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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

THE MEDIAEVAL ACADEMY OF AMERICA

1942

1949

1961

Library of Congress Catalog Card
No. -61-12067

MUSIC LIBRARY

Printed in U. S. A.

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

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 uplay 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. Square4 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 51

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) iJ9

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) l37

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; 0 dolce conpagno

(MS Oxford, Canon. 2/3) • H3

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) 3l6

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) . . . 329

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

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

MuT

RHdM

SchT
SIMG

VfMW
ZfMW
ZIMG

a p. a,

ap.p

c.o.p.

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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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 (c1).
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 - - *

■T

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

1The 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

^ NN

:a.

=fc

-A

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~ps^^g^g

Nf#filr^

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.

1The 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 order1:

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
By 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:

normal:

blackened:

♦

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

m "N'^w

ij!i^iili|iiW«

i*3

^~y

3ZJ5I

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

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: !-£«;» -£0 . 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

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-
latura1 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

Keyboard Partituras
Facsimile 6

IIITfi

1 \

tiiii
i*nei

ill)

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

I I &a Mill

' *1 I4»l I I

1 ! ! I ! '

?4+*i 1 j j j ( j

tt8 I Bit

^♦! 1 i'

»i 1 1 1

111!

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

I I I]

1 ■ *»i 1 r
1 1 *^» 1 1 -

! «-!♦

I I l<5>l

i : w \

IIS*

MM ch 141

urns

I I l<*l

Mill
Mill

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 partitura1 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 0 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

f g

e' P g'

a' b' c"

D E

K L M

NOP

II.

F G

M N O

III.

(E) F

D E

C D E

F(G)

IV.

r a

F G

e f g

-1

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.

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

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

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

- «

tT>

-4

<3 * U-+-

< t*3

* «l

« ' °l

§5

« t «-»

-4 _

*^' *>

i u—

< t^>

■<i hH

l c

t?5

-S>

<SI

1^3

tnj

4-1

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

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

-£. ■©■ Ui L ft y$f «tr 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-

zz:

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

T/r

ag ,# a; #

*&» $" -csr #■ g: «f « «2 .a?

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

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, 5J01), 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 J1 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.

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*

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

? 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

r
j
v

ttft

?T?#

/
J

-r$-r?

ff^ f?w w ^ppp ^^ /

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

*?#? #F? Vr$**

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

Motteten, Canzonetten, Madrigalien und Fugen. Strassburg, 1607

From folio A Iv

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

T-y

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

c Si

; : :i;

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.

The Notation of Soloist Musi

w^^^m-fmm

n^m^^r'^^^ i

Ofeatftcwu fitnp.jj

ffi?.r\l m dft^

EXE

S g«jjgS*g§S^

__riiPiiBJH/*»iirn

3| zjffigg

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

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

(*t7^?HA%8r?fr<

£ «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

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 pedal1 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

Facsimile 15

?^o.

SI 4

v»

3*^.

-1 Ril; V* *) ,F

H ^^o

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 My 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 century3 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#

9
c

30
a'

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^

?5-/-|J/-J5
B*-2*H»3o

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

20 — HnB-aj-H

riattgors 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

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

1234567

The figures 1 to 23 represent

CFG

short octave
3 14 15 16

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

f 1

!>. 17
17; 15 I***

•4

17 !» 171*15 |<

1, 13 #11W?

7 «■

* 4

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

7*7:

13k 13 It I31213lfc

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

II
10

14 13
X II

X j>: 11 10
II| 8;
IO

r r '

1615 14

»4

St
1 1

14
11

14: X t t t

II II IJ 14 13

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'

■

t>. "

«3 X 14

10 s

1 10

11 10

p; 1 1:3,

it iop8 f

n 14 11 11

»4--

4 »7

8 <

; 9: u

X 7 6T- 4

a p

8 p 10:7s

9 a

7 X X

4--

7 3

*•• 4
3=

*••

3-'

l>.

»4

X Xi

10-

t t » »i

ai i8j

x x

t' x

14. 17 1* j

5 »4 ij 11 '18

17:

20 17: i4

11 14 14!

16 18

jt 10: 71 it

X 10

IOJ Ij

13 14. X 1

J »4

U X X

7 7

X •

11. II.

P 7 9

« $

9. 10.

11;

t x X 11 so) sot 301 20:

17 18 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

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

DE JNTOWIO DE QATtECom

iHW i-irl-r-rsiUI

iff

jji

43B

*L7 6SUS-

Jc/o J

'HJiUi '-HHH^H-

c/o c/

"41*

r-7-f-

■H-*

.£

f 7*47

-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.

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 monographs2), 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.

20. 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 lute1 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

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.

