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THE RHYTHM OF WESTERN POLYPHONIC MUSIC FROM ABOUT 850-1300

THESIS

Presented to the Graduate Council of the

North Texas State College in Partial

Fulfillment of the Requirements

For the Degree of

MASTER OF ARTS

Douglas D. Wiehe, B. M.

Beeville, Texas January, 1955 TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ...... iv Chapter I. THE PROBLEM OF RHYTHM IN POLYPHONY TO ABOUT 1150...... * -.- 1

II. THE SYSTEM OF THE RHYTHMIC MODES . . . . 4+7

III. THE MODAL SYSTEM IN THE PRACTICAL MONUMElNTS FROM CA. 1150-1300 ...... 79

BIBLIOGRAPHY...... 103

iii LIST OF ILLUSTRATIONS

Figure Page

1. Some Notational Signs in the Solesmes Editions which Indicate Longer Durations . . . 10 2. Illustration of a Passage Written in Plainsong Notation...... 12

3. A Passage from the Te Deum ...... 23

4. An Example from Guido d'Arezzos Microlo . . 29

5. The Fifth Method of the Ad Organum Faciendum . . 31 6. A Characteristic Passage in the "Sustained4 tone" Style. . * - - * - - * . - * * .. . 34

7. Part of a Twelfth-century Benedicamus Domino . . 36

8. Two Modern Transcriptions of the Modal Patterns. 49 9. An Example of the First and Second Rhythmic ** . ---. . .53 Modes. ------. - - - 10. An Example of the Third Rhythmic Mode . . . . . 54

11. An Example of the Fifth Rhythmic Mode . . . . . 55 12. A Probable Example of the Sixth Rhythmic Mode. . 56

13. Franco's Example of rgnum Purfm ...... 70

14. An Example of Repeated Non-modal Patterns . . . 87

15. Examples of Extensio and Fractio Modi . . . . . 87

16. The Semibreve in the Ars Cantus Mensurabilis . . 96 17. A Transcription of the Semibreves of Petrus de Cruce ...... 99

iv CHAPTER I

THE PROBLEM OF RHYTHM IN POLYPHONY TO ABOUT 1150

The polyphony (organum) of the ninth to the last part of the eleventh century consisted basically of note-against- note settings of plain-chant, sequences and hymns. Examples

and explanations of this music are found in the musical treatises of the period: the Musica Enchiriadis1 (ninth century);

the Scholia Enchiriadis2 (ninth century); the Micrologus3 of

Guido of Arezzo (mid-eleventh century); the Ad Organum j-

endum4 (late eleventh century). In addition there are a number of actual compositions to be found in one of the Win-

chester Troper manuscripts of the first half of the eleventh century.5

Unfortunately, the musical notation in these sources is such that it does not indicate or is vague about the durations of the notes. Dasia notation is used in the Musica

1 Martin Gerbert, Scriptores Ecolesiastici de Musisa Sacra Potissimum, 1,152-173. 2Ibid. ,pp. 173-196. 31bidoII, 1-24. 4 Charles Coussemaker, Histoire de ltharmonie, p. 229, cited by Gustave Reese, Music in the Middle , p. 262. 5Three organa of the same manuscript which preserves the treatise are transcribed into modern notation in Coussemaker, on. cit, pp. 226 ff; one is transcribed in the Oxford Historz OF msac 45, second ed., cited by Reese, 9R, c., p.262 I 2

Enehiriadis and the Sfholia Enchiriadis.6 It comprises merely a text, placed according to the pitch of each syllable in spaces made by lines drawn laterally and parallel across the page. At the left side of this large staff, forming a vertical column, are signs which indicate the pitches of the spaces, and in some examples the letters T and $ (tone and semitone) are placed in the spaces to show the correct inter- val. Staffless neumes are used for the two-part organa in the Winchester Troper manuscript.7 The individual characters of neume notation consist of many combinations of diagonal dashes, at times joined and at times used singly.8 Often, one or both ends of these dashes are curled, and some neume groups employ dots also.9 In neume notation the individual pitches are not given accurately at all, the characters serving to indicate only the general direction of the melodic line and nothing whatever of the durations of the notes. 6 For examples of Dasia notation see Gerbert, Rp..it., I, 166 or Apel, The Notation of Polyphonic Music, first edition, 205-6. ATpel also gives a fuller description of Dasia notation. 7Reese, a. cit., 260.

8Reese gives a comprehensive tabulation of Latin and Gothic neume forms. Ibid., 139.

90ne of the theories about the origin of the neumes is that they developed from the use in Greek and Latin litera- ture of diagonal dashes to indicate grammatical accents. These accents actually involved raising and lowering the pitch of the voice. Neumes," Harvard Dictionary of Music. 3

It is probable then that the musical notation of the

ninth through the eleventh century was used only as a mne- monic aid by the singers and conductors, although some scholars believe that the neumes implied definite durations.1 0

One might expect that the musical treatises of the time would

aid the modern scholar in the task of interpreting the rhythm

correctly by giving explicit instructions for reading the no-

tation or by including discussions of the rhythmic characteristics. But in fact they offer little assistance, and the passages which do deal with rhythm have been interpreted so differently that they are not very useful in establishing what the practice of the times actually was.

The result of the confusion over the rhythmic interpretation of early music written in letters and in neume notation is that much important information about the incipient polyphonic art cannot be uncovered. The most important rhythmic developments in the Middle Ages were those connected with the rise of modal rhythm in the last part of the twelfth century, and it would be of great value historically and practically to know more fully the steps leading up to this epochal innovation. However, the period which encompasses these steps is still that in which the notation does not give any clues as to the rhythmic interpretation Thus, very little can

10Ree 0 Reese, p. cit., p. 143. 11I~bid.,p. 273. 4 be said about the rhythm which is not mixed with a good deal of speculation.

There is the possibility, according to Friedrich Ludwig and Gustave Reese,that the original rhythm of the plain-chant cantus firms was retained in the early polyphonic settings of it. Ludwig says: "What is known as organum up to this time a. 107g is essentially in a note-against-note setting; the cantus firmus is thus able to retain its original rhythm in a polyphonic setting. . . *."2 If this is the case, the rhythm of early polyphony can be approximated by applying to it the principles of interpretation arrived at by the modern scholars of the liturgical monophonic repertoire, which includes plain-chant, hymns, and sequences. It must be kept in mind, however, that no indisputable interpretations exist, and it is possible that for some particular place and time one interpretation is applicable while for another place, different in time or not, another interpretation would be correct. That the actual circumstances warrant such an assumption cannot be completely proved or disproved, but as Reese says, "If, in fact, the three modern points of view all have some historical justification, it may follow that early

l2..#. die bisher genannten Organa gingen im wesent- lichen fiber den Satz Note gegen Note nicht hinaus; die Grundatimme konnte dabei auch im mehrstimmigen Satz ihren originalen Rhythmus beibehalten . . ." Guido Adler, Handbuch der Musikpeschichte, 1924, p. 146. See also Reese, p. cit., p. 2b5. Gregorian rhythm was not definitively systematized at all for universal application. 13 Thus, the immense gap of time between the period we are considering and our day has apparently caused us many insoluble problems; for one thing the gap is too great for the practice to have endured with any semblance of purity, and for another the period itself ended over five hundred years before the advent of systematic research by modern musicologists.14 The following preliminary material presents the possibilities of musical rhythm, in general, from the period before polyphony, i.e., before ca. 850 A.D., to the last decades of the twelfth century, when the introduction of modal rhythm into parts of Leonin's Organa resulted in a corresponding change in notation, making a correct rhythmic interpretation more certain.15

The musical setting of the text and the metrical or non- metrical organization of the text are considered by modern scholars as having been important factors in determining monophonic rhythm. As to the setting of the text, the writer

13 Reese, a. cit., p. 147.

14Armen Carapetyan remarked: "It is at most utopian, at least short-sighted, to expect an absolute or even a fairly exact science out of that which includes non- seientific, imaginative, intuitive--in short, artistic-- elements and comes, furthermore, from an epoch where stand- ardization and scientific method in our sense were surely unknown things." "A Preface to the Transcription of Poly- phonic Music," Musica Disciplina, V (1951), 3-14. 15Apel, M. cit.-, p. 267. 6

of the preface to the Vatican edition of the Roman chant,16

in his instructions to modern performers of the chant, has

seen fit to include the words of the author of the treatise

Instituta Patwum: 17 "In all texts, whether of lessons,

psalmody, or chants, accent and rhythm /concentus?7 of the

word are to be observed as far as possible, for thus it is,

that the meaning of the text is best brought about."1 8

Aurelian of' Reome, a ninth-century theorist and author of

the treatise Musica Diselplina,1 9 states a similar convic-

tion: "In rhythm, however, the provision remains that the

'measure' Lmodulatio7 suitably accompany the words. That is

to say, the melodic line should not be composed unsuitably,

contrary to the meaning of the words." 2 0

l6Li 6LiborUsualis (1938), pp. xix-xxvi.

17 Gerbert, 2. cit., I, 5-8. Jos. Smits van Waesberghe has concluded that Gerbert was wrong in placing this treatise as early as the fourth century. Instead, he believes that it is no older than the twelfth and that it is probably the work of Ekkehard V. Muziekgeschiedenis der Middeleeuwen, II (1939-42), 197ff'., cited by S. A. VanDik,7"Saint Bernard and the Instituta Patrum of St. Gall," Musica Disciplina, IV, 99-109. l8 Liber Usualis, p. xiv. Presumably this is a rendition of the following passage in Gerbert, op. cit., I, 6a and 6b: "In omni textu Lectionis, Psalmodiae vel cantus, accentus sive concentus verborum (in quantum suppetit facultas) non negligatur, quia exinde permaxime redolet intellectss" In- stead of "rhythm," concentus may mean "the accentual structure of a phrase" as J. F. Cronin, professor of Latin and Greek at Southern Methodist University who has kindly checked all the Latin passages herein, suggests.

1 9 Gerbert, 2. cit., 1, 27-63. 2 0 Ibid., p. 35. 7

Other early writers (e.g., Saint Jerome,21 Saint John Chry-

sostem,22 and Saint Basil ) also stressed the importance of

the texts in the liturgy of the Christian church, especially

the fact that the words were the raison deftre for the music. St. Augustine even wrote that it appeared to him to be the way to banish the "melody of all pleasant music" from his

own ears and from the church, because at times he was moved more by the manner of singing than by the text.24

Its importance to the religious stability of the Chris- tian faithful notwithstanding, the composers of the Gregorian repertoire did not always choose a style of text-setting which would best bring out the meaning of the words, or a

style which did not rely on musical value to some extent. In other words, the plain-chant melodies were composed not only as a means of presenting religious texts in the liturgy but also with a view toward ornamenting the liturgy with music

21 Saint Jerome, "Commentary on the Epistle of Paul to the Ephesians," Jacques Migne, Patrologia atina, XXVI, 561-2, quoted in Oliver Strunk, Source Read ing Music History, pp. 71-2. 22Saint John Chrysostem, "Exposition of Psalm XLI," Migne, Protologia Graeca, LV, 155-9, quoted in Strunk, 9. Sit, pp. 67-70. 2 Saint Basil, "Homily on the First Psalm," Migne, Pro- tologia Graeca, XXIX, 209-13, quoted in Strunk, 9. cit.~~4-6. 24 Saint Augustine, Confessions, II, 165-9, quoted in Strunk, . cit., pp. 73T i istine cites the direction of Athanasius, Bishop of Alexandria, that the reader of the psalm was to perform in a manner closer to speaking than to singing. 8

important for its own sake. This ornamentation occurs in

the very fact that music is used instead of mere speech, but it is most clearly perceptible in a melismatic setting, where many notes are sung to one syllable of text.25 Ideally, perhaps, the rhythm of melismatic passages is somehow related to the irregularity of Latin, prose rhythm,26 but a purely musical rhythm actually prevails since only musical materials

(i.e., changes of pitch, organization of the notes into groups by accent or duration) are used.

The close connection between the rhythm of the text and the rhythm of the music in the more or less syllabic passages before ca. 1150 has caused scholars to classify monody into two groups: (1) those with metrical texts; (2) those with prose texts. In the group with metrical texts are the hymns and the later sequences (ca. 1200). The music of this group probably possessed a rhythm of recurring patterns which con- formed to the rhythm of the text rather than to the irregular

2 5 See W. Apel and A. Davison, Historical Ant igy of Muic, I, examples number 12 and 13. 26 Liber Usualis, p. xxx: "We must never lose sight of the fact that Plainsong is vocal Latin music, for this is the key to the understanding of its rhythmic and melodic structure. It has been grafted on, and has sprung out of, the natural rhythm and melody of the Latin words, phrases, sections, and periods for which it was written."

2 7 Curt Sachs, hfl and Te , p. 149 and Reese, . cit., p. 147. 9 prose patterns characteristic of the chant.28 In modern transcriptions the compositions with metrical texts are ren- dered by using long and short notes (e.g., our quarter and eighth) which correspond to the longs and shorts in the meter of the verses or by using equal notes which are grouped by the regular accents of the texts. Plain chant and the early sequences (from about the ninth through the twelfth century) comprise the group with non-metrical texts. The kind of rhythm in these compositions is commonly referred to as "prose" rhythm because of the ab- sence of the regularly recurrent rhythmic patterns found in verse. All the interpretations of chant rhythm agree on this characteristic of irregular grouping, but the means of deriv- ing the irregular groups is different in each of the three chief modern "schools" of chant interpretation (the Benedic- tines of Solesmes, the "Accentualists," and the "Mensura- lists"). Generally speaking, the Benedictine monks of Solesmes, led by Dom Moequereau, believe that the notes in plain chant are of equal value and should be given a duration which would

28As Peter Wagner has said, in the syllabic settings of the hymns "the music had been bound to the text and its metrical content." Adler, . eit.., p. 92.

2 9 For an example of a transcription of a composition with a metrical text which employs long and short notes, see Adler, 9p. cit., p. 94. 10

approximate that of a modern eighth note.30 In their recorded performances of plainsong, there are many notes which are longer than this one basic value, and in their editions there are notational signs which indicate longer values, e.g., the dot, which doubles the value of a note, the oriscus (Fig. la), the pressus (Fig. lb), or the trist (Fig. 10). 3 2

Fig. 1.-Some notational signs in the Solesmes editions which indicate longer durations than the one basic value.

However, these may be regarded as notes of the same value which have been tied together, just as shown in Fig. 1. The rhythm of plainsong is described by the Solesmes scholars as being a "free interlacing of binary and ternary 3 3 groups of notes." In instances where there are more than three notes between one ictus ("beat, rhythmic step, or 34 alighting point") and the next, there is a secondary division, i.e., secondary ictus.35 Such a division into primary

3Libe~rUsualis, p. xxii.

3 1 See, for example, Victor album M87. 32Liber Usualis, pp. xxii-xxiii. 33Ibid., p. xxx.

3bid.,p. xxvii. 3Ibid., p. xxviii. 11

and secondary beats is quite similar to some metrical strue-

tures in more modern music, e.g., the placement in a four- four bar of a primary accent on the first beat and a secondary accent on the third beat.) 6

The Solesmes directions for the placement of the ictus

and its reproduction in performance are puzzling: it appears

from the following rules for determining which note should

receive it, that the ictus is a purely musical division of the basically equal values. First, all sustained notes (e.g.,

the oriscus, the presses, the tristropha, and the dotted

notes) receive the ictus. Second, any note which begins a group (i.e., composite neume of two or more notes) receives

the ictus. Thus, the ictus in effect performs the same function in the Solesmes interpretation of plainsong that the bar-line does in modern music, except that it does not always

receive the kind of accent customary on the first note after

a bar-line. For example, Fig. 2a, shows the plainsong

In occidental music generally, rhythm seems to permit three units of approximately the value of an eighth note (M.M. ca. 80 for the quarter note) to be organized around a single accent (as in a measure of three-four meter) but does not allow the organization of four units without the aid of a see- ondary accent (e.g., the subsidiary accent on the third beat in a four-four bar) . 3 Liber Usualis, p. xxvii. Sachs remarked that "there has alwyj"Teen a natural trend toward the lengthening of accents and, on the other hand, toward bestowing ancaccent on lengths." (Sachs, 9. eit., p. 28).

