early organum.pdf

Theoretical Foundations of Early Organum Theory Sarah Fuller Acta Musicologica, Vol. 53, Fasc. 1. (Jan. - Jun., 1981), pp. 52-84. Stable URL: http://links.jstor.org/sici?sici=0001-6241%28198101%2F06%291%3A53%3A1%3C52%3ATFOEOT%3E2.0.CO%3B2-V Acta Musicologica is currently published by International Musicological Society.

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52

H . Husmann : Zur Harmonik des griechischen Volksliedes

d', ho, g', c' und el liegt. Es nimmt, wie die griechische Musiktheorie immer wieder darstellt, der Legetos (etwa dem gregorianischen Peregrinus als ,,Fremdling" zu vergleichen) als Segah auf e' also tatsachlich die Stelle eines diatonischen 2. (dem Umfang nach plagalen) Kirchentones ein. Ebenso passen Bayati und Cargah zusammen, da sie beide das Interval1 a'b' quasipythagoraisch messen. Das Nebeneinander von reiner und pythagoraischer Stimmung charakterisiert ebenso die turkische Musik und diese hat das Prinzip der Verwendung zweier verschiedener Tonsysteme wieder von der arabischen Musik ubernommen, in der man versteht, wie es zu einer solchen Erscheinung kommt : das pythagoraische System ist das an der antiken Musiklehre orientierte, das temperierte bzw. reine das einheimische persische. So kann es keinem Zweifel unterliegen, dai? andererseits nun wieder die byzantinische Musiktheorie diese merkwiirdigen Verhaltnisse von der turkischen Musiksystematik ubernommen hat, - auch hier ist die Ubereinstimmung wieder so speziell, dai3 sie ohne Annahme eines direkten Zusammenhangs nicht erklarbar erscheint. Nicht nur einzelne spezielle stilistische Eigenheiten des griechischen Volksliedes sind also tiirkischem Einflui3 zuzuschreiben, sondern auch ein grundlegender Zug des Aufbaus des griechischen Tonartensystems uberhaupt.

Theoretical Foundations of Early Organum Theory S A R A H FULLER ( S T O N Y B R O O K I N E W Y O R K )

Naming is a fundamental linguistic activity. It is the means by which mankind identifies what is "out there" in the world and communicates perceptions about the world to others. The needs of identification and communication vary with culture, environment, historical situation. While for us one word suffices to designate "frozen water", the Esquimos have developed an elaborate vocabulary for identifying different ages and topographical characteristics of ice, a pervasive element in their environment, detailed knowledge of which is crucial to their surkival.' Our English word meat started out as a general designation for food, but subsequently shifted its field of reference to "food-that-is-flesh-of-animals" as eating habits changed and animal flesh became a common and important element of diet. In music history, we have adopted organum as the "word for" early polyphony, as well as perceiving it as the early name for polyphony. Hence in his authoritative survey of medieval music, Richard Hoppin speaks of "descriptions o f part singing that establish its distinguishing name, organum", and refers to "the different types of organum'' (i. e. polyphony) described in the Enchiriadis treatises.* This nomenclaRichard Nelson lists over 40 terms employed by North Alaskan Esquimos for kinds of ice in Hunters of the

Northern Ice (Chicago 1969), p. 398-402. Medieval Music (New York 1978), p. 188, 189.

S. Fuller: Theoretical Foundations of Early Organum Theory

53

ture is quite adequate to most music-historical discourse, which assumes the distinction between monophony and polyphony to be of capital import. The suitability of organum as the term for early polyphony is enhanced by its currency in the Middle Ages. In adopting "their" word we preserve a valuable historical authenticity. But in taking this course are we really remaining true to medieval concept? I have come to feel that we are not, and that our casual equation of organum with polyphony is not only incorrect but actively obscures central theoretical issues that confronted thinkers who wrote on organum from the 9th to the 13th century. Recognition of these theoretical issues materially influences interpretation of medieval texts about organum. It also illuminates changes in pedagogy, such as the extraordinary shift from 10th-century methods of generating entire phrases (and, by extension, whole compositions) in two voices to 13th-century formalistic catalogs of two-element voice-leading progressions, severely restricted in interval classes (normally octave, fifth, unison, sometimes the fourth) and utterly divorced from ~ o n t e x tThe . ~ argument to be advanced here is that the word organum as applied in music initially corresponded to a fixed concept of what was, by its nature, organal. Organum was organum not because it was polyphonic, but because it was constituted of organal elements. As musical styles changed, the concept denoted by the word organum became increasingly out of phase with the phenomenon commonly called by the name organum. For a while, theorists managed to cope with this by appeal to new principles of explanation, but eventually even this strategy failed. The resulting theoretical crisis lasted over a century and was only resolved in the 13th century with the advancement of a bold and novel theory that completely redefined the essential nature of organum, revitalizing pedagogical and theoretical discourse about it.

