to the black notes. As a 
matter of fact, one may wonder why, at the beginning of staff 4, a black 
S and M are used without any apparent reason, since the same rhythm 
could be expressed by the corresponding red notes. The explanation is 
that these black notes must be mentally combined with the next group 
of black notes {MB M) in such a way that they participate in the imper- 
fection of this B. x^ctually, this B has not the value of seven (9 — 2), 
but only of four (9 — 2 — 3) M. 

In the subsequent section marked C (middle of staff 4) the black and 
red notes exchange their meaning, not, as Collins surmises, by virtue of 
an 'obscure sign' (see p. 109, footnote 2), but simply because in this men- 
suration the red notes always indicate 'reversed coloration,' i.e., dotted 
values. Here, then, the red M, S, and B (also the red 5-rest) have the 
value of i§, 3, and 6 M respectively. The flagged notes at the end of 
this staff are, of course, Sm, two of which equal one red M. 

At the beginning of staff 5, the sign C appears in red. This means 
that now the red notes are the normal mensuration ([2, j>]), and that the 
black notes are 'coloration,' with three black S equalling two red ones. 



Examples from Other Publications 435 

It must be noticed, however, that here the black S are perfect, i.e., equal 
to three black M, not to two, as would normally be the case. Therefore, 
the passages containing M introduce triplet-groups into the 4-measures 
of the 'coloration.' The black S-rtst near the beginning of staff 5 should 
be red. 

The notation of the short passage marked by a red o (middle of staff 
6) is very problematic. Instead of Collins' emendation (see p. 112, foot- 
note) we suggest interpreting the red notes in [j>, 2], and the black notes 
in the same mensuration, but augmented in the ratio of 3:4, so that 
three black S consume the same time as four red S. If, in addition, the 
red-black S of the ligature are interpreted as dotted (red) S, a satisfac- 
tory transcription results which fits very well with the other parts. The 
final section in G needs no explanation. The dragma is, as in previous 
examples, one-half of the (perfect) S. 

c. As for the three renditions of the discant, only a few remarks need to 
be added to the explanations given in the canon. The initial letter P has 
been removed and has been clumsily replaced, so that notes at the be- 
ginning of the first three staves are misplaced or missing. For these 
gaps, Collins has furnished ingenious and convincing conjectures. Ac- 
cording to him, the first two notes of staff must be one third higher (a' a'), 
while the notes a a c (values: B M M) and P g' g' P g' g' a' (values: red 
S S S M S M S) must be added at the beginning of the two following 
staves (see p. 102, meas. 5; p. 103, meas. 12). Collins has also shown that 
the parts II and III start canonically, each with a full measures (4 and %) 
rest. These two parts are designated in the canon as being in modus 
perfectus. This statement refers particularly to the L at the end of the 
first staff which must be interpreted as perfect in both parts, taking the 
place of three 4- or g-measures. Collins fails to observe this fact in his 
transcription of III (see the correct rendering in the appendix, No. 64 b). 

In the passage of red notes immediately after the 'figura' (middle of 
staff 8) the fifth note should probably be a M, not a S. This conjecture 
allows for an interpretation in simple coloration, while Collins' version 
(p. 113, meas. 2) is somewhat forced. The beginning of the piece as well 
as several sections thereof are transcribed in the appendix, No. 64. 



COMMENTARY 

P. xx. Score arrangement survived in English sources through the 
middle of the fifteenth century (see p. 271, fn. 3; also p. 364). In a 
recent article, 'The Music of the Old Hall Manuscript' (M^ xxxiv, p. 
512), M. F. Bukofzer called attention (p. 515) to a four- voice Gloria 
and a four- voice Agnus 'written in a most peculiar manner: three voices 
in score and one voice separately.' 

P. xxii. 'Music written in part-arrangement is ensemble music.' The 
only exception known to this writer are the organ compositions by 
Michael Praetorius which are included in the parts books of the Hymnodia 
Sionia (161 1) and Musae Sioniae VII (1609), with the remark: 'pro 
organicis: sine textu.' The obvious reason for this procedure is that it 
would have been technically unfeasable to include keyboard scores in 
a publication issued as separate part books. In a 'Nota' Praetorius says 
that an organist wanting to use these compositions may transcribe them 
'aus den Noten in die Tabulatur' (see K. Matthei, Michael Praetorius, 
S'amtliche Orgelwerke, 1930; preface by W. Gurlitt, p. 17b). In other 
words, the actual playing was, of course, from a score, not from the 
separate parts. 

P. 3. Due to the recent discovery (or, rather, rediscovery) of the Codex 
Faenza the use of this method can be traced back to the late fourteenth 
century. See D. Plamenac, in Journal of the American Musicological 
Society, iv, 179 (facsimiles opp. p. 192). 

P. 6. The flag-like sign in syst. 3, meas. 1 of Facs. 2 is a Sm- rest. 

P. 10. A transcription of the music preceding the //. Versus will be 
facilitated by the remark that the obscure sign at the beginning of the 
third measure is a 3, indicating triplets, and that the black S and M at 
the beginning of staff 4 are equivalent to a dotted M and a Sm {minor 
color, see p. 128). 

P. 14. The second rest on the first staff of Facs. 5 (near the end of the 
line) is a M- rest. 

P. 16. The little curve appearing in Facs. 6, staff" 1, near end of meas. 2 
(and elsewhere) is a tie. 

P. 19. To the list should be added the recently discovered Libro di 
ricercate a quattro voci di Rocco Rodio . . . , Naples, 1575. 

437 



4*g Commentary 

P. 26. The second piece of Facs. 7, Creature^ is in four parts, the third 
of which is generally the lowest and is, therefore, best transcribed as 
the bass. In meas. 2 of the first and of the second brace the quick notes 
of the altus should be read an octave higher than written. 

P. 30. In the group of letters: c h c h a g (near the end of the second 
system) the dash indicating the higher octave should extend only over 
the c and h. In Kotter's tablature as well as in most of the later German 
tablatures the higher octave starts with h. See WoHN ii, pp. 23 and 29. 

P. 32. The indication of octaves seems to be rather irregular. Some- 
times the b and h below middle c are written with, and sometimes 
without a dash. Moser's transcription of In dulci jubilo contains several 
errors, owing mostly to a confusion of the letters e and c. The bass part 
in meas. 2 should be exactly like that in meas. 5. 

P. 34. Since these intonazioni are ascribed to Giov. Gabrieli in the 
original publication of 1 593, they must be assumed to be his. 

P. 44. The short strokes appearing in the upper part of the Praeambulum 
bonum super C are not rests but puncti divisiones such as were regularly 
used in the Italian notation of the fourteenth century. There are many 
details suggesting a connection between German organ music of the 
fifteenth and Italian music of the fourteenth century. The lower part is 
notated exclusively in B, often written with elongated heads. The tails 
attached to two of the B are signs of chromatic alteration (b-flat, e-flat). 

P. 47. Following are additional suggestions for emendations. Brace 1, 
meas. last: second note a M\ brace 5, meas. 2: the dragma takes the 
place of a M; brace 7 (p. 77), meas. 2: the fifth note is a S\ brace 7, meas. 
last: the last four notes are a Sm each; brace 8, meas. 2: the third note 
is a M\ brace 9, meas. 4: the third note is a (dotted) M. 

P. 49. The sign in Facs. 16, brace 4, upper part, middle, after 10 9 8 is a 
rest (M). The single dot is the rhythmic sign for the minim. The letters 
D. and M. at the left side mean Destra (right) and Manca (left). 

P. 50. Henestrosa's book has been published by H. Angles, La Musica 
en la corte de Carlos V (Barcelona, 1944), and that of Araujo by S. Kast- 
ner, Libro de tientos . . . compuesto por Francisco Correa de Arauxo 
(Barcelona, 1948). The Spanish keyboard tablature persisted until 1700, 
e.g., in a Portuguese Ms 'Libro de cyfra . . . ' of the Municipal Library 
of Porto (see S. Kastner, Carlos de Seixas [1947?], p. 26). 



Commentary 439 

P. 62. The dots placed below some of the figures are signs for fingering 
(index finger). 

P. 71. The student will readily notice that in this piece the bass strings 
are tuned in D major: G-F#-E-D-Cfc. See the subsequent remarks about 
scordatura. In Gaultier's Ms these changes of tuning are not expressly 
indicated, but are implied by the grouping of the pieces in suite-like 
formations under headings such as 'Mode Dorien,' 'Mode Sous-Dorien,' 
etc. Our piece belongs to the 'Mode Dorien,' which, according to the 
system then in vogue, is the equivalent of our C major (see Harvard 
Dictionary of Music, s.v. 'Church Modes,' end of III). In Gaultier's 
collection, however, most of the 'modes' appear in transposition, for 
instance, the 'Mode Dorien' as D major. 

P. 72. No. 76 of Schrifttqfeln shows the use of stopped bass strings, indi- 
cated by the letters b and d (instead of a). 

P. 77. The little vertical dashes attached to some of the rhythmic 
signs indicate the use of the index finger, while those without this dash 
indicate the thumb. 