38LIber Usualis, ibid. 12 notation which reproduces the original neume groups. Fol- lowing the second rule indicated above, the ictus is placed on the second, fourth, seventh, and ninth notes. The notes are thus grouped as shown in Fig. 2b.

L a. '

A - --Ia Iv !

Fig. 2.--Illustration of a passage written in (a) plainsong notation, (b) modern note-forms according to the Solesmes interpretation, (e) modern note-forms with bars.

Fig. 2c shows how the passage appears with bar-lines added, although the first note after each bar-line would not necessarily be accented. The placing or not of an accent on the ictus "depends on the syllable to which it corresponds and the position it occupies in the melody." The fact that the ictus at times falls on an unaccented syllable is considered by the Solesmes monks as a point of some importance to the

39 Ibid., p. xxviii. 40Ibid. Ibid., p. xxix. 13 musical style of plainsong. They believe that the rhythm of the text was only the starting point for the composers of the Gregorian repertoire, and that the musical artistry of the composers was asserted by purposely avoiding at times the coincidence of musical and textual accents.

According to these prescriptions, the ictus divides the chant melodies musically into the smallest possible groups, but there is a further musical organization of these small groups into larger groups, or, as it were, "phrases." The relative musical importance of the small groups inside the larger ones and the accentuation of the text then determine which of the ictus will receive accentsA.

A second group of chant scholars, known as the "accentualists," is closely related to the Solesmes school because they advocate the use of a single basic time value for all notes. The difference between them is that the "accentualists" believe the accent of the text to be the principal

2Ibid., p. xxxii. According to Dom Jeannin, the word accent I=ihe Solesmes editions coincides with the musical arsis at least two-thirds of the time, quoted by Ludwig Bon- vin, "The Measure in Gregorian Music," Musical Quarterly, XV glanuary, 19297, 27. 3Forexample, in the hymn "Ad Regias Agni Dapes" (Libor Usualis, p. 812) there is the coincidence of the ictus and an unaccented syllable on the syllables "gi" of the word "regiast? and "ni" of the word "Agni" at least. The syllable "um" of the word "eum" in the antiphon "Ecce Puer Meus" (Ibid., p. 424) apparently is unaccented, yet it falls on an ietuiSw ich is even lengthened by a horizontal episema. 14 rhythmic element in plainsong (some believe it to be the only one), and that this accent alone is transferred to the music. In melismatic passages, where there are many notes to each syllable of text, this procedure obviously cannot be maintained, so the accent is given to the first note of each neume group.

Thus, instead of there being two organizing elements of rhythm, musical and textual, as in the Solesmes interpretations, there is only one, the textual. However, because the ietus of the Solesmes interpretations depends a great deal upon the accent of the text to make it perceptible, the two schools appear to be very similar, at least in the passages which are virtually note-against-note. In the passages which are melismatic there would be a noticeable difference, because the "accentualists" accent the first note of each group,45

44 Reese, . cit., p. 141. Reese also explains that the historical basis of their belief in a single basic note-value is the fact that sometime during the fifth century (i.e., before the codification of the plainsong repertoire by Gregory the Great) Latin pronunciation changed from a quantitative basis (the use of different durations for long and short syllables) to a qualitative basis (the use of different dynamic stresses for accented and unaccented syllables). (Ibid.). 4 Dom Jeannin has said that "evidently it was this initial strong beat, which, in the golden Gregorian age, the liturgical castanets sig had to underline. In fact it is this especially strong beat and ordinary place for the liter- ary dynamic accent, which, in the Orient, is emphasized by the instruments of percussion, when they accompany liturgical chant." (quoted by Bonvin, 9. cit., p. 28). Reese says that this conclusion of Jeannina'Tsa based on a misinterpre- tation by Du Cange of the word tabula which he took to mean "castanets." The word actually refers to the covers of chant thile the Solesmes scholars accent only one of these initial

notes of a group out of several which are thought of as comprising a "phrase."

A third interpretation of chant rhythm is that of the "mensuralists," headed by Peter Wagner. Wagner claims that from the beginning (ca. 600 A.D.) the Latin neumes were not

only melodic symbols but also rhythmic symbols, and that

there were two basic durations corresponding to the later

long and the breve instead of just one as claimed by the

Solesmes and "accentualist" schools.46 The following passage

from Guido d'Arezzo's "Prologue Antiphonarii Sui"47 supports

to some extent the contention that the neumes were rhythmic

symbols, but is certainly not proof for two durations:

How sounds are liquescent; whether they should be sung as connected or as separate; which ones are retarded and tremulous, and which hastened; . . . all this is shown in the shape of the neumes itself, if the ueumes are, as they should be, carefully put together.40

The long and the breve are transcribed respectively by the

"mensuralists" as a quarter note and an eighth note, and books which were sometimes made of ivory etc. (Reese, 22, cit., p. 141).

4 6 Adler, ap. cit., p. 79. Curt Sachs holds the opinion that historically this school of interpretation is the most correct. (Sachs, op. cit., p. 152). 4 7Gerbert, . cit., 11, 34-7, translated by Strunk, o . cit., pp. 117-20. 8 Ibid., p. 37, ffrom the translation in Strunk, p. cit., p. 120. there is the occasional use of a horizontal episema (a short

dash) to indicate a slight lengthening of a note and a dot

to indicate a slight shortening of a note.4 9 The use of

these two durations does not approach organization into re-

current metric patterns, except (as would be expected) in the case of a syllabic hymn setting.

Much of the historical proof cited by the "mensuralists"

in support of their interpretations comes from the early pe-

riod of polyphony and is thus especially valuable for the

problem of rhythm in polyphony. For example, a passage from

the eleventh-century treatise of Aribo Scholasticus50says:

"Formerly, great care was taken not only by composers of song

but even by singers, that all should compose and sing accord-

ing to the law of proportion. This consideration is recently 5 dead and buried." 1 The "mensuralists" believe that Aribo referred to polyphony as the recent cause of these proportions 52 in music being lost. The difficulties of singing in more

k9see the transcriptions by Wagner in Adler, a. cit., pp. 93-5 and those in Bonvin, 2. cit. , pp. 24-26. 50Aribo Scholasticus, "Musica," Gerbert, g2. cit., II, 197-230.

5 1 Ibid., p. 227a: "Antiquitus fuit magna circumspectio non solum cantus inventoribus, sed etiam ipsis cantoribus, ut quilibet proportionaliter et invenirent et canerant. Quae consideratio iam dudum obit, imo sepulta est."

5 2fonvin, a. cit., p. 27. 17

than one part, they claim, were great because of the novelty of polyphony, and performance was made easier by reducing the number of note durations to one.53

Not only do the "mensuralists" employ two basic note values, but they also claim that there are definite metrical patterns formed by the combination of these values, albeit these patterns are very irregular. Again, there is some historical basis for this assumption because several medieval treatises closely connect the rhythmic structures of music and poetry. For example, there is the phrase "song is beat according to its metrical feet"54 in the ninth-century treatise Scholia Enchiriadis, and Guido of Arezzo wrote in his

Microlo:.1

By no means, however, is there an inconsiderable resem- blence between poetic meter and music, for the neume groups take the place of the feet, and phrases take the place of verses, since this neume flows in dactylic meter, that in spondaic, the other in iambic, and you

53Reese, p. cit., p. 144.

G54erbert, . cit., I, 182b: "Metricis pedibus cantilena plaudatur." Curt Sachs remarks that three sources of the ninth, tenth, and eleventh centuries (unfortunately without citation) indicate that the chant had a steady tempo which was beaten with the hand, the foot, or otherwise, He concludes that when tempo is beaten, the difference between long and short notes has to be rational. (Curt Sachs, Rhythm and Tempo, p. 154). The short passage above from the Scholia Enchiriadis may be one of the three sources Sachs refers to. 18

see a phrase of now four feet, now five feet, and at other times, as it were, of six feet.5>

That this kind of rhythm (the alternation of longs and shorts) was either a resumption or a continuation of the kind spoken of by St. Augustine can be seen by a comparison of these later treatises and the following passages from St. Augus- tine's treatise on music (ca. 386 or 387 A.D.).5 6 It should be pointed out, however, that St. Augustine wrote during the time when a quantitative basis for Latin pronunciation pre- vailed, and his apparent preoccupation with verse, together with the fact that he was a composer of hymns (both words and music) suggests that the music he refers to may be that of hymns only. If these passages do refer also ttethe "prose" rhythm of plainsong, then plainsong rhythm, at least in

Augustine's time, comprised long and short notes in accord- ance with the "mensuralist" interpretations.

55Gerbert, p. eit., II, 16b: "Non autem parva simili- tudo est metris et cantibus, cum et neumae loco sint pedum, et distinctiones loco versuum, utpote ista neuma dactylico, illa vero spondaico, illa iambico metro decurreret, et distinctionem nunc tetrametrum, nunc pentametrum, alias quasi hexametrum cernes .

56 Eugene Portalie, "Augustine of Hippo," Catholic Eheyelopedia, Vol. II (1913).

57Joseph Otten, "Ambrosian Chant," Catholic Encyclopedia, Vol. I (1913). This article contains some restorations of Ambrosian hymns (composed about the time St. Augustine wrote his treatise on music) by G. M. Dreves. They employ a regular alternation of two values, a long and a short, which are transcribed as a whole and a half note. 19

And suppose an instruments 8 struck in rhythm, with one sound a time's length and the next double repeatedlyQd connectedly, to make what are called iambic feet. . . Those who know these numbers and discern them in the beats and dancing, easily identify them. And those who don't know them and can't identify them, aAit nevertheless they get a certain pleasure from them. 0'When you say " cano or put it in a verse, in such a way as to prolong its first syllable when you pronounce it or in such a place as to make it necessarily long, the gram- marian will censure you . . . But on the contrary the reason of music whose province is the rational and nu- merical measure of words, takes care only the syllable in this or that place be contracted or prolonged according to the rationale of its measures. For if you should

58 The word "instrument" is apparently an interpolation by the translator, because the phrase in Latin reads: "Si quispiam numerose plaudet . . ." The translation should be. "Suppose someone beats musically," etc., which brings the meaning close to that of the phrase from the Scholia Enchiri- adis: "Metricis pedibus cantilena plaudatur."(see P. 17). 59Another passage in this treatise (pp. 50-54) presents the method of measuring metrical feet in verse. The conductor divided each foot into two parts, arsis and thesis, with an up and down motion of the hand. A further division of these two parts into equal units called "times"was made by the performers. A curious thing to the modern reader, who is accustomed to the equal duration of beats within a given passage, is that in some feet the up motion of the conductor's hand was not equal to the down motion in the number of "times" they contained, e.g., the Amphibrach, which contained an arsis (up-motion) comprising a single short of one "time" and a thesis (down-motion) comprising a long and a short of three "times." 6o Saint Augustine, De Musica, translated by R. Catesby Taliaferro, p. 33. (The Latin appears in Jacques Migne, Patrologiae Cursus Cmpletus series Latinag, XXXII, 1098- 109. 20

put this word where two61 syllables ought to be, and should make the first syllable, which is short, long by pronunciation, the 'science of music will not for that be outraged in the least. For these word-rhythi~ have been heard which were necessary to that number.02

From these three interpretations of monophonic rhythm

and from the historical evidence quoted, it is possible to

glean some characteristics of rhythm in the early Middle Ages

which may have served for polyphony. As mentioned before,

the one rhythmic quality which all interpretations share, and

which all the historical evidence touching upon the matter

supports, is that of the irregular organization of the notes,

e.g., the "free interlacing of binary and ternary groups of

notes" which characterizes the Solesmes interpretations, the

organization of the music by textual accent which character-

izes the "accentualist" school, and the use by the "mensural-

ists" of two durations to construct irregularly recurring

rhythmic patterns. Moreover, although there is no agreement

as to whether two basic durations or only one is implied by

the neumes, all three schools are agreed that at least there

are very few of them. This conclusion is of considerable

importance to the history of musical style. Whatever the

6lThe Latin at this point says "duas longas syllabas" (two long syllables) instead of merely two syllables as in the translation here. 62Saint Augustine, De Musica, translated by R. Catesby Taliaferro, pp. 35-36. The Latin a ears in Migne, Patrolo- giae Cursus Completus j eries Latin, XXXII, 1099). 21

reason, whether a desire to set the texts clearly, or perhaps the limited ability of performers (due, for example, to problems of notation and conducting), or even the musical taste of the period, the important fact is that in the only musical repertoire at all widespread and systematized during the early Middle Ages, the rhythm apparently comprised no more than one or two note-values. Furthermore, there is no evidence that there were any additions to these until late in the period. The first patterns of modal rhythm introduced into music in about the twelfth century supposedly comprised only a long and a short,63 and throughout the twelfth century these two were the most used, even after the addition, late in the century, of one longer value, the perfect long of three "beats" (tempora), into modal rhythm.

The application of the rhythmic characteristics of early

Christian monody to the examples of early polyphony as given in the Musica Enehiriadis, the Scholia Enchiriadis, the

Mierologs, and the Ad Organum Faciendum raises a new problem: the musical examples (which are based on plain-chant melodies) in all four treatises are in Dasia or letter notation,64 yet

63Reese, a. cit., p. 274.

6 4Apel, sp. cit., pp. 204-207. Another early example of polyphony in letter notation is the eleventh-century composition Ut Tuo Propitiatus. There is a facsimile of the original from the Codex of the Bodleian Library, Oxford in Apel, 9k. cit., p. 205. A modern transcription appears in Apel and Davison, pp. cit., 1, 22, example 26b. 22

the three interpretations of the Chant (Solesmes, "accentualists,h and "mensuralists") depend to some extent upon the writing of the music in neumes. In the syllabic sections, of course, the textual accents would easily permit the 'ae- centualist" interpretation, but in the melismatic sections

(where the "accentualists" assign the accent to the first note of each neume group there would still be the problem created by the Dasia and letter notation which show no grouping of tones. The fact is that the chant melodies (including their rhythm) were probably well enough known so that only the vertical relationship between them and the newly added parts needed to be demonstrated. This vertical combination of parts was new in music; therefore, it had to be written in a notation which was clear. The exact notation of polyphony was possible only with Dasia or letter notation because they showed the pitches unequivocally. Neume notation at this time (before ca. 1100) was such that it could not show separate pitches accurately, and even at a later period it presents great difficulties for aligning the parts properly.6 5

Neumes were apparently not used for this reason, even though

they showed the grouping of notes. Curt Sachs' conclusion

that "in the western world, the use of a rhythmically non-

committAl notation in times when a metrical script was

65Apel,j. cit., pp. 210-214. 23

66 available indicates a free or optional rhythm" does not

appear as necessarily valid for this particular case. As an example of a chant melody set polyphonically,

there occurs in the Musica Enehiriadis part of the Te Deum which serves in the treatise to show various methods of com-

bining two voices.67 The corresponding monophonic version 68 can be seen in the Libor Usualis. A comparison of them shows that the polyphonic version in the Musica Enchiriadis

(Fig.3b) does not have more than one note to a syllable, but in the monophonic version from the Liber Usualis (Fig.3a) there are two notes set to the syllables "Pa," "ter," and

"ego.