I The earliest treatises to deal concretely with organum are the Musica Enchiriadis and the Scolica Enchiriadis. Neither work is primarily about polyphony. The aim in each is to lay out a coherent pitch system and to explain significant relationships among its elements, the pitches. Prime significance attaches to the symphoniae-intervals of fourth, fifth, and octave-because pitches so related join together in sweet agreement.4 Discussion of organum is undertaken not for its own sake, but in illustration of the properties of symphoniae. In the Musica Enchiriadis, the subject is announced by the heading De proprietate symphoniarum and approached thus :

. . . nunc id, quod proprie simphoniae dicuntur et sunt, id est qualiter eaedem voces, sese in unum canendo habeant, prosequamur. Haec namque est, quam diaphoniam cantilenam vel assuete organum nuncupamus. Dicta autem diaphonia, The so-called Vatican organum treatise, with its concrete melismatic elaborations, is a striking exception. It has been edited by F. Zarniner (Tutzing 1959). Musica Enchiriadis, edited M. GERBERT, Scriptores Ecclesiastici de Musica I (St. Blasien 1784, repr. Hildesheim 1963), p. 160, col. I. Hereafter cited as GS I.

54


quod non uniformi canore constet, sed concentu concorditer dissono. Quod Iicet omnium simphoniarum est commune, in diatessaron tamen ac diapente hoc nomen ~ptinuit.~ (Now let us pursue what symphoniae properly are and are called, that is, how these same pitches relate to each other when sung together. This is indeed what we call diaphonic song or, customarily, organum. But it is called diaphony because it consists not in singing uniformly, but in the concordant agreement of separate sounds. Although it is common to all symphoniae, this name nevertheless applies best to fifth and fourth.) The writing makes clear that "singing in symphoniae" is known by two names, diaphonic song or diaphony and organum, and that these names best apply to two symphoniae, the fourth and the fifth.6 The Scolica Enchiriadis presents a similar though not identical viewpoint. Its successive chapters on "organum" are simply headed by the name of each symphonia in turn: De diapason ac disdiapason, De diapente, De diatessaron. The Scolica never actually calls the music produced by these intervals organum, but it does refer to the added part as the vox organalis. The essential property of the vox organalis is its symphonic relationship to the principal voice.

Principalem enim vocem absolutam cantionem dico, organalem vero, quae huic subiungitur symphoniae rationee7 (I call the principal voice that which is sung absolutely [literally], the organal voice that which is subjugated to it by the relationship of a symphonic interval.) By implication, the Scolica limits the notion of organal to the symphoniae of fourth and fifth. The term vox organalis is absent from the chapter on the octave but occurs repeatedly in the sections on singing at the fifth and the fourth. The octave, moreover, is characterized as not so much consonus but aequisonus (the same sound), which puts it in a class apart from the other two simple symphoniae.' The association of organum with symphoniae was not restricted to theorists of Daseian persuasion. Hucbald too finds a reference to organum the most direct way to express the nature of symphoniae (which he terms consonantiae).

Consonantia siquidem est duorum sonorum rata et concordabilis permixtio, quae non aliter constabit, nisi duo altrinsecus editi soni in unam simul modulationem conveniant, u t fit, c u m virilis ac puerilis vox pariter sonuerit; vel etiam in eo, quod consuete organizationem v ~ c a n t . ~ Quoted from the edition of E. L. WAELTNER, Die Lehre vom Organum bis zur Mitte des 11,lahrhunderts I, Miinchner Veroffentlichungen zur Musikgeschichte 13 (Tutzing 1979, p. 2. Hereafter cited as WAELTNER. Waeltner includes page references to the older, and less reliable, GS I. F. Reckow has pointed out that diaphonia and organum stem from quite distinct, somewhat incompatible, traditions (Organum-Begriff und Friihe Mehrstimmigkeit, in: Forum Musicologicum I, Basler Studien zur Musikgeschichte I, p. 133). WAELTNER, p. 22. WAELTNER, p. 20. This characterization of the octave parallels Hucbald's description of the unison, see GS I, p. 104, col. 2, or, in English translation, Hucbald, Guido and John On Music, translated by W. BABB (New Haven 1978), p. 13. Hereafter cited as BABB. GS I, p. 107, col. 1.