♦ o ♦

* * o ^

nmunm "M

♦ ♦ ♦ ♦ Q

~* zj r*J

J- J J- ,LJ J HF — 3-2320

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

- ° , -, *

inmunu^ « uauui

■f-f-

-5-^70 — 0 2 j

■*-*■

■j-*

-3-^-0—0-2-

-D-2-4-0-*

---0-

■j-a-

m i 1 ' 4 ' 111 ?n

^ O v< 6 <y $ $ $ 0 ^^$^4

— 5— 2— 0 1 :

ioiiii

iillll

♦ ♦♦

fc=

— ■ — 3— 245-a-o— 0-2-

1 0 * -»

■J -2

■J-

"3 J 0

O J ■

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 manoy intitulado El Maestro. Valencia, 1535

Folio G VIV

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:

0 12 3 4 5 6 7 8

I g gt a b\> b 0 4 <* &

-/ — ft *"ff "et a WZ

/// "a tfc b""\ — 0 c$ d eV-

IV — / ft g """gf a" bl b""\ — 0 c#-

V — 0 4 d e\> 0 f ft — ""g 'M'

VI — IcPIl'gf^ZlAl^Jii; jfl — 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

/
//
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

^-H

U±

!£..<>

<)<T

I
I
I

L.
L.

L,
L.

LL.

LL—

Lt—t

f
*
C

h
>

t
LL.

£
L

«<

)

>♦

i
I
L

L.
L.
L.
L.

n
>

>
>

t
LL.

LL.
LL.

I"*

1
1

LL.
LL.

LL.
LL,

1
1

k
»>
1
>*

LL.

LL,
LL-
LL—
LL—
LL-f
LL-t
LL-

r
t
C

1
>•

)

L-.

••(»

df>

<>"h

..<> LL-

f VI

«!•
• I*

f Ms

<>•

<T «

-<<

>-*

•

£—

««

**— «

zo_

)

LL—

LL—
LL—

i
«

«•

«^(

LL
LL—
LL—

f
<

<
->
l»

>♦

LL—

)

LL—

■>

r.<

■>•

LL.

)

»n<

*<•

C5^

^-;

<•

LL—

\»

LL—

s»

LL—

s»

LL—

LL.

\»

L—.?

<•

*■>«

■»

n . .

-s

LL—

» •

f ^

■»

..(

LL—
LL—

•C

t
r

l«

<r>-

s
5.

•i: to

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

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 iCA — h

©€-»<

•A-e-D-

■AC A A A

4~€-

e-A-c-

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

*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- PC AC 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) =

•- I

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):

The Notation of Soloist Music

, rhrt

Routine a bitconru for mop. if

AtttflHtlflllfll^

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

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

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
(Paris, 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

bib^i •» b •

IbAb-B •

^ c-» •

v7 . ^

a. •

^ Ui

!fv^

a* o-b flu

.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?,

lO. 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-
ture1 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.
SchTy 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

LADEDICASSE.

O cw

s:^:

Oi a . _ r~ —

^ ^^CW-

13ZSZL

^=jg

^12

/ ^

a r

£3=^=^

^4*=

4* ^

4*^

^Sf

r r

<*t^\

rttfjtf

^ r~ fa

-*£-

<& <f \Y>

j r> 1 tMg^\ ac^ CL llj2

U-CL

(*+>

tt^±

-t*-e-

Jk — c-

jrA f &

-¥*-

O o*~

tt^t

^<*al

*4r

W<%^

& — *a r r , r

-if-"

tfi 0 r

-&-

42 (£ 1^

^1 <*-

^* — F-

r r -p

■#=-

«j> g r~

<V,

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

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' = 0 -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.

0
4—

—4—

— i —

— 0 —

— i—

—7-

—2—

i —

3—

— 0 —

— h—

— s —

— * —

— c

hr-

— n —

— s

///

■h

-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

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

7
nkl

0 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 scordaluray 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

FFFFFFF

JDMbhtViifitne

rrrr

hynt

PFFFPFF

FFFFFFFF

togf2fe»

rrrr

voir

nt e

irr

rrFFFF

0 e

FFFF

I 2o*

FFFFIFFFFrr

2?gp tSppyro

rrrr
« ?p

y?8?

rrrr

ittm

Z ry

rr*r

rrrr

«P

irrr

yp*j>

rrrr

?rrr

nmfy

rrrr

i*Si

FFFFFFFFFF

FFFFrr

2 n
Hnytj

FFFFrrpFFrr

c p \1 1

rFFrr

2 8im«

FFFFrr

c *

rrrr

eny£>

rr
n 1

#'»&»

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
QTgttmgg and) vi\ anba: tatg ana) auff ban $ng fcfrlagot*
fraPlubot Cant* tm|i 1 11 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 ./. |, TJ, ,|, ,/
' LJ- eJ 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-

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 notation1 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.

