The harmonic effect of mediaeval polyphony; a study of vocal compositions for two and three voices

Item Type text; Thesis-Reproduction (electronic)

Authors Hollis, Esther Rasche, 1913-

Publisher The University of Arizona.

Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.

Download date 25/09/2021 20:53:17

Link to Item http://hdl.handle.net/10150/553501 THE HARMONIC EFFECT OF MEDIAEVAL POLYPHONY

A STUDY OF VOCAL COMPOSITIONS

FOR TWO AND THREE VOICES

by

Esther Hollis

A T h e s is submitted to the faculty of the

Department of Music

in partial fulfillm ent of

the requirements for the degree of

Master of Music

in the Graduate College

University of Arizona

1940

A pproved: Director of Thesis D ate Z ^ e n r t " / 9 y a

2~ TABLE OF CONTENTS Page

Introduction ...... 1 Contemporary Theory (1100 A. D. • 1300 A. D •)...... 6

Analysis of Two Part Com positions ...... 9 Summary of Analyses of Two Part Compositions ...... 22

Analysis of Three Part Compositions ...... 27

Summary of Analyses of Three Part Com positions ...... 37

Conclusion ...... 40

Bibliography

k 'u eic

Two P a r t C o m p o s itio n s ...... 43

Three Part Compositions ...... 44

b General References ...... 45

13U7.il - 1-

INTRCDUCTICK

An Inquiry Into the musical thought of tte ^alSSle ages necessarily Involves some conjecture and speculation. The passing of centuries has sot up Inmanerable barriers, not

only to the translation of dead music Into modern symbols, but more especially to the Interpretation m 2 understanding

of that music as an emotional and artistic expression. It is difficult, if not impossible, to discard the rich and varied

tonal experience of succeeding centuries when listening to

the minimum of tonal m aterials employed In mediaeval music*

It Is difficult to forget, even momentarily, the conventions

of modem musical thought when listening to'an Immature music

obviously composed with a different esthetic. It is not the

purpose of this thesis to demonstrate either artistic merit

or emotional significance but to study objectively the harmonic

effects of certain representative specimens of mediaeval vocal

polyphony, assuming that the aural experience of such harmonic

effects, even though unrecognized as such, was a necessary

preliminary to the harmonic accomplishments of later periods.

The m aterials used as the basis of this study are the

compositions for two and three voice parts reproduced as

facsim iles and translated in E. de Coussemaber"s Hiatolre de

1 "Harmonle au Woven Age. ( See bibliography of music•) Certain

other sources of aural experience prior to the development of

polyphony in the tw elfth and thirteenth centuries, which^

though not in themselves giving rise to any notable develop! ments in the recorded history of harmony, have contributed to the total background of musical experience from which

the harmonic consciousness emerged # These may bo summarized briefly as follows! 1* Sounds of man's natural environment distinguishable

from noise • 2 * Overtones of a single instrumental note, 3 * Harmonic instruments (magadis)* 4. Vocal phenomena" price' :to the development of poly­ phony in the tw elfth and thirteenth centuries*

While many of the sotmds known to prehistoric man were

hardly distinguishable from nolee, other sounds of his natural environment were a direct source of Inspiration and object of

imitation for his untutored artistic impulse, which, even in

paleolithic times, had manifested itself In the invention of

instrum ents.

Prehistoric man listened to the wind vibrating through

the dried river reeds and conceived the syrinx, or flute, the

archetype of all wind instruments. The warrior warded off his

enemy’s blow with a shield made of dried animal skins stretched

tautly over a wooden frame, and heard the first rudimentary

drum beat. The huntsman let fly an arrow and heard the musi­

cal twang of his bow string, the predecessor of harp, lute and psaltery, and of all plucked, stringed instruments A

GeOLpin, F r a n c i s W. A Textbook of European Musical Instrum ents. Dutton & Co., N* Y« 1937 p» 37 - 3-

Every note sounded upon these first imperfeot instrwm nts contained within itself a harmony of overtones, even as do notes sounded upon our present, improved instruments# Whether or not the prehistoric man or the musician of late antiquity ever consciously perceived the component parte of a single instrumental note, is not known# There is no evidence suf­ ficient to prove that early musicians listened with the interest and Intensity necessary to perceive the faint harmony of over­ tones# It is possible, however, to cite as evidence the re­ presentations in ancient bas-relief and frescoes of various instruments being played simultaneously.

"The early musicians were not at all times intent upon the mere design which the plucked strings of their kit haras, harps or psalteries, or the long-drawn notes of their reed-pipes, wove rhythmically into melodies# As the finger plucked the string or the performer's breath thrilled through the tiny mouthpiece into the reed-pipe, a mass-chord of harmonic overtones rang out, f oil owed by the natural polyphony due to the pi ay of harmonies in varying rhythms and intensities • • . "1

Some contemporary m usic-historians have attempted a schematic explanation of the evolution of harmony, based upon the theory that all harmonic m aterials have been derived from the overt one a or parti ale of a single note. Superficially, there seems to be considerable favorable evidence. The first recorded harmony employed the octave or Interval between the first and second partlals of the harmonic series. The harmony of the octave, itself a natural harmony inherent in the multi­

1 Settlesinger, Kathleen. The Significance of Musical Instruments In the Evolution of Music. Oxford History of Music, introductory Volume. p. 86 «*4"»

voiced utterance of a people, Is as old as the human voice. It was not consciously perceived, however, until the fourth century, B. C., when It was observed by the Greeks, who called the harmony antluhonv to distinguish it from the homoohonr of voices in unison*