Tu PaTrlb St"Pi-'rqrnU5 es r4i-V

Fig. 3.--A passage from the TeDeum in a) the monophonic version from the Liber Usualis and in b) the polyphonic version from the iuTea Enehiriadis.

66 Sachs, Rhytm and Tpo p. 178. 67 Gerbert, a. eit., I, 171. 6 8Liber Usualis, p. 1833 (fifth stave).

69Reeses.20' ei., p. 254. 41I

As one can see, where there are two notes to a syllable in the monophonic version, the second of the two notes is absent in the Musica Enchiriadis. The Libor Usualis version may represent a later embellishment or the Musica Enchiriadis version, a simplication. That the difference occurs because of a simplication of the polyphonic version in deference to the difficulties of polyphony (perhaps similar to the difficulties which the "mensuralists" claim caused the use of fewer note values, see pp. 16-17) does not appear likely because part of an alleluia which has two notes to a syllable in two places is also used as an example in the Musie aEn- chiriadis.7 0 The tempo direction "slowly and deliberately"71 given in the Musica Enchiriadis for orggnum has led to two different opinions among modern scholars: 1) that the tempo was very slow and awkward; 7 2 and, 2) that the original tempo of the chant could be maintained generally. It is conceivable

70Gerbert, a. eit., I, 156. 71Sachs, R and Tempo, p. 157 and Reese, 2.- e1it., pp. 253 and 26?neither writer quotes the exact location of the passage). 72This view is supported by Sachs and Ludwig Bonvin. Bonvin cites a "Hucbaldian source" which says that the slow tempo of organum destroyed the proportions between the long and short notes. (Sachs, h and TeMo, p. 157 and Bonvin, a. eit., p. 16).

73 This view is supported by Reese. (Reese, 2. cit., p. 265). 25

that, after some of the new problems created by org were solved, the tempo of the original chant melodies was attempted in polyphony. The lttclihood of eventually regaining the old tempo and the other subtleties of plainsong rhythm is increased by the fact that the polyphonic sections were sung by a few picked soloists, reducing the problems of performance as compared with polyphonic singing by large groups.

Sometime during the two or three centuries (ninth through the eleventh) of basically point-against-point or-

g, perhaps in the early part of the eleventh century, one of the most important rhythmic techniques of the Middle Ages began to develop: the use of more than one note in a part against a single note in another part. The combination of this technique with the greater freedom of motion between the parts, i.e., a mixing of contrary, parallel, and oblique motion (as, for example, in the eleventh-century compositions Cunotipotens genitor, Ut tuo propitiatus, and Alleluia lus Domini),75 marks the end of the first period of polyphony, in which the liturgical melody dominated the polyphonic composition both melodically and rhythmically. The use of

74 manfred Bukofzer, "The Beginnings of Polyphonic Choral Music," Papers of the American Musicological Society, 1940, p. 23. See also Apel and Davison, . eit., , 217 (commentary on example 26c).

75 .Apeland Davison, _2. eit., 1, 22 (examples 26a, b, and c). 26

various kinds of motion between parts, i.e., the divergence from simple parallel motion, apparently precedes the rhythmic development by more than a century. We can see an occasional example of this divergence in the earliest expositions of polyphony, the ninth-century Musica and Scholia Enehiriadis,76 although in them it arose incidentally from the avoidance of the tritone rather than from any musical consideration of the different motions for their own sake.77 The lengthening of a note in one part may have been a result of the more independent voice-leading, because the use of oblique motion (on, voice on the same pitch while the other voice changes pitch) in a melismatie passage would force the singers who stayed on the same pitch either to articulate the separate notes without a new syllable to give the articulation definiteness or to just hold the notes as one for a duration equivalent to their combined values. The Micrologus of Guido d'Arezzo (ca. 1095-1150), the Ad OrSm Faciendum (eleventh century),, the few actual compositions of the eleventh century, and the Musica of John Cotton 8 (ca. 1100) mark the beginning in polyphony of differing

76Gerbert, a. cit., I, 169-171, 188, 190. 6ee the discussion in Reese, pp. eit., pp. 253-260. 8Jos.Smits Van Waesberghe remarks that the surname "Gottal for the writer of this treatise is historically un- founded. He suggests the name "John of Afflighem" insead. (Jos. Smits van aesberghe, "Some Musical Treatises and Their Interrelation," Musia Disciplina, III (1949), 95-118). 27

rhythmic structures in vertically-combined parts. In the earliest of these sources, the Micrologas, Woobridge79 and ReeseBO believe there is sufficient evidence to assume that the writer sanctioned the use of more than one note of the plainsong melody to a single note of the added part. The following passage from this treatise undoubtedly supports them:

On the other hand, when the singer admits tones lower than the third tone, we often sustain the organum at the third tone; then indeed it is necessary that the singer should not make a pause in the lower tones, but let him remedy this aforesaid third tone by returning fjn the prinipalis, or plainsonrs7 with swiftly-running notes, and he shoud retard his own Jar and that of the other by a pause in the upper tones.

Although the grammar of the last clause of this passage is somewhat obscure, it can readily be seen that the organum,

79 Harry Wooldridge, The Polyphonic Period, Part I, Vol. I of The Oxford Hi of Music, edited by Percy Buck, p. 28. BOReese, 2p. cit., p. 260.

l"Saepe autem cum inferiores trito voces cantor admi- senit, organum suspensum tenemus in trito; tune vero opus ist, ut in inferioribus distinctionem cantor non faciat, sed discurrentibus cum celeritate voeibus praestolanti trito re- deundo subveniat, et suum et illius facta in superioribus distinctione repellat." (Gerbert, 22. cit., II, -22a). Apparently, the references to the "thirdtone" (trito) in this passage refer to the lower limit placed onthe movement of the added part, or organum (see the discussions in Wool- dridge, g. _mfil'., pp. 21-32 and Reese, 9p. cit., pp. 259-260). 82 Another difficult passage in the Micrologus also probably refers to this difference in the rhythm of the parts in polyphony: "Aliae voces ab alliis morulam duplo longiorem, vel duplo breviorem, aut tremulam habeant, id est, varium tenorum." (Let the other voices have a little delay longer 28

or organizing voice (the lower voice in Guidoe's two-part examples) was at times rhythmically different them the plainsong to which it was added, and that this difference meant a

sustaining of the added part while the plainsong continued.

Moreover, the passage about the singer "returning with swiftly-running notes" apparently means that when the singer of the plainsong melody descended below this "third tone," he was to sing all the notes in that ptrt of the scale

quickly, and was to continue this until the plainsong went on to a higher part of the scale. The sacrifice of the normal plainsong tempo is surprising in so early a treatise as the Mierlogus (first half of the eleventh century), and it may be that the performance of such passages in a faster tempo represents one of the earliest important effects of polyphony on plainsong rhythm. Before the icrologus the

original rhythm of the plainsong melody was probably main-

tained in polyphony, and this was apparently the case in the polyphony described by Guido, except in those instances where

the plainsong went below the "third tone." It is obvious that this principle of altering the tempo of the plainsong

represents an influence upon rhythm by extra-rhythmical elements of music, and it offers a case somewhat similar to that

than a doubled note Luplof7 or shorter than a doubled note, or a tremulo, that is, let it have a varying length.) Gerbert, * cit., II, 15a. The connection here between notes whih are a little longer or a little shorter than (or in) the dupj with the tremulo may indicate a type of free, rabato-like treatment of the rhythm in some passages. 29

of the influence of consonance and dissonance upon rhythm in the organa dupla of the late twelfth century (see Chapter II, p.73, The examples of polyphony in the Micrologus also apparently support the assumption that vertically-coincident notes were not always of the same durations3 although the principle of sustaining the added part, brought out in the text of the treatise ("organum suspensum tenemus in triton) , cannot be detected from the letter notation in which the examples are written (see Fig. 4a).

CF F D F CD D C DF E C E D veni ad docendum nos viam prudentiae C C C C C CC A CCC C COD

Ve-_4 a"do -c t ;%.d-

Fig. I.--An example from Guide d'Arezzo's CI3ol in: a) the original notation; b) a transcripti7nbAiibros; c) a transcription by Wooldridge.

83Wooldridge, 2. cit., p. 37.

8 4Gerbert, 2* cito., II, 23a. 30

Ambros has transcribed the examples in the MI los so that the durations in one voice are always the same as in the other voice (Fig. 1b), 85 just as they appear to be in the original notation. However, Wooldridge has transcribed them as having rhythmically different parts (Fig. 4c). 86 He evidently has applied a principle similar to the conclusion stated on page 26: the use of oblique motion in melismatic sections may have led to substituting a single protracted tone for what is notated in the Mierologs by repeated letters. Actual compositions of the eleventh century also have similar passages, and the transcription of them by more recent scholars than Wooldridge shows that they have reached a similar conclusion about tying together notes such as these.87 The late eleventh-century treatise Ad Organum Faciendum describes five modes, or methods, for using the polyphonic technique. The fifth is of interest in the study of the changing rhythmic relationship between parts in early polyphony because it (the fifth method) "arises from the multi- plication of opposite notes by augmentation or diminution." 8 8

85August Ambros, Geschichte der usik, 3rd ed.,II, 181. 86Wooldridge, E. cit., p. 27.

87Apel and Davison, R.. cit., p. 22 (example 26b).

88 "Quintus per multiplicationem oppositarwm vocum, augendo vel auferendo." (Charles Coussemaker, Histoire de l'Harmonie au Mo en Age, p. 233, cited by Wooldridge, 2P. cit. , p. 39) . 31

89 The following example (Fig. 5, a transcription by Wooldridge? is given in the treatise to illustrate the "fifth method."

Fig. 5.--The fifth method of the Ad Organum Faciendum.

In its original notation this example90 (at the close, or occursus) may show an instance where the principle just mentioned of tying together notes in certain passages could be applied; that is, unless some notational sign was used to indicate a longer value. Whether or not Wooldridge used this principle in transcribing the examples cannot be seen from the example91 (the bottom part merely has one note set against five notes in the upper part), and he does not mention it in the text of his book. It is conceivable that he did, however, because of the way he transcribed the examples in the Microl-

a treatise a little earlier than the Ad pOranum Facien-w dum and also written in letter notation.

89wooldridge, p. cit., p. 39. 90Charles Coussemaker, Histoire de ItHarmonie au Moyen Age, p. 233, cited by Wooldridge, _2. cit., p. 39. 9 1 The original notation was not available to the present writer for comparison. 32

The examples in the Ad Organum Faciendum show the plainsong melody to be below the added part.92 Thus, the illustration (Fig. 5) of the "fifth method" may be one of the earliest uses of more than one note of the added part against a single note of plainsong. It will be remembered that in the earlier Mierologus there are at times more than one note in the plainsong melody to a single note of the added part, but almost never is the opposite to be seen, i.e., more than one note in the added part to a single note of the plainsong melody.93 The Ad Ora Faciendum apparently stands midway between the Miroloas and Cotton's Musia concerning this relationship between the rhythm of the plainsong melody and the rhythm of the added part. The passage quoted previously from the Ad Organum Faiendum which describes "the multipli- cation of opposite voices by augmentation or diminution" could conceivably mean that either one of the two voices contained more notes than the other at times,9 while Cotton describes only the use of two, three, and perhaps more notes in the added part against a single note of plainsong:

92Reese, ,. *cit., p. 262. 930ne exception to this occurs in an example from the MicroloAs transcribed by Wooldridge. At the occursus the added part has two notes set to the last note orthe lain- song melody. (Wooldridge, o. cit., p. 25).

94 Wooldridge apparently translates "oppositaram voeuxu" as "organal notes" (see page 42), because he remarks that "the fifth mode arises from the augmentation or diminution of the organal notes." (Wooldridge, g. c.it., p. 39). 33

You ought to notice however much I should lace simple organum in simple mode jnote-against-notW, still to any singer of the organizing part j he added parj it is permitted to double or to triple the simple mode or to bring together any suitable mode, if he chooses.A5 It would seem to have been some time in the second half of the eleventh century that the technique first described by Guido (the use of more than one note of the plainsong melody to a single note of the added part) gave way to the other alternative, i.e., increasing the duration of the liturgical melody's notes in order to sound against each of them several notes of a newly-composed melody. Guido's method of setting longer notes in the added part against the eantus firms was very limited in its possibilities. Its development would have resulted merely in a type of sustained accompaniment to the old melodies instead of the composition of new melodies. After the Mierologus it seems to have been gradually abandoned, as was shown in the passages from the

Ad Oram Faciendum and Cotton's Musia (see pp. 30-33). An early culmination of the technique of using more

than one note in the added part against one note of the cantu firms was reached in the two-part organa of St. Martial

9 5 "Animadvertere etiam debes, quod quamvis ego in simplicibus motibus simplex organum posuerim, cuilibet tamen organizanti simplices metus duplicare vel triplicare, vel quovis modo competenter eonglobare, si voluerit licet." (Gerbert, . cit., II, 264b). Wooldridge remarks about this passage that Cotton "probably also intends to sanction the use of two or three notes of the plainsong against one of-organum." (Wooldridge, . cit., p. 37). 34~ and Santiago de Compostela. These two schools of composition flourished in the first half of the twelfth century, soon after the date (ca. 1100) of Cotton's treatise, in which (as we have seen) polyphony employing two, three, or more notes in the added part against one note in the plainsong melody was described. There apparently were precipitous gains made by this technique in the first quarter of the century, or else Cotton was a somewhat conservative theorist, because in the polyphony of St. Martial and Compostela there are at times as many as thirty-seven notes in one melisma of the added part against a single note of the borrowed, litur- gieal melody.9 7 This many notes in a melisma of the added part does not occur very often; instead, from two to ten notes in the added part to a single note of plainsong is characteristic of the style, as in the following example

e a

Cvvn- ttio - e Fig. .-A chargeteristic passage in the "sustained-tonen style of polyphonic writing.

96See Appendix I for the sources of transcriptions of these organa.

9 73ee the Benedicamas Domino transcribed by Handschin in Heinrich Besseler, Die Musik des Mittelalters und der Renaissance, Vol. II, Handbu6h diierMusikwissenschaft, edited by ErnstBdeken, pp. 97-8. 98 From the two-part organum Cuntipotens Genitor (School of Compostela, ca. 1125), transcribed in Apel and Davison, . cit., 1, 23 (example 27b). Of considerable interest is the use of this new style, the "sustained-tone" style, and the older note-against-note style in the same composition. The organum Viderunt Hemanuel9 shows this combination of styles in a single short section.