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-all •

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

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.

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 cy=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_ . _^_, -CvJ_ = B; BB

5. DX,(^,XD = 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 closy 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: 0 H=«*« o = i^i

Mensuratii

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, <?];
0 = [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>.

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 [*,*]

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- iJ Jl

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

(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

i^N^'k \t

ffl*

^*Tfw 4*&4 p«M» «~*«V».

.f|=- «Vf..

4 j 1

pjgp

fiS~~& v

: Nhi ■ TTA —

WV / ^U»3» U»MUM«

J±\m:x> •

rv^H**.

j K jj«-J

un.^.|H< 'Vstfc

■■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 ' S

1 ~;r

f i-.^

|HJ

fei-

- £

Iftssi

o
U

>^ ^

1-, ^*-
-2 «

i—l bo

in,

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

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

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 S3 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

xThe 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: Ga ♦*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 Ruey
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

if-i-a,.

4Zp[

5*Lf

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

«c.^«*

HDC

P^E

^H-

Ar...ft

^.^Au"'

:ezr

fl-V 31 ^

3=±

"° Eg "<hr

A»^<fi>v-wm fi»«« vnS>«J. fXweH <g*u

^~TBT

-*-*

•^TT

M-f

J— == — ~ Lps»

j°

'ffwi^ **•»* . /«V.tT<.

^-Vrfcr*^

4-H-4--

f-J

0/ Vt/ :t±r:

gfe^zj^

E=^k

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*iUUNui-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

— <•

— - 5

*~=^

— <
i

• -
<>-

■

• '

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 By 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) modusy 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 prolationisy 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:

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=[JJ/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 Sy 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 S3 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.
52> 107), 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 Sy 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)

[2J 2\ 0 + 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

20 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
ptaysantey 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 !

.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 meay
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.

JThe composer's name is given in the MS Modena, Bibl. Estense, L. 471.

Coloration in Tempus Perfectum
Facsimile 28

i3S

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 J1. 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'

*Q OO

S 8

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. Cf *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

Coloration in Prolatio Perfecta
Facsimile 31

141

v^r*

rf^m "^ <\cg

^cfcw^ jrfi*"^

±^4

r'-er

HAS. .^3j

f^'^y''^^^'

-./

°^wg\J

T\^'<. ggggj

ffi-

tea ^H^ag

mggeg <^pr

1 fy* ft>-Cf ^T1^ '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^

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|sUpJii|; 0.#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

Facj

SIMILE -12

9^ f+£-m fcfi~3

y i-m-^Sw. ^""vE^-gj*1^ a m

rf- V a jf1')^^.^^'!^, ,J*zb'

...... "re.. &3X*w?7,i*fiM£w^

^mmwm

feaa

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, sesquialleray 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 :Lt. 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 ; 0 : 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.

i48

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

o I J J J I

(2) 0 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 0 . 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, 0 , 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 0 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

<t [H,2]

0 [111,2]

C3 [II, 3]

03 [HI, 3]

Actual
♦ I
[2, 2]

[2, j]

[3>J]

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 P1C

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

I52

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 sesquitertiay 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 61 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

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*

ggastpfligi

±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 perfectumy our explanations
concerning its rhythm may be illustrated by the following passage, from
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

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 0 ,
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 MuTy 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

jfe 4.iwrtlfrrt**i*tU^

Difouutu Integer

Diarinutus

^^1t^Q!J^pt^ty4::

Ptoporttenatus

!!l*'Ufl»."t*ii.«i«gJ

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

The sign \ indicates diminution in the ratio 5:1, so that 5 S of the pro-

Other Proportions

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

aifetejgjjfflifefe

§8

■ ■

ia^^"^^i

TENOR

g^jgjfflpfe

te$

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 Sy 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)

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 g2 is cancelled by the signa-
ture 12 (see DTB xvm, p. 154). It goes without saying that in this period the sign g2 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 .. ..

(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

i67

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 Ly 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 0 , 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
0 (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

■8

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:

* ♦

IIJ J

♦ ♦ ♦

IIJ J

j 1

♦ ♦

1(1)1 J.

0 ♦ ♦

I (1)1 J.

(t(C2)

1=1 W

fU J

WWW

IIJ J*

j 1

<t2((t Djw W

11 n

♦ ♦ ♦

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 0 ). 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 ^0

De tadice

IcfTc

propaginis

linis ma nu

Sol vcri Luminis

fapicnti*

*ft|jEl

tcmplum tern plum glo-- tue.

sfc * g B-fej^^r^r^rQjtyt *

Dc radicc Ic&e

propagini* jhanc cduxit

i^^^iBtk1B 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

Oil I
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.