The philosopher, A ristotle, askedl

"Why Is symphonous singing (antiphony) more agree­ able than homophony? Is it not because antiphony is the consonance of the octave? For antiphony is bom of the voices of young boys and men whose notes are distant from each other as nete from hvoate.* (the highest and lowest notes of the octave scale)x

The conscious artistic practice of the octave harmony,

called magadizing. seems to have been named after the magadis,

an Instrument capable of producing concords at the octave,

of two kinds of tone, in im itation of vocal antiphony • Again A ristotle considers 8

"Why is the consonance of the octave the only one which is sung? for in fact this consonance is magadized, but not the others. Is it not because this consonance alone is antlphonous? For in the antiphones, when one of the two notes is sung, the same effect is produced as in the case of the other, so that a single sound of this consonance being sung, the entire consonance is sung; and when the two sounds are sung, or if one is taken by the voice and the other by the flute, the same effect is produced as if one were given alone. This why this consonance is the only one which is sung, because the antiphones have the sound of a single note ." 12

1 'Pindar, in his scolion to Hlero, describes the sound of the magadis as responsive because it gives a concord, at the octave of two kinds of tone, namely those of men and boys.* Athenaeus XIV 3 6 . From t h i s p a s s a g e we a l s o gather that the recognition of the octave was as old as Pindar, 1. e., 0 . 522 B. 0. Wooldrlge, Oxford History of music. Vol. I, p. 5, footnote. 2 Op, cit. p. 5, footnote. 'S~

During the time of Plutarch,, some three centuries after

A ristotle,, the harmony of the fifth,, or the Interval lying between the second, and third partlals of the harmonic series,, and the harmony of the fourth, or the Interval lying between the third and fourth partlals of the harmonic series, were - ' -1 used In both vocal and Instrumental music. So far as Is known, the Intervals of the octave,, fifth , and fourth,, const!-. tuted the total of the Greek contribution to the art of harmony.

Hot until the end of the ninth century, A. D.» was the harmony of the major third, or the interval lying betwamn the fourth and fifth partlals of the harmonic series, admitted to use by Huobald, a monk of St. Amand In Flanders. In order to avoid the trltone or "Devil in !.!uslc” Hucbald introduced the third in the occursuo or close of a composition otherwise written in the parallel fifths and fourths of strict organum*

In the free organum of Guido of Arezzo In the succeeding cen­ tury, the harmony of the minor third, or the interval lying between the fifth and sixth partlals of the harmonic series, and the harmony of the major second, or the interval lying between the eigth and ninth partlals of the harmonic series, both described as discords, were used as passing Intervals be­ tween the concords of the octave, perfect fourth, and major t h i r d .

Although the first five of these harmonies correspond with

1 Oouesemaker, E. de H lstolre de l lHarmonle aa Moven Age. p . 4 - 5 a - the first intervals of the harmonic series, it Is not the pur­ pose of this thesis either to confirm or refute any sueh theory

of harmonic development.

Although most of the extant specimens of mediaeval poly­ phony are for voices, the rele of Instruments may have been a more Important factor in the evolution of harmony than the

amount of instrum ental music which has survived, would Indicate.

In the preliminary sketch ©f tw elfth and thirteenth cen­

tury musical theory, only such ideas and conventions as are pert­

inent .to the study of harmonic effects, w ill be considered.

In the analysis of the vocal compositions, a ll questions

of form, rhythm, notation, biographical details concerning per­

sonalities, and the controversial subject of national origins,

are arbitrarily excluded. The harmonic effect of music con­

ceived in melodic strata is the chief subject of investigation^ - 6 -

G onrm m m m theohx (1100 a . d * - 1300 a . d *) Contemporary mediaeval theory had little vital connection with the expanding nuoical practice of the tw elfth and thirteenth eenturles. The theorists propounded quaei-m theaatical eystoms of voice progression* often disregarded by the creative composer.

Typical of tho systems of the period ore the rules for two part compositions (organum or dlscant) contained In a treatise dating from tho beginning of tho tw elfth century. Instructions for the novoment of voices were as follows:

If the chant rises* take tho octavo. If the chant rises one note, take tho dlncant at the octave abovo and descend two notes. If tho chant rises two notes* take tho dlscant at the octave and descend one noto. / If tho chant rises three notes, take the octavo and remain on that note* If tho chant rinoo four notes, take the octave and rlco one note. If the chant falls, take the fifth. If tho chant descends ono note, take tho fifth and rloo two notes. Every time tho chant descends* take tho first note of tho dlscant at the fifth, and the next noto at the octav#* Every time tho chant rises* take tho first noto of the dlscant at tho octavo, and tho next note at ■ the fifth. ... ■ ■ Hben tho melody continues to ascend or descend, use parallel fifths; , Closo the dlscant upon tho octave.

Although the harmonic effect of such progressions was

1 Couoeomaker, E. do H istolro p . 245 either that of a fifth moving to an octave* or an oot&va moving to a fifth* the intervals were not eoncelved as harmonic entitles* ■. . . ;

The possibility of three part oonnoooltion was recognized by JohanneeCotto (e* 1100 A* D*)* The first rule* apparently the result of theoretical speculation rather than of musical

Insight* was given by Franco of Cologne (c* 1150 A. D .) a n d

- • was considered adequate guidance for a^l three part oospeeltlonsi

When the third voice produces a dlssomnee with one voice, it must form a consonance with the other voice, and vice versa . 1

Franco recognized three types of consonances perfect con­ sonance s, such as the unison and the octave; Intermediate con­ sonances, such as the perfect fourth and perfect fifth* and ■ Imperfect consonances, such as the major and minor third* .He recognized two types of dissonance: perfect dissonances (sounds intolerable to the ear), such as the minor second, trltone, major and minor sevenths; and Imperfect dissonances (sounds not

