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TENSION ENVELOPE CORP
1 1 H 1
IL2I
'. ] I**
L*
Iff ji.) v
C 9
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
Fourth edition
Revised and with Commentary
THE MEDIAEVAL ACADEMY OF AMERICA
CAMBRIDGE, MASSACHUSETTS
1949
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 Weyrnan Foundation of the Department of
Music of Harvard University.
Copyright by
THE MEDIAEVAL ACADEMY OF AMERICA
1942
Printed in U. $. A.
TO
ARCHIBALD T. DAVISON
Quid valet subtilitas
ubi perit utilitas.
Speculum Musicae.
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 1915:
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that a score of years has by no means outdated it or rendered it useless,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 y 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
vii
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 1 100
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 3 in particular, to their secretary, G. W. Cottrell Jr 5 for his active
interest and his most efficient handling of the many problems involved
in the preparation of the publication. I 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
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 careftil 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 Gustavfc 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 of polyphonic mu$ic>
85) a totalement fausse le probleme de la notation mensuraliste,' and that, in
the same writer's view, *La fausse perspective de Toiivrage4e M. Apel est encore
mise en evidence par Fordre antichronologique de ses demonstrations/ The
reader is warned.
W A
February 1949
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 ai
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, prolatio > and modus 96
B. Tempus imperfectum cum prolatione imperfecta . . 100
C. Tempus perfectum cum prolatione imperfecta . . . 107
Imperfection 107
Alteration 1*2
Punctus divisionis 1*5
D. Prolatio perjecta i-
E. Modus and maximodus 124
xi
xii Contents
Page
III. COLORATION ............. 126
A. Coloration In tempus imperfectum cum prolatione im-
perfecta ............ 127
B. Coloration in tempus perfectum cum prolatione im~
perfecta ............ 130
C. Coloration in prolatio perfecta ....... 136
D. Half-Coloration ........... 142
IV. PROPORTIONS ............. 145
A. History and Terminology ........ 145
B. Proportio dupla and tripla in General . . . . 148
C. Proportio dupla ........... 151
D. Proportio tripla ........... 155
E. Other Proportions .......... 157
Proportio quadrupla ......... 157
Proportio sesquialtera ........ 158
Proportio qulntupla y sesquitertia ..... 160
Successive Proportions ......... 161
F. Augmentation ........... 163
G. Examples ............ 168
H. Canons ............. 179
I. Proportional Time Signatures and Tempo . . . 188
PART III: THE NOTATION OF ENSEMBLE MUSIC:
BLACK NOTATION
I. INTRODUCTION ............ 199
II. PRIMITIVE NOTATION .......... 204
III. SQUARE* NOTATION ........... 215
A. General Characterization ........ 2ir
B. Modal Notation ......... ] 22O
The Rhythmic Modes ........ 22O
The Ligatures ......... i 223
Repeated Notes .....
Examples ........ , ... 230
Extensiomodi ....
Tn *"*
Fractio modi ..........
Conjuncture ........ ! ! 1 040
Consonance and Dissonance ...... 244
Contents xili
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
1X1
IV. PRE~FRANCONIAN NOTATION"
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 Fauvei 325
The Tenors; modus and maximodus .... 327
Red Notes 3 28
Notation of the Upper Parts 330
Semibreves signatae 33 2
Conjuncture*, and plica 333
Examples 334
VI. FRENCH NOTATION 338
A. The Innovations of the Ars Nova 33^
B. The Notation in the Works of Machaut .... 343
Imperfection and Alteration 344
Determination of the Mensuration .... 346
xiv Contents
Page
Ouverf and clos " 34^
Examples 352
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 370
Note Forms 371
C. Examples of Italian Notation 374
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 40^
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
1. Marcantonio da Bologna, Recerchari^ motetti^ canzonl . . . 5
2. Attaingnant, Vingt et six chansons musicaks 7
3. MS London, Br. Mus. Add. 29996 n
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. Bibl. F IX 22 (Kottcr) 29
10. MS St. Gall 3 Stiftsbibl!othekjjo (Sicher) 31
n. Bernhard Schmid, Tabulatur Buck 35
12. Vienna, Stb. Ms. 18491 (Regina Clara Im Hoff) .... 36
13. Bach, Orgelbiichlein, MS Berlin, Stb. P 283 39
14. Ileborgh tablature, Philadelphia, Curtis Institute . . . . 41
15. Conrad Paumann, Fundamentum^ MS Wenigerode Zb 14 . 45
1 6. Antonio Valente, Intavolatura de cimbalo 5 1
17. Antonio de Cabezon, Qbras de musica 53
1 8. Luys de Milan, Libro de musica . 57
19. Petrucci, Intabolatura de lautv 63
20. Denis Gaultier, La Rhetorique des dieux, Berlin, Kupferstich-
kabinett Ms. 142 73
21. Hans Judenkunig, Am schone . . . Underweisung ... 79
22. Hans Newsidler, Ein newgeordnet . . . Lautenbuch ... 81
23. Dufay, Qudjronte signorille (MS Oxford, Canon. 213) . . 103
24. Benet, Sanctus (Trent Codex 92} ........ 105
25. Dangler tu m'as tollu (Chansonnier Laborde) 109
26. Dufay, Ave regina (MS Oxford, Canon. 213} 119
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. dm. 3510) 13?