335

S2SS

tndi^- 4. Wf Cc rvc *e m3V|cGm$ue

enov-. <un<an£-

"'"^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

0 03 c er © 02 ©3

e e
e 2e e 3e 3^e e

B = 6e 3e 6e

3e 2e 4e 2e 9e 9/2e 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

¥4=3

ggg= ^^^^^^^g

&**ttn« -wi-»v^ — *Kf**)

^wn-

" ^"fy'i fcf^ "f fry «»»•■>/

jg ^hl^^f «t |g§i J

m-r^H'S j

pp&

fc**Pu\J

h ji0h^\p

%%f

MS Oxford, Bodleian Library Canonici misc. 213 (ca. 1450)
Page 47

i78

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).

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 0 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&±>«-fe

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: *

gilig^^.lii^^^^1^

y^^^^^iJiUMm^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, A2, A3) and three
of B (Bi, B2, B3), which have to be read in the following order: Ai Bi A2
B2 A3 B3 . A2 and B3, both of which are in [2, 2], are composed of six im-
perfect By inclusive of the two 5-rests at the end. In A3 and B2 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 Ax 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 Obrechty
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:

SJdrdfio

fcltnf linr

t.,.LW...il^l»lliliMilii»ilillWli

^^^^^fa^^y
^^^^^^^^g.

iiiiii%iiHf|iin!miiA,i|ll"iif %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^v0"'

»*qH,0,i<K),..»c£e^j

For the Crucifixus of the mass, the same melody is used in sixfold
augmentation:

P ..w(_. I

C inciSnw

fai 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: /JOU9X> 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 0 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 diapentey 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, Sy 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 Tempo2

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 0 , 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 i7, 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. xixy 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

0 ^.m^f V 0

<£tt*S

^^»gNg.Ujj)| ..,=*£

w?*fcs)

p^'^ll,^

ggg:

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 0 . As has already been pointed out, this sign, if used as a
common time signature, always calls for ternary mensuration of the Bs 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 Sy 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.

i94

White Mensural Notation

b«n m# Ad U^jcmmt'^wV.

| -uu atH^UUa» i 0iiHi4rtHMMM^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

"Mr"

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:

0;(J:

C3:CI

144

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 (9th-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.

,Tw . , (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 (W2).
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, lt 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

ftf tnCCtyifn*' \ Vj

fl'einptthuT

ef U

iltffernpttmif' \

k
4;

trtffeirrptirwf

f>r vr

tffep»

i^S

/4 w
r

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 book1) 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^

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 faciendum1, 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 cheironomic1 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- 15I'/IS'2) maY 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

^t^tf

n^r

-a_JE^

\bwmtJHi»*~ja&^ —

T"?

■*-=*

1 « *******

^ill.

c, - ;

.f-f ,f5r

<* twrn-JL^iltwiv

*. • ^L_^ 2 3_

' ! ' -— - S

— =— XT- *-, . * ■■ C ^ —

*->

* _ - ^T £.

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*Jat

■ Sc 31

3i Si •» ■ _,

* \ :^ •• ^

■%aN. ♦

• V«.3rf

•Si

Al- - -

le- -

- - lu- - ia.

\\ Vo- - ca-

- - vit

j 1

a •

■ ■ 1

1 ■

1 PL ■

5 — J

1 g

1 Ik

■

■ ■* J I

t" \%

■ ■ ■

■ fmm

•Vr,]» j

■ -1 ■ r

* ' V *.

% a a % J

■V J^V

1 • a1 ,

■\3 ■

1 » ' •♦rk

Jhe-sus Ja- -

•• ' *

co- - bum,

■

• 1

■,

■

•

— — *-■ — $-

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.
2Cf. Handschin's measured transcription of a three-voice Congaudeant Catholici from the same
MS in ZfMW viii, 336.

Primitive Notation
Facsimile 45

213

fx jt - ^JjU.t 1 ' ! > yl^

-^r^

r^y^^l^^XX^

title

Jin y r-rj

T-r,

Iftr

-r^r

c-d&nr

t+Ji

H^t — ZJZ

■JH-fo

-f-

^•j'fo}

CA\ utc -— ^ tfv fttf U. co !n«rt

«-/W-:-t/

~ ... _. ~ 1 ■ " ~« ~l j "*"""? ^

v-^|.

-*n— ^-^— *~y*~

VVl. . , i rr

aB/

^3~E5

< tut: tc

^r:^tri:

«»f§(l ..f»j0*

&&*-*<*-& u* «*fcl

bo a'

' ^.7 fcr -*■**"

j^"^

*?'— 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

2I4

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 consonance1 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 Anonymous1 — 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,342.