Intolerable to the ear but, nevertheless, discordant), such as the major second, and major and minor sixths*

Joan do Garlands (1240 A.D.)ivho ruled that the third voice must form a consonance with each of the other voices, conceived of the consonance in the same fashion as Franco, but dlstlngulsh-

1 Goussemaker, E. de Hlatolre de l tHarmonle au Woven Age. - 8- ed three types of dissonance: perfect dissonances, such as the minor second*tritone, and major seventh; the imperfect dissonances such as the minor, seventh and major sixth; and the intermediate dissonances, such as the major second and the minor sixth*

The mediaeval th eo rist. made, no attempt to:.analyze or elassi- fy the possible combinations of consonant aoi dissonant intervals*

His brief rules for three part composition* allowed, mary unpredict­ able and otherwise unmanageable harmonic effects* 9-

AMALXSIS CF TWO PART OCBU’OSITIOES

The compositions in two voices have been analysed to determine the kind and proportion of intervals , the most frequent interval progression, or habits of intervallic thought? the role of the suspension and appogglatura, and the oadentlal effect of the closing progressions*

Key to abbreviations used in following tables*

CoBposltion# (^ e blbllographv)

M # L * M ira Lege Ve B ♦ • • Agnus F ill Virginia L e R # Lone Rien De La Fontaine A cb # # ! Dames Sent En Grand Earns!

A * C # Ascendit Chrlotus A S ■wmmm. A l l e l u i a T e S * «*»«- Tumba Sanoti N icolai

V. N . — Venes a Nueaches

P5 — perfect fifth or perfect twelfth

8va-- octave o — u n is o n

P4 — perfect fourth

M5 — major third * 10*

m3 — minor third

MS —- major sixth m6 —. minor sixth .

M2 »— major soecmd m2 -i- minor second W — major seventh m7 — minor seventh A4 — augmented fourth

tot.-- total

% of in t. ch. — percentage of total number of progressions

involving interval changes - 11-

INTERVAL8 USED HI TWO PART COfefPOSITICHS

P 5 8va P4 M3 m3 M6 ir.6 ■ M2 m2 L7 m7 A4

— o r j 2 H.L* 24 23 9 3 1 3 3 1 3 1

V.B* 6 4 81 1 4 26 31 6 4 7 2 — 6

A *F * 18 1 4 5 3 6 ' :2 , 3 2 1

L a . 25 15 1 5 8 8 2 7 3 •x D.O. 1 5 19 6 5 1 4 2 4 7 2

A.C. 14L 49 1 5 2 3 16 1 1 6 5 1

A. 9 3 3 1 1 2 1 1

T.S. 57 1 3 1 9 21 5 1 3 5 3 5 1 0 2

V.N* 1 5 30 6 1 0 2 1 4 3 5 1 1 7

T o ta l 368 247 92 7 9 7 0 62 17 3 4 4 1 4 39 5 Per cent 35*69 23*95 8*92 7*64 6*78 6*01 1*64 3*29 *30 1*35 3*75 *48 Total number of Intervals— 103L •12-

SUSPENSimS USED IN TWO PART OCEPCBITICNS

M2 8 P 4 m2 m? MS P5 m3 M3 A4 MT

M .L. 3 1 1 v. B . r 6 2 6 4 2 6 2

A . F . 2 3 1 1 1 1 L* R . 6 9 3 1 5 5 3

D. O . 4 3 4 1 1 1 1 2

A . C . 1 7 3 6 5 1 4

A» 1 3 2 2 1 1

T . S . 2 1 4 9 2 8 6 4 9 1 3

V . N . 3 1 0 4 1 6 3 8 1 0 1 4

29 11 50 3 32 10 28 36 16 1 8 3 7

Total number of euB^nalcms*—243

243 GUBpenBionB equal 23*56 per cent of to tal number of Intervals used - 13-

APPOQO-IATURAS USED IN TWO PART COMPOSITIONS

MS P5 P 4 A4 m3 nfT %2

M.L*

V.B. A.F. 1 1 1 1 L.R.

D\C. A.C. 6 3 4 : 1 1

A- 1 1 T.8. 1 11 1

V.N.' 1 1 ... 2

8 2 5 7 2 1 2 2

Total number of appoggiaturas — 29

29 appoglaturaa equal 2 .8 per cent of the total number

of interval b u s e d PROG-RESSICUS CF THE PERFECT FIFTH

P5 ii.L« V.B. A.F. D.O-. A.C. A* T.8. V.H- tot. % Of to Int. oh.

8 o r 0 12 21 7 2 3 28 - 4 9 86 3 9 -0 9

F5 3 18 4 18 1 8L 3 18 2 140

P 4 4 8 2 6 1 1 3 2 1 3 1 50 2 2 .7 m3 3 5 2 - 1 1 1 - 1 3 5*99

M6 1 - 2 3 12 1 7 2 28 1 2 .7 2

M3 7 1 3 2 2 1 8 - 2 4 19*99 m5 - 2 - - 1 1 - 2 1 7 3 .1 8

W • 2 1 1 1 - 1 - 6 2 .7 2

IT > - 1 - - 2 - 3 1 .3 6

M2 — - 1 - - - 1 - 2 .9 9

A4 - - 1 - . - 1 •45

P5 — P5 —— 3 8 . 8 ^ o f t h e t o t a l num ber of progressions uslns the perfect fifth P5 P5 M2 P4 P4 r o 8va m3 M2 M3 o r o 8 87 — — a