30. Ockeghem, Et resurrexit (MS Rome, Chigi cod. C. VIII,, 234) 139
31. Lan tins, Ce ieussefait (MS Oxford, Canon. 213) .... 141
32. Bartholomeus de Bononia, Vince con lena; dolce conpagno
(MS Oxford, Canon. 213} H3
xv
List of Facsimiles
Page
33. Tmctoris, Proportionate musices (MS Brussels) . . . . 153
34. Ockeghem, Kyrie (MS Rome, Chip cod. C. Fill, 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, Bibi Nat. lat. 3549} ... 211
45. Alleluia vocavit Jhesus (Codex Calixtinus) 213
46. Go; Flos jilius est (MS Florence, pluL 29.1) 229
47. Descendit de cells (MS Wolfenbiittd. 1206) 233
48. Instrumental dances (MS Brit. Mus. HarL 978) . . . . 239
49. Eenedicamus Domino (MS Florence, plut. 29.1) . . . . 247
50. (a) Scio cut credidi; (b) Alleluya (MS PariSj Bibi Nat. lot.
15139) 249
51. Various clausulae (MS Florence, plut. 29,1) 255
52. (a) Mulierum; (b) Domino (MS Florence, pluL 29*1) . . . 257
53. Hac in annijanua (MS Wolfenbiittd 6jf) ...... 259
54. Hui main-Hec dies; Uautre jor-Flos jilius (Chansonnier Roy,
Paris, Bibi. Nat. frf. 844) 273
55. 56. Laus Domino Eius; Homo quo vigeas Et gaudebit (MS
Wolfenbiittel 1206) 275,281
57. Candida virginitas Flos Jilius (MS Brit. Mus. Add. 30091) 285
58. Ave beatissima Ave Maria Johanne; Salve virgo Ave lux
Neuma (Codex Montpelller) 291
59. Diex je Amors qui ma Et super (Codex Montpellier) . . 293
60. Moutmefu Robins Portare (Codex Bamberg) . . . . 305
61. Hei diex Mai latus ? (MS Torino, Bibi. Reale 42) . . 307
62. Et in terra pax (Codex Huelgas) 309
63. Huic utHuic ut? (Codex Montpellier) 316
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) . . - 33 1
68. Machaut, Ne pens ez pas (MS Paris, B. N./rf. 1584) ... 353
69. Machaut, Dous amis (MS Paris, B. N./rf. 1584) . . . -357
List of Facsimiles xvii
Page
70. Machaut, Eiaute qui toutes (MS Paris, B. N./rf. 9221) , . 359
71. Kyrie (MS Cambrai, Bibl. Comm. M>. 6) 363
72. J. Tyes, / * A?m3 jp*# (Old Hall MS) 365
73. Jacopo da Bologna, AquiP altera; Fortune (MS Paris, B. N.
ital.s68) ,. .... .^ .... 375
74. Bartolinus de Padua, Perche can^ato (Codex Reina) . . . 377
75. Eenedicamus Domino (MS Paris, B. N. ital. $68) .... 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 Squarcialupl) 391
79. Landini, Nessun ponga (Codex Squarcialupi) 393
80. Paolo (tenorista), Benche partita (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 n'estes (Modena, BibL Est.
L.s<%} 4"
83. Je ne puts (Codex Chan tilly) 413
84. Anthonellus, Dame gentil (MS Modena, BibL Est. L. 568} . 415
85. Tout houme veut (MS Torino, BibL Naz. J II 9) . . . . 419
86. Eiaute parjaite (Codex Reina) 421
87. Jacopinus Selesses, En attendant (MS Modena^ BibL Est. L.
568) ^ 4^3
88. Baude Cordier, Belle bonne (Codex Chantilly) 427
AfMW
AEdM
AM
CS
DTOe
GdM
Gr. Rom.
GS
HdN
JJMW
Km. Jb.
MfM
MuT
OH
RHdM
SchT
SIMG
VfMW
ZfMW
ZIMG
a.p.a,
a.p.p
B
c.o.p.
D
F
L
M
I. BOOKS AND PERIODICALS
Archivfur Musikwissenschaft, Leipzig, 1918-1927.
G.KdltT ^Handbuch derMusikwissenschaft^ 2 vols., Berlin,, 1929.
Acta Musicologica^ Copenhagen, 1928-.
E. Coussemaker, Scriptorum de musica medii cevi nova series^
4 vols., Paris, 1864-1876.