P. 85. Other early organa written in staffles neumes are found in manu- 
scripts from Chartres, Fleury, Einsiedeln, etc. 

P. 96. The use of a whole circle for 'perfect', and of a half circle for 
'imperfect' is plausible enough, and the indication of the same qualities 
by means of a dot would seem to be hardly less plausible, through the 
coordination: presence = perfect, absence = imperfect. Actually, the 
latter explanation is wrong. Originally, that is, in the fourteenth century, 
prolatio perfecta was indicated by three dots (perfect = three), prolatio 
imperfecta by two. This method occurs in some Italian sources of c. 1400 
(see WoGM'i, p. 96, 322). Some time later the number was reduced to 
two for perfecta and one for imperfecta. An example of this practice 
exists in a late- fourteenth- century ballade, 'Ung lion say' (see W. Apel, 
'The French Secular Music of the Late Fourteenth Century,' AM 
xviii/xix, p. 22). Finally, the number of dots was reduced to one and 
none respectively. 

P. 102. Recent studies of the problem of partial (or, as it is also called, 
'conflicting') signatures are: E. E. Lowinsky, 'The Functions of Con- 
flicting Signatures in Early Polyphonic Music' (MQ xxxi, p. 227) and 
M. Johnson, 'A Study of Conflicting Key-Signatures in Francesco 
Landini' {Hamline Studies in Musicology, vol. ii, 1947). Specialized 
studies like the latter are much needed in order to get more definite 
results. 



44Q 



Commentary 



P. 104. The MS contains a few errors which we leave for the student 
to find. 

P. 112. According to strict theory this example is wrong, since im- 
perfection is caused here by a note which forms part of a binary group 
(2 M = S)> while properly it can be caused only by a note forming part 
of a ternary group (such as the S in the preceding examples). Correct 
examples of imperfectio ad partem remotam would be: 

O t=j « = f| JJJJiy J! or G ^ I = f| JJJJ «DI 

However, as early as the fourteenth century composers admitted 
imperfection by a note of a binary group (see the remark on p. 345)* 
On the other hand, it is interesting to notice that the application of the 
above rule automatically leads to the correct reading of the passage from 
Pierre de la Rue's Missa Vhomme arme discussed on p. 112. Here the 
imperfection is caused, not ad partem remotam by the M, but ad partem 
propinquam by two M, that is, the valor of a S. 

P. 118. M. Bukofzer, in an interesting article, The Beginnings of Poly- 
phonic Choral Music' {Papers of the American Musicological Society, 
Annual Meeting, 1940) has pointed out (p. 23) that simultaneous rests 
are a frequent and characteristic trait of duo sections in English compo- 
sitions of the fifteenth century. The tenth note on staff 2 of the recto- 
page of Facs. 24 should be a M. 

P. 122. Facs. 30 is a section from the Credo of Ockeghem's Missa 
VHomme arme. At the beginning of the tenor part of the Credo the 
canonic inscription, 'descendendo in dyapente' is given (see Johannes 
Ockeghem, Sdmtliche Werke, ed. by Plamenac, vol. i, p. XXXVa). This 
accounts for the seemingly faulty pitch. 

P. 124. Yet in other words: the equivalent of a maximodus perjectus 
is always represented by a group such as L L L {y\-y^-'S), or Mx L 
(6+3), never by a single Mx (9). 

P. 134. Numerous examples of split groups of coloration in [2, 3] occur 
in Ockeghem's Missa Prolationum, a complete facsimile of which is given 
in Johannes Ockeghem, Collected Works (ed. by Plamenac), vol. ii, plates 
II-IX (e.g., pi. VI, Contra, first line, starting with the last black ligature, 



Commentary 441 

S S y which is completed by the first S of the next ligature). The facsimiles 
of this publication (subsequently referred to as Ockeghem \\) provide 
most valuable material for the study of the more complicated aspects 
of White Notation. 

P. 136. Mr Bukofzer has identified this composition as Bedingham's 
Mon seul plaisir (after Ms Oporto 714). 

P. 138. See the remark to p. 122. 

P. 148. Regarding the proportional signs used in the subsequent expla- 
nation see the Commentary to p. 155. 

P. 152. The following corrections of Stainer's transcription are sug- 
gested. The S on a', middle of first staff (above the word orgoglio) 
should be perfect, as is indicated by the dot. This means that the last 
of the three ensuing M goes to the next measure, imperfecting the B. 
This version not only is notationally correct, but also makes much better 
musical sense. In the three-note ligature near the beginning of the 
contra the initial S remains perfect in spite of the preceding M- rest, since 
it is followed by another S y and it is this second S which is imperfected 
by the M- rest. This method of producing syncopation occurs frequently 
in the sources of the late fourteenth century (see p. 395ff). Possibly 
the passage near the end of the first staff of the contra should be inter- 
preted in a similar way, that is, with the M- rest imperfecting, not the 
preceding S, but the second S of the ensuing ligature (as in our tran- 
scription, No. 20). In the 'clus'- section of the contra the eighth note 
(omitted by Stainer) should probably be a M (once more imperfecting 
the second-next S). 

P. 155. Very likely the solution (or, at least, a partial clarification) of 
the intriguing problem presented by tempus perfectum diminutum exists 
in the fact that a distinction must be made between the signs O 2 and 
, to the effect that the former indicates notated [111,2], the latter, 
notated [11,3]. Hence, the former sign calls for a rendition in 3 / 4 (as in 
the example (b) of p. 154), the latter for one in 3 / 8 or, if two perfections 
are combined, in % (as under (a) of the same page). A good illustration 
of this practice is found on pi. XIII of Ockeghem ii, containing the Rex 
gloriae of the Requiem. Here the entire cantus and bassus are notated 
in O 2, while a section of the contra (beginning near the end of the third 
staff) is notated in . Under the former sign we find groups of three 
imperfect B to the equivalent of a perfect L\ under the latter groups of 



442 Commentary 

three (imperfect) S to the equivalent of a perfect B. Isaac also seems 
to have followed this practice. The student may compare the example 
quoted on p. 154 (from De radice Jesse, Facs. 38, p. 173) with his Dico ego 
(Facs. 37, p. 174; discussed on p. 170). The question would certainly 
be worthy of further investigation. 

If the above theory is confirmed, our general explanations given on 
pp. 1 48 to 150 would be correct only if the sign <fc) is replaced every- 
where by the sign O 2. 

P. 163, top. For a transcription of the whole example it is advisable to 
use irregular measures in the tenor as well. 

P. 163, bottom. It is entirely possible that the time signatures in this 
source and in others of the period still retain to a certain extent their 
proportional meaning, serving to regulate the tempo (see p. i88ff). 

P. 164. Two other early examples of this practice exist in Helas merci 
and A qui fortune by Matheus de Perusio, who flourished in the first two 
decades of the fifteenth century. They are transcribed (from the Codex 
Modena) in W. Apel, French Secular Music of the Late Fourteenth Century 
(1940). 

P. 167. While Ockeghem's Missa L Homme arme is an example of the 
later practice, his Missa Prolationum is based on the earlier interpretation 
olprolatio perfecta (see below, remark to p. 181). The 'Exemplum Quinti 
Toni Johannis Ockegem' reproduced on p. 167 is taken from the Missa 
Prolationum. Therefore our remarks regarding 'lack of correctness in 
late documents' and Seb. Heyden's failure 'to use the signs correctly' 
are without foundation, all the more since Heyden in connection with 
this and other examples from the Missa Prolationum expressly says that 
this use of the 'signa integra' (i e., of the signs of prolatio perfecta without 
the sign of diminution) is 'contra artem ac usum aliorum,' ascribing it 
to scribal error (see Ockeghem ii, p. XXIII). Another very interesting 
example of this type is the ^uam olim Abrahae from Ockeghem's Requiem 
{Ockeghem ii, pi. XIV). 

P. 168. As is explained in the commentary to p. 155, the sign used in 
this example indicates notated [II, 3], actual [2, J], so that a transcription 
in 6/8 appears proper. 

P. 170. See the commentary to p. 155. 

P. 172. Possibly they are a late remnant of the 'reversed coloration* 



Commentary 443 

which is often found in the sources of Mannered Notation (see p. 406, 
par. 3). If so, they would suggest perfect B y resulting in a shift of accent 

from B SS B to BS SB (i.e., from 3 / 4 to %). 

P. 176. See the commentary to p. 155. 

P. 179. It will be noticed that our two renditions (p. 178 bottom and 
p. 179 top) show yet another inconsistency in the reading of the discant, 
that is in the two passages marked D ( 2 / 4 meter), the first of which is 
transcribed in: S = eight-note, the second in: S — sixteenth-note or, in 
the final rendition on p. 179, in sixteenth and thirty-second notes re- 
spectively. It is possible to avoid this inconsistency by doubling all the 
values of second passage (spreading this passage over two, instead of 
one, %-measures of the contra, but only by the admission of another 
inconsistency of the same nature, that is in the two passages marked , 
the second of which (beginning at the end of our transcription) would 
then have to be rendered in half the values used for the first (initial 
measures of the transcription). The former of these alternatives (used 
in our transcription) is, no doubt, preferable on stylistic grounds, as it 
results in a much smoother counterpoint. By the way, exent means not 
'exhausted' but 'superior' or 'outstanding', a designation equally not 
devoid of significance. 

P. 181. This composition is the final Agnus Dei from La Rue's Missa 
VHomme arme. Ample additional material for the study of.mensuration 
canons as well as other devices of White Notation exists in the facsimile 
reproduction of Ockeghem's Missa prolationum which are given in 
Ockeghem ii, plates II to IX. A brief explanation of the notational 
principles of this work is given on p. XX of the publication In the 
title of this famous composition the term prolationes is used in the 
older sense of the word (Philippe de Vitry, see p. 340), synonymous with 
what we call mensurations. Each of the four voice parts is written in 
a different mensuration, the two upper parts forming a canon in [1,2] 
and [3,2], the two lower ones a canon in [2,3] and [3,j]. The relationship 
between imperfect and perfect prolation is based on the equality of the 
M, in conformity with the older practice recommended by Tinctoris 
(see p. 166; also commentary to p. 167). 