0 && SS E5 55 5 — L. .L d 7 1 1 1 5 17 3 5 2 8 0 a v ) 12 B. .B V 20 I — 22 • 22 — I 6 1 2 6 6 1 2 2 4 2 RSESQS F H OCTAVE THE UNISON OR OF PROSRESSIQNS ng t ave or son o is n u r o e v ta c o e th g in s u F. .F A 1 1 4 3 2 1 2 6C u e of s n o i s s e r g o r p f o ber num l a t o t e h t f o 36JC R.D. . .G D . .R L 1 3 2 1 1 4 2 - 3 1 3 2 1 1 2 1 4 15 - O•A • A •O • 27 1 1 7 1 1 3 2 5 1 1 S. .S T 1 2 1 6 1 1 1 N. .N V ) 1 ) 1 ) 9 ) 1 ) 1 2) ) 1 ) 2 ) 1 ) 2 ) 1 3) ) ) ) ) ) ) ) ) ) t o t 8 6 2 1 4 1 5 1 27 53 12 21 7 3 Anlzsh- % 56.92 67 .6 4 1 41 .4 1 1 f o 6 - 7 2 .5 6 63 3 .6 1 6.52 15 .1 8 71 .7 2 .8 3

*»2.6—

PROGRESS! QIS OF TIE PERFECT FOURTH

P4 V.B. A»F» L«R. D ,e * A »0. A ♦ T*S« V.K. to t. % or to Int.oh.

P 4 i 1 3 i - 1 1 8

P5 i 3 2 2 2 13 2 8 33 3 8 .4 8 L76 i -- 1 2 1 5 5 .8 1 8va or 0 2 5 1 3 2 2 1 3 19 22.61 b6 1 - ~ 2 3 3*5T

M2 1 ; • - — — V 1 1.19 m3 2 3 1 6 1 — - 4 - 17 2 0 .2 3

M3 2 1 1 1 — 1 2 8 9.5

P 4 — P 4 — 8*56/0 ofi.the total numl^r of progreeslona using the perfect fourth -17

PROEiRESSICES OF THE UAJQR THIRD

M3 M.L. V.B.A.F.L.R * D.G # A %G • A . T •S # V»N. t o t . * o f t o I n t .o h *

M3 '• 5 • 1 - --- 3 9 m3 1 1 - - - -- 1 - 3 5 .4 5 0 1 1 2 2 4 - i - - 2 22 4 0 .0 0

? 5 1 - - 1 5 i - 6 1 1 5 2 3 .6 3

M2 - 5 - - - - 1 1 . - 7 1 2 .7 2

P4 - 3 1 2 - — ■ - 1 - 7 1 2 .7 2 A4 ------■ 1 - 1 1 .8 1

M3 — M3 — 14.06* of t h e t o t a l num ber of progreaoiona using major third

PROORESSICNS OF THE MINOR THIRD m3 M.L.V.B.A.F.L.R. D.G. A eC e A « T #5 * V .N . t o t . * o f t o I n t .o h m3 1 - 1 1 3 ■ * .?* - 0 2 1 - 11 1 6 .6 6 7 - - 1 - ■ -V. -

* ' ‘ M6 1 1 1 .6 6

P4 . 1 - 1 3 - 5 6 .9 M2 1 1 2 - 1 5 6 .9

P 5 4 19 1 — 1 2 1 3 31 4 5 .9 6

M3. 1 4 1 1 - — — — 7 1 0 .6

8 1 — ■ - - - 1 1 .6 6 m2 1 1 1 .6 6 m7 - - - - . 1 1 1 .6 6 m3 * — m3 4*54^ of the total number of progressions using minor third .. - 18-

KICGRISSIONS CF THE MAJOR. SIXTH '

M.L. V.B. A-F. L-R. D.G. A-G. A. T-S. V.H« %ot. % Of ^ ...... ■ ...... - ...... : .... ®3 1 ' ' ' ' • V * ‘ " ‘ 1 . 1 .7 5 . 1 4 2 1 6 1 6 6 27 47.36

KS 2 ■; ■ 3 5 : 8 1 2 8 1 2 1 15 26.31

0 1 1 1 .7 5

P4 1 1 2 2 1 7 12.28

^ 3 3 5 .2 6 m& 3 3 5.26

iS6 — 16 — 12.4^ of the total .number of progmseisms msisg

the major sixth

PROGRESSICKS CF THE MINCB SEVEITOH m7 M.L. V.B. A.F. L.R. D.G-. A.C. A- T.S. V.M. tot. % o f t o ______• ______-______I n t .o h . m 1 . 1 2 .7 0

%6 2 3 3 8 21-61

8 2 . 11 1 3 8 2 1 .6 1

b6 ...... 2 2 5 -4 0

P5 3 4 6 1 17 45.94

m? - 2

P4 1 1 2.70

b7 — — 5.127$ of tM total mmWr of progressions using

the minor seventh - 19-

raCBRESSICES (F TIE M4JCR SEWStH

U6 M.L. V.B. A.F. L.R. D.G-. A .C . A . T .S . V -N . t o t . % Of t o . . V - ■' - - ____ — ____ ;______; ...... 8 ■ - ..... ; .... 1 ■ ...... 1 ...... 2 ' 1 3 -3 3

M6 1 12 13-33 P5 ,1 6 3 10 66*66 m? ■ ; 1 ' ‘ 1 ' 6*66 • - ' ■ . . ■■ . ‘ ■ ■ V ^

PROGRESSIONS CF THE MINCH SIXTH m6 K -L . V.B. A.F. L a. D .G. A.0 . A. ""T.S. V.N. tot. ^ of t o _____ ;______■ ______Int .c h .