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: WXi Fly fV2i 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: Quadratnotation1) 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 {Wx 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

y\)H *t 0 — 1 **~ ♦ 1 J.-— ^-77 **^—H

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. 64\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" Ju 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 iy273):

[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

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 Wx. In F and JV2 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> 233)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> and the second mode, 222. Here follows the transcription:

(3) Facsimile 47 (p. 233) contains an organum triplum Descendit de
celis from JV2. 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

11 imri

% •?* "V *:

■a ' "-; 3 ,ir ,;:

: ' r

2 iL =1 =rr 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: -rr ;Sr "j V sw *

;l -ri *i ;^ .. % ii ?- f

234 Square Notation

In Fly 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 {JVX 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 fry\
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\ByBBL\
L' — /. The first three ordines of the upper part are given in transcrip-

Extensio, Fractio Modi
Facsimile 48

239

^V^Ai

^rV^^:^^V^h,l

Twptir

Sj^^^feiS

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. 242.

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
semibrevesi 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 By 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 fVu 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 243

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 Sy 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 Wx (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,
t928).

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

246

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

im n&

ym^F!,&

• ^

^»

•*f-

;^=^g^^' W^/^y/«\^^

muf

^tx>

^"\.^ :V'^^Aw^^

♦— - — *-+

1 VT%/* ■ ■.',>■ 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>J7|J JlJr|JJiJr|

ia'i3 13 hbijij Jwju jyjyjg

'lc|j. J. |j. }. |J. J. |J. J. |J.J.Ij.).|

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^MSjgE

MS Paris, Bibliotheque Nationale lat. 15139 (T3th 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. 3Sy

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.

ffl7

^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:

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^

^%iyJv'^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 Dy 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 / + 2y
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 — Gaudebity 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

W7'*M>

.^VV^^M

a=a«

Sggplg gjj = A,, mi,;j1i/

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
Wiy 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 Ly 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 \ jj-jtzzzJA «Jii

< . 1 ■> /T?

acm flam lAnufr foe tn t&mfrtt toftftnutf aS

333 1 ' AiL^nj

S5tt

j^tiaurrtitnm\(UVft>wa*ttbia tat ttumiA

£ P Z1 »f *W^»±5

MS Wolfenbiittel, Herzogliche Bibliothek 6jjy 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:

/?>

/?\

firm3

/C\

1 -

I i

8
Hac in

an -

ja -

nu - a,

hoc

i I i

Ja"

nu -

- 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

J-3

J~H

jVj

JT1

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, i89fF)

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 omnesy in two versions, from
W\ (p. 71) and from the Codex Hue/gas (p. 97):

HP 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,IV'''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

1The most likely explanation of these terms is that per se means 'in two parts' (organum duplum) ,
cum alio, 'with a third part' (organum triplum).

2Judea 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.

3Anon. 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 longay 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 scholars1 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 (rV2)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.

4The 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

±3EZ£

HtJ:

^L.|L.LijLt:

-tie u &uu • to urn Aineta • lu tturaot &

-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?Tf

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

X=3t

"uai ♦ ^ cottns &MW - ctter or oai - ft own

.twrcBjonr cfmai • amcrfat qnen frra

— r O :> —

-Hv-.-4-

<fifr to ftnf qnc <ntf nuf Mejammt

p. ... ,Jl"»i*l/nA *»NAi til Jtrr^iflri"
1 fD \t*tt*1r*rrm- '^|jtttgil_JLk.l

fulfil**. , ,iL .

jtifftmw Citwi (tit (bttew"

•mcfcuctf Ctttttr. 5cy fw «t Iwtn tattr.

qiunr metct tie mtifenn -cnunr

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, W2) 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

:5i

? 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
motet1 — 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):

fto-UutC jwteGntftoUuC'ic nxtmw ttiAtvtttoiici mm*

*i g " ; 1 V

^^T^ll 1 1 * , , , , I

■hi

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 JV2
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

!■

life ira

3=r

■Hisa

o 0+

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 perfectumy 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 3Z~~

1 1 1

1 2 1

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 0 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

Ij|

II.

\n\3\

III.

\J2 . . . 2\

IV.

\22 ■ • ■ 3\

\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^ 239)

(He) Fifth: lJjJ.|J.|..|J.|J.|J.|..| 17 (e.g., nos. 23,

42, I35» 240

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 |sia-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 581 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:

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...-rIJJ|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 By the
other on a binary:

as ternary:

P'r

as binary:

£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
3s
°3

r- s

J J

JJ(JJ)

h '

J J

"4 J

^ Lf

(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
2s, 3s: lig. cum proprietate and sine perjectione
s2, sj: lig. sine proprietate and cum perjectione
°2y °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 s2 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 s2 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 2s = 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. 461

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 sj-ligatures,
to denote B LB (see the tenor Pro patribus). The tenor Optatur (p. 57')
reproduced below shows the use of s2 in the meaning of L B (the reverse
of 2) as well as that of js in the meaning of B B B. It may be noticed
that in Ba the shape of the s2 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 2s 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#i«

i^ — L " - |i - g . ~ zz

-en&'opBlatf

1 : jZPEi

IZt-tit

ntctagattt toutetna

g£^

EEJ^JSg

quat-neiuusttrnteirfijlas

4mittJ at uaiurt&crr

! cti

ncftula* y

ttuelSnta

UCtJjl&li

S=?