Denkmaler der Tonkunst in Qesterreich, Leipzig, 1894-.
J. Wolf, Geschichte der Mensuralnotation^ 3 vols., Leipzig,
1904.
Graduale Romanae Ecclesiae, 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 fur Musikgeschichte, Berlin, 1869-1904.
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. i, Oxford,
1901.
H. Riemann, Handbuch der Musikgeschichte, 5 vols., Leipzig,
1904.
J. Wolf, Musikalische Schrifttafeln, Biickeburg, 1930.
Sammelbande der Internationalen Musikgeselhchafl^ Leipzig,
1899-1914.
Vierteljahrsschrift fur Musikwis sens chaff, Leipzig, 1884-1894.
Zeitschrift fur Musikwissenschaft, Leipzig, 1918-1935.
Zeitschrift der Internationalen Musikgesellschaft, Leipzig,
1899-1914.
II. TECHNICAL TERMS
MX
p.a.
a parte ante
a parte post
brevis
JL
cum opposita proprietate S
duplex longa Sf
fusa Sm
longa t
minima
mamma
punctus additionis
punctus divisionis
semibrevis
semifusa
semiminima
tactus
xvin
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.
xix
xx Introduction
Although there are certain ties of relationship which 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, Stimmbiicher). 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, Mtcrologus, 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 if.).
: Score-arrangement gave way to part-arrangement in the second quarter
of the thirteenth century (see Facsimiles jftff). 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
term's '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-
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-instrumentaF and, consequently, our
substituted dichotomy of soloist and ensemble, attain acute importance
(ca. 1250-1600), 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 (mensuralj notation (1250-1450) and that of
white (mensural) notation (1450-1600). 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 Musieological 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 FOiseau de Lyre, Paris, 1934), in which these
compositions are offered as organ music wilh pedals(!) and all manner of modern registration.
Introduction xxiii
1175-1225)5 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 Trench 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
partitura.
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
XXV
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PARTI
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, Recercharij Motetti,
Canzoni (Venice), a page of which is shown on Facsimile i. Two staves
of six lines each are used, the upper staff for the right hand, and the
lower staff for the left. From the standpoint of contemporary mensural
notation (see p. 85 ff) two features are particularly interesting since they
indicate an advance which was not reached in the writing down of
ensemble music until several decades later. These features are the bar-
line and the tie. As they are both employed in a very consistent and
logical manner, one might well conclude that various prior attempts in
this direction had been made (regarding bar-lines see p. 9).
The clef sign at the beginning of each staff indicates middle c (c 1 ).
The mordent-like sign at the end of the staff is the custos (guardian, also
called 'direct') which refers the player to the first note of the same part
in the next staff. The note-values are: brevis (5), semibrevis (), minima
(M) 3 semiminima (Sm) y 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.
B S M Sm F Sf
Old form of notes: 2 lilt
Modern form of notes: w) J J J^ J*
Old form of rests: i z: ZL IE 31 ZL
Modem form of rests: x ^ ~ ^ y *?
Each note (or rest) Is equal to two, and only two, notes (or rests) of
the next smaller value. This is another progressive feature of keyboard
and lute notation in contrast to contemporary mensural notation, in
which a note was equal to two or to three notes of the lower grade, ac-
cording to the 'mensuration' (perfect or imperfect, see p. 96). The
1 The abbreviations: B (brevis), S (semibrevis) , M (minima), Sm (semiminima), F (fusa), and Sf
(semifusa) will be used throughout the book.
8 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 al.
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 m 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. i. An inter-
esting feature of the piece is the 'Freistimmigkeit' (cf. four voices in meas. 4, 5; three in
meas. i, 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 152.9-30. Facsimile 2 is taken from one of these
books, Quatorze gaillardes y neuf pavanes, sept brunles et deux basses danses %
k tout reduit de musique en la tabulature de jeu d* argues . . . (Paris,
1530).
Keyboard Scores
FACSIMILE I
JJ
i-
2IL,
f
cj
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1
tt
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15
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i O
*s
O
4-J
c
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cct
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 100 years later that this method
became generally accepted. The notes of smaller value are slightly
different from those of Marcan tonic's book. The Sm does not appear
here as a blackened M, but as a white M with a flag, . Accordingly,
the F appears as a white note with two flags s , whereas the Sf is a
blackened F, I 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
che signature, as is illustrated by the following two examples (in example
b, the dot belongs to the higher, not me lower note) 1 :
not =
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 i).
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, Accldentun und Tonality Strassburg,' 1937, p. 49 (examples 146, 148).
Keyboard Scores
FACSIMILE 2
8
1
E-E
$4=$=%
Attaingnant, ^uatorze 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. 2. 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. 1520-1560) and that of the
virginalists (ca. 1570-1620). 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. 30513, Mulliner Book (circa 1560)
Among the composers are: Hugh Aston (1480?-! 522), John Red ford
(i4 9 i?-i543?), William Blitheman (?-i59i), 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 Tui 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.