P5 1 4 2 7 41.6?

8 4 2 1 7 41.67 m7 ,, 1 1 5-88

P4 1 1 5-88

M3 7 ; ' " 1 1 5.88 PROGRESSIONS OF THE fiAJCR SECdfi) (CR IVkJOR MIRTH)

M2 M.L. V.B. A.P. L.R. D *G* A.G. A. T .S. V N. t o t * % o f t o i n t . c h . M2 , - ' - 1 ' : : ■ - " 1 2

P5 1 ■ 2 ':: ' - 4 1 1 9 3 4 .6 1

0 1 5 2 2 1 1 12 4 6 .1 5 m3 1 1 2 7 .6 9

M3 1 - 1 3*84

8 . 1 1 3 -8 4

07 1 1 3.84 :

M2 *- - M2 —7 of the total number of progressions using th e major second

. PROGRESSICMS OF THE MINOR SECOND (OR MINOR NINTH) m2 M.L. V.B* A .F» L .R . D43-. A .G . A . TiS. V.N. t o t . % o f t o A n t .c h . m3 1 21 3 07 1 1 2 1 -

CL05ITO PROBESSIGKS WITH C/UDENTIAL EFrECT

Gfflaposltlons

1 * L• in3 —**— (M2) —• o

m3 — P5

V. B. m3 — o

P4 — o

M3 •——* O O — o CO P m ! A* F. v m

L. R. L'6 (P5 — P4 — M3 ) -

D. G * P4 — 8

A. C . P5 — 8

A. P4 — P5

T .; S. P4 — P5

V. N. P5 — 8 — 8 — 8 -22-'

SUMMARY OF ANALYSES OF TWO PART COMPOSITIONS

INTERVALS USED

The intervals most frequently used in this sampling of ‘ twelfth and thirteenth century music were the perfect fifth; the octave, and the perfect fourth. However, major and minor thirds and major sixths were used extensively to decorate the main structural skeleton of perfect fifths and octaves. These intervals were found in approximately the following proportionsl

P5 ......

8va or unisons P4 ......

M3 ...... m3 ...... M 6 ......

Sevenths, seconds, minor sixths and rare augmented fourths were heard occasionally i

ml 4^

M2 3 ^ m6 2% m If* m2 _*

A4 *

* Less than 1% - 2>

SUSPENSIONS AND APPCXKHATURAS

The suspenDion was a well-establIshed device. Twenty- four per cent of all the Intervals used In these compositions were heard as suspensions. The appogglatura, used less fre­

quently, constituted approximately three per cent of the total number of intervals.

The Intervals used least frequently were heard most often either as a suspension or appogglatura. The augmented fourth,

for example, was heard only as a suspension or appogglatura. Three out of the four minor seconds used were also heard in that manner. Other intervals were heard as suspensions or appog-

giaturas in the following proportions*

M2 ...... • 91%

m? * '• • . . . & . «i * . * &T% ' W * ...... 64*

P4 ...... 62* m6 ...... 5^

...... 55% m3 . . . . . ♦ . . . 24*

M3 ...... 23* P5 V ...... i i *

PROGRESSIONS

Parallel progresolons of perfect fifths, octaves or

unisons, and perfect fourths were prominent. Of the total

number of progressions containing the intervals, the foi- lowing percentages were paralleli

P5 ...... 39*

8va or o ...... 22* PA . . * ...... 9 *

Major and minor thirds and major sixths were Infrequently heard in parallel progresalone.

The perfect fifth usually progressed either to itself

or to the octave or unison, less frequently to other intervals$

■ , P5 8 or O'...... 39* .

P5 — PA . . . . . • . . 23*

P5 — M3 ...... 20*

P5 __ MS ...... 13*

P5 — m3 • . . . • . . V 6* The octave progressed .to Itself or to the perfect fifth!

lees, frequently to the minor, third, minor seventh, major

second, or perfect fourth. ,

8 — P5 *. #,'* # •: e, *. # . 37^

8 — . m3 .

8 — m? + » * * * * * * * 1 1 ^

8 — PA * », +, *. *, *, * * The perfect fourth progressed to. Itself or to perfect

fifth, octave, or minor third. . . .

PA — P5 ...... • 38*

PA — 8 ...... 23*

PA «•— m3 ...... 20* - 25-

The major third progreaeed most frequently to the unison and perfect fifth .

10 — o V ......

M3 — ?5 ...... 2h% The minor third prc^reseed most frequently to the

perfect fifth or unison.

m3 — 3 5 . • • • • • • • • Xrfr m3 — o ...... 17$

The major sixth progressed most frequently to the

perfect fifth, octave,or perfect fourth. MS — P5 ...... 47$ . MS 8 2o$

MS — P4 . . < . . . . . 12$ The minor seventh progressed most frequently to the perfect fifth, octave, or major sixth.

■ nf? — *■ P5 m7 — 8 . . . . 22^ m? — : MS * * *• .' .■ * .' 2256

The major seventh likewise progressed to the perfect

fifth, octave, or major sixth• •

The minor sixth progressed most frequently to the perfect

fifth, or octave.