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 — %-

*♦

For a more detailed study of the MS the reader is referred to the above-
mentioned publication which also contains numerous transcriptions from
Wx 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"% ,■,!.»'

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 Bi 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

a -ji(W

■(&) ■«» B(b)

e2B

j(a) ■ (a)

°2

if V

value
B L
LL
BB
LB
S S

type

; X'

iwr

■(d) m& Kb)

S3S

J0) J(«

°3

; u*

taur

°3S

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.

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*, sjs)3 as well
as of ligatures cum opposita proprietate and sine perfectione ("Js).

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: sj 2 2 2 2 2 B ^33j(s4 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

v(U CO
5 ON

ft M

T3 bo

Examples
Facsimile 64

317

\ *

■ r S«

■"it

lit

(U (U
T3 bfl

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 Sy 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. jjjjjj i

(a) '

1 Jr 3 °^TtT

iOOOiu

,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

J>J

J- 3

JT3 or: JTJ

jttj

J li : or: J-J J-J

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

111

!,:

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' 3S 4S $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 narrative1 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
Sy 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

£tkml

F=F^g^

pv vvTuy'fj,

>', , '.♦i\

J>?*ft|iityftF

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

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.

328

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

i >

Ij i.fWi'i II -e flN^t

IE: 11

*-.*■-.?¥

fil

14
r

J I OKU

•f

.a 1
jJ, a . t

tLiJ

(».-.

5 J--IU :j

;

> ^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 — 0 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«ci>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 jpm1 itunt.n tut ^Itftauir iniWucf mrlinn* iuct.H-T.iCii iiiunirw

... ,. ...t-'1 ' " gg ' '«• ' ,'.':^r7T^T

<fi0rdcard(Rjtiui tuPV- cor Imnfe (ill JUj^Hnnry <ift. »x?in.i mt. 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-^. cM'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 *"uf*

*T^f t . #. jjjjgl 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** sf ♦ .
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 | || 0 |

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 [IIIy 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 By 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

1SeeHdNi, 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, 46, 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 Ly 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 Sy 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: ■ \ =FJ: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|cJ.|JJJ|iJ6JJ| .

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

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,^]):

waSBj

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

irr»w*te;

fc (cm /icwr nc Doufl Mop .^ Of
-n ton nc . , , T* *Un

gg§

en Twin awM^^Wewri^.wncitfqiufin; 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* \

sou -
cuer

- vent
en

ne vous voy.
♦

bonne foy.

■wit f4' 1 >. r r~ \f nr r irr r rip* rrj: 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,0 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

Ti.r,1i,,,T.,^>wrT>jV^

&%.

OJ-

d|n.frl ♦s*1

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

JllHTjpl|lJ'hli11iAl|blCLJ>il'fl1|^
flnomifl. Ccno? . ao tc ftjftmntmtg ymcmre ft watt -if.' vlifx funr

crftor • «r Rutec iiiqierfrnr Xnuu a «

jimvcrc . tt Bigg intjicrfrftt

flli I «. 01 m_ '

tus) includes six perfect Z,, equal to eighteen Bi 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:

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
l2> 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

till illn. j B ^"'jp.r E ,U'I il ■ 53 S&

*n in^pm- magiM gtanrnn ma

'■"V1* "".<*

*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.*

rrili.lT'lli:,ilHI.-vA„|,u,l-l,lir

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"iiii.jli4yjlkt^

tmitiw

I ni iot.1 p»rliwiniotin»rituiHiMiuni< tenmiiiVinirom iu|«trMD.>nm4

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 Ss My
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, prolatioy
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 signataey 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 Frenchman1 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

ternaria
3

divisio secunda:

quaternaria senaria imp.
4 6

senaria perf. novenaria
6 9

divisio tertia:

octonaria

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 ♦iitii-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 tiii-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 Tm .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

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

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 ;yl=!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»£

n "

<& ft--

e _:"

r^dir

r-u

1 _ -- s 1 _

fe .

: e- -=.