Apparently, the missing composition from an anonymous Tracta- t de Musica100 of the period (which Handschin assigns to the 101 St. Martial circle) also employed both styles, because the text includes this passage: "Note that the organum of the

Benedicamus corresponds now to the eantus and now to the discantus; note in what way the discantus is different flom the cantus and the organum different from the discantus."0 In a preceding passage the writer distinguishes between discantus and organum:

Certainly, between disantus and organum, it is clear that there is this difference, that discantus corre- s onds to its cantus by an equal number of notes junctoLm7 . . .; or anum, on the other hand, does not have the same number of notes as its cantus, but agrees with it by an infinite multiplicity and a mar- velous flexibility.103

991bid., (example 27a). 1 0 0 Jacques Handschin, "Zur Geschichte der Lehre vom Organum," Zeitschrift _fr Musikwissenschaft, VIII (1926), 333-336. 101Ibid-.,p. 337. 102"Nota quod suprascripti Benedicamus organum nune cantui, nune discantui respondeat; nota qualiter discantus a cantu, a discantu organum differat." (Ibid., p. 335). 1 0 3 "Inter discantum vero et organum hoe interesse pro- batur quod discantus equali punctorum munero cantui . organum autem non equalitate punctorum, sed infinita multi- plicitate, ac mira quadam flexibilitate cantui suoe concordat." (Ibid.) 36

Handschin interprets the last passage quoted to mean that discantus was a note-against-note style, and that or- ganu was a rhythmically decorated contrapuntal style. There are actually two musical examples missing from the treatise,

one illustrating organum and the other illustrating organum with discant, so Handschin has printed a three-part Benedid camu domino from the Compostela school (ca. 1140) to take their place.lO 4 The fragment in Fig. 7 is taken from this composition. It will be noticed that the combination of

Fig. 7.--Part of a twelfth-century Benedicamis domino which illustrates organum with discant. styles, note-against-note with the "sustained-tone" style, is accomplished in a way quite different from that in the example cited previously, the organum Viderunt Hemanuel.lO5

O4.Ibid., pp. 336-337.

105Apel and Davison, g. citi., I, 23 (example 27a). 37

In the Viderunt there is the linear juxtaposition, as it were, of the two styles, but in the Benedicamus the combination is a vertical one, with the two bottom voices moving in a note-against-note style, or distant, while the upper voice has more or less regularly two and four notes to one in the lower voices.lo

This twelfth-century distinction between distant (note- against-note style) and organum ("sustained-tone" style) was apparently one of the earliest differentiations to be made between the two terms.107 About this time polyphony began to develop strongly in both directions, and continued to do so for about a century. Naturally, this point of terminology would not have arisen during the centuries of polyphony preceding St. Martial because the compositions were virtually note-against-note. As has been shown previously, the Musica of John Cotton, written about twenty-five years before

St. Martial, described the use in polyphony of two, three, or more notes in the added part against a single note in the

cantus firmus. Cotton, however, did not differentiate between the two styles but included them both in his two terms

for polyphony: "diaphonia" and "organo."108 Although the

106Another transcription of this composition (by Fried- rich Ludwig) appears in Reese, a. eit., p. 268. 1 0 7 Reese, G., a. cit., pp. 268-269. 108Gerbert, 2. cit., II, 263. 38

St. Martial circle apparently did make such a differenti- ation, the close relationship of everything polyphonic (at this very early stage of its development) is perhaps demonstrated by the fact that the word discantus was the new term chosen to designate one of the styles, and discantus is merely another word for diaphone. or organum.lg It is strange, however, that the new word was used to indicate the older, note-against-note style, while the old word organum was chosen to indicate the newer style.

Reese points out that this terminology was probably not very widely accepted at first and that the word distant later

(in the thirteenth century) came to mean measured music as opposed to organum, or unmeasured music.110 It is significant, however, that the qualities of the music which caused the distinction in terminology between distant and organum, i.e., whether the parts were combined in a note-against-note style or in the sustained-tone style, are also the qualities which differentiate distant and organum in the later terminology of Johannes de Garlandia and others. For example, Garlandia defines discantus as "the simultaneous sounding Leonsonantia7 of different melodies according to mode and according to the

109Reese, G., o. eit., pp. 268-269.

11O0id 39

equivalence of one to another," and in organum he says,

the equipollentia that is, relationshi of the upper to the lower part in this type of music/ is limited to a single tone 1inisono: the sustained note of the tenor7, till the end of each punctus section based on 112 one tenor note7, where the two parts meet in consonance.

Disregarding for the moment the implications of modal rhythm, these characteristics correspond exactly to the description of organum and diseantus given in the Saint Martial anonymous

Tractatus de Musica. Thus, it appears that the essential distinctions of the early twelfth century writers, with regard to the vertical combination of similar or dissimilar parts, were carried over intact into the treatises of the mid-thirteenth century, with the addition, in the later works, of rules concerning the treatment of modal rhythm.

The problem of rhythm in the St. Martial and Compostela organa is clouded by the deficiencies of the neume notation.

Even though the two-part compositions are written with the neume characters on a staff ("diastemitid,"or "heighted" neumes), there are still no durations indicated for any of the notes or groups of notes. Moreover, the vertical alignment of the parts is not by any means beyond doubt. Just a

From a translation by William Waite, "Diseantus, Copula, Organum," Journal of the American Musicological Society, V (SummerT1952),"T6.76"Te"atin occurs in Charles Coussemaker, Sriptorest . . . I, 106b.

11 2 From a translation by Willi Apel, "From St. Martial to Notre Dame,"Journal of the American Musicological Society, II (Fall, 190p9),71.97. T eatin occurs in Coussemakero- Scriptores#. . . I, lkb. 4+0

glance at the original notation1 1 3 is sufficient to convince

one that there must be many knotty problems connected with 1l4 the transcription of these compositions into modern notation.

Concerning the vertical alignment of parts, Willi Apel be-

lieves that the original manuscripts should be followed as

closely as possible. Furthermore, the tenor should change

notes at the beginning of a note-group, and, generally, there

should be a consonancel formed when the two voices coincide

at the beginning of each tenor note. Peter Wagner's tran-

scriptions of the Codex Calixtinus117 do not exhibit any im-

provement over the original manuscripts in the matter of

vertical alignment. Wagner used modern plainsong notation

See Apel, Notation, facsimile 144, p. 211 and fae- simile 45, p. 213.

ll4Apel cites the transcription by F. Ludwig of a St. Martial composition Viderunt Hemanuel (Adler, 2R. cit., p. 14k8, ex. II, saying of it that"the act that a transcription presented by so outstanding and scrupulous a scholar as Ludwig is open to severe question only goes to illustrate the difficulty of the situation." (Apel, Notation, pp. 209-210). 115 The consonances of the period immediately succeeding St. Martial (those of the earliest Notre Dame compositions) are thought by Apel to have been the unison, octave, fourth, fifth, major, and minor third. (Apel, "From St. Martial to Notre Dame," Journal of the American Musicological S00isty, II (Fall, 1949), l51-12T~ The treatise Discantus Positio Vulgaris of ca. 1225 says that "it is to be obserVed-that the unison and octave are perfect consonances; the major and minor third imperfect; the fourth and fifth intermediate" (translation from Wooldridge, o. eit., p. 88). 116 Apel, Notation, pp. 210-214. 11 7 See the facsimile from Wagner's Die Gesange der Jakobsliturgie in Apel, Notation, p. 212. 41

for these transcriptions, a point in favor of such notation being that it preserves quite well the original neume groups of the manuscripts and does not imply any kind of measured rhythm. The transcriptions of Apel, on the other hand, indicate the neume groups by phrase marks, and "free" rhythm is implied by noncommital, round note-shapes without stems; the vertical alignment is shown unequivocally although Apel admits that he is not absolutely sure of the correct alignment at all times.ll8

The melismatic upper parts of the St. Martial and Compo- stela organa are obviously more important than the lower parts, the latter (the tenors) following along in a suitable, concordant accompaniment resembling at times a type of

"drone" 11 9 or perhaps a pedal point. The rhythmic style of this type of upper part is described by modern scholars as that of plainsong, i.e., a free, "prose" rhythm. Friedrich

Ludwig says: "The basis of the melodies in these _ -fi

St. Martial comes from a very strong artistic feeling for solo-art."1 2 0

The irregular groups of notes in the upper parts occur 121 in two ways: 1) over a very long tenor note, which

ll8 Apel, Notation, p. 214. 9 Reese, j.. cit., p. 265.

1 2 0 Adler, o2* citp.* p 150.

12 1 See the Benedicamus Domino in Besseler, p22.cit., pp. 97-98. 42

necessitates a performance of the musical and textual accents

similar to that of melismatic chant; 2) over tenor notes which occur more often and virtually always on the first note

of every neume group, 1 2 2 giving further emphasis to what were

evidently points of stress. The conclusion of Apel's123 that

the notes of the tenor should change on the first note of a

neume group may offer some support for the belief by the

three schools of chant interpretation that the first note of

a neume group in plainsong should receive some sort of

special emphasis. Conversely, of course, Apel's conclusion

is supported by these schools of chant interpretation. The

practice of placing a new tenor note at the beginning of each neume group stresses the irregularity in length of successive

note groups in the St. Martial and Compostela organa: thus,

the "prose" qualities of the rhythm are stressed.124

In the performance of the organa in the "sustained-tone"

style (those of St. Martial and Compostela) the durations of

the long tenor notes could not have been determined in the

same way that such notes are counted out by performers today.

This is due simply to the fact that the period (the mid- twelfth century) is prior, evidently, to any strict kind of

12 2 See the example in Besseler, 9. cij., p. 96. I23t is evidently Besseler's also because he transcribes a Compostela piece using that method. See Besseler, 2. cit., p. 96. 12lsee parts of Davison and Apel, 9. eit., examples 28a and 28b. 1-3

measure in music. Some type of counting in "times" temperaa), such as that described by Saint Augustine for the reciting of verse could have been used, but apparently the singer of the tenor part merely held a note until the notation of the upper part or the conductor indicated that the melisma in the upper part was over.125 Even in one of the rare three- part compositions of the early twelfth century, a Benedicamas 126 trope Congaudeant Catholici, the singers of the two lower parts could have held their notes until the proper meeting place with the more melismatic part. The difference between this practice and the modern one is especially notable in much of the modern instrumental music for several instruments.

The music used by the individual performers in such compositions is usually not in score form, as was early polyphony to about 1225;127therefore, the unit of time indicated in the music and beat by the conductor (a unit common to all the

125Apel, Notation, p. Besseler says that keeping the two parts together depended on the immediate understanding (Runmittelbar VerstAndigung") between the performers. Besseler, _ cist.., p. 98. 6 JacquesJ2 Handschin, "Zur Geschichte der Lehre vom Organum," Zeitschrift fdr Musikioissenschaft, VIII (March, 1926), 336. This cMoition actually comprises two lower parts in exactly the same rhythm and a slightly embellished upper part; therefore, with the exception of the examples of polyphony in the Musica Enchiriadis and the Scholia Enchiriadis in which the two parts are exactly alike rhytthe rhythm of this three-part piece is very similar to the two- part compositions of the period. 1 2 7 Apel, Notation, p. 262. 44~ performers) is the only means by which long tones can be accurately measured.

The period from the ninth century to the thirteenth is particularly distinguished by devices and techniques for ornamenting and enlarging upon the liturgical musical repertoire: the tropes of the eighth or ninth century;128 the introduction of polyphony in the ninth century; 1 2 9 the use of independently moving parts in polyphony; the lengthening of the notes in the liturgical melodies so that more freely composed parts could be written above them. This chain of developments appears to have been caused by an urge on the part of musicians to ornament and enlarge the liturgical repertoire according to the musical practice of their times, or perhaps it was largely a matter of the composers wanting to exhibit their skills in a medium (liturgical music) which

8 12 Reese, a. eit., p. 185.

1 2 9 "We can easily realize the connexion which exists between the art of tropes and early polyphony, the latter having been cultivated at the same centres as the former: this is because polyphony, or at least liturgical polyphony, was considered, like tropes, as an embellishment of the Gregorian repertory; polyphony did by superposition what the tropes did by interposition." (Jacques Handschin, "The Two Winchester Tropers,R Journal of Theological Studies, XXXVII (1936), 36, quoted in Reese, . cit., p. 264. would insure the best performance of their work.130 At any rate, the final result of these developments was that in the polyphonic compositions, the former balance between the part taken from the liturgical, monophonic repertoire and the new, added parts was completely upset: the predominant musical element became more and more the voices added to the old melodies rather than the old melodies themselves, as had previously been the case.

The lengthening of the notes of the borrowed, liturgical melody is important to the history of musical style for several reasons. First, it represents the beginning of elabo- rate polyphonic compositions on a cantus firmus. Second, it marks the beginning of the end in Western polyphony of the

"free," "prose" type of rhythm which polyphony had obtained from its close association with and development out of plainsong. The original rhythm of the plainsong melodies used in polyphony as bases for the tenor partsl3l became un- recognizable in the passages where a great many notes were sung over one note of plainsong. In the St. Martial and

1 3 0 "The canonical 'Gregorian' repertory could not be supplanted by another one; thus it was amplified, added to, interpolated . . . to creep into the liturgy was for the new art the only chance to live, because the church was the foremost concert hall of the epoch." (Handschin, id., p. 35, quoted in Reese, a. cit., p. 186.)

1 3 1 Compare, for example, the Kie shown in Apel and Davison, 2. cit.., I, p. 13 (example l5a) with its lengthened adaptation for the tenor of the polyphonic composition Cunctipotens genitor, also in Apel and Davison, Ibid., p. 23 (example 27b). Compostela pieces some of the plainsong melodies are set in a note-against-note style with the added parts, but more often each note of plainsong is sustained too long to allow any recognition of the melody's original rhythm. In the sue- ceeding polyphony of the Notre Dame school and in the thirteenth-century motets, this subsidiary role is always given to the Gregorian melodies (or parts of them), and they continue to be of subsidiary rhythmic interest. However, though the "prose" rhythm of the old plainsong melodies was corrupted by the lengthening of its notes, "prose" rhythm, as a type of organization based on irregularly recurring patterns of notes, was to continue to some extent throughout the twelfth century: notably, in the upper parts of the

St. Martial and Compostela organa and in sections of Leonin's and Perotin's organa dupla. "Prose" rhythm was therefore the rhythmic basis of polyphony until about the thirteenth century when modal rhythm began to develop. CHAPTER II

THE SYSTEM OF THE RHYTHMIC MODES

Between the early eleventh-century organa of St. Martial and Compostela and the rewriting of the Magnus Liber Organi de Graduali et Antiphnarie1 in modal rhythm by Perotin early in the twelfth century, what are possibly the most important developments in the history of Western rhythm took place: the steps connected with the change from a "prose" style of rhythm to a rhythm based upon the repetition of rhythmic patterns, or modal rhythm, and the establishment in music of a unit of measure whereby a note could be given a specific duration.

We see the culmination of this new rhythmic organization

in its codification into the six principle modes, or patterns, which comprised modal rhythm. Johannes De Garlandia, in his

De Musica Mensurabili Positio of about 1250, describes them:

A complete year's cycle of organa composed first by Leonin and later revised by Perotin. Only copies of this work are extant. See pp. 79"8% Chapter III.

2 There had been a system for measuring duration in verse centuries before the twelfth century, e.g. see Chapter I, pp. 1l-26.

3 Reese says that "the creation of a mensural system . constituted a revolutionary step in music history, a step more difficult of achievement and hardly less important than the creation of the staff. Gustave Reese, Music in the Middle Ages, p. 293. 48

The first mode comprises a long breve, a long breve, etc. The second, a breve long, breve long. The third, a long and two braves, a long and two braves, etc. The fourth, two breves and a long, etc. The fifth, all longs. The sixth, all breves.4

The modern transcriptions of these modal patterns generally utilize a reduction of the note values in the ratio of either 1:8 or 1:16, depending at times on the character of the composition or the preference of the transcriber.5

One scholar has even recommended for the Notre Dame composi- 6 tions a ratio of 1:32. Figure 8 shows the modal patterns

in the two most common reductions: a) 1:8, which changes

the old long to a modern half note and the old breve to a modern quarter note; b) 1:16, which changes the long to a

quarter note and the breve to an eighth note.