P. 184. In the bass part the fourth note from the end of the second 
staff should be a Sm. On the third staff there are three groups of two F. 
In each group the second of these F should be a Sm. 



444 Commentary 

P. 1 86. The solution is correct, as is confirmed by the recent publication 
of the piece in S. Clercx, Johannes Ciconia (i960), vol. ii, No. 22 (based 
on Bologna, Lie. mus. ^ 75, olim Cod. 37). In the Tenor the last pair of 
'rests' is actually the sign for repeat and the two subsequent L are the 
beginning of the Amen which is omitted in the three other parts. In 
Bologna the first of the two long ligatures is separated after its sixth 
note, the second after its fifth note, whereby both of these notes auto- 
matically become L. 

P. 202. Regarding doubts as to the existence of a 'y oun g er Johannes 
de Garlandia' see G. Reese, Music in the Middle Ages (1940), p. 287, 
fn. 42. 

P. 206. It may be noticed that the intervallic indications of this ex- 
ample are in contradiction to the principle, stated in the Musica En- 
chiriadis, that the fundamental vox principalis (in the present case, the 
second voice from below) cannot be chromatically altered. The adoption 
of this principle would mean that the second and fourth parts are to be 
read with F-natural, the other two with B-flat. 

P. 207. For a photographic reproduction of the original, together with 
more detailed explanations see W. Apel, "The Earliest Polyphonic 
Composition ..." {Revue Beige de Musicologie x, 1956, p. 129). 

P. 208. P. Wagner, in AMW vi, p. 405, fn. 2, gives a plausible ex- 
planation of this sign, saying that it is 'the oriscus or strophicus well 
known from neumatic notation, that is, a portamento transition from 
one main note to the next, which later was performed as a simple pro- 
longation.' 

P. 212. Goslenus (Josquelin de Vierzy) was archbishop of Soissons 
from 1 1 26 to 1 1 52. The prevailing opinion is that the ascriptions fre- 
quently given in the Codex Calixtinus are fraudulent. See G. M. Dreves, 
Analecta hymnica, xvii, p. 5; Liber Sancti Jacobi: Codex Calixtinus 
(Santiago de Compostela, 1944), iii (Estudios e Indices), p. LII, fn. 1. 

P. 219, top. Modal rhythm is clearly indicated for the clausula- sections 
of Leoninus' organa. Whether the organal sections of his compositions 
should also be interpreted in modal meter, is still a controversial question 
(see p. 2676*). The Benedicamus Domino of Facs. 49 (p. 247), although 
not necessarily by Leoninus, illustrates the style of his period. 



Commentary 445 



P. 219, middle. Our distinction between these four types should not 
be construed as implying that they represent different systems of no- 
tation. Rather are they different manifestations of one unified system, 
that is, of Square Notation. 



P. 222. The rules regarding the rests in the various modes are implied 
in the statement that the final note of a mode (or of an ordo) has the 
same value as the first (\ . . terminatur per eamdem quantitatem qua 
incipit;' Anon. IV, CS i, 328b). The only mode which does not conform 
with this rule is the fourth. 



P. 223. Both Anon. IV and Joh. de Garlandia (CS i, io2fT) explain the 
imperfect modes in such detail that a few more words of explanation 
(and, to a certain extent, correction) seem to be in place, particularly 
since the descriptions given in HdN i, 232 and G. Reese, Music in the 
Middle Ages, p. 280 are incomplete. The imperfect modes can be defined 
as modes in which rests appear at regular distances in such a way that 
each group of notes closes with a value different from that which opens 
it (Garlandia, p. 97: 'modus imperfectus . . . terminatur per aliam quam 
per illam in qua incipit'). As an illustration there follow examples of 
the first and second mode: 

Primus modus imperfectus 

Primus ordo: |J J) | 7 7 J>| J 7 I 

Secundus ordo: | J «M J M 1 t M J J>U 1 I 

Tertiusordo: |J J>| J J* I J J>l 7 7 J> I J J>|J J> I J 7 

Secundus modus imperfectus 

Primus ordo: | J) J | y J | J> j 7 | 

Secundusordo: |J>J|J>J I 7 J | J>J |J>yy| 




446 Commentary 

The only example I have found in the practical sources is the tenor 
of the motet Seje sui — Jolietement — Omnes {Mo y No. 316): 

etc. 

According to strict theory, however, the third measure should have a 
quarter note (B) followed by two rests. 

P. 232. An unusually clear description of the various meanings of the 
pausatio is given by Anon. IV (CS i, 350b): 'There is another kind of 
pausatio which seems to be a pausatio but actually is not, and this is 
called suspirium. It has no time value as such, but takes its time from 
the preceding note. This, by the way, is often done by the singers 
whether there is a dash (tractus) written or not. . . . There is yet another 
kind of dash found in the lower part. This is sometimes longer, some- 
times shorter, and does not have a definite time value {nullum tempus 
signai). It is written because of the change of syllables {divisio sylla- 
barum) . . .' 

P. 237. 'The mode never changes within the main part of a clausula.' 
Aside from internal evidence (writing of ligatures) this theory is sup- 
ported by the fact that all clearly notated motets show uniformity of 
mode. Some scholars (Bukofzer) are inclined to extend this principle 
to the final copulae, preferring (in the example under consideration) a 
rendition in the first mode, with upbeat. Since the copulae were never 
included in the motets, it is difficult to arrive at a decision in this question. 

P. 256. At the end of the first brace the last note of the duplum coin- 
cides with the initialis of the last ligature of the tenor (as suggested by 
the vertical alignment), while the finalis of this ligature coincides with 
the first note of the next line of the duplum. The second section of the 
duplum (coincident with the second statement of the c.f. in the tenor) 
starts with a D on c'. The penultimate note of the preceding section, 
on g, is also a D. Aside from this, each single note of the duplum is a L s 
each binaria B L, and each ternaria L B L. 

P, 258. According to Mr Bukofzer this clausula should be transcribed 
in the first mode. In this case the L of the original would indicate 
perfect longae, the 1?, imperfect longae or breves. 

P. 260. There exist a number of conductus in which the caudae are 
of extraordinary dimensions, occasionally leading to an almost complete 
obliteration of the syllabic sections. Two such highly embellished con- 
ductus, Pater noster commiserans and Salvatoris hodie (the latter by 



Commentary 447 

Perotinus, according to Anon. IV; see CS i, 342a) are reproduced in OH 
(pp. 252, 292; the transcriptions given there are not correct, particularly 
in the melismatic sections). 

P. 261. The introduction of bar-lines is contingent on the metrical 
structure of the poetic text, the obvious principle being that the accented 
syllable should fall on the first beat. The great majority of conductus texts 
show the versification of Hac in annijanua, that is, of four trochaic feet 

(the last catalectic) :-•-•-•-. In the case of iambic feet, • - • } 

the first syllable falls, of course, on the upbeat. An example in point is 
the conductus Luto carens et latere (tV h p. 73) r 1 

In not a few cases the versification changes within the poem, for in- 
stance from trochaic to iambic feet. An example is the conductus Roma 
gaudens jubila (IVi, p. 107). Following is the first stanza of the poem (the 
second stanza has identical versification), arranged in musical measures: 
Ro- . . . ma / gau- dens / ju- bi- / la — / Men- tis / pro- cul / nu-bi- / 
la Splen- / dor ex- / pel- lat / nu- bi- / la Splen- / dor pa- / cis et / 
glo- ri- / e Fi- / de- li- / bus Lu- / gen- ti- / bus Or- . . . / tus de / 
tu- o / prin- ci- / pe — /. 

The dots indicate the places of melismatic passages which occur in this 
conductus not only at the end of the composition (as in Hac in anni 
janua), but also at the beginning of several lines. 2 

From the preceding explanations it appears that an understanding of 
the vers structure of the poetic texts is of great importance for the tran- 
scription of the music. 3 The great majority of conductus have trochaic 
or iambic feet and therefore can be rendered in two-beat measures (f), 
with or without upbeat. In the case of dactylic or anapaestic feet (- • • 
or • • -) three-beat measures (J) would have to be used. Naturally the 
possibility of irregular groups must be admitted, either if the music 
clearly calls for a modification of the regular scheme, or if the text shows 
irregular versification. 

Examples showing irregular versification are found particularly in the 
nth fascicle of W x (pp. 176-197) which contains a singular repertory of 

1 In the transcription given by L. Ellinwood (The Conductus,' M^, xxvii, p. 191) the bar-lines 
are wrongly placed. 

2 The entire conductus is transcribed in A. T. Davison and W. Apel, Historical Anthology of Music, 
i (1946), No. 38. For a somewhat different rendition see G. Reese, Music in the Middle Ages (1940), 
p. 309. 

3 Many of the texts of the repertory in question are reprinted in G. M. Dreves and C. Blume, 
Analecta hymnica, vols, xx, xxi, or in G. Milchsack, Hymni et sequentiae (1886). Nearly all of them 
are listed in U. Chevalier, Repertqrium hymnologicum (i892ff). In dealing with conductus from W\ 
the references given in A. Hughes, Index to the Facsimile Edition of MS. Wolfenbiittel 677 (1939) 
are useful. 