• |4::

. j£-*

■= z ;

-=g •

i= -- -

i -

-5

""/§ -In

Af*S «

bfl

■M

376 Italian Notation

position falls into two sections the first of which is obviously in octonaria.
Typical combinations are:

♦ru.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 61, 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

:\Wli/flir\;i lb."! 'fill Mill

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 Sy ♦ , 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

1 |MHiii|in mm

U>«iMK

* ! I Tl^f T T IT ! HI

■ nr riii 1 fat

in [|| |[ |||[ ih ,1,'"

llVTlUZH'lVUII

,liin^i,ilikpiigpi

* ** ■ iff II /

379

MS Paris, Bibliotheque Nationale ital. 568 (ca. 1400)
Page 138

38o

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

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 I1 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 quaternariay 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

C «
u ^

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

386

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

is--*—

ii —

^ 3

-=5

!" •

r?'<

-s?

*" *

-kr

= 2

j'S " :

■ $1*

e fe

1 ■

r « a

j- -V.

-Z

■ «H -3i

!• 1

-5

" 3 .

;=' 3 ^=

n. --:

.5^

=:r - = ?

§v| =

'- vP"i -

*- i

" ' if fB>

- ::i

111

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

II JTflfiTHffl

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

|XJ 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 ochiy 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

1? p*ntot*wfr 19 Iwcmafcjiifi

■f&

3zn:

a4«ffin<it;

Hfl^'iUil,,ll

re fc»u»t nt m»« 1 ill,, , **'• \ &

j_ji

cix

1 1 a wilt

•a

u«. Tt<r (unrthhc tatsatelfvoa u&<

i ■■a- ii7.»i:iT7v *n unpntKin a 5s: > ' ■: ■v:1 g w mm pgn r«H.i?

5 pnnss >r? n ( j ::t ri7">'"F

WtttH* U-ifefefe

ass

ytento Tionfara liitfwj ie»l fa

^tt

frpfTnhen pe.

US ♦

l^^g

buHtfo manca

*+4

'■Sr>tf«»i

*eTp^t ^' lofpT^r^ ntfty m w &c

■rur

^ * u-4

u<>

(n lEgkWta* fcft ^elfrW

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

>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):

XlfV w*»fwte t»ti -mAWui ^v"3^mi^m^

^mte

JHffl(l>i$ fWfc«|U<>T»wn»>u^}-

Hrr-T

t. *&£

VHt+

'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 • In 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#»Uil

325

bcmnoctc^t

*«a

t11***

av i e wo

p^^M«|lffP%

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 Sy 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 diminutumi 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)

3 M (82)
2M(F)
49 M (R)

'(A, L)

M
(W4)

§M

(87, wo

(WO

(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

against:

■ = 6M

♦

= 3M

| = 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

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

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 imperjectumy
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

a<A.1..l ."V.I i=F^

tv... ^y/Pfiy ■ '■> ,

:V"»a... j

■*J

-C" L» rcmirc din* »«<nlii

^^Nw,,.,1,;>^^^i^N«.i,1^

£tfn

^■f^ryfi

jgggg

J I j jmcljhOntea «mcnr~"fclrtwc»im\«-(«ni»'m«fiiie>

b • -y>g

* J ^f '

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: ^_^

3m«-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 WL^Li-^ Mtii.jJJi

fflonourqwcftUnncf ft *V t> \

wortourqmwUnwi ft no/

*2Elto»3

^A^tp^cpy^^ryr^^^l^

|lH>^^,.,"-,t>>,ro!v^vt-t^f|f|tf,),'(!)()()p

ft>llttllttll^,>FA^>^-lif^WB

j^.l|^l,»-1rT|llljg!^j^

mw**'*

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-

UiuMp'km^mmd

d tut Qen hi

^m4Vma.

i.-..i[„>tilli,il.ii|iii 1 HHa^

ffsfrrttltf*- "Vtft**

4AJ-4

/ r

Mv^

rfto* fpiir m«*n

I'icn cr im"i cpnfeii

«i^

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 ZQTZ1

♦ — ^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
Abgesang1 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<ctergesanges 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 tempusy 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

kjjk'%V'iLk- litis

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 :

rrlj.jj>trr,rnrr

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 61,' 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

■%fMilill EldES

i/.msAifiiiinii3«i.,inMnw!Mfiir

gijP}p

»Wy vn ''#

" JaS irjgtgt

JrVi, J«'#i

f My*

nfi^SUe<f<MSe« B^Sr

swama

iff

II J-

lAWkllt|HVWSi

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 ballade1 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 Sy 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)> and 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

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-lC/r.lJ)J.lrIJ^IrrrU..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:

lPP!Jjj!PP|swiJ-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.jPr jjuj. !r|J)JiP/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.i64ff).

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\ (orJ 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
t2> 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 prolationisy 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,232]

[3>j]b b, 2} dim*

[2,3]

[3, 2]*

3B = 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

3B = 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 4M 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 Sy 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 Sy 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
0 , 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 0 . 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 By 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 0 ,
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 'younger 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 {Moy 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 Ls
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 (tVh p. 73) r1

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 Wx (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 05 the values
under 0 (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 Chy 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.