4Charles Coussemaker, Scriptorum de Musica Medii, I, 97. The account in the Discantus Positio Vulgaris(Coussemaker, Sjriptorum de usica Medii, I, 9bb) is essentially the same as Garlandiats. It was written in about 1225 (soon after the Notre Dame school distinguished by the strict, modal compositions of Perotin) and was probably the first exposition of the modes.

5Reese, p cit., p. 276. As recently as Harry Woold- ridge's publicationl"of volume I of the Oxford History of Music there was the reduction of i:{.,i.e., the transcription ofawhole note for the long and a half note for the breve.

6Hans David, "Problems of Editing Old Music," American Musicological Soeie andanPapers Proceedings, 1937,p.269 David also suggests that the lively character of these compositions by Perotin and his contemporaries could be better suggested by printing the notes closer together, as was certainly the case in their original or copied form, instead of the "spacious print of modern de luxe editions." 49

it Ii XA

3-i IiL I~N i I i I I .4 4 1~!I1 dio s $'c'W '..I''

Fig. 8.--Two modern transcriptions of the modal patterns

The necessity for making such changes comes on the one hand from the fact that as the vital quality of new music fades there is apparently a new emphasis on its classical qualities; this emphasis is usually accompanied by a reduc- 7 tion in tempo. On the other hand, the continual introduction of faster notes over a period of several centuries causes the durations of the notes to become longer and longer. The extent of this process can be realized by a brief comparison of the durations of the longs and breves mentioned by Garlandia and the Discantus Positio Vulgaris with their

durations today. The long of the early thirteenth century was probably equal to one beat of our tempo Riusto, or about eighty per minute; the normal breve was three times that fast. Today we do not even have a note form for the long, and the breve is equal to a double whole note.

7lIbid., p. 25. Heinrich Besseler, "Studien zur Musik des Mittelalters,t Archive flr Musikwissenschaft, VIII (1926), 214. See also Curt Sachs, Rhythm and Te po, pp. 171-173. Apparently, no mention of how the durations of the longs and breves were measured in performance is to be found before the Ars Cantus Mensurabilis, written by Franco of

Cologne in about 1260.9 In this treatise we find a system of counting the long and breve by means of a unit of measure called the teEisus, which is defined by Franco as "that which is a minimum in fulness of voice." 1 0 The perfect long had three tepora; the imperfect long had two tempora; and, the duplex long, which stood for two perfect longs, had six tpmpora. The proper breve had one teMpus and the altered breve two tepora. The major semibreve received two-thirds of one tempus and the minor semibreve one-third of one teus.II

9The Latin text appears in Coussemaker, . cit., I, 117-135. An English translation is in Oliver Strunk, Source Readings in Music History, pp. 139-159.

1 0 The term "tenpus" used here reminds one of St. Augus- tine's descriptionTof the t times" used to regulate the reciting of verse (see p. 25, footnote 3). Unfortunately, details concerning the motions made by the conductor are not given in France's treatise as they are in St. Augustine's. In fact, a conductor is not mentioned. However, from a passage in the treatise of Jerome of Moravia, written in the last half of the thirteenth century, we might conclude that the omission by Franco was not because a conductor was not known or used during his time, The passage says that "however many good singers there may be they should designate one to be pre- centor and director and to whom they should pay attention." Coussemaker, . cit., I, 93b. lThree minor semibreves stood for" a proper breve, and a major semibreve comprised two minor semibreves. Strunk, a. cit., p. 145. The smallest unit of rhythmic organization resulting

from the modes and these measured units of duration was

called a "perfection" by Franco. He defined a "perfection"

as any combination of longs, breves, and semibreves which equalled three tempora.13 Franco's period, however, is

rather late in the development of modal rhythm, actually

falling during the time when the modes were beginning to give way to other rhythmic devices. 4 During the rise of modal

rhythm and its strict use during Perotin's time (ca. 118040

1210), the organizational unit, although conforming precisely

to Franeo's definition of a "perfection," would probably have been thought of merely as comprising one pattern of notes in modes one and two, one-half a pattern in modes three and four,

one long note in mode five, and three short notes in mode

six. It would appear that there was no preconceived idea of

a ternary rhythmic structure, or "perfection," as it was

called later, but that there was a recognition of the struc-

ture as being ternary after it was already in use.15

Since Franco's period is late in the modal era, the

musical examples in his treatise reflect the fact that the

development of the modal system was at this time advanced to

the point that one modal pattern was not used for very long

in any of the parts, with the exception of the tenor (the

12Ii~d.,pp. 1344 and 156. 13 , p.14 14see pp. 91-119, Chapter III. 15Reese, #cit., p. 277. 52

tenor part during the modal period was characteristically lacking in the rhythmic variety and development shown in the upper parts). That the rhythm is modal, however, cannot be questioned, because in the opening sentences of section four of the Aras Cantus Mensurabilis France says:

A figure is a representation of a sound arranged in some mode. Figures are either simple or composite. The composite figures are the ligatures. Of simple figures there are three species--long, breve, and semibreve . . .

Since all music1 7 was written in these "figures," i.e., either

in ligatures (groups of notes) or in longs, breves, and semibreves (single notes), the passage must mean that all music was in modal rhythm irregardless of the modal system's advanced state of development.

In Franceo's treatise there is no exposition of the modal

patterns as such. That is, nothing is said specifically

about the structure of each pattern. However, his examples

must be in modal rhythm ("a figure is a representation of a

sound arranged in some mode"), and there are specific direc-

tions given by Franco concerning the duration of each note;

therefore, it would appear to be justifiable to draw conclu-

sions about the kinds of notes and their durations in the

various modal patterns from his examples and his explanation

of them.

16Strunk, _9. cit., p. 142. 1 7 Franco defines "mensurable music" as "melody measured by long and short time intervals." Ibid., p. 14.0. The first and second rhythmic modes, according to Gar- landia, comprised a long, breve and a breve, long respectively. Figure 9 is an example of Franco's (transcribed by

Strunk) which exhibits these two modes (the long is the note form with a stem; the breve has no stem) .18

. I I

Fig. 9.--An example of the first and second rhythmic modes.

Franco says of the example that "the first long is imperfect ftwo tempora7 and the second also, while the breves will both be proper fone tepus."19

The third mode, according to Garlandia, comprised a long and two breves, and a good example of it appears in Franco's treatise. There is no example of the fourth mode, probably because it was rarely used in actual compositions,20 How- ever, it is apparently universal practice to merely reverse the two perfections of the third mode, and from Garlandia's

18_Ibid Apel Th14e N i 9f 20Willi Apel, The Notation of Polyphonic Music, p. 231. description of the fourth mode as comprising two breves and a long, this practice would appear to be justified. Fig-a ure 10 is an example of Franco's and Strunks transcription of it which exhibits the third rhythmic mode.21

Am A

Fig. 10.--An example of the third rhythmic mode

Franco says of this example that "the long is perfect Lthree tempora7 . . . and7 of the two breves, the first, moreover, is called a breve proper Une tempus7, the second an altered breve /two tempora.t#2 2 By Garlandia's definition the fifth rhythmic mode comprised all longs and the sixth all braves. As in the case of the fourth mode there is no good example of mode six in

Franco's treatise, possibly because of its scarcity in

actual music up to the time of the Ars Cantus . . . There

are successions of proper breves in some of the examples (this was apparently the structure of the mode rather than a succession of altered braves), but these could very well 21S22 Strunk, g. c~it. , p. l1f3. 2Ibid. be instances of the fractio modi device, i.e., the division in a modal pattern of a note of normal duration into several notes. The most comon application of fractio modi was the division of an imperfect long into two proper breves. 2 3

Most of Franco's examples containing successions of proper breves apparently show this type of derivation for them, one such succession appears in Figure 11 which is an example of the fifth rhythmic mode.2+

SIiz

Fig. ll.--An example of the fifth rhythmic mode

Of this example Franco says that "if long follow long, then the first long, whether it be a figure -a note7 or a rest, is measured under one accent by three "tempora" and called perfect long."25

Figure 12 is an example from the Ars Cantus . . . which may exhibit the sixth rhythmic mode (and, incidentally, the 26 fifth); if the division of the perfect long into three

4 3Apel, g. ci. , p. 21+3. 2 Strunk, . cit., p. 142. 25 d2 6 ~b d.Ibi._d. ,p p.1"4t+ proper breves is fractio modi, then, as pointed out previously, it is not a very common use of this device.

ii_ I I)

4H? t)

Fig. 12.--A probable example of the sixth rhythmic mode

Of this example France says that

the case is the same as before j/Fhe same as in the example (Figure 10) showing the third mode, in which the first breve is proper, and the second breve is altere#7, except that the one which we called altered breve in the f rst instance is here divided into two breves proper. 7

Briefly, the application of Franco's rules for certain of his examples to the long-breve structure of the modal patterns as expounded in Garlandia's treatise and in the Discantus Positio Vulgaris gives the following results: the first rhythmic mode comprised, an imperfect long of two tempora and a proper breve of one tempus; the second rhythmic mode comprised a proper breve of one tepusI and an imperfect long of two teMora; the third rhythmic mode comprised a perfect long of three tempora, a proper breve of one temU 27Ibid 57

and an altered breve of two tempora; the fourth rhythmic mode comprised a proper breve of one t2Epus, an altered breve of two tempora, and a perfect long of three tempora; the fifth rhythmic mode comprised a succession of perfect longs of three to each; the sixth rhythmic mode comprised a sue-

cession of proper breves of one p each.

It is necessary for a clear perspective of the period

to point out that both Garlandia and Franco did their work

at least seventy-five years after the innovation of modal

rhythm in the compositions, presumably, of Leonin (ca. 1175).

There apparently is no doubt that the system of the modes

did not begin with a fully codified set of patterns as was

first exposed in the Diseantus Positio Vulgaris (ca. 1225).

In fact, the first modal rhythm was probably the mere alter-

nation of long and short tones28 with the others being added

later to allow a greater Variety within the strict framework

of triple meter; even at the time these theorists wrote, some

modes were not used enough for them to be characteristic of

the rhythm, i.e., the fourth and sixth modes. The complete

system of modal patterns, however, forms a convenient basis

for the examination of musical rhythm from about 1175 to

1300. Therefore, the discussion of the modal system and the brief summary of Franco's and Garlandia's remarks about the

structure of the modal patterns should be considered as only

8 2 Reese, op ct., p. 271.. a basis for examination and should not suggest that all these patterns are characteristic of musical rhythm for the entire period, i.e., from ca. 1175 to 1300.

In many of the articles on modal rhythm in the diction- aries and encyclopedias there is the application of the names of the Greek poetic meters to the modal patterns. These names and their supposed modal counterparts are: trochaie, first mode; iambic, second mode; dactylic, third mode; ana- pestic, fourth mode; molossic, fifth mode; tribrachie, sixth mode. The connection of these names with the modal system has persisted to the present day, yet the first and apparently

only medieval writer to mention the matter was Walter Oding-

9 ton, who wrote in the last quarter of the thirteenth century.2

Because of this single instance of the poetic names being

applied to the musical patterns during the Middle Ages and

because of Odington's "antiquarian studies" (which possibly

influenced him to use such names), Willi Apel believes the

terminology to have insuffietent historical justification.3 0

Among other scholars, however, the opinion prevails

that sufficient evidence is extant to justify the conclusion

that the poetic meters were connected in some way with the

structure of the modal patterns, perhaps to the extent that

the musical patterns were actually imitations of the poetic

29Apel, g. Cjt.. 230. 3 0 Ibid* patterns and as much like them as the nature of musical rhythm would allow.3 Part of the supporting evidence for this opinion lies in the fact that old part-songs written originally in neumes have been found also in later copies written in a mensural notation; in the neumatic versions the rhythm of the words was transferred to the music, and in the

later, mensural copies the discernible note-values are just

those which the meter of the text requires.3 2 This would

suggest that at a time early in the development of the modal

system (when a neume notation was used) there may have been

some conscious application of principles which caused musical

rhythm to be either derived from or influenced by the poetic meters.

In regard to this matter it would seem a striking coinei-

dence to the present writer that in the original codification

of the modes in the Discantus Positio Vu is as well as

the later exposition by Garlandia (both several decades be-

fore Odington) the structure of each modal pattern coincides

with the structure in longs and shorts of one of the poetic

meters mamed above. The long, short pattern of the trochee

coincides with mode one, the short, long pattern of the

3 1 Ourt Sachs goes so far as to say that "the 1lng-short organization of the modi is poetic, not musical," and that the concept of "metrical feet" was extant in the ligatures of Gregorian Chant at the time the modal patterns were devised. Sachs, . cit., pp. 160-163.

3 2 Reese, . cit., p. 272. 6o

iamb coincides with mode two, etc. Yet, with the number of available durations it would have been possible to construct each of the first four modes in another combination of longs

and braves, and each would have sounded exactly the same.

For example, mode one or mode two could have comprised two

braves, (one a proper breve of one tempus, the other an

altered breve of two teMpora) instead of one long and one

breve; also, the one perfection containing two breves in

modes three and four (the second in mode three, the first in

mode four) could have comprised, instead of the two breves,

an imperfect long of two tempora and a proper breve.

In a reversal of this logic it would also have been

possible for the musical patterns to have struck upon others

of the many different names to be found for the Greek poetic

meters33 merely by coincidence, if the patterns had been

constructed to sound the same but in other combinations of

longs and breves. For example, either the first or the sec-

ond rhythmic mode would have corresponded to the pyrrhic

meter if the two notes comprising one pattern of each mode

had been called braves (one proper and one altered) instead

of one proper breve and one imperfect long; the third mode

would have corresponded to the amphimacer meter if the second

perfection had comprised an imperfect long and a proper breve

instead of one altered breve and one proper breve; the fourth

33 "Verse," Encyclopedia Britannica, Vol. XXIII, 1951 ed. 61

mode would have corresponded to the bacehius meter if its first perfection had comprised a proper breve and an imperfect long instead of two breves. Yet, it is to be remembered that although comprised of different combinations in these hypothetical structures the musical patterns would sound the same as they do in their actual long-breve structures.

Despite these chances for coincidence between the musical patterns and the poetic patterns, it would nevertheless appear likely that the poetic meters had some influence upon the structure of the rhythmic modes because of the nature of the Greek metrical terminology. This terminology is charac- terized by pairs of patterns, one of the pair being just the opposite of the other and often having a name which links it to its opposite, e.g. the amphibrach (short, long, short) and the amphimacer (long, short, long), the bacehius (short, long, long) and the antibacchius (long, long, short). Also, the iambic meter (short, long) is the opposite of trochaic

(long, short), and the anapest (short, short, long) is the opposite of the dactyl (long, short, short).0 4

The musical patterns do not coincide at random with their poetic counterparts. Instead, two musical patterns of

opposite structure coincide in their long-short arrangement

34There is apparently no connection between the Greek words "iambic" and "trochaic," although there obviously is between the long-short structure of the iambic and trochaic patterns. The derivation of "anapest" is: Latin anapaestus, from the Greek word meaning "struck back," "reversed" (as compared with a dactyl). "Anapest," Century Dictionary (1927). 62

in every case with two poetic patterns of opposite structure, i.e., the iamb (short, long) with the trochee (long, short), the dactyl (long, short, short) with the anapest (short, short, long), and the tribrach (short, short, short) with the molossus (34ng, long, long). There is no instance in these pairs of patterns in which there 4xv paired a pattern with any other pattern than its logical antipode, as would be the case, for example, if the first or second rhythmic mode comprised two breves instead of a long and a breve.