448 Commentary 

sequences and tropes for the Ordinary of the Mass, mostly composed in 
two- voice syllabic style. 1 A composition such as the Kyrie super celos 
{JViy p. 177) is best transcribed without bar-lines, possible also in free 
rhythm rather than in modal meter. 

*"V",., ,V y 

P. 262. There are, however, instances showing that it is advisable to 
approach this question with an open mind. A particularly interesting 
case is the conductus Die Christi Veritas (F/, p. 203). At three places of 
the tenor, each time for the first syllable of a verse ('die,' 'die,' and *u-') 
we find a binaria with a prolonged head for the initialise a shape which, 
no doubt, is intended to indicate the rhythm L B, and which possibly 
proves ex contrario that the normally written binariae mean B L> an 
interpretation which is also strongly supported by the contrapuntal 
context. 

As regards the groups with three or more notes, numerous mistakes 
have been caused by the fact that these notes occur preferably in de- 
scending motion and, consequently, appear in the misleading form of 
conjuncturae (see p. 241 ; also the explanations in 0//, p. i\ii). There can 
be hardly any doubt that the conjuncturae have the same rhythmic 
meaning as the ligatures. 

P. 263. A rendition in the second mode would lead to a more acceptable 
result. 

P. 271. Attention is called to the exchange of Communications between 
W. G. Waite and me in JAMS v, 272ft*. Mr. Waite's reply does not (as 
he hopes) "satisfy my questions." Aside from any points of debate or 
disagreement I want to say that I consider my explanations not as a 
'theory' (as is, to a large extent, the 'modal theory') but only as an 
exegesis of statements given by some of the most eminent writers of the 
13th century. Whoever finds fault with the 'principle of consonance' 
(and I am not entirely certain about its validity myself) will have to take 
it up with them. 

t J. Handschin has made a plausible case for the surmise that the entire contents of this fascicle 
is of English origin. See his article, 'A Monument of English Mediaeval Polyphony' (The Musical 
Times lxxiii [1932], p. 510 and lxxiv [1933), p. 697). 



Commentary 



449 



P. 306. The codex is published in A. Auda, Les "Motets IVallons" du 
manuscript de Turin , Vari 42 ', 2 vols. (1953). The major part of its con- 
tents turn out to be in Franconian, partly even Petronian notation. 

P. 308. Mr Angles informs me that the reasons for his methods of 
transcription are set forth in his Introduction and Critical Commentary. 

P. 325. Published by L. Schrade in Polyphonic Music of the Fourteenth 
Century, vol. I (1956). Concerning Schrade's interpretation of the small 
values see my review in Speculum xxxii, p. 863. 

P. 328. The other is Quomodo cantabimus. Its tenor closes with three red 
L, each of which is perfect, while the preceding L are all imperfect. Thus, 
the red notes have here the meaning of reversed coloration (see p. 406). 

P. 233- A strong argument in favor of Wolf's view is supplied by the 
organ arrangement of the motet Firmissime — Adesto — Alleluia (Facsimile 
66), which exists in the Ms Brit. Mus. Add. 28550 (Robertsbridge 
Codex), the earliest extant source of keyboard music (see p. 37). Here 
the various conjuncturae of the motet are reproduced in single notes 
which invariably show the rhythm B SS, not SS B. Following is the 
beginning of the organ arrangement, which may be compared with the 
transcription of the motet given on p. 335: 




Since this organ arrangement is only about twenty years later than 
the Roman de Fauvel, it carries great weight in all the questions presented 
by this source. On the other hand, it carries no greater weight than 
older sources, such as Mo and Fl, which have several pieces in common 
with the Roman de Fauvel and which, naturally, show the older rhythm 
of the conjuncturae (see the examples in WoGM i, 52). The only safe 
conclusion is that matters were in a fluid state between 1300 and 1325. 

It will be noticed that the above example also furnishes additional 
evidence in the question of the groups of S, supporting the rendition 
favored by F. Ludwig (see p. 327). The same rhythm is consistently 
used in the organ arrangement of the motet Tribum quern which, to- 
gether with the original version from the Roman de Fauvel, is reproduced 
in WoGM ii, iii, No. 78. 



450 Commentary 

It is not impossible that a full investigation, long overdue, of the 
Roman de Fauvel may yield more definite results for the various problems 
which this source presents. 

P. 335. In the discant, at the end of the second long line, notes to the 
value of a L are missing in the MS. According to Brussels, Bibl. Roy. 
Ms. ip6o6 the notes to be supplied are g' P-e'-f'-e' (B S-S-S-S). 
P. 336. Or, very possibly, of the delight in grotesque shapes which 
appears so clearly in the pictorial representations of this period, for 
instance the gargoyles and hunchbacks that adorn the Gothic cathedrals. 

P. 338. "In Navarino" does not refer to the kingdom of Navarre but to 

the Collegium Navarrense of Paris, founded in 1304 by Jeanne de Navarre, 

wife of Philippe IV (le Bel). Cf. the remarks by A. Gilles in Revue Beige 

de musicologie x, p. 150, concerning the possibility of de Vi try's association 

with the College either as a student or as a teacher. 

P. 340. The literal meaning of prolatio is 'manner of delivery.' 

P. 345. See commentary to p. 112. 

P. 358. Both sections are perfect, I in maximodus perfectus, II in modus 
perfectus, but with an imperfect group at the end. 

P. 364. The tenor is repeated in diminution. 

P. 367. In a recent article, 'The Music of the Old Hall Manuscript' 
(Mg xxxv, No. 1), M. F. Bukofzer makes a remark to the effect that my 
assumption of a clerical error in the use of the mensuration signs does 
not provide a satisfactory explanation (p. 49, m. 31). However, his 
criticism is evidently based on the arrangement of these signs as they 
occur in the original Ms, not on the exchanged order which I suggested. 
If the signs are arranged as I suggested, that is, © (E 5 the values 
under (that is, in the first section) are triple of those under O (that is, 
in the third section). This little controversy is included here because 
it will contribute to clarify our explanations of the notation of this tenor. 
As regards the duplication of values which takes place in the second 
section (that is, according to my theory, under the sign G ), a plausible 
explanation can be given if this section is considered in relationship not 
to the third section (as is done in the main text), but to the first. In 
fact, the signs © and G designate respectively 9 and 6 units, and there- 
fore correctly indicate the ratio of 3 to 2 which exists between the first 
and the second sections. See the table of values given in Collins' edition, 
vol. iii, p. XXVIII. 



Commentary 451 

P. 369. Petrus de Cruce came from Amiens in Northern France. 

P. 374. Giovanni da Cascia and Giovanni da Florentia are identical. 
Cascia was a little place near Florence. 

P. 380. This argument loses some of its weight in view of the fact 
that the divisiones .0., .p., and .q. are indicated in the tenor, possibly 
to direct the singer to use different values for the B in the different 

sections. The sixth note from the end of the first staff in Facs. 75 should 
be omitted. 

P. 382. The sign .sg. means senaria gallica. Marchettus de Padua in 
his Pomerium musicae (GS iii, p. 121 ff; see also CS iii, p. iff) comments 
in detail upon the difference of the French and the Italian interpretation 
of the smaller values (i.e., groups of S taking the place of a B), and sug- 
gests using the letters g {gallic e) and y {ytalice) for the purpose of dis- 
tinction (GS> p. I75ff). The following table illustrates the main points 
of his theory: 

gallice ytalice 

3* j. j j) n j 

5* m j J> in n 

6 s m m rmn 

According to F. Ludwig {Guillaume de Machaut, Musikalische IVerke, 
ii, p. 24b, fn. 1) the signs g and y are both found in the Rossi Codex. I 
am not in the position to say whether their practical use in this source 
conforms with the theoretical explanation of Marchettus. The de- 
scription of the codex, given by J. Wolf in Peters Jahrbuch, vol. 45, 
contains no information on this question. 

P. 384. The word probably means Retrove (not Petrone). 
P. 404. On the basis of recent investigations the situation can be more 
clearly outlined. The system of mixed notation can, for all practical 
purposes, be identified with the late Italian school, while the system of 
mannered notation developed in France after the death of Machaut, 
where it was in vogue from c. 1375-1400. The main difference between 
the two systems is that the Italians, in spite of all refinements, never 



452 Commentary 

abandoned the idea of 'measure music,' that is, of music whose rhythmic 
life unfolds within the limits of measures. In Italian music the measures 
vary, if at all, only from section to section (horizontally), never from 
part to part (vertically). Moreover, syncopation over the bar-line is 
practically non-existent in Italian music. These limitations are com- 
pletely abandoned in the French music of the late fourteenth century, 
a music which may well be said to represent the most complete reali- 
zation (in a way, the only realization in all music history) of the poly- 
rhythmic ideal. It is probably not by chance that the polyrhythmic 
composition Fortune, which has been studied as an example of mixed 
notation, bears a French title. It would find its proper place among 
the examples of mannered notation. The manneristic school was located 
mainly in southern France, at the papal court of Avignon and the 
splendid secular courts of the Duke of Berry, of the Count of Foix, of the 
King of Aragon, and others. This school included, in addition to numer- 
ous Frenchmen (Solage, Senleches, Trebor and others) some composers 
of Italian extraction, notably Anthonellus de Caserta (a town near 
Naples), Philipoctus de Caserta, and Matheus de Perusio (Perugia). 
Philipoctus can definitely be associated with Avignon. 