'The practice of notating all the parts of a piece on one single staff should not be confused with
a method widely used in early music (prior to 1250; see Facsimile 53 and Coussemaker. Histoir, de
Lharmoms au moyen-a^ Pans, 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 star? 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 fe.g., Sebastian Virdung, Musica getutscfo, Basel, 1511), 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 tabkture (see p. 40 ff, Facsimile 14), and in the tablature of Wolf-
gang Neuhaus (see p. 40). See also HdN LI, 259.
Keyboard Scores g
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 (IL
versus] serves as an example. Here, as in many cases of manuscript
music, the chief difficulty lies in the obscurity of the handwriting rather
than in the intrinsic problems of notation. The clefs are those of
modern practice, namely the G-clef in the upper staff, the F-clef in the
lower one. The G-clef is a G with a loop added whereas the F-clef is
a sort of C followed by a sign which looks like two minims turned head
to head. This shape is explained as a gradual transformation of the
letter F. Here follow certain of the main forms of the F-clef, in chrono-
logical order 1 :
It should be noted that, in all these shapes, the note f is on the middle line of the staff
although with the first three characters the dots or strokes appear a semitone higher
than with the other, more recent ones.
The signs above and beneath the clefs are flats (B-flat). For the
transcription, a reduction i :2 (M = quarter-note) appears to be appro-
priate. The system of barring depends upon whether \- or |-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 $, thus leading to a cadential
1 See the Facsimiles nbs. 44 (twelfth century); 49, 50, 64 (thirteenth century); 73, 74 (fourteenth
century); 31, 33 (fifteenth century); 27, 35 (sixteenth century). Examples of the C-cief 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 f or \. 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 Mon b, or else the S should
be dotted.
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
froprietale, which is characterized by an upward dash to the left side of
the first note. Such a ligature embraces two notes which appear either
in form of two adjoining squares or that of a diagonal body (ligatura
obliqua) the beginning and end of which determines the two notes it
represents. The value of these two notes is always an S each:
A third peculiarity of English keyboard notation is the use of blackened
notes. For certain purposes, which will be explained later, the white
B, S and M were replaced by others which show black heads, a change
which was referred to as coloration or blackening. Special forms were
used for the 'blackened' Sm:
B S M Sm
normal: p o ^ i
blackened: | ty
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 *y 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
ii
MS London., British Museum Add. 29996 (ca 1540)
~
12
The Notation of Soloist Music
mark off a middle voice from the neighboring ones. An example of this
practice is to be found in the Sahator withe a meane from the Mulliner
Book (Facsimile 4). Here the middle voice is written in blackened notes
which have the same value as the corresponding white notes. More-
over, the middle voice is parcelled out between the upper and lower
staves,, indicating whether it is to be played with the right or with the
left hand. Why this blackening of the middle part was used in some
pieces, and not in others, is a difficult question to answer. In the present
instance, one might suppose that it has some connection with the expres-
sion 'meane' of the caption, a term which, in all probability indicates a
middle part of special importance, perhaps a cantus firmus. 1 Still, such
coincidence is not present in every case.
More interesting, but more difficult also, is the use of coloration for
another purpose, that is, the introduction of ternary rhythm. In this
function, coloration represents an important feature of mensural nota-
tion and will be explained later in detail (see p. 126 IF). 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: i-^;*-|* . Therefore, a blackened S and M together equal
a white S, and so do three blackened M: ^i = ^ ; |j| = <> . 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) :
M 3
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 |-meter. However, the latter value is also 'indicated by a dotted
black S (beginning of the 6th staff). The sign .32. at the beginning
1 Cf. C. Pfatteicher, John Redford, Kassel, 1934, pp. 63-65
Keyboard Scores
FACSIMILE 4
13
1
vcH>
I
I I I I I ill.
y- '
^
Mulliner Book
MS London^ British Museum Add. 30513 (fa. 1560)
From page 47'
FACSIMILE 5
a
"ff 1
MS London, British Museum ^^. ^999^ (^. 1540)
From page 9'
14 The Notation of Soloist Music
means 'three against two' (proportio sesquialtera), 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 f-measures are replaced by one l-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 f-rneasure) is formed by the initial black
M and the final black S; however, these two notes are separated by five white S in the
value of a dotted half-note each. See the transcription in the appendix, No. 4.
Let the foregoing suffice to show the beginnings of that musical nota-
tion which today has the most extended usage, and which is now the
only one employed for keyboard music. To be sure, its further develop-
ment and eventual universal acceptance were not achieved immediately.