The major second progressed most frequently to the

unison or perfect fifth 4 CLOSING PR08RBS8ICKS

All of the two part ooffiposltims closed variously on the unison, octaw , or perfect fifth, usually preceded by the perfect fmirth, perfect fifth, or minor third. One v o i c e , either upper or lower, approached the final hot® In stepwise fashion. Chains of unisons, octaves, or perfect fifths sometimes reiterated the cadential effect of the close, either through simple repetition or unison progression, through a major second to the final note. ANALYSIS OF THREE PART 6CKF08ITXCB8

The compositions In three voices have been analysed to determine the ueo of tonal potentialities, !• e», the proportion­ ate parts w ritten•

(1) with three voices in uniboh (2) with two voices in unison and the third voice 'sing­

ing a different note

(3) With one voice doubled at the octave and the third

voice singing a different note

(A) with three voices singing three different notes

(3) and (A) above are further analyzed to determine

the chords or harmonies present or implied.

KEY TO ABBREVIATIONS

Compositions (See Bibliography) D* J* Bleus Je Me Puis la Mult Dormier

C. M. Oust oil Hob

D , D u lc ia

S* S a n c tu e

B t • B e n e d ic tu s

Be* Benedlcamue

R . A* R ondeau A T r o is P a r t i e s

A R« Autre Rondeau A* Trois Parties

H* A« He C e le Amour . 28:

- M e m M

Where one Interval Is found euperlmpoeed upon another in the following manner, P4, the chord Ind loeted lo forced of t the two Intervals pyramided in conjunction* 49*

i:: - ; . : u se . of tonal potentialities - •; , - - a » t tvt -. >

m i . m m B t* BO^ m m .m A i.isia r : - U n iso n 1 1 2 4 .5 7 , 1 :■ • :■ - - 2 1 2 -

I n t e r v a l 19 29 T 53 34 17 16 41 221 32.08 2 ? 2 .2

' .‘O ctave 23 20 7 29 16 16 3 15 43 172 24.85 2 2 ■ ; - f

Chord 21 23 9 6 0 32 20 10 39 81 295 42.61

...... • -______■ ' : ^ "

: :: ' ■ - ; - f: : ' . " ■ 12 "• •":

J:: KE2

~ 1 Unlsozu— throe voices in unison

Interval — two voices in unison,third a different note

Ootave — one voice doubled at octave, third a different

( n o te Chord — throe voices oingins.three different notes - 30".

C hord D.J.C.N. D . S . B t • 1 Be * R *A • A *K • N .A . t o t . 2

P4) P 5 ) 1 5 1 5 * 5 25 1 3 11 3 - 1 0 20 * 117 6 2 -5 0

III . 2 1 3 3 . -.. I 2 1 2 6 -9 0 ' ;• „c. *>' U6) m3) 2 1 4 7 4 .0 6 ■ y- . ; - ■ . » srxV - . m6) 3 3 6 3.4T t . ■ ' "r ‘ • •; s ■: 4 »6) M3) i 3 3 1 8 4 .6 5 j'-' M6) 1 1 2 2 1 6 1 2 6 .9 0 : ■■. V" m2) -B 7 . 2 2 1 .1 6 .. * . ' m7) M2) 1 1 2 1 .1 6

, M2) m7) 4 6 3 .4 7 f . \ J .

Total number of Incomplete chords — 172 TRIADS

D'.J'. b.s. DV S . B t . Be • R *A * A.R. N>A. t o t . $ m3) M3) 1 4 1 1 3 6 16 1 6 .3 2 P4) m3) 2 1 2 1 3 . 2 2 3 3 6 1 5 .3 M3) P4) 3 2 2 7 7 * 1 4

,11 4 1 6 3 1 1 4 2 22 2 2 .4 4 P4) M3) 1 2 2 5 8 19 1 9 -3 8 m3) P4) 1 2 1 4 4 .0 8 M3) M3 2 2 2 .0 4 m3) m3) 1 1 1 1 1 5 5 .1 P4) m3) 5 3 8 8 .1 6

- Total number of t r i a d s - -99 M W M . .. w _ -33.55$ of the t o t a l num ber o f c h o rd s

composed of three different voices*

KEY

m3 M3 — major triad in root position 1:3 m3 — minor triad in root position - 3*.

P4 m3 — major trial In first Imversicii >.!3 P4 — major triad in second Inversion

M3 — minor triad In firat inversion- r;m3 ■ ' ' „P4 — minor triad in second inversion

; m3; „ ' : m3 — diminished triad P4 ' ■■ : m3 — diminished triad in first Inversion

. » ■ M3— augmented triad - 33^

IHCCtiPIETE SEVENTH CHCRDS

i‘ ; . : ■ ; ; '

D • J * C.N . D » S• Bt»* Bo * R »A • A *R • t o t .

H?<5> . . 2 v 1 % / ' • • ----8 7 24 25-44

7 1 (5 ) 1 3 • ,-;I .■-■..‘3 ' • - 'I-:. 1 : — 5 15 15-95 7 1 1 1 (5 ) 1 : -'v: 3 - : 1: V 3 , 8 8 .5 R 7(3) 4 1 4 2 2 2 1 1 6 23 24.45 7 1 1 (3 ) 3 2 3 3 11 1 1 .6 9 7 1 1 1 (3 ) 6 1 4 11 11.59

D7 1 1 2 2 .1 2

Total number of Incomplete oeventh chords — 94

Total number of Incomplete seventh chords — 31. 86^. of the total

number of chords composed of three different notes

KEY

B 7 (5 ) - s e v e n th c h o rd In r o o t position with fifth o m itte d #H * M w 7 1 (5 ) - # f i r s t in v e r s io n W w « W W w 7 1 1 1 (5 ) W t h i r d w M w w R 7(3) root position t h i r d * #W w w ## # 7 1 1 (3 ) second inversion #. * # w w w 71X 1(3) * t h i r d - 34-

eoi*© D• J • C.K• D * S* St* • B e » R*A• A*R • N »A• t o t « ch o rd o Implied 8 9 5 IT 15 10 2 10 28 102

T o ta l ■number o f Im p lie d d is o o n a n t c h o rd s — 102

Total number of Implied dieaonant chords —34;57^ of the total

number of chordo eompoeed of three different notea. 35^

CLOSING PROGRESSIONS

Composition Vi J«

bS —— c P4 P4 f — S o r ni3 *5 a — c

C . N. o — a P 5 P4 r - s or fa o. ? 5

D.

f -— e m3 o a — e o r ?5 P5 6 — a

6 ••••. f P4 P4 b — o o r M3 P5 B — f

B t .