The decline, after 1400, of the manneristic extravagances of this 
school brought about a return of a simpler style. This change entailed 
the abandoning of mannered notation and the return to the principles 
of French notation. 

Recent publications dealing with this period are: G. de Van, 'La 
Pedagogie musicale a la fin du moyen age' {Musica Disciplina ii); N. 
Pirrotta, 'II Oodice Estense lat. 568 e la musica francese in Italia al 
principio del '400' (Atti delta R. Accademia di Scienze Lettere e Arti di 
Palermo, serie IV, vol. V, parte II, 1944/45) ; W. Apel, 'The French Secular 
Music of the Late Fourteenth Century' (AM xvin/xix); W. Apel, French 
Secular Music of the Late Fourteenth Century (1949). 
P. 405. For a variation in the meaning of these signs see the article in 
AM xviii/xix, p. 22. See also the commentary to p. 96. 
P. 408. In two other sources, Paris, Bibl. Nat. nouv. acq.frc. 6771, p. 80, 
and Paris, Bibl. Nat. ital. 568, p. 1 267127, the composition appears 
with a text for the upper part. 

P. 412. Even in those cases where the text is incomplete or missing 
can the form be determined from the position of the clos- ending. In a 
ballade this short group appears at the end of the first section, in a 
virelai at the end of the second section, while in a rondeau there is no 
clos- ending since neither of its two sections is repeated immediately. 
Thus it appears that Je la remire (Facs. 82) is a virelai. 



Commentary 453 

P. 418. In examples like this may be seen the first adumbration of the 
modern principle of notation according to which binary values are used 
for the writing down of ternary (as well as binary) meter. A particularly 
interesting case exists in Senleches' Je me merveil (Ch, p. 44'), which 
is reproduced and discussed in French Secular Music (No. 48). 

P. 420. For further clarification of the problems presented by this 
extremely involved specimen see French Secular Music, Commentary 
to No. 23. 

P. 422. For a new attempt of evaluation, on the basis of Ch y see French 
Secular Music, Commentary to No. 49. 

P. 425. Both the 'Musical Heart* and Cordier's equally interesting 
'Musical Circle' (Tout par compas suy composes \ facsimile in P. Aubry, 
Les plus anciens monuments de la musique francaise (1905), pi. 22; see 
also RHdM, I. ii, p. 351) are later additions to the main repertory of 
the Chantilly Codex, written, probably by Cordier himself, on separate 
front leaves. 

Commentary (by A. T. D.) 

Our ingenious friend, Baude Cordier 
Sat him down one Saint Valentine's Day 

And made him a heart 

Which he sent to his tart 
(Wish to hell she had thrown it away!) 



INDEX 

Extended discussions are indicated by figures in bold type. Musical illus- 
trations (in original notation) are indicated by asterisks. References to modern 
scholars are not included if these are only named as authors of books. 



Abgesang 4 i7 

Accidentals 16, I04ff; see Chromatic 
alteration; Musica ficta; Partial 
signature 

Accord 71 f 

Adam von Fulda 90, 99 

Ad organ um faciendum 201, 207 

Agricola, Martin 72 

Al Farabi 55 

Alia breve 148 

Alia longa 157 

Alia semibreve 148 

Alleluia (Ba y Hu) *3o6 

Alleluia vocavit Jhesus {Cod. Calixtinus) 
212, *2i3, 267 

Alleluya (St. Victor) 248, *249 

Allwoode 8 

Alteration 108, 112, 122, 221, 344 

A madame playsante *i 3 3 

Amans ames *iys 

Amerus 202 

Ammerbach, Nicolaus 22, 32 

Amo *255, 256 

Amor da po *394 

Amor tu solo 407, *4<D9 

Anapaest 222 

Angelica 55, 72 

Angles, H. 214, 308, 447 

Anima mea 134, *i 3 $ 

Anonymus: A. II (GS i) 21; A. Ill 
(CS iii) 202, 320, 392; A. IV (CS i) 
202, 218, 240, 243^ 270, 282, 310, 
444, 4455 A. IV (CS iii) 320, 392; 
A. V (CS iii) 202; A. VI (CS i) 
340; A. VII (CS i) 202, 296; A. de la 
Fage 268; A. Sowa 202, 246, 268, 339 



Anthonellus de Caserta 414, *4i5 

Antonius de Leno 203 

Apostropha 210 

Apt, Codex 202 

Aptatur (Ba) *303; (Mo) 315, *3* 7 

AquiV al tera ferma 374, *375 

Arnaldi *94 

Aron, Pietro 114 

Ars Antiqua 322, 324^ 385 

Ars Nova 106, 311, 320, 322, 326, 332, 

339, 3*5> 403 
Aston, Hugh 8 

Attaingnant, Pierre 4, 6, *j, 56, 64 
Aubry, P. 241 
Aucun ont trouve — Lone tans — Annun- 

tiantes 319, *32i 
Audi filia 215 
Augmentation 163 
Ave beatissima — Ave Maria — Johanne 

289, *29I 
Ave regina 117, *i 19 

Bacfarc, Valentin 69 

Bach, J. S. 32, 33y 37, *3 9 , 127, 132 

Ballade 417 

Ballata 151, 390 

Bamberg, Ed. IF. 6 202, 302 

Bar (form) 417 

Bar-line 3, 9, 16, 28, 67, 85, 101, 416 

Bartholomeus de Bonorha 140, *i43, 

429 
Bartolinus de Padua 374, 376 
Bass courses 69^ 72 
Basse danse 6~/( 
Beat 97, 147, 324, 343 
Beck, J. 274 



455 



456 



Index 



Bedingham 440 
Beethoven 100 
Belle bonne 425, *427 
Belle que vous 166, *i6j 
Bellermann, A. 87, 132 
Bene he partito 398, *399 
Benedicamus Domino 216; (Fl) 245, 
*2 47 , 267/, 2 7 of, 444; (// 568) 378 

*379 
Benet, Johannes 102, *io5, 106 
Berlin, Mus. Ms. Z 26 (Kleber tabla- 

ture) 30. P. 283, see Orgelbuchlein 
Bermudo, Juan 47^ *^S 
Bern, Bibl. Bongarsiana Ms A 421 *^6i 
Bernelinus 21 

Besardus, Jean-Baptiste 69 
Besseler, H. 102, 322, 343 
Biaute parfaite 405, 418, *4i9 
Biaute qui toutes 356, *359 
Bitonality 78, 102, 104 
Black notation xxii, 199 
Blackened notes, see Coloration 
Blitheman, William 8 
Blume, F. 67 
Boethian letters 21, 208 
Boethius 146 

Bologna, Bibl. Univ. 2216 *94, 202, 362 
Bologna, Lie. Mus 3/ 94, 364 
Boumgartner 22, *i$ 
Brahms 132 
Branle commun *y 
Brevis 3, 87, 220, 269, 282, 370 
Bruger, H. 68 
Brumans est mors *303 
Brumel, Antoine 158 
Brussels, Bibl. Royale MS 6428 *i42; 

Proportionate (Tinctoris) 152, *I53, 

158,161 
Buchner, Johannes 24 
Bukofzer, M. F. 230, 264, 364, 437, 

440, 445, 448 
Burgundian cadence 106, 117 
Burgundian School 26, 106 



Buxheimer Orgelbuch 22ff, *25 
Buxtehude 37 

Cabezon, Antonio de 5of, *53 

Caccia 368 

Cambrai Ms 6 202, 362, *^(>3 

Candida — Flos filius 252, 284, *285 

Canon 179, 403, 433 

Canonic inscriptions i86f 

Canonici MS> see Oxford 

Cauda 260, 445 

Cavazzoni, Girolamo xxi, 14 

Ce ieusse fait 123, 140, *i4i 

Cest la jus *2jy 

Cephalicus 210, 226f 

Chansonnier: Labor de *I09, *i3o; 

Noailles 201, 271, *277; Roy 201, 

27 if, *273,3 3 8 
Chantilly, Musee Conde 1047 91, 164, 

203, 404, * 4 i3, 425, * 4 27 
Cheironomic neumes 208 
Chitarrone 55 
Choi gli occhi *387, 390 
Choir book arrangement xx 
Choralis Constantinus i68ff, *i69, *I7I, 

*i73, *i74 
Chromatic alteration 4, 6, 2 if, 23, 24^ 

44, 5o 
Ciconia, Johannes 202 
Cithrinchen 55, 72 

Clausula 145, 215, 217, 230, 237, 267 
Clef 3, 9, 16, 107 
Climacus 240 
Clivis 88 
Clos, see Ouvert 
Codex Calixtinus 201, 212, *2i3, 214, 

443 
Coelho, Manoel Rodriguez 19 
Collins, H. B. 188, 366, 4 32rF 
Coloration 10, 12, 126, 142, 405. See 
Courante-coloration, Half-colora- 
tion, Minor color, Triplet coloration, 
Reversed coloration 
Color prolationis 127, 138, 140 



Index 



457 



Color temporis 127, 138, 140 
Compostela, School of 212 
Conductus 216, 219, 258 
Conductus-motet 263, 274 
Conjunctura 224, 240, 254, 296, 304, 

333, 447 
Conradus de Pistoria 429 
Consonance and dissonance 244, 27of 
Convenientia modorum 288 
Copula 234, 237, 248, 256, 445 
Cordier, Baude 175, 425, *427 
Correa de Araujo 50, 438 
Corona 94 