'

S . Fuller: Theoretical Foundations of Early Organum Theory

55

( A consonantia [symphonia] is then a proportionally determined and concordant mixture of two sounds, which will not come about unless two sounds, produced from different sources, come together simultaneously in one musical idea, as occurs when a man's voice and a boy's sound at the same time or indeed in that which they usually call "making organum".) Other treatises associated with the Enchiriadis pair also press home the association of organum with symphoniae, omitting the fifth and mentioning only the fourth when it suits their pedagogical purpose.

Adhuc de diatessaron symphonia, quomodo melos diaphoniae nascatur, videamus, quam usitato vocabulo organum n ~ n c u p a m u s (Paris . ~ ~ Treatise) (Now let us see how the melos diaphony, which we call by the customary word organum, is born from the symphonia of a fourth.)

Diaphoniam seu organum constat ex diatessaron symphonia naturaliter dirivari." (Cologne Treatise) (Diaphony or organum is derived naturally from the symphonia of a fourth.) Dyaphonia vel organo dupliciter uti possumus, id est vel per dyapente vel per dyate~saron.'~(Se'lestat fragment) (We can practice diaphony or organum in two ways, that is, either by the fifth or by the fourth.) The notion that organum as a phenomenon embodies basic relationships of symphoniae lies behind the doctrine of parallelism which is central to the organum pedagogy relayed in these treatises. For organum at the fifth, parallel movement of the organal with the principal voice is unproblematic. Under the Daseian pitch system, the organal voice can hold rigidly to the fifth without ever deviating from this symphonia or altering any of the pitches postulated in the given pitch-system. Organum at the fourth, however, poses vexing problems, for the voices cannot proceed unswervingly in fourths, but inevitably encounter tritones in moving from one tetrachord to the next (Diagram 1, p. 5 6 ) . In pedagogy, the response is to abandon strict parallelism and allow the organal voice to dwell on boundary tones determined by behavior of the principal voice and by tetrachordal or modal context. In theory, the response is to proclaim a special law said to govern organum at the fourth. The theorists's representation of the deviation as law-bound, and their further characterization of the law itself as divinely inspired (Musica Enchiriadis) or as natural (Scolica) betrays a deliberate effort to invest the deviation from fourths with authority, to preserve it from the taint of arbitrariness.

lo

WAELTNER, p. 72.

l2

WAELTNER, p. 68.

" WAELTNER, p. 54.

5. Fuller: Theoretical Foundations of Early Organum Theory

Diagram 1

Daseian Pitch System13

Fifths

Fourths

Daseian Symbol Daseian flame b "

L e t t e r Name Tetrachord Name

f

A

6

Graves

C

D

E

F

Finales

G

a

b

c

d

Superiores

e

f

'

g

a

,

Excel l e n t e s

At in diatessaron quoniam non per omnem sonorum seriem quartis locis suaviter sibi ptongi concordant, ideo nec absolute ut in ceteris simphoniaca editur cantilena. Ergo in hoc genere cantionis sua quadam lege voces vocibus divinitus accomodantur.14 (Musica Enchiriadis) (But because with the interval of a fourth sounds do not concord sweetly at a distance of four notes throughout the whole series [of pitches], so the symphonic song cannot be [relproduced literally as in the others. Therefore, in this genre of singing, by a law proper to it, pitches are adjusted to other pitches in a divine way.) Sequitur diatessaron symphonia. Ea est, ubi quartanis locis in unum pangitur. Sed sciendum, quia non ita simpliciter, ut in ceteris, quae maiores sunt, sed et alia quadam naturali lege organum exinde derivatur, unde et post dicetur.15 (Scolica Enchiriadis) (There follows the subject of the symphonia of a fourth. This is when singing together is done at a distance of four notes. But know that this organum is not sung so simply as in the others, which are larger, but is diverted from thence [the fourth] by a certain other natural law, as will be discussed later.) The necessity for this special law is explained differently in the Musica Enchiriadis than in the Scolica-one of many telling indications that these treatises did not stem from a single mind. The Musica Enchiriadis justifies it in observing that the fourth note below the deuterus of any tetrachord always makes an interval larger than a fourth with the deuterus above, thereby creating a non-consonance (See Diagram 1).