6 — i P4 ?4 b — c o r - %3 P5 g — f - 3 6 -

B d.

f — g . .r.’lMf' o — d o r P 4

g

R . A* '

P 4 .2 4 g * — — a o r m3 ' ■ P5 i 0 (1 -

A . R .

e — f P'4 P4 b — c or — ' . . M3 ... . P5 g — f

N • A •

O ; — . d P5 P5 f — g o r m6 """ 8 a — g SUMMARY ;OF AI-IALYSIS OF THREE PART GO:POSITIONS

In three part compositlono* the proportionate use of tenal potentialities was as follows t

(1) Three voices in unlsmA

(2) Two voices in unison with tbs thlrtl voice singing a different not® 32%

(3) One voice doubled at the octave, with the . :

third vole® singing a different note 25^

( 4 ) Three voices singing three different notes 43^

} ' Incomplete Chords •

The perfect fourth superimposed upon a perfect fifth constituted 68^ of the incomplete chords composed of one voice doubled at the octave with the third voice, singing a different note• Other Incomplete chords were used less frequently *

(P5) 1 (P.4) 7* (m 3): (M6) 7% (m6) (M3) ' : 5% ■ : r' (m l) 4% SI! S f

1 less than 1% 2 low percentage If the doubled note ie*considered as a tonic of the

chord In v?hlch It 1b found, the following intervalllc com­ binations may be translated Into modern harmonic concepts

In the following manner. , (FA)- (P5) — major or 61ti<^ triad in root position with : third omitted - : " v : 'r:; ,

(F 5) ; 1. V.. - ; J . .. .u .* - •(FA) — major or minor tried in second Inversion with third omitted : v v ; ."• . ' 'V . i ■ v, 7; • \ :.v'? V: ' "• I': - - ' ' ^ • (m3) (t6)— mihor triad in first Inversion with fifth omitted

(e 6 ) r . - r-. .7. ! ' (1,13) — major triad in root position with fifth omitted_

minor triad in root position with fiftti emitted

8 1 1 major triad in first inversion with fifth emitted

(AA) — diminished seventh with third- and seventh omitted (M2) :'v. -:V:.7 7 . ; v.,.. ; r., ■ / '" (m?) — seventh chord with third and fifth omitted - ;

T r ia d s -

:: :;-••;TrImla -@md ,th eir inversions were represented in the

following proportions i

minor triad 22/9 1 minor triad in first Inversion 19%

major triad 16%

major triad In first inversion 15% Second inversions, diminished, and augmented triads, heard•infrequently, were present in small percentages.

v Incomplete Seventh Chords

H ; Implied seventh chords, i . e ., .three note chords out­ lining seventh chords w ith:third or fifth omitted, were formed by a variety of interval combinations, suggesting.all types of seventh chords. The skeletal outlines of seventh

©herds were found; in the following proportions:

Seventh chords in root position with fifth omitted - 2596

” - ”: M 51M third . 24/j .

* w ! first inversion " fifth - * V ” * M second • .« . w third W

: M " "third ", " . " 11^

tt " " " v V " fifth " . 9>

These seventh chords were foimd both as suspensions

accented chords. Resolutions of the seventh chord to triads

were found in rare instances but not frequently enough to in­

dicate an established habit of thought• The seventh of the

chord moved Indifferently up or down in stepwise fashion,

skipped an interval, or preceded a rest.

Dissonant Chords

A variety of chords more dissonant than the seventh chords were suggested but were not sufficiently defined by the three

notes possible in three part harmony to permit exact analysis.

130731 , , e m e m s i c *

Both the mediaeval theorist and composer were concerned with the perfection of a melodic idiom and only incident ally * with the eubeidiary harmonic effect of simultaneous sounds.

The theorist, either through speculative Invention or deduction from musical practice, provided a schematic, if not comprehen­ sive, systematization of musical m aterials (melodic intervals) and rules for their use (progressions) in compositions for two voices. The composer, in actual practice, enlarged the imtmrrml vocabulary and Introduced new progressions thrtmgh frequent use of tto suspenslcm and appogglatura, and more rarely through direct use of the intervals, as an expression of hie personal musical and imaginative feeling. Although both composer and theorist were aware of the harmonic effect of the vertical interval resulting from the simultaneous orogreoolon of melo- die intervals, they never conceived of the harmonic interval

Rs a unit or entity capable of progressing to another harmcmlc interval. However, the music to which they listened, and which they themselves emposed, produced the harmonic effect of vert­ ical units progressing to other vertical units, either directly or indirectly, by means of suspensions and appoggiaturas. The main structural framework consisted of octaves, perfect fifths and unisons, ornamented by major and minor thirds, and major s i x t h s . ... ; . . . ; . The discovery of the possibility of composing music for three voice d found the theorist, unable either to systematize the new tonal m aterials or devise an adequate theory of their function* The brief rules which he formulated for composi­ tions In three parts indicate that, he thought of the harmonic

Interval as a vertical unit which might be superimposed upon a similar vertical unit by conjunction. Although the resuit­ ing harmonic effect of two such Intervals was that of a three- note chord. the theorist never perceives the chord as an entity or harmonic unit, but continued to think in terms of intervals.