Abgesang4i7

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 (Bay 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 *i33

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, *i3$

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, *39, 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,
*247, 267/, 27of, 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, *273,338
Chantilly, Musee Conde 1047 91, 164,

203, 404, *4i3, 425, *427
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, 432rF
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 *345, *349

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,

*293

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, *3o9; {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, I91, *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, 269f, 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,

*275, 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,

*l73, *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, *i84; (Di
dadi) *i84, *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,
*i4i, 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, 242f

Longa 87, 220, 261, 269

Ludwig, F. 100, 209, 217, 220, 224,

230, 245, 274, 284, 322, 325, 333,

346,354,355, 368,448
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, 3i9f, 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; 0 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, *i94; L. 568 203, 4o4f, *4u,
♦415, *423

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,
*29i, *293, 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,

i84,*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
0 dolce compagno *i43, 187
Old Hall MS 91, *i24, 362, 364ff, *2^

♦366, 432ff, 437
0 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, *n9, 123, *i4t, *i43, *i75,
*i77

Paix, Jacob 32

Paolo Tenorista 374, +394, 398, *399,
407, *409

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,

*329>*33i>448
Rome, Bibl. Vat.: Chigi cod. C. VIII

234 *l39, *i65; Rossi 215 203, 374,

382, *3«3
Rompeltier 154, * 155, * 193

Index

463

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)
*i85; (Fl) 237, *255, 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 (Wx) *235; (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)

*i24; {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 (Wx) 201, 217, *235,

♦236, *252, *259, *264, 446, *447;

1206 {W2) 201, 217, 231, *233, *275,

279, *28l
Wooldridge, H. E. 262

Zacharias, Magister 431
Zoppa, Alia 129

APPENDIX

TRANSCRIPTIONS

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No. £

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No. 3

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No. 4

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No. 15

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No. 16

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r» cKia-mat'i ahan qua

, k

11^1 — a

ios- to. Bo-cha ne-gra toy toy. bianco p«lo sta qui sta d7u-no eha moxaa mi-nw par

cfua con- p«q- ni qua cum 5 ran p!a- c«- r» ehia-nufi

No. 51

gf ,— ■

■fc

(Facsimile 77)

Qua-

■ . ^.

•>l

1'era scalzae

|L_ SJ_

piu rum v« dir qudn-to qtwl di mi piac-

No. 5:

(Facsimile 78)

Jf ^1

•»

—3

(

O.'

pron-

non

sa-

1 uom

> j1 y"**"

No. 53

(Facsimile 79)

n«-

1. Che s«'l a in se vo- 9h«

No. 54

(Facsimile 80)

lfo flp. — |r <|> c flTr

r.lr frrr^lftrrffr 1 ftf GIT CfT TrlrfT ^ — Pi
b b

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ir r \^M r ir if =i

fi/brfff Pdr *• If- r If ftyrfilf ftf rjr r r r r ^ IJ J

b b b

ft r"^1i ill f Hi i _ I llli_ m pf IP f\ pf

IF |»'

• »

1 — ~^ 1

-f-n — ^"K

1 D

-j f

No. 55

(Facsimile Si)

No. 56

(Facsimile 82)

No. 5-

(Facsimile 8j)

No. 58

(Facsimile 84)

1 — k — 1 n

JtTTT — if'ftr

} 1 J f)]

_^* '*c y —

|J- pJ' ',,'

[J- J.

_Mfc -— j-

fm fj »l ■>

■f fr|J' r

1 1 p —

f |» \u. ' |fr.

f] »•

# *

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;

B«l- i« bon-na so-
ft T

plai -

«ante «t

1 Ct'

U£*ft 1

i^L 1* * J

No. 63

(Page 431 Sumite karissimi)

(Page 432 Patrem omnipolentem)

f @ ^ M , . -

^g — s ==E=|' pf 3p=: — fe=ferpr^r i^~x' p p*Crf P* ?^fflf r/'

m »f»

crni

^w r 7

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

SPP ?(

NOV i? ii

>74

MAR 1 1 1£

A*'»7

b0d i i m

0 197

DEC x 9 --

JAM « g

.jsovYY

Library Bureau Cat. No. 1137

ML431.A61961

MUSIC

Ape,.w25002 00369 0190

The notation of polyphonic music, 900-16

431

T36T

AUTHOR

Apel

The Notation of Polyphonic Music,

DATE DUE

JUL

1 x 197 -

PEC 2 2 V1+fiA .<&^£tu/

—

OCT

BORROWERS NAME

9791V-

MUSK LIB

ML
431
A6
1961

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