Courante coloration 14, 68, 127, 138 
Coussemaker, E. de 262, 284, 319 
Covered play 70 
Creature * 2 5, 437 
Crucifigat omnes *264, 265 
Crucifixus *i86 
Cunelier, Johannes 428 
Currentes 240, 270 
Custos 3, 94, 418 

Dactyl 222 

Dame gentil 414, *4i5 

Dangler tu m'as 107, *io9, 129 

Dannemann, E. 175 

Dasia notation 204, 206 

De petit po *3 4 5, *3 4 9 

De radice Jesse 171, *I73, 441 

Descendit de cells 23 if, *233, 241 

Detractor est — §>ui secuntur — Verbum 

inlquum 330 
Diastematic neumes 208 
Die Chrlstl Veritas 447 
Dlco ego 170, * 1 74, 441 
Didier le Blanc 129 
Dietricus 202, 223, 296, 302, 314 
Dleux gart 426 f 
Dlexje — Amors qui m'a— Et super 289, 

*2 93 

Diminutio 147, 149, I5if, 155 

Discantus 21 8f 

Dlscantus posltio vulgaris 201, 220 



Divisio modi 225, 231, 245, 282, 302 

Divisiones 370, 389 

Dodekachordon 108, 180, *i8i 

Dominicus de Feraria *i43, 187 

Domino *257, 258 

Dona I ardentl 94, 102, *io3 

Dot 4, 122. See Punctus 

Dous amis 355, +357 

Dragma 392, 400, 408, 412, 420 

Ductia 238 

Dufay, Guillaume 102, *io3, 1 17, *i 19, 

134, Hi, *i66, *i94 
Dunstable, John *I24, *i87 
Duodenaria, see Divisiones 
Duple meter 290 
Duplex longa 224, 245^ 286, 288, 310, 

328 
Duplum notation 219, 267 
Dusiacki 70 

Ellend du hast *45, 47 

Ellinwood, L. 262 

En attendant esperance 422, *423 

Ensemble music xxi 

Epiphonus 226 

Epitrita 161 

Erlangen, Univ. Bibl. J2g 40 

Ersatzklausel 215 

Et gaudeblt (/F,) *252, 279; (Fz) 254, 

♦255 
Et in terra (Ockeghem) *i67; (Huelgas) 

308, * 3 o 9 ; {Old Hall) 364, *3*5, *3*6 
Et occurrens 245, 254, *255 
Et resurrexlt *I39 
Extensio modi 223, 234 

Falscher Schaffer 34, *$6 

Favellandl vlclum *233 

Felix virgo — Invlolata — Ad te susplra- 

amus 358, *36o 
Flllls sass 34, *36 
Finalis 89 
Finger notation 54 
Finis punctorum 104, 290 



458 



Index 



Fitzwilliam Virginal Book 8 
Firmissime — Adesto — Alleluia benedic- 

tus *329, 330, 335, 447 
Florence, Bibl. Laur. Pal. 87, see 

Squarcialupi Codex 
Florence, Bibl. Laur. Plut. 29.1 (Fl) 

201, 215, 217, *229, *247, *248, *25o, 

*25i, 254, *255, *257, *266 
Florence, Bibl. Naz. Magi, xix 112 bis 

*i35, I9 1 , *i92 
Florence, Bibl. Naz. Pane. 26 203, *387 
Flos filius *229, 238, 251, 274, 279, 284 
Flos subirus 334 
Fortune *375, 40of 
Fortune a bien couru 64, *65, *66 
Fractio modi 223, 235 
Franco of Cologne xxii, 202, 220, 270, 

296, 3 1 off 
Franconian notation xxiii, 199, 310 
Freistimmigkeit 4 
French notation 199, 338, 404 
Frescobaldi, Girolamo 67 
Friderici 70 

Fuenllana, Miguel de 62 
Fuhrmann, Leopold 69 
Fundamentum organisandi 40, 44, *45 
Fur non venit *3iJ 
Fusa 3, 87 

Gabrieli, Andrea (Giovanni) 34, *35 

Gafurius, Franchinus 9of, no, 116, 
145, 152, *i6o, *i62, 163 

Galilei, Michelangelo 70 

Garlandia, Johannes de (the elder) 202, 
220, 234, 244, 26 9 f, 283, 298, 302, 
343, 444; (the younger) 202, 338, 443 

Garrit gallus—In nova jert 328, *33i, 

335 
Gaultier, Denis 701", *73 
Gennrich, F. 278 
Genus (multiplex, etc.) 146 
Gerle, Hans 76 
Giovanni da Cascia 374 
Giovanni de Florentia 374, 386, *387 



Glarean, Heinrich 108, 120, 172 

Glogauer Liederbuch xx 

Go *229, 230, *248, *25o 

Gombosi, O. 61 

Goslenus 212, 443 

Grossbrummer 748" 

Group style l6${ 

Guido 426 

Guido d'Arezzo xx, 21, 85 

Guilelmus Monachus 145, 202 

Guitar 55 

Hac in annijanua 258, *259, 26off, 265 

Hadrianus, Emanuel 69 

Half-coloration 142 

Hamilton Codex 71, *73 

Hanboys, Johannes 338 

Handel 132 

Handschin, J. 212, 243, 262 

Heckel, Wolff 76 

Hei diex — Mai latus *3oy 

Hemiolia 131, 158, 348 

He mors — Quare non sum ^358 

Heyden, Sebaldus {De arte canendi) 

*I54, 157, 159, *i6o, *i67, 442 
Hieronimus de Moravia 334, 341 
Hodie perlustravit *255, 256 
Homo quo vigeas — Et gaudebit 265, 

*2 7 5, 279, *28i 
Hucbald 21, 207 
Huelgas, Codex 202, *264, 306, *309, 

324 
Huic ut — Huic ut 315, *3i6 
Hui main—Hec dies 272, *273, 274 
Hupfauf 78 

Iambic 222, 446 
Ideoque quod nascetur 168, *i69 
Ileborgh tablature 8, 4off, *4i 
II n'est si grand possession *^6 1 
Imperfection 107, 122, 129; Imper- 
fectio ad totum, ad partes, ill, 112, 

344, 43 9f 
In campo aperto 208 



Index 



459 



In dulci jubilo *3i, 32, 438 

Initialis 88 

/» seculum {Mo) *igo\ (Ba) *302 

Instrumental music xxi 

Intavolatura 14, 16 

Integer valor 52, i47ff, 388 

Isaac, Heinrich 144, i68ff, *i6g, *iji, 

* l 73, *i74 
Isochronous 263, 265, 266 
Ivrea, Codex 202 

Jacobus (of Liege) 318,338,340^ see 

Speculum music ae 
Jacopo da Bologna 374, *375, *38o 
Janequin, Clement 159 
Je la remire 408, *4i 1 
Je ne puis avoir 410, *4i3 
Je ne puis — Flor de lis — Douce dame 

♦292 
Je suy exent 176,* 177 
Jobin, Bernhard 76 
Josquin des Pres 152, *I54, 180, *i8i 
Judenkunig, Hans 76ff, *79 
Judentantz, Der 78, *8i 

Kargel, Sixt 76 

Keyboard partitura xxiv, 16 

Keyboard score xxiii, 3 

Keyboard tablature xxiii; German 
21; Spanish 47 

Kinkeldey, O. 28 

Kleber, Leonhard 30 

Kleinbrummer 74, 78 

Kleinsaite 74, 78 

Koczirz, A. 78 

Koller, O. 284 

Korte, O. 6of 

Kotter, Hans 28f, *29 

Kyrie (La Rue) *i2i; (Ockeghem) 
*i65; (Obrecht) *i83, *i8 4 ; (Di 
dadi) *i8 4 , *i86; (MS Cambrai) 362, 
*3^3 ; Kyrie super celos *^rj 



La dedicasse *J3 

Lambert, Magister (Pseudo-Aristot- 
eles) 202, 226f, 292fF, 296, 298, 302, 
310 

Landini, Francesco 374, 386, *387, 
390, *39i>392, *393 

Lantins, Hughe de 123, *I33, 140, 
*i 4 i, i76fF, *i77 

Laudamus te *94 

Laurentius de Florentia 374 

Laus Domino — Eius 265,274^275,279 

Lautenkragen 75 

Leoninus 215, 219, 245, 267, 271 

Le Roi, Adrian 68 

Letter notation 2 if, 24, 30, 32, 34, 37f, 
7i, 74, 77, 207f 

Uhomme arm'e (Josquin) 180, *i8i; 
(la Rue) *ii2, 118, T20, *i2i, 180, 
440, 443; (Ockeghem) *i39, 163, 
*i65, 180, 440, 442 

Liber usual is 210 

Lieto, Don Bartolomeo 33 

Ligatures 10, 87, 223, 282, 296, 312; 
rules for ligatures 91; ligatura bin- 
aria, ternaria, etc., 91, 224, 241; 
ligatura obliqua 10, 90 

Lombardic rhythm 129 

London, Brit. Mus.: Keyboard scores 
8 ; Egerton 274 201 ; Egerton 2615 201, 
*242, 27 1 ; Add. 28550^ see Roberts- 
bridge Codex; Add. 2gg8j 203; Add. 
jooyz 201, *284, *285; Harl. 978 

238, *239, 2 4 2f 

Longa 87, 220, 261, 269 

Ludwig, F. 100, 209, 217, 220, 224, 

230, 245, 274, 284, 322, 325, 333, 

346,354,355, 3 68 ,448 
Lute tablatures xxiii, 54; French 64; 