Such an arrangement would make a pair from a pattern comprising two breves and a pattern comprising a long and a breve; this is certainly not as logical as a pair of patterns, one of which comprises a long plus a breve and the other a breve plus a long. Likewise, if the structure of the fourth mode were thought of as being in the bacchius meter, or breve, long, long, then the third mode could not be its logical

antipode, i.e., in antibacchius meter, since the antibacchius

structure is long, long, short: the second long could not have a duration of one tempus as is necessary in the musical

pattern.

Because of this circumstance that the long-short arrange-

ment of the musical patterns coincides with the long-short

arrangement of the Greek poetic patterns, and that the termi-

nology used for both systems agrees very closely, it would

appear that the idea of coincidence between the systems may be at least as old as the Diseantus Positio Vulgaris (ca.1225), 63

in which the structure of the modal patterns was first set forth. Because the account of the modes in this treatise probably was a codification of an established practice, the connection of the poetic and musical patterns may even be older.

If it is true that in devising the modal system some care was taken to follow the structure of the poetic patterns, then this means of arriving at the modal "feet," so to speak, was not the okLy consideration involved. It will readily be perceived that had such a plan been pursued completely there would have been some binary modal patterns included in the system, e.g., in constructing the third and fourth rhythmic modes if an imperfect long had been used in place of the per- feet long, and two altered breves had been used in place of one proper and one altered breve. However, all the modal patterns were ternary; therefore, there apparently was a purely musical decision involved which resulted in the changing of some binary poetic meters into ternary patterns for use in the modal system.35 What this musical decision was

can only be a matter of speculation, but if it is true that

the pattern called the first rhythmic mode (merely an alter-

nation of short and long tones) was first chronologically,

35Sachs, p. cit., pp. 160-161. Yvonne Rokseth says of the modes that Tthe rhythm of verse and musical rhythm will be perceived then as essentially bound together, as if to prove that the system of modi was a simplified adaptation of the old system of prosody." Yvonne Rokseth, Polyphonies du X111 Siecle . . ., IV, 39. 64

then the problem of combining two or more voices in polyphonic writing would have made necessary the adaptation of the remaining patterns to the ternary unit of mode one. And, this adaptation of various patterns could have been accomplished without the realization that the patterns were organized in a triple meter. 6

Several attempts have been made to answer the question of why the modal patterns were all ternary. The first apparently came from so close an observer as Franeo, but his argu- ment that "the ternary number . . . 3s7 the most perfect number because it takes its name from the Holy Trinity . . appears to have been made "after the event."3 8 Two modern writers Dom Anselm Hughes3 9 and Curt Sachs4 O believe that the apparently ternary unit of rhythmic organization was actually a unit of six in practice. Thus, two perfections comprising six teMora would have been the smallest unit of rhythmic organization instread of one perfection comprising three tempora. This would have given composers the opportunity to vary the rhythmic structure of one voice by using three groups of two notes or two groups of three notes and by using three groups of two notes against two groups of three notes

6 37 3 See p.51, Chapter II. Strunek, . 2 jt., p. 142. 38 Reese, p. cit., p. 274.

39 Dom Anselm Hughes, Worcester Mediaeval Harmony, p. 14, cited in Reese, a. cit., p. 270. 4. Sachs, .22cit., pp. 168-173. in setting one part against another in polyphonic compositions. Therefore, in some modern transcriptions a duple, compound meter such as six-eight is used in preference to a triple, simple meter such as three-four, allowing in most cases a more natural metric organizations

Going further into Sachs' explanation of this particular rhythmic phenomenon and thereby, into his classification of rhythm, we find that he believes the small ternary unit of three tenpora to be "the logical combination of additive, metrical and divisive, accentual rhythm"and that it was a rational choice for these reasons by the composers who first used such a unit. To sum up his classification briefly, divisive rhythms are those which equally divide a given duration, e.g. a two-four measure into two quarter notes or a four-four measure into two half notes or four quarter notes.

Divisive rhythms are usually accentual because their equal and equidistant parts are dependent upon accent of some kind to establish meter. Additive rhythms are those which un- equally divide a given duration; the separate parts which result from such a division thus appear to be added together

to form a measure or other metrical units, e.g. in a five-

four measure a half note plus a dotted-half note or vice versa and in a three-four measure a quarter note plus a half

note or vice versa, etc. Additive rhythms are usually

4iApe:L, o. cit., p. 229. 42Sachs, p. cit., pp. 168- 171. 66

metrical in the sense that their rhythmic content is dependent solely upon varying and thus, measured, durations.3

Using Sachs' classification as a basis, the ternary unit offered several varieties of metrical organization: additive and metrical rhythms in such combinations as the imperfect long of two tenpora plus the proper breve of one tempus or vice versa; divisive and accentual rhythms in other combinations such as three proper breves of one tegpus each in a perfection or, with the linking of two perfections the division of this unit of six teMora into two perfect longs of three tempora each. The division of the six-te pora unit into two longs would, of course, have provided a kind of binary organization.

On the next level of rhythmic organization beyond the basic unit of the modal pattern is the ordo, or ordinatio.

Garlandia defines an ordo as the number of notes before a

rest but says nothing about the characteristic arrangement

13Ibid., pp. 21-32. 4 Although the selection of the ternary unit was the result, primarily, of its adaptability to several kinds of rhythmic organization, Sachs believes that in the Gothic Age there was a definite tendency toward additive structures, not only in music but in other arts. Other musical evidence for this additive tendency would be the composition of polyphonic music by adding one part to another and the rhythmic construction of a single part, which was often a matter of a small pattern plus another small pattern and a group of such repatlorsplus another equal or contrasting unequal group. Ibid., pp. 169-170. 67

of the modal patterns.45 The passage in which he mentions ordinatio concerns discantus, which he defines as "the sinul- taneous sounding of different melodies according to mode . .

Therefore, we know from his account that the ordo is a type of measurement in distant. There is, however, a more de- tailed terminology for the various forms of ordines: the number of the ordo corresponds to the number of successive patterns in a single mode and before a rest, e.g., the first ordo comprises one complete modal pattern before a rest, the second ordo comprises two complete patterns before a rest, etc. In the fifth mode two perfect longs comprise ordo one; in the sixth mode three proper breves comprise ordo one.

The ordo is perfect if the first note of the mode is used once again after the last complete modal pattern; the ordo is imperfect if this note is not used as the last one, and instead the ordo ends with the last regular note of the modal pattern.' The terms "perfect" and "imperfect ordo" are similar in their application to musical phrases to the modern

"masculine" and "feminine" cadences. The masculine cadence always ends on a strong beat, as does the perfect ordo, and

45Coussemaker, a.* cit., I, 106b. Translated in William Waite, "Discantus, Copula, Organum," Journal of the American Musoloical Society, V (Summer, 19572T,77. 46Ibid

7SeeReese, _P*. cit., p. 275, Sachs, p. cit., pp. 161- 162, Apel, _. cit., pp. 230-231. 68

the feminine cadence always ends on a weak beat, as does the imperfect ordo.c 8

The two units of modal rhythmic organization, the modal patterns and the ordines, comprise the basic structural com- ponents of the modal system. A pure, unvarying use of the modes and the ordines, however, is not characteristic in polyphonic music for any part of the period under consideration, which is roughly the modal period. Instead, the following devices for changing the basic six patterns were used to obtain more variety: 1) fractio modi, which was discussed previously 2) extensio modi, which is the omission of a breve, at times adding a breve value to the previous note and at times substituting a rest for a breve;50 3) rests, of which Franco designates six kinds, corresponding in name and duration to the six kinds of notes (not including the double long).51 Rhythmic techniques on a larger scale were: 1) distant, the combination of several parts all of which were in modal rhythm; 2) organum e , organum pr se, or organum duplum, the combination of two parts one of which (the , or upper part) was in modal rhythm and the other (the tenor,

48 The end of an ordo is marked by a small vertical dash, "the so-called divisio modi," which in the Notre Dame compositions has the character of a short breathing sign, or of a sign of orientation or sectional division. Apel, 92. cit., p. 233.

Seep.55, Chapter 11. 50 Apel, . cit., pp. 242-245.

5lStrunk, pp.eit- p p.149-151. 69

or lower part) unmeasured; 3) hocket, the extensive use of rests in alternating parts. Concerning these techniques there is not a consistent terminology among the medieval theorists. The meanings of some terms overlap, and some terms are not used by more than one writer. Other problems are involved also, and these will be discussed in the following section.

Both Garlandia52 and Franco53 state in their treatises that they consider plainsong as music which is not measured.

This is in contrast to organum which Garlandia says encompasses all of measured music (organum generale) and at the same time is a type of measured music (organum speciale. He states:

Whence organum is both the species of all measured music and at the same time, in a different sense, a genus . . . you must know that there are three generally accepted species of organum endiscantus, copula, and organm I. iae/._)

These two meanings for the term organum are apparently referred to by Franco as "its proper sense" and "the sense commonly accepted." He is still more specific and says that organum duplum, or organum param, is the proper sense, but

52 Coussemaker, . eit., I, t175a, translated into English in Waite, 2. cit., p. 5.

53Strankt, . cit., p. 14-0. >4 Coussemaker, a. cit., I, 175a, translated into English in Waite, 02. cit., p. 85T 70

that commonly it is used to mean "any ecclesiastical chant measured by time."55 Orgau npr or oranum in "its proper sense," is shown in Figure 13.

Fig. 13.--Francols example of Organum Puram

From this example, which is commented on very briefly by

Franco, 56 we see that organum purIam was a two-part composition in which the tenor, or lowest voice, had very long notes and an upper voice, the , proceeded in faster notes and in modal rhythm. The tenor's notes were apparently unmeasured in organum pnkm for Franca says:

Organum, in the proper sense of the word, is a sort of music not measured in all its parts. Be it known that there can be no organum purum unless the tenor sustains a single tone, for when the tenor take several tones in succession, distant begins at once."

From Franco's brief reference to discant in his definition of organum, it is clear that distant had not only measured upper parts but also a measured tenor. In his more

55Strunk, .. cit., pp. 14O-lo1. 561bid..,p. 158.

57Strank, 12..cit., p. 158. 71

complete discussion of distant we find, as in Garlandia's definition, that it was on the one hand a style of organum and on the other hand a term used to designate the upper part, or duplum, of any two-part composition: it is "something based on a cantus.158

As a style in which all the parts were measured, discant was not limited to two parts. In fact, it could be written in three, four or five parts; the third part was known as the triplum, the fourth part as the Ruadruplum, and the fifth part as the quintuplum (the terms trilum,

were also used to designate modal compositions in three, four, and five parts respectively).59 In distant, as well as in the triple, uadrupla, and quintuple, Franco advises the observance of

equivalence in the perfections of longs, breves, and semibreves . . . that there may be as many perfections in the distant, triplum, and so forth, as there are in the tenor, and vice versa counting both actual sounds and their omissions . . .60

There are three species of distant named by Garlandia:

1) distant in which modus rectus is set against modus rectus;

2) discant in which modus per ultra mensuram is set against modus ptr ultra mensuram; 3) distant in which modus rectus 61 is set against modus pultra mensuram. The m reeti

58;:.bid.,p. 153. I59_bid., pp. 155-156. 6oIbid., p. 156. 6 lCoussemaker, a. cit., pp. 106b-107a, translated into English in Waite., op. cit., pp. 80-81. 72

comprise the first, second, and sixth rhythmic modes; the modi per ultra mensuram comprise the third, fourth, and fifth rhythmic modes. 6 2

In the two-voice compositions in which the lower part characteristically holds its notes, and the upper part moves in faster notes and in measured rhythm (organum purup, organum plum, or organum per se) there are two ways of employing the meqsured notes of the upper part: 1) in a modus rectus; 2) in a modus non rectus.63 For the comparison of these two terms Garlandia defines the modus rectus as that mode "by which discantus is made" and modus non rectus as a mode which

differs from any normal mode in which the longer and breves are first and foremost used correctly and in the proper way. In a modus non rectus a longa and a brevis are, indeed used in the first mode , though only incidentally. 4

The last sentence of this passage appears to be the crux of a contention between Willi Apel65 and William Waite6 6 over the solution to certain rhythmic problems in the p

Waite, . cit., p. 80 (footnote). Reese explains that the longer of two teMora in modes one and two were called l rectae (normal longs) while the longae of three tpora in modesThree, four, and five were called ultra mensuram (beyond measurement). Reese, ., cit., p.~2'7.

6 Wfaite, op. cit., p. 82. 6 1 bid.

65Willi Apel, "From St. Martial to Notre Dame," Journal of the American Musicological Society, II (Fall, 1949T71T5-

6 6coussemaker, oP.. cit., p. 114a, translated into English in Waite, op. cit., p. 73

of organum parua. Apel stresses the fact that n incidentally was modus non rectus in the first mode, i.e., only by coincidence. The principle determining factor of a note's length according to his view was its harmonic relationship with the tenor if it was consonant, then the note was long; if it was dissonant, the tone was short. His principal support comes from the last chapter De Modis Irregularibus of the treatise by Anonymous IV. 6 Here the rule of consonance and dissonance is stated as applying to music written in ligatures. Since the dupla are written in ligatures, Apel believes that they were affected by this rule. Concerning the modus rectus and the modus non rectus Apel believes that Gar- landia may have meant the sometimes strictly modal passages in the d (such as the clausulae) as contrasted with those in which the long and short tones were determined by consonance.

Commenting on Apel's work, Curt Sachs agrees with him generally. He adds, however, that the soloist would probably not have deprived himself of his characteristic freedom and style by singing the longs and breves in an unvarying ratio of 2:1. Such strictness in the organal sections would have destroyed the effect of contrast between the measured clausulae and the more loosely organized rhythm of organum. 6

67Coussemaker, . cit, I, 361-364. 68 Sachs, _p. cit., pp. 157-158. see also Reese, 2R. cit., p. 298. 74'

From the above passage of Garlandia's, William Waite has concluded that anything but modal rhythm in the organa d would be erroneous. Instead of the variance from modal rhythm that Apel believes is the modus non rectus in the dupla Waite believes that the modus non rectus meant an ad libitum performance of strict modal rhythm in the dupla. A similar rhythmic arrangement, perhaps the same one, is mentioned by Anonymous IV in speaking of a modus in organum duplum which is different from a true modus: "the longs are too long and the breves too short, and it seems to be an irregular mode in comparison with the modes of discantus, although in itself it is regular."6 The regularity this writer speaks of here might be interpreted by Apel to mean the strict maintenance of a 2:1 ratio between the long and short notes; as interpreted by Waite it would be the basic use of modal rhythm.

There would apparently be the possibility that in the dupla of Leonin the rhythm was not exactly a measured one, as Apel states, in the sense that Franco's system was measured, i.e., a measurement of durations by means of some unit such as the tempus in the Ars Cantus Mensurabilis. From the

&ombined views of Apel and Sachs on this problem7 0 it would

Coussemaker, p. cit., I, 306b, translated in Waite, 2. cit., p. 82.

70ee pp. 72-73, Chapter II. 75

seem possible that the long and short notes of the d may have been merely relative terms and did not connote any idea of exact measurement such as two units for a long note and one unit for a short note as was probably the case during

Perotin's time and certainly a short time after him. This kind of rhythm, based upon relatively long and short notes, could more logically have led to modal rhythm (for the reasons stated above) than could have a rhythm based upon what are possibly the more advanced ideas of strictly measured longs and breves. At least part of the reason for modal rhythm being introduced was an attempt to gain greater facil- ity in combining several parts; since its early use by Leonin involved only the setting of mode five in the tenor against one of the faster modes in the duplum (usually mode one or two), modal compositions, at least for the early period, would have been quite practical with a technique based merely on relatively long and relatively short notes. Later, of course, with the complication such as that to be seen in some of

Perotin's compositions, there would have arisen a need for a more accurate notation and a more strict observance of a certain ratio between notes of different durations.