The keyboard score found least objection in England, where it became,
in the hands of the virginajists, a convenient means of notating music
composed in an idiomatic keyboard style. It was retained in France
and Italy, though a rival appeared in the form of the keyboard partitura,
which, because of ease of polyphonic reading, was frequently preferred
around 1600, especially for works in a contrapuntal style, such as can-
zonas, ricercares, etc. Germany, on the other hand, was the last country
to adopt the keyboard score. Joh. Ulrich Steigleder's Ricercar Tabu-
latura 1 of 1624 appears to be the earliest German example of this nota-
tion. In southern Germany, because of the Italian and French influence
which prevailed there, this manner of writing quickly became established
in general usage. In northern and central Germany, however, even to
the end of the seventeenth century, the organ composers remained true
to the national method of notation, the German organ tablature (see
p. 21 ff). Not until the beginning of the eighteenth century, after the
decline of the great north-German tradition in organ music, and the rise
of the musical rococo (Mattheson, Telemann) was the keyboard score
universally accepted in northern Germany.
The notation on two staves was called in Italy 'intavolatura/ a name
which occurs already in the second-oldest source of Italian organ music,
that is, the Intawlatura doe 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
l The only extant copy of this publication, for which Steigleder himself engraved the copper
plate*, 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. Wolfs Handbuch der Nota-
tionskunde (HdN), n, 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 n, 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.,
6 I 95 etc - ^ n 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
KlavSertabulaturen' is made, it should include German publications
(Pachelbel, Froberger) which appear elsewhere in Wolfs list. The name
'Deutsche Klaviertabulaturen' should not be confused with the name
'Deutsche Orgeltabulaturen/ which indicates an entirely different sys-
tem of notation (HdN n, 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
Partitttra (di canzone) or (Canzone) spartiti; while titles like Intavolatura
(di cembalo) or (Toccate) intawlate 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: || . The sharps appear in a
diagonal position (see tenor, second measure, second note).
As in Attaingnant's publication (p. 6), the notes within a measure are written here
without regard of their vertical coincidence, in order to save space. The bar-lines
(which are omitted at the beginning and at the end of the staff) mark off groups of two,
three or four S. Since a transcription without reduction appears to be musically cor-
rect, each bar of the original divides into several measures in the modern writing. In
the last bar, the altus seems to be too short, since there are only three S as against four
in the other voices. However, from the standpoint of early notation the writing is cor-
rect, since the missing S is supplied by a part of the final L which, therefore, sounds
ahead of the L of the other voices. See appendix, No. 5.
Of particular interest is the absence of sharps in various passages
such as the third bar of the original which, from the point of view of
nineteenth century tonality, would seem to call for a sharped F. Cases
of this sort which, as is well-known, abound in early music, raise the
question as to the necessity or justification of the 'editorial accidentals'
which appear no less abundantly in many modern editions of early
music. A thorough discussion of the problem of accidentals or, as it is
frequently called, of musica ficta, would far exceed the limitations of
this book. Instead, another approach to this important matter has been
adopted, that is, short discussions of the special cases arising with the
various musical illustrations to be considered. Only this much need be
said in general: the generosity with which editorial accidentals have been
inserted in most modern editions of early music far exceeds what can be
supported and justified by scholarly evidence. Preferences created by
16
Keyboard Partituras
FACSIMILE 6
17
is
fe
^
S
cs
o
jg 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 modem 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
*See, for instance, D. Plamenac, Johannes Ockeghem, Samtluhe Werke, Messen I- Fill, p. xv;
L. Ellin wood, The Works of Francesco Landing Cambridge, 1939, p. xlii.
2 See W. Apel, Accidentien und TonaUtat^ pp. 29, 43.
8 For a discussion of these works, see W. Apel, 'Neapolitan Links between Cabezon and Fresco-
baldi' (M%, 1938).
keyboard Partituras 19
The earliest documents of keyboard partitura 1 are certain Italian
publications of the late sixteenth century, for instance: 2
1577: Cipriano de Rore, Tutti i madrigali . . . a quattro voci spartiti et
accomodati -per sonar d'ogni sorte 96); Hucbald (GS i, 118); Bernelinus, (GS i, 326).
IV: Oddo of Chmy (GS i, 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: t (b molle) for the B-flat, and square: L (b quadratum) for
the B-natural. In later usage, the square b assumed the following
shape: \\ , and was, especially in Germany, falsely identified with the
1 Letters were also used in Greek notation; see HdNi, 16 ff.
21
22 The Notation of Soloist Music
letter h, the round form being called simply: b. This nomenclature and
manner of writing, i.e., h for B-natural and b for B-flat, is found in all
German tablatures and persists to the present day in Germany. It may
be noticed that another variant of the square b lead to the sign t| 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 tablatures 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),* where it was adopted exclusively for the writing down
of keyboard music until Scheldt'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
tablatures. 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.
i. 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 hands chriftliche Uebcrliefcrung der altesten Instrumentalmunk^ Bonn, 1931;
W. Apel, 'Early German Keyboard Music' (M^ 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
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 15ne 3 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: Hjj* , 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: Xjl (cf. the first measure), the last note is
not a Sm, but a M, the whole group being equal to: Sm, Sm y 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: t 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-
menium sive ratio vera y l ca. 1520) is called a mordent. It may be
transcribed by our modern sign of the simple shake i**, although its
execution was probably somewhat different. According to Buchner 5
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: f
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:
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 VJUW v; see also E. V. Werra, in Km. Jb. 1895, and W. Nagel in MfM xxin.