German 72; Italian and Spanish 56 
Lute ornamentations 70 
Luto carens 446 



460 



Index 



Mace, Thomas 6gf 

Machaut, Guillaume de 99, 124, 145, 

202 (Mss), 343 (Notation), *353, 

*357, *359, *3^o 
Madrid, Hn i6j 201, *240 
Madrigal 390 
Magi videntes *I94 
Magnus liber organi 200, 201, 215, 217, 

230 
Mandora 55, 72 
Mannered notation 199, 403 
Marcantonio da Bologna 3, *5, 14 
Marchettus de Padua 203, 322, 334, 

368ff, 449 
Maxima 87, 124, 328 
Maximodus 99, 124, 327^ 440 
Mayone, Ascanio *I7, 18, 48 
Meane 12 
Media 91 

Melismatic notation 2i7f 
Melismatic style 212, 216, 219 
Mensuralists 271 
Mensural notation xxii, 3, 85 
Mensural notes 3, 87 
Mensuration 3, 96, 346, 404f 
Mensuration canon 118 
Mensurstrich 101 
Mertel, Elias 69 
Michalitschke, A. 294 
Micrologus xx, 201 
Milan, Luis de 56, *57, 62, 190 
Minima 3, 87, 3 i 9 f, 325, 328, 338 
Minor color 46, 108, 127, 128, 136, 

144 
Missa: Di dadi *i84; L'homme arme, 

see L'homme arme; Je ne demande 

*i84; quam suavis *i88; Prola- 

tionum 440, 442, 443; Si dedero 

i82ff, *i83, *i85 
Mittelbrummer 74, 78 
Mittelsaite 74 

Mixed notation 199, 385, 404 
Modal notation 199, 219, 220 
Modal rhythm 263, 444 



Modena, Bibl. Est. L. 471 134, 136, 
193, *i 94 ; L. 568 203, 4 o 4 f, * 4 u, 
♦415, * 4 23 

Modes, rhythmic 220; perfect, imper- 
fect 223, 444f; rectus, non rectus 
269f 

Modus 98, 124, 327; modus major, 
minor 98; modus perfectus, imper- 
fectus 131, 292, 294, 303, 318, 327, 

340, 347 

Mon seul plaisir 440 

Monsieur 136, *I37, 440 

Montpellier///5p 21; H ig6 202, 284, 
*2 9 i, *2 9 3, 315, *3i6, *3i7, *32i 

Mora generalis 94 

Mordent 24, 30, 49 

Morley, Thomas 116 

Morleye, Guillaume 68 

Mors *235 

Motet 219, 263 

Motet notation 219, 271 

Moult me fu — Robins m'aimme — Port- 
are 304, *305 

Mudarra, Alonso 66 

Muffat, Georg 194 

Mulierum 256, *257 

Mulliner Book 8, 12, *I3 

Munich, Mus. Ms. 2987 47; Cim. 351a 
*137; Mus. Ms. 3725, see Buxheimer 
Orgelbuch 

Muris, Johannes de 117, 145, 182, 202, 
322, 340, 395 

Murschhauser, Franz Xaver 163 

Musica enchiriadis xx, 201, 204, *2o5, 

443 
Musica ficta 10, I04ff, 120 
Musica mensurata, plana 87 
Musica reservata 118 

Narvaez, Luys de 66f 
Naschoso el viso 386, *387 
Ne pensez pas 352, *353 
Nessun ponga speranza 392, *393 
Neuhaus tablature 8, 40 



Index 



461 



Neumes 88, 208, 209, 212 

Newsidler, Hans 56, 756% 78, *8i; 

Melchior, 76^ 
Niemann, W. 220, 228 
Nos qui vivimus *2o6 
Notatio cum (sine) litera 218, 286, 

294> 3°4 
Notker Labeo 21 
Notre Dame, School of 201, 215, 219, 

267 
Notum fecit *2^6 
Nouveau ton 70, 72 
Novenaria, see Divisiones 
Nulla pestis — Vergente *32y, 337 

Obrecht, Jacob xxi, 114, 129, 182, *i83, 

i8 4 ,*i85 
Ockeghem, Johannes *I39, *i65, *i67, 

1 80, 440, 442, 443 
Octaves, Indication of 24, 28,30,34,37, 

438 
Octonaria, see Divisiones 
Oddo of Cluny 21 

Odhecaton 113, *I28, 154, *i55, *I93 
Odington, Walter 202, 220, 221, 268, 

338 
dolce compagno *i43, 187 
Old Hall MS 91, *i2 4 , 362, 36 4 ff, *2^ 

♦366, 432ff, 437 
Maria — Nostrum 284, *285 
Opposita proprietas 10, 90, lybi 
Optatur *303 
Ordo 222 

Organ tablature xxiii 
Organum 208, 215; organum duplum 

267fF; organum purum (etc.) 268f 
Orgelbuchlein (Bach) 37, *39 
Oriscus 443 

Ornithoparchus, Andreas 150 
Or qua conpagni 382, *383 
Ouvert and clos 94, 152, 335, 349, 412 
Ovid 336 



Oxford, Christ Church College MS 
371 8. Oxford, Bodleian Library: 
572 21, *2o5, 207f; Can. misc. 213 
♦103, *n 9 , 123, *i 4 t, *i 43 , *i75, 
*i 77 

Paix, Jacob 32 

Paolo Tenorista 374, +394, 398, *399, 
407, * 4 09 

Paris, Bibl. Nat.: ital. 568 203, *375, 
*379> *399> *4°9; l&t. 11266, 202; 
lat. 15139 (St. Victor 813) 201, 246, 
*249; see Chansonnier Noailles, Roy{ 
Machaut (Mss); Reina, Codex; Ro- 
man de Fauvel; St. Martial 

Part arrangement xx, 437 

Part books xx 

Partial signature 102, 104, 140, 378, 

439 
Partitura xxiii, 16 
Patrem omnipotentem 432ff 
Paumann, Conrad 40, 44, *45, 74 
Pausatio 445 
Pavane *57, 66 

Perche canqato e'l mondo 376f, *377 
Perfect, imperfect 96, 292, 439; see 
Tempus, Imperfection, Modes, Mo- 
dus 
Perfectio (in ligatures) 88, 224, 3i2f 
Perotinus 145, 215, 218, 267, 271, 446 
Petrucci 56, 62 

Perms de Cruce 3i8ff, *32i, 324, 369 
Philippe de Vitry 202, 322, 330, 338f, 

34°f> 395 
Piae voces 170, *i7i 
Pierpont Morgan Library 410 
Pierre de la Rue *ii2, 118, *I2I, 157, 

180, *i8i 
Pisador, Diego 56, 62, 66 
Pitch notation 54 
Plica 226, 235, 260, 298, 311, 314, 333; p. 

duplex longa 230 p. -note, p. -tone, 

227 
Ploures dames *346, 351 



462 



Index 



Podatus 88 

Porquoy je ne puis *I28 

Power, Leonel 134, *i^S 

Praetorius, E. 130 

Praetorius, Michael 437 

Prague, Univ. Bibl. XI E 9 202 

Preambulum 42f 

Pre-Franconian notation xxiii, 199, 
263, 282 

Priamel *79 

Prima (seconda) volta, see Ouvert and 
clos 

Proceleumaticus 222 

Proh dolor 3031", *304 

Prolatio 96, 120, 319, 323, 340, 347, 
443, 448; p. perfecta diminuta 167 

Pro patribus *303 

Proportional notation 145 

Proportional time signature 52, 188 

Proportions 52, 62, 145; p. dupla 147, 
148, 151; p. tripla 62, 147, 148, 155; 
p. quadrupla 157; p. quintupla 160; 
p. sesquialtera 146, 157, 158, 166, 
348; p. sesquitertia 146, i6of, 166 

Proportz 157 

Proprietas 88, 224, 3i2f 

Prosdocimus de Beldemandis 145, 182, 
202, 203 

Pseudo-Aristoteles, see Lambert 

Punctum (neume) 88, 210 

Punctus: p. additionis 101, n6f, 348; 
p. divisionis 11, 1131", 115, 295,299, 
318, 344, 348, 352, 369, 385, 396; 
p. syncopationis 367, 396; p. alter- 
ations, perfectionis, etc. 116 

Punktpaar 397, 410 

Pyrrhichius 222 

Quadratnotation 217 

^uant florist — Non orphanum 254 

Quant revient — U autre jor — Flos filius 

252, 272, *273, 284 
Quare fremuerunt 325^ *326, 334 



Quasi non ministerium — Displicebat 

3271", *328, 337 
Quaternaria, see Ligatures, Divisiones 
Quel front e signorille *io3, 134 
Que pena 4298* 
Quia respexit *I42, 155 
Quintsaite 74, 78 

Ramis de Pareia 164 

Redford, John 8 

Red notes 328, 348, 356, 358, 405; see 

Coloration 
Reduction (of note values) 4, 6, 9, 16, 

26, 30, 33, 97, 222, 282, 324, 343 
Regina Clara Im Hoff 341", *36 
Regnat 250, *25i 

Reina, Codex 203, *377, 380, *42i 
Relegentur ab area 265, *266 
Renvoisiement *iyj, 278 
Repeated notes 225 
Repertorium (Ludwig) 230 
Resolutio 184, 186 
Resonet *3i, 32 
Rests 3, 87, 347, 445; see Divisio modi, 