Per omnem enim sonorum seriem tritus subquartus deutero solus a simphonia deficit et inconsonus ei efficitur, eo quod solus diatessaron simphoniae mensuram excedens tribus integris tonis a praefato sono elongatur, cui extat subq~artus.'~ l3 The relationshi~s shown here hold for anv tetrachord pair, for all tetrachords are uniform in , adiacent , construction ( T S ~ )and disjunct by a tone. l4 WAELTNER, p. 10. WAELTNER, p. 28. l6 WAELTNER, p. 10. Inconsonus has the sense of "an improper interval". Note, in this connection, Guido's definition of the consonantiae as the six intervals from semitone to fifth, excepting the tritone (Micrologus, edited J. SMITS VAN WAESBERGHE, Corpus Scriptorum de Musica 4 [American Institute of Musicology 19551, p. 105). Hereafter cited as Micrologus. The Musica Enchiriadis elsewhere refers to this sound as an absonia (WAELTNER, p. 14).


57

(Throughout the whole series of sounds only the tritus a fourth below a deuterus abandons [the interval of a] symphonia and produces an inconsonus with the deuterus, so that exceeding the size of the symphonia of a fourth, the tritus is removed by three whole tones from the precedent sound of which it is the fourth [pitch] below.) To avoid the unacceptable sonority inevitably produced by the tritus pitch with the sound four notes above it, the organal voice is instructed to remain fixed on the tetrardus note of any tetrachord when the principal voice sounds the bottom notes of the tetrachord above. That this procedure both breaks parallelism and introduces intervals that are not symphoniae is of far less consequence than that it eliminates the inconsonus or absonia of three whole tones. The explanation in the Scolica Enchiriadis takes a quite different tack, appealing not to quality of sound but to the concept of mode. Whereas in organum at the fifth the organal voice remains always in the same mode as the principal one-as evidenced by the equivalence of the Daseian symbols for each, protus invariably answers protus, deuterus answers deuterus, etc.-in organum at the fourth it does not-protus will answer tetrardus, deuterus will answer protus, and so on (Diagram 1). The resulting discrepancy in mode between the two voices forces the organum sometimes to deviate from the fourth. D[iscipulus]: Quare non potest in diatessaron symphonia vox organalis sic absolute convenire cum voce principali, sicut in symphoniis aliis? Mlagister]: Quoniam ut dictum est, per quartanas regiones non idem tropi reperiuntur, diversorumque troporum modi per totum simul ire nequeunt, idcirco in diatessaron symphonia non per totum vox principalis voxque organalis quartana regione consenti~nt.'~ ( S t u d e n t : Why is the organal voice unable to agree with the principal voice literally in the symphonia of the fourth as it does in the other symphoniae ? M a s t e r : Because, as already said, the same modes are not found at the fourth and the characteristic manners of different modes cannot go through the whole (pitch system) together. Therefore, with the symphonia of a fourth the prior voice and the organal voice do not concur at the fourth through the whole range.) Although the natural law of organum at the fourth permits intervals that are not symphoniae, the writers yet emphasize that such intervals are not to be accepted as organal. The Musica Enchiriadis theorist insists that the first three notes of Rex caeli domine (Example l a ) lack an organal response (in the theoretical sense) even though the vox organalis in fact sounds from the beginning of the phrase. Similarly, in the subsequent phrase of this prose, which begins on GI there is no ratum responsum for the tetrardus, protus and deuterus opening the principal voice (Example Ib). The so-called Paris treatise (an insertion in some versions of the Musica Enchiriadis) is similarly strict about where legitimate organum may be said to begin. l7

WAELTNER, p. 36.


59

(Sometimes, for lack of natural space, we put a false organum in some phrases, by bringing [the voices] together at the second or the third.) This attitude is echoed by one of several comments on organum imbedded within a work on organ pipe mensuration:

Quod vero organum invenitur in secunda et tertia similiter sicut in quarta et quinta, non naturale hoc dicitur." (Truly, when organum is found in the second and third pipes, just as it is in the fourth and the fifth, this is called unnatural.) Passages such as these deepen the impression that the term organum was considered to'apply properly only to symphoniae. They reveal too that the theorists already confronted a paradox. Certain intervals that existed within organum (loosely construed, as the phenomenon) were not legitimately organum in the technical sense. While the necessity for such intervals could be supported by arguments about modal consistency or false sounds, and while the rules by which they were generated could be granted the status of natural law, these intervals yet remained outside that set of entities which were understood to be organal by nature. Fourth and fifth remained the sole legitimate organal intervals. The theoretical bias toward organum manifested in the treatises of the Enchiria~' Guido's discussion of organum dis orbit did not extend to Guido of A r e ~ z o . Indeed, in the Micrologus (Chapters 18 and 19) is remarkable for its indifference to guiding theoretical principles. Although in the earlier part of the work Guido engages with such abstract issues as the generation of a diatonic pitch system through division of the monochord and similarity relationships among the resulting seven pitch classes, in the organum chapters he claims just to report local usage. . . . gravem a canente succentum, more quo nos utimur e x p l i c e m ~ s . ~ ~ (Let us explain the low voice following below the cantus in the way that we practice it.) Guido's one reference to the relationship between symphoniae and organum even reverses the association postulated in Northern theory. Whereas in the Enchiriadis treatises the symphoniae provide the rationale for what is organal, Guido writes as though the practice of organum reveals what is symphonic. Et quia hue tres species tanta se ad organum societate ac ideo suavitate permiscent, ut superius vocum similitudines fecisse monstratae sunt symphoniae, id est aptae vocum copulationes dicuntur, cum symphonia et de omni cantu d i c a t ~ r . ~ ~ WAELTNER, p. 68. These few sentences have been gathered together by Waeltner to form what he calls the Sdestat treatise. I include among organum treatises "of the Enchiriadis orbit" those works whose transmission is linked with the Musica or Scolica Enchiriadis or one of their offshoots. In practice, this encompasses all the texts edited by Waeltner except the Micrologus and, in addition, the treatise Prague, Stami Knihovna CSR, Ms. XIX C26. The actual teaching of the treatises is not a criterion for this grouping, since the works differ considerably in this respect. Micrologus, p. 201; and WAELTNER, p. 92. Guido's shift in perspective is noteworthy and reflects upon the relative status of these two realms of music. Plainsong theory is presented as possessing universal validity; organum teaching as having only local reference. 24 Micrologus, p. 198; WAELTNER, p. 90. A complete English translation of the Micrologus is found in BABB (cited note 8). 21

60

S . Fuller: Theoretical Foundations o f Early Organum Theory

(And because these three species [of interval, i.e. fourth, fifth, and octave] so thoroughly mingle in organum with companionship and sweetness-just as they were shown above to effect similarities of pitches-they are called symphoniae, that is, fitting unions of pitches, although all song can be called symphonia.) One of the central pillars of Guido's organum teaching is a hierarchic ranking of intervals (the other is occursus). Of the four intervals which he accepts in organum (the fifth and the semitone are specifically excluded), the fourth ranks highest, the minor third lowest. The major second stands next below the fourth and the major third falls below it. The high status of the fourth presumably follows from its prestige as a symphonia, although Guido does not explicitly state this. The status of the three lower-ranking intervals seems to derive from their role in occursus, the unison conjunction required at most phrase endings. tonum vero et ditonum et semiditonum cum diatessaron recipimus, sed semiditonus in his infimatum, diatessaron vero obtinet principat~im.~~ (We admit the tone and major third and minor third with the fourth, but the fourth is the principal one among these, the minor third the lowest ranking.) Qui occursus tono melius fit, ditono non adeo, semiditono n u m q u ~ m . ~ ~ (Occursus is best made by a tone, not so much by a major third and never by a minor third.) Guido makes no gesture toward defending this ranking on general theoretical grounds. As with his pedagogical precepts, his hierarchic ordering has no inherent claim to authority. It rests neither on natural law nor on abstract properties of sound but simply derives from local custom. Although Guido's theoretical stance and pedagogical approach differ materially from those of the Enchiriadis theorists, the style of organum at the fourth resulting from his dicta is substantially the same as that resulting from their teaching. This (along with just as sharp differences in pedagogy evident among treatises of the Enchiriadis orbit) suggests that these theorist-pedagogues were trying to control, explain, teach a way of making music that was already common practice. As with the modal theory they were concurrently devising for chant, their task was mainly to devise reasonable and relatively coherent doctrine to fit what was already happening. Unlike most of the teachings put forth in the Micrologus, Guido's approach to organum seems not to have attracted adherents, possibly because practice was already in the course of change. The main commentaries on the book virtually ignore the organum chapters.27The next generation of writers on organum adopts neither his instructions for making organum nor, more importantly, his notion of a hierarchy among intervals which is established by convention. Indeed, the central 25

26 27

Micrologus, p. 201-2; WAELTNER, p. 92.

Micrologus, p. 204; WAELTNER, p. 92.

Expositiones in Micrologum Guidonis Aretini, edited J . SMITS VAN WAESBERGHE (Amsterdam 1957).


61

work that initiates what we may call the post-Guidonian phase of organum teaching, the A d organum faciendum, aggressively attacks Guido in its opening lines, characterizing his guidance as worthless.