A freer interpretation of the terms "long" and "breve" would apparently also be applicable to the type of rhythm

Waite believes is correct for Leonin's dpja and distant sections. Conceivably, the "modus in organum duplum different from a true modus" spoken of by Anonymous IV and the 76

71 modus non rectus mentioned by Garlandia could have comprised these relatively long and short notes. Both writers lived during a period when the rhythm was strictly measured; therefore, the approximate values given these notes would appear to them (in an occasional performance of the old dupla, perhaps) as a mode produced by an abnormal measurement and as a mode in which "the longs are too long and the breves too short . . ." Thus, the passages which Waite believes may refer to an ad libitum performance of the first rhythmic mode may actually note a preservation in performance of what was actually the earliest modal rhythm.

From the separate conclusions reached by Apel and Waite two historical sequences are possible for the changes in rhythm between early organum and the system of "measured" rhythm found in Franco's Ars Cantus Mensurabilis. If Apel's theory is correct, there was a progression from the "free" or "measured" rhythm of the earliest organa to "measured" rhythm in Leonin's dupla and modal rhythm in his discant sections to "measured" rhythm at about the time of Garlandia and Franco. If Waite's theory is correct, there was a progression from the "free" or "measured" rhythm of earliest organa to modal rhythm in both the dupla and discant of Leo- nin to the "measured" rhythm of Franco's system.

7lSe pp.71-74. 72 See pp. 2Q-25 of Chapter I. 77

The development implied in Waitets conclusions appears

to be the most natural one; if Apel is correct, there was a

brief use of "measured" rhythm by Leonin, then a choice of

modal rhythm, as seen in the compositions of Perotin, in

preference to it. Although it was not known during the mid-

dle of the twelfth century, the ultimate goal of the times

was apparently "measured" rhythm, a type which has lasted

(with characteristic metrical structures) from the thirteenth

century to the present. Once achieved it would appear that

this type of rhythm would have shown such a capacity both

for present uses and for further development that modal rhy-

thm would not have been a necessary step. This is provided,

of course, that the modal patterns would not have been chosen

except for their utilitarian purpose of aiding the combination

of various parts in polyphony. The musical choice of modal

rhythm in preference to measured rhythm would appear, in it-

self, as unlikely since the modal patterns took shape in the music one or at most, a few, at a time. Therefore, during the

early modal period there would only have been from one to

three modes (probably one, two, and five) available to the

composer. Had there been a "measured" rhythm extant at the

time (even without the semibreve duration, which developed

early in the thirteenth century), the modal patterns would

surely have been a poor choice; with measured rhythm all of the 78

patterns would have been possible from the beginning besides 73 many variations of them. The fact that a mensural notation was some seventy to eighty years in the future at the time modal notation was invented apparently does not indicate that notational difficulties retarded the employment of measured rhythm. Recalling the statement of Reese that "the notation was brought into being by actual music and not vice versa, it would seem more likely that the modal patterns were exactly what the inventors of modal notation wished to depict, and that these patterns were the substance of the period's rhythm in polyphonic music.

73 The practical use of semibreves, of course, had been part of musical rhythm even in the works of Leonin (see, for example, W. Apel and A. Davison, Historical Antholg of Music, Vol. I, example number 29); however, their use was quite limited, and they do not constitute a principle duration.

74At about the time of Perotin, i.e., the last decades of the twelfth century to the second quarter of the thirteenth. See Apel, Notation . . ., pp. 215-219. 75Reese, .. cit., p. 292. CHAPTER III

THE MODAL SYSTEM IN THE PRACTICAL MONUMENTS

FROM CA. 1150-1300

Modal rhythm was introduced into polyphonic music during the early period of the Notre Dame school, around 1160-1180,.

For this period (to ca. 1225) only two composers are known by name: Leonin is the earliest and is called "9ptimus organ- 2 ista" by Anonymous IV; Perotin was an immediate successor to Leonin and is called "optimus discantor" by Anonymous IV.3

The compositions of both men are to be found in four prin- cipAl manuscripts containing copies of the Magnuj Liber Or-

n de Graduali et Antiphonarie, a year's cycle of organa composed for parts of the Mass and the Office first by Leonin and later revised by Perotin. The manuscript Wolfenb1ttel

677 contains the oldest version of the Liber . .

1 Handschin gives the dates of the Notre Dame school as ca. 1181-1236. These dates, according to Leopold Delisle, encompass certain historical events alluded to by the texts of the Florence ma. Jacques Handschin, "A Monument of English Polyphony. The Ms. Wolfenbfttel 677," Musical Times, 73 (1932), pp. O510-513. Reese thinks that Leonin's time may have been before the laying of the Notre Dame Cathedral's cornerstone in 1163. Reese, *. cit., p. 296. Yvonne Rok- seth places Leonin at between 1160 and 1180. Yvonne Rokseth, Polphonies du XIIIe Sicle, IV, 39. 2 Coussemaker, _P. cit.., p. 342. 3lbid. 79 80

and thus is probably the one which best preserves Leonin's styleA. The other copies of the work are in the Wolfenbuittel ms. 1206 (Helmstedt 1099), the Madrid Bibl. Nac. ms. 20486, and the Laurenziana of Florence ms. Plut. 29, 1. Friedrich

Ludwig at one time classified all four manuscripts as belong- ing to the Notre Dame school but was later induced to change his mind by the work of Jacques Handschin who believes that the Madrid ms. had its origin in Spain and that some parts of the Wolfenbilttel 677 ms. were of English origin. Almost all the compositions in the latter manuscript are also in the Florence ms., so these compositions are probably from the

Notre Dame school in Paris. The entire manuscript was probably written at or at least for the community of St. Andrews, the ecclesiastical metropolis of Scotland in the Middle Ages.6

The notation in all these manuscripts is called "square notation" by Apel, the term reflecting only the general shape of the individual notes and the notes in ligature, or group form. This type of notation developed from the Aquitanian neumes of the mid-twelfth century and exhibits a clarity in

4Reese, p. cit., p. 297. 5 Friedrich Ludwig, Repertorium Organorum Recentiowis et Motetorum Vetustissimi StiliX(1909), eited by Handschin, "r Monument of English Polyphony. The Ms.Wolfenbfittel 677," Musical Times, 74 (August, 1933), pp. 697-704. 6 Handschin, "A Monument of English Polyphony. The Ms. Wolfenbittel 677," Musical Times, 74 (August, 1933), pp. 697- 704.

7Apel, The Notation of Polphonic Music, pp. 215-220. the relationship of parts and in the placement of individual notes that is more easily read by the present-day musician.

Aside from some problems involved in the transcription of the early organa duplaand some conducti the notation from the Notre Dame period on does not hinder the study of rhythm as does the notation and the lack of explanatory treatises on rhythm before this period.

The names "optimus organista" and "Optimns diseantor," applied to Leonin and Perotin respectively by Anonymous IV, emphasize. the most obvious difference in each one's polyphonic contributions to the MagnsLiber 0ga . #

Characteristically, Leonin's style is that of the "organ- point" or of organum pura in which many notes are set in an upper part to a single note in the tenor. Perotin's style, on the other hand, is characteristically that of distant, which is nearer a note-against-note style than is organum pures and which has all its parts in modal rhythm. In an examination of a number of compositions by these composers it will be found that each of them did not limit himself to this characteristic style; Leonin used the discant style (in fact, it is found for the first time in his compositions), and Perotin used the organum parwa style. However, in a generalization which compares their work as a whole the des- ignation for each of them of one typical style is justified,

8 See pp. 71-76, Chapter II. 82

and it serves, of course, to indicate the trend of rhythmic development during the latter part of the twelfth century.9

In the distant sections of both composers the rhythm is much the same. In rewriting the Magnus Liber Organi .

Perotin used modal rhythm in more of the organa than did

Leonin10 but at the same time apparently maintained approximately the rhythmic style that Leonin had begun. This is true even in the triple and Quadrupla of Perotin. This rhythmic style comprises the use of principally one rhythmic mode in the tenor and one rhythmic mode in the upper part.

Mode five, comprising all perfect longs, is by far the most frequently used mode in the tenors, and its equal notes are arranged in both regular and irregular phrases, or ordines.

Mode one is used most in the upper parts,11 and it is arranged characteristically in irregular ordines, repetitive passages occurring occasionally. The mode and the ordo of the upper part or parts are characteristically not the same as in the tenor. The ordines of the upper parts in triple, cuadrupla, etc., usually do not coincide with each other or with the

9 Jacques Hautmhin, "Zur Notre Dame Rhythmik," Zeitschrift ffir Muikwissenschaft, VII (192L4), pp. 386-389. 10 Fora comparison see Friedrich Ludwig, "Musik des Mittelalters in der Badischen Kunsthalle Karlsruhe," Zeit- schrift fur Musikwissenschaft, V (1922-23), pp. 13+-4+0~ Reese prints part of Ludwig's examples from this article. Reese, . eit., pp. 300-302.

11 Ibid., p. 302. 83 tenor; this produces an alternation of rests between voices which is similar to the device of hocket except, of course, that the rests do not occur as often.

In the tripla composed by Perotin, several of which are in the Montpellier Codex,12 there is exhibited a characteristic which shows the trend of rhythmic development of the time and also a greater rhythmic complexity than in the compositions of Leonin: these tripla employ a greater number of the modal patterns than do the Leonin organa. Leonin used modes one, two, and five almost solely, but Perotin used in these triple modes one, two, three, five, and six (the latter rarely, however). 13

Three styles of tenor-writing are shown in these compositions, two of which were later used in the thirteenth- century motets (even in the last decades of the century):

1) a kind of organum pur tenor which utilizes long notes while over each of them the p and triplum proceed in faster notes (almost note-against-note) and in modal rhythm;

2) a tenor in short, reiterated patterns and in modal rhythm with the other two voices; 3) a tenor in longer, more connected phrases and in modal rhythm. Numbers two and three are of importance in the later thirteenth-century motets.

12 Yvonne Rokseth, .2. cit., fascicle I. 1 3There is one example of Perotin's (number 14, fascicle I) which employs the sixth mode extensively, but this is very rare for Perotin's period and was to remain almost unused until the second half of the thirteenth century. Ibid 84

In fact, virtually all the motet tenors of that period fall into one or the other category.

The most frequently used regular pattern in the tenors of the Notre Dame organa is that of three perfect longs before a rest.l4 A close variant of this is also found quite often: a duplex long plus a perfect long before a rest. It will be noted that in each case the pattern has a duration of nine tempora. In the modal system the double long-perfect long pattern could have been derived, possibly, by a kind of extension modi, i.e., by the omission of a long which would add three teMora to the duration of the first note.15

In the system of ordines the three-long pattern was designated as "perfect ordo one of mode five."1l In a strict ternary system with the triple unit equalling three teMora., this ordo, or phrase, would have no meaning in a comparison to the present-day masculine and feminine cadences since each note would begin on the first, or strong, beat of every triple unit. However, as concluded by Hughes and Sachs4the

lkThe pattern of three longs in the tenor was not re- stricted to use in the Notre Dame school but was also important in the motets of the thirteenth century. See III, 12.

l5The most usual application of extensio is the change in a three-breve pattern of the first two braves to an imperfect long or in a succession of mode one patterns to extend the imperfect long to a perfect one. 16 Apel, Notation . . ., p. 230. 1 7 See p. 64, Chapter II. See also the transcriptions of Apel in W. Apel and A. Davison, Historical Anthology of music, Vol. I, pp. 26-32. metrical organization of successive triple units was capable not only of a ternary organization but also a binary one, i.e., an organization in duple-compound meter (perhaps 6/8 in a modern transcription) which was the result of the music being organized in units comprising two perfections instead of one. In binary metrical organization the ordo of this pattern and the modern cadential terminology are logically applicable, i.e., a pattern of two longs establish a recognizable unit, the first long falling on the first, or strong, beat and the second falling on the second and weaker beat

(comprising, for example, one 6/8 measure). This would comprise imperfect ordo one of mode five and also a feminine cadence since the pattern ends on a weak beat. To make it a perfect ordo one of mode five and, therefore, a masculine cadence the first note (a long) must be repeated after the two-long unit. This makes it fall, in a 6/8 meter, on the first, or strong, beat of the succeeding measure.

Throughout thirteenth-century polyphony the technique of repeating rhythmic patterns in the tenor on the phrase, or ordo, level was an important structural device; and it apparently developed into the iso-rhythmic technique of fourteenth-century music. Although the tenor appears to have been the more frequent choice for the application of this technique, one finds it in the upper voices also. More often, however, the upper parts have faster notes, a variety of phrase lengths, and a much more frequent use of mode 86

alterations. Later in the thirteenth century there was a greater rhythmic freedom in the tenors, 1 and, of course, between the freely-composed tenors and the upper parts of conducti a much greater coincidence existed than was apparently the rule in the late twelfth and early thirteenth- century 2ogana.

All the compositions employing modal rhythm, even from the very early use of the modes in the works of Leonin, con- sistently employ alterations of the modal patterns;19 they are characteristic of the upper parts of the organa but not of the tenors. The alterations, of course, are not merely haphazard ornaments inserted occasionally to relieve the monotony of continuous modal patterns. Rather, they are used with the musical taste one would expect from a leading school of musical activity such as Notre Dame was in the late-twelfth and early-thirteenth centuries. In fact, the alterations at times establish a rhythm quite apart from the modal patterns as in Figure 14 (which also shows a sequential tenor constructed mainly of double longs).

8 1 For example, compare the tenors with the upper parts in any of the early, modal compositions printed in Apel and Davison, 9. cit., pp. 25-39. The tenor to the motet On Parole - A Paris - Frese nouvele is an exception. It was written, however, in the last half of the thirteenth century when departures from the techniques of the Notre Dame school were not uncommon. 19tExamples of this pure type /of modal techniques are relatively rare and uncharacteristic. Usually the elementary pattern of the mode is modified by either omission or addition of tones. . ." Apel, Notation . . ., p. 242. 87

Alk An

As-

An Aft As 40 AL qqww

Fig. 14w.a-An example of repeated non-modal patterns

This example is part of an organum from ca. 1200.20 The upper parts are apparently written in mode one, but by the

use of extensio modi the characteristic pattern of mode one, imperfect long, proper breve, is changed to perfect long,

imperfect long, proper breve. This results in a pattern closely allied to those of modes three and four: the pat-

tern's length is two perfections, but it differs in that a

long comes before the breve in the second perfection.

The next illustration (Figure 15) is part of an earlier composition, supposedly in the style of Leonin. 2 1

11-

Fig. 15.--Examples of extensio and fraetio modi

2 Supposedly in Perotin's style. Apel and Davison, . .cit., I, example 31, p. 31. 2 1 Ibid., example 29, p. 29 (first staff). 88

This example, in parts of two lausula sections, shows instances of both extensio and fractio modi. The first three measures are basically in mode one, but the division of the imperfect long (a quarter note in the transcription) into two breves in each of these measures creates by fraction modi a different, repeated pattern. At the beginning of the new clausula the mode is again one, but in every other measure extension modi is used, providing for the omission of a breve.

In this case there is a breve rest instead of an extension of the long by a breve value.

In these instances as well as many others it might well have been difficult for the listener to discern just what mode a particular composition er a part of one was written in. It may well have been the composer's intention in an artistic design, to make more subtle the appearances of a modal pattern. And, even though these devices would apparently have weakened the modal system insofar as the six basic patterns were concerned, modal rhythm was still the basis for the rhythmic structure of polyphony long after the period of these compositions (ca. 1160-1210).