Pausatio 
Reversed coloration 406, 412, 420, 442 
Revo hit *255, 256 
Rhetorique des dieux 71, *73 
Ricercare 61, 63 
Riemann, H. 67, 97, 172, 187, 208, 221, 

262 
Rippe, Albert de 69 
Robert de Handlo 202, 318 
Robertsbridge Codex 22, 37, *38, 384, 

447 
Rokseth, Y, 286, 295, 299, 300, 320 
Roma gaudens jubila 446 
Roman chorale notation 88, 210, 378 
Roman de Fauvel 202, 315, 325, *326, 

*3 2 9>*33i>448 
Rome, Bibl. Vat.: Chigi cod. C. VIII 

2 34 * l 39, *i65; Rossi 215 203, 374, 

382, *3«3 
Rompeltier 154, * 155, * 193 



Index 



4 63 



Rondeau 140, 276ff, 304, 417 
Rore, Cipriano de 19, *I27 
Rose lis *349 
Ruina *yri 
Rules of the B 104 

Sachs, C. 67 

S abator withe a meane 12, *I3 

Salve mater — Salve templum — In nom- 
ine *366 

Salve regina *27, 28 

Salve virgo — Ave lux — Neuma 289, *2<?f, 
298 

S' amours ne fait *35o 

Sancte spiritus 237, *255, 256 

Sanctus: (Benet) io2f, *io5; (Obrecht) 
*i8 5 ; (Fl) 237, *2 55 , 256 

Scheidt, Samuel ig{, 22 

Schering, A. 43 

Schlick, Arnolt 26, *27, 56, 76 

Schmid, Bernhard (the elder) 32; (the 
younger) 32, 33^ +35, 49 

Scholia enchiriadis 21, 201, 204, *2o6 

Schrade, L. 61 

«SWo <•«/' credidi 245, 246, *249 

Scordatura 71, 78, 438f 

Score arrangement xx, 364, 437 

Scotch snap 129 

Se Galaas 428 f 

Se je suis — Jolietement — Omnes 445 

Selesses, Jacopinus 422, *423 

Semibrevis 3, 87, 295^ 304, 311, 318; 
s. major 326; s. caudata (signata) 
306, 320, 325, 332, 337, 369, 370, 
381, 405; s. minima, see Minima 

Semifusa 3, 87 

Semiminima 3, 87, 319 

Senaria, see Divisiones; s. gallica 449 

Se pronto 390, *39i 

Sesquialtera, see Proportions 

Shepard 8 

Short octave 47, 49, 438 

Sicher, Fridolin *3i, 32 

Si dedero, see under Missa 



Signum congruentiae 94, 102, 118, 

167, 180 
Silbenstrich 231 
Simplex groups 245, 254 
Sources of black notation 201 ff 
Speculum musicae 202, 318, 322, 339, 

341 
Spiess, L. 204 
Spinaccino, Francesco *6% 
Squarcialupi Codex 203, *39i, *393 
Square notation xxii, 199, 215 
St. Gall, Stiftsbibliothek 530 *3i, 32 
St. Martial, School of xx, 201, 209, 

21 8f, 267, 268, 271 
St. Victor S/J, see under Paris 
Staff 3, 6, 8, 23,48, 69, 204 
Steigleder, Ulrich 14, 22 
Sthokem, Johannes *i28 
Stimmbucher xx 
Stollen 417 
Strophicus 443 
Subsemitonium 120 
Subtonium 120 
Successive proportions 161 
Sumer is icumen in 243 
Sumite karissimi 43 if 
Sweelinck, Jan Pieterszon 20 
Syllabic notation 217, 219, 258 
Syllabic style 2i6f, 265f 
Syncopation 14, 28, 133, 342, 347, 356, 

362, 367, 395, 4Hf 

Ta (W x ) *2 35 ; (Fl) -255, 256 

Tablatures, xxii, xxiii, 21, 54 

Tactus i47f, 150, 190, 191, 343, 389 

Talea 356 

Tempo 4, 97, 188, 324, 343, 388 

Tempus 96, 282f, 3o2f, 34of; t. im- 
perfectum 100, 322, 330; t. per- 
fectum 107, 311, 319, 322, 330, 340; 
t. perfectum diminutum 155, 441 

Tenors, Notation of 245, 286, 303, 327 

Text, Underlaying of 1 1 8 



464 



Index 



Theodoricus de Campo 202, 320, 324, 

384, 392 
Tie 3, 85,385 
Time signatures 188 
Tinctoris, Johannes 9of, 1 14, 145, *i 53, 

156, 164, 166, 180 
Titelouze, Jean 19 
Tonschrift 54 
Tordion 68 
Torino: Bibl. Naz. J II 9 203, 404, 

405, *4i9; Bibl. Reale Far. N. 42 

202,306, *3©7, 315 
Tout houme veut 417, *4i9 
Trabaci, Giov. Maria 18, 48 
Transmutatio 246 
Trent Codices 102, *io5, *uo, 114 
Tribrachic 222, 446 
Triplet coloration 127, 130, 138 
Trochaic 222, 446 
Trop plus — Biaute paree — Je ne suis 

3°4 
Tut sunt cell 8 

Tuning 561", 7of; see Scordatura 
Tunstede, Simon 202, 344 
Tu patris sempiternus 204, *2o5 

Un bel sparver *38of 

Unison, see Repeated notes 

Upper parts, Notation of 252, 294, 304, 

330 
Ursprung, O. 92 
Ut tuo propitiatus 21, 201, *2o5, 207 

Vado *255, 256 

Valente, Antonio 19, 48, *5i 

Venegas de Henestrosa 50, 438 

Vent sancte spiritus {Old Hall MS) 

*i2 4 ; {Trent Cod.) *i87 
Veri almi pastoris 429 
Verulus, Johannes 202, 398 
Via artis (naturae) 372fF, 382 



Victime *303 

Viderunt Hemanuel 209, *2ii 

Vieil ton 72 

Vienna, Staatsbibliothek Ms. 18491 

34, *36 
Vierhebigkeit 208 
Vihuela 56 

Vince con lena 123, 140, *i43, 151 
Virdung, Sebastian 8, 26 
Virelai 151, 412 
Virga 88, 210 

Vitry, see Philippe de Vitry 
Vocalisation 219 
Vocal music xxi 
Vox organalis, principalis 207 
Vulpius, Melchior 130 

Wagner, P. 443 

Warner, S. T. 117 

Warsaw, Library Krasinsky MS 52 

186 
Wasielewski, J. W. 6of 
Wecker, Hans Jacob 76 
Weiss, Silvius Leopold 71 
White mensural notation xxii, 85 
Wilkin tablature 22, 40, 43 
Willaert, Adrian xxi 
Winchester troper 85, 201, 208 
Wir Chris tenleut *29 
Wolf, J. 15, 40, 44, 46, 48, 55, 61, 64, 

65, 72, 129, 163, 222, 228, 319, 320, 

3*5, 33o, 333, 346, 368, 374, 397, 447 
Wolfenbuttel: 677 (W x ) 201, 217, *235, 

♦236, *252, *259, *26 4 , 446, *447; 

1206 {W 2 ) 201, 217, 231, *233, *275, 

279, *28l 
Wooldridge, H. E. 262 

Zacharias, Magister 431 
Zoppa, Alia 129 



APPENDIX 

TRANSCRIPTIONS 



No. i 



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No. 3 



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No. 4 



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cfua con- p«q- ni qua cum 5 ran p!a- c«- r» ehia-nufi 



No. 51 


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(Facsimile 77) 
































Qua- 


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piu rum v« dir qudn-to qtwl di mi piac- 



No. 5: 



(Facsimile 78) 



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No. 53 



(Facsimile 79) 




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1. Che s«'l a in se vo- 9h« 



No. 54 



(Facsimile 80) 



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b b 




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No. 55 



(Facsimile Si) 







No. 56 



(Facsimile 82) 




No. 5- 



(Facsimile 8j) 




No. 58 



(Facsimile 84) 



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No. 59 



(Facsimile 85) 




No. 60 



(Facsimile 86) 




(J- J) 



(J>.J>) 



(J-J) (>-» 







The equations added in parentheses indicate the relationship between the note 
values of the soprano and those of the tenor. 



No. 6 1 




No. 62 



(J\\c>iMii.i: SS; 













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No. 63 



(Page 431 Sumite karissimi) 




(Page 432 Patrem omnipolentem) 




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Date Due 


IIC 17 


1965 uU 


1 8 J39§ 




P* 13 


' V ' : 






DEC 16 1 


970 ^ 


£ 8 1386 




-FEB 2 


197? DEC 


2 1 1988 




m : 


1971 MAS 


: x ,iW 




(MAY 1 -■ 








, 








™» ^ i 


J ii.2 






FOV 6 19 


73 






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NOV i? ii 


>74 






MAR 1 1 1£ 


75 






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197 


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DEC x 9 -- 








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Library Bureau Cat. No. 1137 



ML431.A61961 



MUSIC 



Ape,.w2 5002 00369 0190 

The notation of polyphonic music, 900-16 



ML 

431 

kb 



T36T 



AUTHOR 

Apel 



The Notation of Polyphonic Music, 



DATE DUE 



JUL 



1 x 197 - 



PEC 2 2 V1+fi A .<&^£tu/ 



— 



_^ 



OCT 



:_ 



^y 



BORROWERS NAME 



U^ 



9791V- 



Mr 



MUSK LIB 

ML 
431 
A6 
1961