He was unable to discover or formulate any rules for the pro­ gression of two voices in relation to a third voice but left such considerations to chance or the discretion of the composer.

The composer» intim idated, perhaps, by the lack of theo­ retical guidance and his own JhaAblllty to control the unpre­ dictable effects Of his new tonsil resources, did not immediately exploit the potentialities of three part composition.

Large portions of the compositions analyzed in the present sampling of tw elfth and thirteenth century music were w ritten with the doubling of voices in unison, producing the effect of a composition for two voices, or a composition for three voices with one voice doubled at the octave.

In such portions of the music as were w ritten with each of the three voices singing different notes, a variety of harmonic m aterials was found 2 major and minor triads in root position, first and second inversions; augmented and diminished triads, .formed by suspensions and appoggiattiras; seventh chords# with the fifth omitted, in root position, first and third Inversion; other more dissonant chords suggested but not clearly defined by the three volees.

Because the mediaeval composer did not perceive or under­

stand the harmcmic nature of ..the nev? tonal m aterial, he was unable to master the complex harmonic effects of composition for three voices. He merely began, in tentative fashion, the tonal experiments in harmonic effect.which enabled the com­ poser of later centuries to define and establish the harmonic

foundation and structure of modern music. BIBLIOGRAPHY-

MUSIC

TWO PART COMP OS ITIONS

AKnug F ill Vlrglnle. Bibl. de" L ille. Ms. 95 Gmemaaker,* Mmmmnta, P I . XXVT jteicendlt Cbrletu#. Bibl. Mat. de Parle. Me. 8L2

Coussemaker,Monumente, PI. XXVIII

A l l e l u i a . B i b l . N a t. de P a r l e • M s. 03.2

Coueeemaker,* Mommenta, P I. XXX

Dames Sont-En Grand .Bsmal. Bibl. Nat. de Parle, Ms. 813 Coueeemaker,# Monuments, P i. XXVII

Lone Le Rlen Pe La Fontaine. B ibl. Nat . de Parle. Me. 813 Couesemaker,* Monuments, P I. XXVII

Tumba Sanct 1 N 1colal., B ibl. Nat. de Paris, Ms. 812

Ctsiseemalrer,* Monuments, P I. XXX

Venes a Nueeches. B ibl. de Cambral.

Coussemaker,* Monuments, P I. XXXIV

Mira Lese* Bibl. Nat. de Parle, Me. 1139.

Couesemaker,* Monuments, PI - XXIII

Verbum Sonum et Suave. Bibllottoque de Doual, Ms. 124

Causeemaker,* Monumente, Pi* XXIV

*CouBsemakery E. de, H lstolre de l 1 Harmon le au Woven Ace. THREE PART COMPOSmOHS

Autre Rondeau A Trols Parties (D*Adam Do La Hale). Bibllo-

theque de Cambral, Cousaomakcr^, Monuments, PI* XXXI Benedlcaznun. B lbl. Sat. do P a r i s , Usi 812, Cousooiaaker», Bonumpota, PI* XXX Benodictua. Blbl* Nat. de Paris, I£s. 812, Cousaemaker^,

M onum onts, P I . XXIX

Custodl NoSeiBlbl. Nat, do Paris, Ms. 813, Coussomaker*, Mommeata, PI. XXVII

Pious Je No Puls la Hult Dormler* Blbl; Hat; de Paris,

Ms. 813, Coussemaker*, Monuments, PI. XXVII

Dulcla. Blbl. Hat. do Paris, Ms; 1817, Couasemaker*,

Monuments, P I. XXVII

He Cole Amour. M bliotboquo de „ Cambrai, Coussemaker*, ; ' ' . M onments, ;P i; XXXV

Rondeau a Trols Parties (D*Adam De la Halo), Blbliotheque

do Cambrai, Cousaemakor*, Monuments, PI. XXXI

Sanctug. Blbi; Nat. do Paris, Ms; 012, Coussemaker*, Monuments, PI, XXIX

^Coussemaker, E. P aris, MKJCCLII. - 4 5 -

QENERAL REFERENCES

Ikirney, Charles• A General History of Music* ed* Frank Mereer

Opusaemaker, E« de H latolre de 1*Harmonle au Moyen Ane,

P a r i s , LtDCCCLII

Ftergusem, Donald N* A History of Hu b leal Thought.

C rofts & Co., Now York, MCMXXm

Finney, Theodore M. A History of Kusic.

Rareourt, Brace & Co., Sew York, 1935

Calpin, Francis W. A Textbook of Euroooan ilialcal Instruments.

Dutton & Co., N. Y. 1937 p. 37

Cray, Cecil• The History of Music.

Alfred A. I^iopf, Not; York, 1931

B&ydon, Clen The Evolution of the Six-Four Chord.

University of California Press,

Berkeley, California, 1933 Jeppeaon, . Counterpoint. tr. Cion Hayden

Prentice-H all, Inc. Hew York, 1937 Kit son, C* H* TheArt of Counterpoint Qxfozti Clarendon

Press, 1924 lacran, Henry S. The Harmonics of Arlstoxenua

Oxford Clarendon Press, 1902

Oxford History of Music. Introductory Volume ed. Percy

Buck. Oxford University Press, London, 1929

Oxford History of Music* Polyphonic Period. Part I H. E.

Wooldridge. Clarendon Press, Oxford, 1901

Bhlrlaw, Matthew The Theory of Harmony Hovello & Co.,Ltd.London - mb cs

£ 9 7 9 / I y^