German Keyboard Tablatures
FACSIMILE 7
-rrr
f ++9Te#+f & \\k
1 ' Vi \\J
^
rf^**
t i t i
~ "
?
I ' i !
i
P
^tt
PP
f.
Buxheimer Orgelbuch
MS Munich, Staatsbibliothek Mus. Ms. 3725 (ca. 1460)
Page 6 1
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 iise 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
\ h h
For the transcription (see appendix, No. 6), a reduction 1 14. 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-naturai
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 Tabulaturen etlicher Lobgesang und Lidlein uff die Orgeln
und Lauten (Mainz, 1512). Except for a single musical illustration
contained in Sebastian Virdung's Musica getutscht of 150, 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
A * !
Chromatic alterations are indicated by a small loop attached to the
note (of. the sixth note of the example),
In the letter-notation, tones of the great octave (below c) are desig-
nated by a horizontal dash beneath the letter a. It is probably from
German Keyboard Tablatures
FACSIMILE 8
%J
it
X
, iv,
-40
40
40
to
-10
h
-
* iu H
4 , ja -t
<:i
01
' tOi "
- lu
-_D
VT)
K4
E^
. a h
I^u ^T
-0i ^
O)
H
c
a8 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 3 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 Crests affixed to a fragment of a staff 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 0. 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 1513 (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
1 In modern usage, the term contra-octave signifies the octave below the great octave.
2 Or%el und Klavier im 16. Jahrhundert, Leipzig, 1910, p. 190.
* The inscription reads: Anabole (Greek, prelude) inja, 7(haimes)
German Keyboard Tablatures
FACSIMILE 9
-M
w
u
whereas its actual value is only M + F. The whole piece is reproduced in W. Apel,
Musik ausfruher Zeit, vol. i (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. Z26}i
F G A B H c c# d d$ 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 u,
26 and in SchT, p. 16.
German Keyboard Tablatures
^^^s*fWSES
V &L LFI y S fifft&'w !ir~*'* %&
H- -& -jHf 9* f/~ fW^-V rt ^ ^^^ *^
VF ff
J^^^
"7^7
'MI* YI ~wJn
~2~V~" ten w ^ j 1^
^>
err
wr
r T/
- CC
prp
~&~
TV*
F~
, r
r _ _ __ _ jfifrfi f7 *rv >**t3^
/>r ^^* pT^r- /^- ^rSF ^r~ ij^r ^^ K*|v^i-*o
j 7 o 1**^* ^f^> IV ^* fif/^ f 9 ^ JF? f^< J-i-*~*"*<*i *
^'v XE nr- *% * r" -/CAv- -/r- /^- .* j
^jzi/tf" fiy ft jftoittoitr-ftf-
? <*' J *< !*'**' *
rr
&
F
i?>-
ff
\rr rr
r
5f
MS St. Gall,.Stiftsbibliothek5JO (*.
Page 10
32 The Notation of Soloist Music
A page from Fridolin Sicher's tablature of about 1525 (Library of the
Monastery St. Gall, 5J0 1 ), written in more hasty characters, may serve
as a final illustration of the old German keyboard tablature (Facsimile
10). It contains an In dulci jubilo, and the beginning of a ResoneL A
peculiarity of this tablature is the writing of the rhythm JJ in this
manner VJ" 3 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
~Friihmeister 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 n, 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. GaTier Organist Fridolin Sicher und seine Orgeltabulatur' (Schweizerisches
Jahrbiich/ur Musikwissemchaft, vn, 1938).
2 Qrgelbuchhin (Berlin, Staatsbibliothek, Mus. Ms. P 2#j), pp. 9, 17, 22, 26, 30; see Facsimile
German Keyboard Tablatures 33
a rather confusing variety of rhythmical signs (see the explanations in
HdN n, 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 S 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 S/
mensural notation (figure de musicd] : $ I j J |
tablature (figure de sonator'i] : I f f* p ^
The Italian names are those of Don Bartolomeo Lieto's Dialogo quarto di mmica y icco;
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 14 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
J For instance, W. Merian in: Der Tanz in den deutschen Tabulaturbuchern^ Leipzig, 1927.