As long as parallel movement in symphoniae was the guiding principle of organum, theoretical explanations of the kind advanced in the Musica Enchiriadis and the Scolica Enchiriadis could be held valid. But as the organal voice became more independent of the principal one (even though still adhering to symphoniae), the old reasoning could no longer adequately account for choices of organal pitches to pair with tones in the principal voice. The course of the organal line in a two-voice phrase such as that shown in Example 2 can be understood neither in terms of single-interval parallelism, nor of modal consistency, nor of forced avoidance of harsh intervals. New theory was needed to support new practice and pedagogy, and it was supplied most imaginatively by the anonymous author of a treatise entitled A d organum faciendum. Example 2'' First modus organizandi from A d organum faciendum 0 = cantus, = organal voice

While obviously familiar with Guidonian teaching, the author of A d organum faciendum yet shows a consciousness of fundamental principles that allies him with Northern tradition as represented by the Enchiriadis treatises and their offshoots. His ,sensitivity to theoretical issues is immediately manifested in the way he presents the two names for polyphony : organum and diaphonia. Rather than simply juxtapose them, he explains the connotations of each in separate definitions.

Organum est vox sequens precedentem sub celeritate diapente vel diatessaron. quarum videlicet precedentis et subsequentis fit copula, aliqua decenti consonantia. Dyaphonia vocum disiunctio sonat. quam nos organum vocarnus, cum disiuncte ab invicem voces concorditer dissonant. et dissonanter concordant. Qua organizatores ita utuntur, quatinus diapente vel diatessaron discurrant, ut .A, ad .D.29 Ad Organum faciendum. Lehrschriften der Mehrstimmigkeit in nachguidonischer Zeit, edited H. H. EGGEBRECHT and F. ZAMINER, Neue Studien zur Musikwissenschaft 3 (Mainz 1970),p. 52. Hereafter cited as EGGEBRECHT and ZAMINER. 29 EGGEBRECHT and ZAMINER, p. 46. Sub celeritate seems to have the sense of archaic English "quick", vital principle, that which is active. Voxis equivocal in meaning. It can (and does) stand sometimes for a pitch, sometimes for a line. On consonantia see note 16 above.

62

S . Fuller: Theoretical Foundations of Early O r g a n u m Theory

(Organum is a pitchhoice following a given pitchlvoice under the control of fifth or fourth. These two, i.e. the given voice and its follower, make copula by any appropriate interval. Diaphony sounds as a disjunction of pitchesllines which we call organum because these pitches, which are distinct from each other, sound separately harmoniously and concord in sounding separate. Those making organum practice this [diaphony] thus, by proceeding at the fifth or the fourth, as A to D.) This definition of organum incorporates the central principle held by the Enchiriadis treatises: that fourth and fifth control the action of the organal voice with respect to the cantus. Only just before copula-union in unison or octave-are other intervals admitted, and the theorist is indifferent to what they might be.30The definition of diaphony is closely modelled upon Guido, who in turn seems to have imitated the Musica E n ~ h i r i a d i s This . ~ ~ name refers to the duality or separation of sound perceived in two-part music. Singing in two parts is both organum and diaphony because it possesses qualities signified by both names. It is organal because it adheres to precise symphonic intervals, the fourth and the fifth. It is diaphonic because the voices moving in fourths and fifths do not blend fully as at the octave or unison but sound distinct. The A d organum faciendum theorist prefers the name organum and the concepts conveyed by it over the name diaphony. He not only gives organum precedence by elucidating its meaning first, he also' pulls diaphony into the sphere of the organal by a qualification concerning its practice: singers in fact produce diaphony by singing at the fourth or the fifth. Although the A d organum faciendum concurs in its concept of organum with the Enchiriadis treatises, the kind of polyphony it teaches differs radically from theirs and from Guido1s. It does not distinguish an organum at the fifth and an organum at the fourth, each bound in principle to a single interval, but teaches one organum in which fourths and fifths are intermixed (see Example 2). It incorporates copula as an essential syntactical element and allows it to take place at the octave as well as at the unison.32 Other differences such as voice-crossing and position of the organal voice above the principal one may be passed over here, as they do not bear directly upon theoretical stance. The critical problem, from the theoretical viewpoint, is how to justify the mixture of allowed intervals: unisons, octaves, fourths and fifths. The old arguments citing avoidance of tritones or modal integrity can no longer apply, since with the abandonment of parallelism untoward intervals can easily be skirted, and what might be meant by modal consistency cannot easily be determined. The A d organum faciendum theorist responds by invoking a new principle to account for choices of organal pitches. He chooses his ground carefully, not appealing to the Note the incipient sense of function in this licence, for by means of it copula/cadence can be distinguished in sound quality from other moments in the piece. See the passage quoted above, p. 60. It is possible that this theorist drew directly upon the Musica Enchiriadis, but there is no internal evidence that he knew that work, while he does mention Guido explicitly. 32 The occursus taught explicitly by Guido, and implicitly in examples of the Enchiriadis treatises, is similarly an essential element of organum at the fourth, but occurs only at the unison.