The change from the compositions of the Notre Dame school, i.e., the organa and conducti, to the motet, characteristic of the thirteenth century, was accomplished by merely adding full texts to the upper parts of the two-part blausulae of Leonin, Perotin, and their contemporaries. 89

Because of such a direct derivation from oranum there is no new problem in the rhythmic structure of the motets, at least in the early stages of their development which began in about

1225. Later, of course, the most important rhythmic changes in the thirteenth century were to take place in this type of composition, and as far as polyphonic writing is concerned the three-voice motet was cultivated almost exclusively in the last half of the thirteenth century.2 2

The new words for the upper part of the motet were apparently adapted to the previously-composed music and not vice versa. The bonds of modal rhythm at this late date in the modal period were well enough established to allow the addition of a text without a corresponding change in the musical rhythm. This in itself is an important innovation since before the modal period there is the possibility the rhythm of a text influenced the rhythm of the music to which it was set.24 However, insofar as the development of rhythmic practice was concerned, this characteristic was probably only a by-product of the trend toward measured rhythm instead of a basic consideration.

22 Rokseth, a. eit., IV, 77. In motets, especially the later ones, "each time the composer wanted to give the text a good accentuation, he had to depart from the rigidity of the modes. In reality, the modes were more frequently chosen for their musical interest and without regard to the binding with the verse." Ibid., p. 251. 2)See pp. 5-9, Chapter 1. 90

The Montpellier ms. H 196 is an important source for the thirteenth-centtxry.motet. It contains more motets of all kinds from the first half of the century than does any other manuscript25 and also two fasicles of late thirteenth- century motets. There is some overlapping throughout the manuscript due to the fact previously mentioned that there is such a direct connection between the clausulae and the motets; therefore, in some of the three-part motets of a relatively late date we find that a triplum has merely been added to an earlier plausula or two-part motet. This has been done to a small degree throughout the manuscript, but practically all the motets in fasicle III (written before

1240 with the exception of one triplum) were constructed in this manner.26

The tenor construction in the motets of the Montpellier ms. composed before 1280 (fascicles VI, VII, and VIII) is essentially the same as that of the Notre Dame compositions: principally the use of short, constantly reiterated patterns in modal rhythm with only one syllable or, at most, very few syllables for a text and in slower notes thah the upper voices. Early in the second half of the century, however, there are some examples of the tenor becoming more interest- ing rhythmically by the use of: 1) longer phrases; 2) a use

25Reese, P. cit., p. 312. 26See Rokseth, _. cit., IV, 139. 91

of more modal patterns (the sixth mode was quite an important 27 innovation); 3) semibreves. Also, there are a few examples with a full French text for the tenor part instead of just one or two syllables. These changes, although indicating a progressive rhythmic development during the last half of the thirteenth century, did not become frequent enough to constitute a characteristic style of the Ars Antiqua. Instead, the tenors were principally deployed in the style used before

1280.

Concerning the number of perfections used to make the constantly repeated tenor patterns, it would appear significant that in the early motets of fascicle VI there are about seventeen which employ three perfections and about fifty which employ two. In the later motets of fascicles VII and

VIII there is a reversal of this ratio, with more compositions employing three perfections than two. It will be remembered that two particular patterns of three perfections were used in the organa of Leonin and Perotin; these same patterns (long, long, long and duplex long, long) are also the most frequent in the early motets which roughly correspond in date to the organa. A pattern very similar to the duplex long, long pattern in the thirteenth-century motet is the long, duplex long pattern found in the compositions of the Roman de Fauvel and in the motets of the early Ara Nova

271 . 78 92

and Machaut, i.e., a pattern comprising a perfect long plus a duplex long. In fourteenth-century music this pattern was called the modus maximorum.28

Around the time of the motetts inception there was the predominant use in the upper parts of rhythmic modes one and two (there are very few early motets which employ the sixth mode in the upper parts). At this time the tenor parts were characteristically in mode five so that the upper parts in relation to the tenor had faster and more notes. This relationship continued throughout the development of the thirteenth-century motet: as the tenor gradually used more of the modal patterns,and thus, faster notes, the upper parts correspondingly gained -in speed. In the compositions from around the middle of the century (in fascicles VII and VIII of the Montpellier ms.) there was an increase in the use of mode three and mode six in the upper parts, and there are several examples of the top part (the triplum) gaining in rhythmic interest in comparison to either the tenor or the duplum. 2 9 This is especially true in the motets of Petrus de Cruce in which a great number of semibreves are set to slower notes in the , or motetus, and the tenor: up to nine semibreves are used against one long of the tenor,30 28 Apel, Notation . . ., p. 328. 2 9 See, for example, Rokseth, 9R. cit., nos. 306, 307, 334. 3 0 See, for example, Rokseth, py. cit., nos. 253, 254-255. For the rhythmic interpretation of these large groups of semibreves see p. 99 of Chapter III. 93 resulting in a style which is reminiscent of Leonin's and

Perotin's organa dupla and in a way the sustained-tone style of St. Martial and Compostela.

The conductus is a kind of composition to which the characteristics previously discussed of tenor construction and the relationship of the tenor with the upper parts do not apply. The tenor was often a freely-composed part and, as Odington said, "sk composed from suitable songs either already known or newly composed, in various manners styles7 and iterated points /iotes7, in the same mode or in diverse modes." 3 1 In fact, the lowest part of the conductus is not a tenor in the sense that the tenor is a part in which notes are held. This part proceeds in approximately the same rhythm as the other parts, so that in looking at this type of composition it appears to comprise only the upper parts of an organum or motet. In describing this characteristic the author of the Discantus Positio Vulgaris says that "a conductus is a part-song set in a single meter."32 The conductus was cultivated during the first half of the thirteenth century and declined in use as the motet rose in importance after ca. 1250.33

3lCoussemaker, . cit., I, 21;7, translated in Leonard Ellinwood, "The Conductuf &MusicalQuarterly 27 (191), 178. 3 _bbid.,p. 169.

33Ellinwood, 2R. cit., p. 166. 94

The increasing use of the semibreve is a very important facet of thirteenth-century rhythmic development. The development begins in the earliest motets (ca. 1220) in which two semibreves are characteristically used in place of the first breve in a pattern of three proper breves. Yvonne Rokseth has maintained that this was the earliest use of the semibreve. Later, between 1220 and 1260, there was a great advance in the use of three semibreves, and between 1260 and

1280 compositions were written in which the triple comprised semibreves entirely. In these p the number of semibreves used in one perfection was at times as many as seven, which, of course, was but a short step away from the still more advanced, and later, use of semibreves by Petrus de

Cruce.

At first the three semibreves which took the place of one proper breve "were used as ornaments, as melismas on one syllable of the text. Then they progress to three independent semi-breves set one to each syllable." 35 The progress

34 Ibid., IV, 78. The early use of this division of the first breve into two semibreves can be seen in the triple of numbers 77, 84, 103, and 143. The division of the first breve into three semibreves can be seen in the triplum of number 40.

3 5Rokseth,po. cit., IV, 78. This view of Rokseth's is in accord with Johannes Wolf's contention that shorter durations came into use as embellishments of longer ones. Johannes Wolf, Geschichte der Mensural-Notation vbn 20- .# gI, 3. made in the use of separate syllables for each semibreve is not only discernible in these late thirteenth century motets but also in the early ones. In the motets before 1220 there are many examples of two semibreves used in place of one breve and a few examples of a breve divided into three semibreves. However, in none of these is there a separate syllable of the text used under consecutive semibreves. In the tripla of the motets between 1220 and 1260 there are many examples of syllables under two consecutive semibreves, but for the many instances that a breve is divided into three semibreves there is only one example of a syllable of the text under each of them.36 In the motets from 1260 to 1280 are found the first examples of two syllables of the text under two consecutive semibreves in the , and toward the end of the century there are the innovations of Petrus de Cruce mentioned previously.

The period of the breve divided into three parts is probably a little before 1250.37 Franco of Cologne's Ars

Cantus Mensurabilis of about the same time (ca. 1260) exhibits such a division of a breve. Franco's example of it with Strunk's transcription appears in Figure 16. Of the example Franco says that "there cannot stand for a breve proper more than three semibreves (called minor semibreves, since they are the smallest parts of the breve proper)."8

36 Rokseth, . it., no. 307. 37 Ibid. 3 8 Strunk, cp.jt., p. 145. 96

Fig. 16.--The semibreve in the Ars Cantus Mensurabilis

The year 1260 is also about the time that Petrus de Cruce began his work in which, claims the writer of the Speculumn

Musicae, occurred the first instance of a breve divided into four parts.3 9 This assertion, according to Rokseth, "is not strictly true." One of the triple (number 40) of the Mont- pellier ms. shows the same division, and Rokseth claims a slightly earlier date for it than Petrust first work.t

The significance of these changes is two-fold. On the one hand the tempo of compositions employing many semibreves probably was slower than the early ones which employed only two and three semibreves to a breve, and as the groups of semibreves increased in individual importance and decreased in their ornamentative importance there probably was a further slowing down, especially when the text was set

3 9 Coussemaker, p. cit., ,II401a, cited in Rokseth, 2R. cit., IV, 79 (footnote 9).

40Ibid. 97 syllabically. On the other hand the extent of Petrus' employment of semibreves helped, along with a greater use of the sixth mode, to break up the system of modi. It can well be understood that the time necessary to sing seven to nine semibreves set to the text in a syllabic style would be such as to render almost useless an organization of rhythm based upon three short notes (breves). The breves would tend to become as long as the old longae to which were set three breves. Since there were many examples throughout the century of the breve divided into two semibreves, a new, long duration for the breve could possibly have led to a binary organization on the same scale as the old ternary unit of perfection, provided the two semibreves were of equal duration. In fact, at about this time there begins to be developed in notation as well as in practice such a binary organization.

It Is in about 1280 (approximately the time when consecutive syllables of the text were finally used under semibreves in the dwpla parts) that Besseler believes the note getting one beat of the e giusto changed from the long to the breve. Besseler, 2. cit., p. 214.

2Rokseth, 9k. cit., IV, 78.

43R'okseth transcribes them as equal notes, but Apel interprets them as being unequal. He assigns a quarter note to the first semibreve and an eighth note to the second. He supports his conclusion by the passage from the SpeculUm Musicae which says: "For one and the same tempus, namely, that of the brevis recta they Jhe old masters/ used two semibreves unequal in value, or three, four, five, six, seven, eight, and nine equal semibreves." Coussemaker, _o. cit., II, 429, translated into English in Apel, Notation . . ., p. 322. 98

Concerning the innovation of the modus iperfectus, as binary rhythm was referred to in the fourteenth century, the treatise of the Pseudo-Aristotle (ca. 1250) reads:

Therefore, if someone were to ask whether a mode or a natural song can be formed by imperfect longae exclusively just in the same way as it can be formed by perfect , the approved answer is: no; since npr body can sing a succession of pure imperfect longae.44

This, of course, represents a very conservative opinion of the capacities of binary rhythm at a time (ca. 1250) when the modal system, and therefore a ternary organization, was still very much in force. It does, however, give us an idea as to the attitude with which the modus imerfectus would be approached a few years later. Opinions such as this theorist's notwithstanding, shortly after the beginning of the fourteenth century the modus iperfectus dominated musical rhythm instead of the triple modus perfeetus.45

In the Montpellier ms. only number 278 of fascicle VII

(composed towards the end of the century) and number 328 of fascicle VIII (composed in the first years of the fourteenth century) are transcribed by Rokseth in binary meter. However, a few compositions in fascicles V, VII, and VIII, she believes, could just as well have been transcribed in the imperfect modus as well as in perfect, and "it is possible that

44Coussemaker, 2. cit., I, 271a, translated in Apel, Notation . . ., p. 292.

45"Apel, Notation . . ., p. 294. 99 both interpretations were made at times by the various per- f ormers . 11 6

The Roman de Fauvel is the last extant document of the Ars Antut. ,8It was completed in 131)4 and contains motets and monophonic songs inserted into a narrative. There

are examples in it of fourteenth-century distinctions between

semibreves, i.e., the so-called semibreves signatae and semibreves caudatae. However, Apel has concluded that the stems on the semibreves which make them different from thirteenth century semibreves were actually added to the manuscript at a later date and do not indicate such distinctions for the thirteenth century. The semibreves are apparently to be interpreted by the rules of Petrus de Cruce which results, according to Jacobus in the Speculum Musicae, in the interpretation to be seen in Figure 17.50

SLi 35 41 7$

Fig. de Cruce

o~. cit., IoV, 83. 47Paris, Bibliotheque Nationale fonds frr. 146, cited in Apel, Notarion . . ., p. 331. 48 See Apel, Notation . . ., p. 322 (footnote 1). 49Ibid. 50 .bid., p. 323. 100

The binary modus imperfectus is used more frequently in this manuscript than in earlier sources, and the indications to the reader notifying him that it is to be used are clearer.

In fact, there is used for the first time in this manuscript the device of coloring notes red to indicate a change in the tenor part from modus perfectus to modus imperfectus.5

During the period when the system of rhythmic modes was being developed, apparently beginning around 1160 with Leonin and continuing with Perotin in the latter part of the twelfth century, it would seem possible that as a structural element or as an artistic facet rhythm was not as important to music as were the elements of melody and harmony.52 On the one hand it is likely that during the very early modal period in the dupla of Leonin, the length of notes was not determined by a musical choice of rhythmic structure but instead, was merely coincidental to harmonic considerations. If this historical assumption is false, then the alternative of a strict, modal rhythm54 does not appear to have offered to

5Ibid.,pp. 325-330. 2 5 Curt Sachs believes that "medieval man . . ., never inclined towards preponderantly rhythmic expression, he was just then, in the Gothic Age, building up the third dimension of music in a coincident counterpoint, indeed in the roots of harmony, so much so that his rhythm could not wit the prominent position as a functional quality of melodic expression that it had of necessity in the two-dimensional music of Greece and the East." Sachs, _k. cit., p. 171. 53 Apel, "From St. Martial to Notre Dame," pp. l45-158. 54Waite, P.. cit., p. 82. 101

the composers much more with which to devise a characteristically important rhythmic element; the different note- durations were too few (basically one, two, and three teMora), and the repetitive arrangement of these durations in groups of three tempera was certainly not an aid to ob- taining variety. Devices such as the rests, fraction modi, and extensio modi made inroads upon the strictness of modal rhythm early in the period, but it was a long time before there was added to the system an independent semibreve duration' and still longer before the adoption of binary structures. After the accomplishment during the first half of the twelfth century of adding to the system a semibreve duration and of using the modal patterns in a less repeti- tious way the rhythmic element in polyphony became increas- ingly capable of a more artistic application.

The importance to rhythm in Western polyphony of the period from immediately before the innovation of modal rhythm to the Ars Nova lies in two fundamental changes in the concept of rhythmic structures: 1) the change from an irregular, 'prose-like" organization of groups of durations to the strictly organized, "poetic" type of rhythm in which there is a regular recurrence of certain patterns: 2) the development of a binary rhythmic organization. The reasons for the change to poetic meters is obscure. In part it may have

55See pp. 92-97, Chapter III. 102

offered a solution to the problem of combining several voices in polyphony, and in part it may have been a musical choice.

However, whatever the reasons for the development it is looked upon as an innovation on a level with the invention of the staff, 56 and with the binary structures introduced into polyphony in the late thirteenth century comprises a large and important part of the various rhythmic structures devised from then until modern times. Because of these far-reaching ramifications the period from ca. 1160-1300 must be regarded as one of the most important for rhythm in the history of

Western music.

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