34
The Notation of Soloist Music
values are combined in fence-like drawings similar to those of the tabla-
ture of Kotter (Facsimile 9). Likewise, the lines indicating higher oc-
taves are drawn as uninterrupted horizontal strokes for an entire group of
notes: a g f e (end of the first line). If, in such a group, some notes
belong to the two-line octave, separate dashes are added on top of the
long dash: c b a g. Note that the letter c has the shape of the modern
letter r (see the explanations on seventeenth century French lute tabla-
tures 3 pp. 7i 3 72). Apparently, the one-line octave begins here with
the letter h, not c 5 as appears from a consideration of the bass line at
the top of the page.
The pieces on this page 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 GaMeli, et di Gio: suo mpote* 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 transpodtus per quintain superiorem (the first C-sharp on the page cor-
responding to the G-sharp at the beginning of the fourth column). Of particular interest
Is the dash 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 Intonazzoni contained in L. Torchi's UArt musicals in Italia^ vol. m, p. 131 ff.
Torchi and many other writers ascribe these pieces to Giovanni Gabriel!, whereas B,
Schmidt names Andrea Gabriel! 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 Jungfmu Regina Clara 1m
Hof (Vienna, Staatsbibliothek Ms. 18491) of 1629, serves as an example: 1
419**
In both pieces of our facsimile (FilBs sass m tinen Botgen, and Falscher Schaffer ist das
reckf) the number of voices alternates between three and four, in a manner characteristic
1 Compare these characters witli thosrof Kkber's tablature, p. 30.
German Keyboard Tablatures
FACSIMILE n
35
TT
ffTT 5
. " .
o
^
m
_
Num. 4.
Secund? To
fittvperquin
tamfupcrio-
u
J
3C
7
T_ _ r
7 ]'] f'
J.
T
T
*
J
T
A
Bernhard Schmid, Tabulatur Buck von allerhand . . . Praeludiis> Toccaten,
Motteten^ Camonetten, Madrigalien und Fugen. Strassburg 5 1607
From folio A F
The Notation of Soloist Music
FACSIMILE 12
____
'' /C y
r
cfe
A-''
^ &
*
~3r r
? J T ** <* * -f =T*y X- <*
^ , z rl x> "T
^ ^%
^'
f
*'
f
/ 1
"-"^ ^ ^ "7 s
*-* **
4 f
* a 4 * <\
5"^ 7^Z
I !
^ S ^
... i 7*^ ^1*<
y
Klayierbuch 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 Orgelbiichlein 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 less 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. 28530 (Robertsbridge Codex). The upper voice
of the two- voiced composition (an instrumental estampie, not a prelude;
cf. the erroneous designation in Frotscher, Geschichle des Orgehpiels
[Berlin, 1935], I, 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 Music
iogical obscurities of the original, there follows a transliteration of the
first line.
I 3 asasaagaf g^ agf
Peirone. primus puncju&.
cu&. \ , ,
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 \ (modus perfectus). The smaller
values are combined in groups equalling a brevis and marked off from
one another by dots (punctus divisionis). Rhythmical differentiations
within such a group are obtained by the use of stemmed semibreves.
The S with a downward stem is half of a B; the plain S is half of a B
or a quarter of a B depending upon whether there are two or four such
notes in a group; the S with an upward stem (minima) is one-eighth of
a B. The small circles on top of the first two S are probably orna-
German Keyboard Tablatures
FACSIMILE 13
39
4 o
The Notation of Soloist Music
merits (mordent?). The white B would seem to indicate prolongation
of the preceding black 5.
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
j-n j 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
1. Tablature of Ludolf Wilkin, 1432 (Berlin, Staatsbibliothek, theoL lat.
quart. 2gd)
2. 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 organlsandi magistn 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 jnodum
1 For further studies of this MS see the facsimiles in H. E. Wooldridge, Early English Harmony,
London, 1897, i, pi. 4 2 ~45> a well as the transcriptions and explanations by J. Wolf (Kirchen-
musikatisches Jahrbuch, 1899; AfMW i; GdM i, 357; GdM in, no. 78; HdN n, 5) and J. Handschin
(ZJMW xn, xm). The primus punctus of the above piece is also contained in W. Apel, Musik aus
fruher Zeit, n. The transcription in Early English Harmony, n, 1913 (H. V. Hughes) contains
numerous errors.
2 Literature (a) general; L. Schrade, Die altesten Denkmaler der Orgelmus'ik, Miinster, 1928; W.
Apel, 'Early German Keyboard Music r (M^ xxin). (b) Special: W. Apel, 'Die Tabulator des
Adam Ileborgh' (ZfMW xvi); F. Feldmann, Ein Tabulaturfragment des Bresiauer Dominikaner-
klosters' (ZfMIPxv); F. W. Arnold andL. BeUermann, 'Das Lochamer Liederbuch . .' (JfMfTn);
K. Ameln, Locheimer Liederbuch und Fundamentum organlsandi y Berlin, 1925 (facsimile edition).
German Keyboard Tablatures,
FACSIMILE 14
Tablature of Adam Ileborgh (1448)
Philadelphia, The Curtis Institute of Music
Page i
4 2 The Notation of Soloist Music
subtiliter et diligenter collecta cum mensuris diversis hie inferius annexls 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., I . 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 modurn 7 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 longa^ a brews or a semibrems^ 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 i, pp. 298, 306, 327, 352, 354; HdN i, 313. See p. 405 of the present book.