''


63

privileged status of symphoniae but appropriating from the Micrologus (Chapters 7 and 8) the doctrine of affinitas vocum or affinity. Affinity is a crucial topic in the theory of chant finals.33Through it, Guido demonstrates that the seven notes within the octave are not completely independent entities but adhere each to one of just four final patterns, or modi vocum. A and D are allied in having a tone below and a tone, semitone and two tones above; B and E in having two tones below and a semitone and two tones above, etc. These affinities are intrinsic to the pitch system itself. Besides holding true for pitches of the same letter name, the affinity relationship exists only between pitches a fourth or a fifth apart (Diagram 2 ) . The doctrine of affinity thus offers a perfect rationale for the new organum. The test of a legitimate organal response to any cantus pitch becomes that it possess affinity with the given pitch. Diagram 2

Micrologus Figure showing Similarities among Pitches34

[Fourths side] [Octaves] [Fifths side]

Sciendum est autem organales voces affinitatem habere cum p r e ~ e d e n t i b u s . ~ ~ (Know then that organal pitches have affinity with those of the given voice.) The theorist even introduces his teaching of organum as though it were simply a further exploration of affinities. 33

For an exposition of its importance in Guido see R. L. CROCKER, Hermann's Major Sixth, in: J A M S 25

(1972). , , =D. 22-25. - \

34 Micrologus, p. 129. I reproduce the second of Guido's figures. As Crocker points out (op. cit., note 33), this

figure seems to argue for just 3 Finals.

35 EGGEBRECHT and ZAMINER, p. 46-47.

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C u m autem affinitas v o c u m i a m satis patefacta sit, per diatessaron et per diapente et per diapason, natura eorum persequenda e ~ t . ~ ~ (Since then the affinities of pitches through the fourth, the fifth, and the octave have already been demonstrated sufficiently, their nature must be explored.) The doctrine of affinity can account in principle for all four intervals regularly permitted by the teaching. The pitches of unison or octave possess affinity by identity, those of fourth or fifth by the pattern of surrounding tones and semi tone^.^' The initial element of copula is the only pairing exempted from this criterion. The doctrine of affinity is the theoretical cornerstone of the post-Guidonian stage of theory initiated by the A d organum faciendum. The important Milan verse treatise, an independent companion of A d organum faciendum, stresses the bond thus created between the parts, playing on the resonance between affinitas and amicitia. Prestolatim colloquendo amicus duas iungamus.

N a m tantae affinitatis sunt tantaeque amicitiae.

Prima conducit alteram causa beni~olentiae.~'

(Let us join together two friends ready for conversation

For so much affinity is allied with so much friendship

That the first leads the other out of benevolence.)

The reworkings of A d organum faciendum retain the affinity principle in their texts, even when the practice they allow contradicts it. The purpose of invoking the principle of affinity-which, as Guido presents it, is part of plainchant theory-seems to be to fortify the traditional understanding of what is, by nature, organal. The A d organum faciendum closes with a highly philosophical passage that brings the full battery of contemporary dialectic to bear on this matter.39The argument maintains that the real concept of organum pertains uniquely to the fourth and fifth, and runs as follows. There are two kinds of significatum organi, one natural, the other remote from nature. Natural organum consists in two distinct entities or states of being: fourth and fifth. Organum remote from nature is anything other than these two entities. Such organum, the theorist states, is no organum. His analogy is to the concept of man. As a living being, a man must be either well or sick. If neither of these conditions holds (as with a cadaver) EGGEBRECHT and ZAMINER, p. 47. Note the similarity of approach to that of the Musica Enchiriadis theorist, who introduces organum as a means of exploring the symphoniae (quoted above, p. 53f.). Contrary to the impression given in this passage, the author has not carehlly explained affinity. The preceding line, lifted from Guido, suggests that he had the Micrologus in mind. It is also possible that Ad organum faciendum as it exists now is a portion of a longer work which did include a substantial discussion of affinity. 37 This theorist gives no heed to the obvious objection that if a pitch stands in an affinity relationship with the pitch a fifth above, then it cannot possess affinity with the fourth above, and vice versa. To explain the primary intervals of organum, it suffices to show that affinity relationships other than identity are generated by fourths and fifths only and by no other intervals. Specific affinities-such as whether D can belong to G as well as to A-are left vague. 38 EGGEBRECHT and ZAMINER, p. 111,lines 5-7. 39 A penetrating exegesis of this passage and its roots within contemporary tradition is provided by MAX HAAS, Der Epilog des Mailander Organum-Traktates, in: Schweizer Beitrage zur Musikwissenschaft 2 (1974), p. 7-19.