2 See W. Apel, 'Die Tabulator des Adam Ileborgh' (ZfMW xvi), p. 193.
German Keyboard TaUatures 43
difficulty. If one tries to play them together with the corresponding
tones of the upper voice, he will easily see that the resulting two-part
composition does not make sense. Especially strange is the fact that
the last note of the lower voice should be g which fits very poorly with
the C-tonality of the whole piece. The solution of the puzzle lies in
the fact that two successive letters always are to be played simultane-
ously in pairs, as if they were arranged vertically,, instead of horizontally*
Thus, the single row of letters actually represents two voices:
This curious manner of writing loses its apparent oddity and becomes
logical and plausible if perceived as an expression of a special technique,
i.e., of the double pedal The letters, then, indicate tones to be played
on the pedal 1 in such a way that, with each pair, the first one is to be
played with the left foot and the second with the right foot. A tran-
scription of this preamble follows: 2
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 pedals sive manu&le.
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 Geschichte der Fruhrenaissance, Leipzig, 1914, p.
144 &
2 See the article in JVfj xxm, 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 SchTy 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 v 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 Magistri Conradi Paumanni Ceci de
Nuerenberga Anno 1542 (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. 1 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 | , known to us from the Ileborgh tablature,
occurs frequently in the Fundamentum y 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 9 p. 97.
2 J. Wolfs remarks about the chromatic alterations in the Fundamentum (HdN n> 15) are some-
what obscure, particularly the statement: 'Merkwurdigerweise gewinnt er den Ton b ebenfalls als
Kreuzton von der Stufe h aus.' The inherent contradiction of this remark results from Wolfs
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 Wolfs book (p. 14, Des Kla/ers
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 i6th cen-
tury music.
German Keyboard Tablatures
FACSIMILE 15
45"
c*
CD
I
CO
W
c
(5
*u
O
1
I
DH
5
U
4 6 The Notation of Soloist Music
rhythm: l|44 = J-J . Occasionally, (for instance, on p. 79, st. 5, meas.
2 of the facsimile edition) it follows upon a Si J*l which this combination represents, is a modification of
what originally was a triplet rhythm: *i- o_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 8892 are insertions of a later band) the forms f
and t occur repeatedly, probably with the meaning of an ornament
(mordent). 2
1 See the explanations and transcriptions in JJMW n and in HdN n, 13.
2 The ornamentations in the Fundamentum are explained by J. Wolf as follows (HdN n, 16):
*Nur als Verzierungen sind die Formen A und i zu deuten. Vielleicht verbirgt sich hinter ihnen
hannonicus 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
Wolfs 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 vertical dash
indicating the higher octave appears frequently in the form of a scroll
reminiscent of the modern sign for the mordent. The metrical values
of the letters are indicated by small red notes wherever deemed advisable
for clarity's sake.
Facsimile 15 shows a two-part composition Ellend du hast (Misery,
thou hast), a section of which, beginning with measure 6 of the third
brace, is transcribed in the appendix, No. 8.
The piece contains various clerical errors, particularly in the upper part, some of
which are obvious whereas others require conjecture. In measure four of the fourth
brace we suggest changing the second note to an M y and the last note to an S y 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.
B. SPANISH KEYBOARD TABLATURES
The scarcity of documents , on Spanish keyboard music of the
sixteenth century 3 makes it difficult to investigate the early history
of notation in that country. It is not unlikely that Spanish composers
of organ music prior to 1550 employed a notation similar to that of the
Italian keyboard score. At any rate, shortly after 1550 various attempts
were made to introduce a national notation based entirely on figures.
The Spanish theorist Bermudo, in his Dec/aracion de instrumentos musi-
cales (Ossuna, 1555)3 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 I 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 Accidentun und Tonalitat^ p. 23.
2 See W. Apel, 'Du Nouveau sur la musique Franchise pour orgue au xvie siecle' (La Revue
Musicals xvni, 97).
3 For a survey of sixteenth century Spanish organ and lute music see W. Apel, 'Early Spanish
Keyboard and Lute Music" (Mj-Jxx).
4 Cf. O. Kinkeldey, Orgel und Klavier im 16. Jahrhundert t 1912, p. 20.
48 The Notation of Soloist Music
His figures then represent these tones:
123456789 10
CFDGEABbBccft
ii 12 13 14 15 16 17 18 . . 30 . .
d eb e f fft g g# a .. a' ..
42
a' 7
In applying this material to actual compositions, Bermudo uses a
staff 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 Bermuda's
example:
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 n, 266)