36


65

then the phenomenon cannot be subsumed under the concept man. Similarly, if a sound between organal and principal voices is neither a fourth nor a fifth-that is, if it corresponds to neither condition of organum-then it cannot be called organum. The logic may be summarized in a syllogism: All natural organum is either at the fourth or the fifth Some polyphonic sounds are not at the fourth or the fifth Therefore such sounds are not organum. Organum remote from nature, polyphonic sounds which are not fourths or fifths, is organum only by resemblance, as a portrait might resemble its subject. Though less dogmatic in tone, the Milan verse treatise also holds to the conceptual identification of organum with fourths and fifths. This is advertised in its opening lines :

[ C ] u m autem diapente et diatessaron organizarnus. Succincte et egregie c ~ r r a m u s . 4 ~ (Since we make organum at the fifth and the fourth Let us carry it out with precision and excellent execution.) The centrality of relationships by fourth and fifth is further pursued in the teaching, for the student learns that for any given pitch there exist but a limited number of legitimate organal companions: G and a only are organal to D, D and E pair with A.41The prudens cantor is exhorted to learn perfectly not only the pitches of the scale, but also the pitches of organum, for these, too, are fixed entities.

Flagito te prudens cantor has perfecte discere. Omnis quia fere cantus ibi possit psallere. Organum vocesque suas perfecte dinoscere. Quarum labor cum sit gravis honos est d ~ l c i s s i m u s . 4 ~ ( I entreat you, skilled singer, to learn these [pitches] perfectly Because all song can usually be sung with them, And to distinguish perfectly organum and its pitches While this task is difficult, it is most wonderfully honorable.) Despite extreme differences between the musical style of organum taught in the post-Guidonian treatises and that taught in the Enchiriadis treatises and by Guido, the concept organum remained intact. New styles and a radically different pedagogy did not yet menace the concept, but they did force reconsideration of its rationale. The chosen doctrine, affinitas vocum, was neither newly invented nor restricted in application to polyphony, but was appropriated from plainsong theory. Such mining of earlier writings on music for ideas that might be of use to theory of part-music recurs in subsequent phases of change. The tendency reveals a cast of 4"GGEBRECHT and ZAMINER, p. 111, lines 1-2. Note the resonance of the verb curramus with the language seauens . . . sub celeritate of the wose treatises. E G ~ E B R E C H T and ZAMINER, p. 111,'lines 10-11, 21-23. 42 EGGEBRECHT and ZAMINER, p. 111, lines 26-29.

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mind both cautious-as though theory of this kind of music should keep to known paths-and imaginative-for such appropriations involved fresh perceptions of the breadth and power of concepts not originally associated with organum. I11 Revised versions of A d organum faciendum testify to a deepening gulf between the concept of organum and the practice of polyphony. Revision of the organum definition in the version known as Berlin B reveals the course of disintegration: Organum est vox sequens precedentem sub celeritate diapente vel diatessaronvel dittoni vel semidittoni. quarum id est precedentis vel subsequentis fit copula aliqua decenti c ~ n s o n a n t i a . ~ ~ (Organum is a pitchlvoice following a given pitchlvoice under the control of fifth or fourth or major third or minor third. These two, i.e. the given voice and its follower, make copula by any appropriate interval.) The definition so emended becomes merely a statement of practice, lacking a theoretical foundation. With the acceptance of thirds as intervals proper to organum, the principle of affinity no longer justifies choice of organal pitches. The anonymous redactor of Berlin B eventually allows that fourth and fifth are more central to organum than thirds because they make up the octave and because organum sounds more "tempered" in them. However neither of these reasons has the persuasive force of the argument from affinity.

Medie siquidem voces per lIIl.Or supradictas consonantias incedunt quarum diapente et diatessaron, principatum organi possidere dicunter eo quod modulantius in eis organum resonet et constitutive diapason c o n ~ i d e r e n t u r . ~ ~ (The middle notes [of the phrase] indeed proceed by the four intervals mentioned above, of which the fifth and the fourth are said to possess the foremost place, because the organum sounds more measured in them and they are considered as an octave when arranged together.) The Montpellier treatise provides even stronger testimony on the weakening of the original concept organum. To be sure, it repeats without significant emendation what seems to be the standard definition for this stage of theory,45but the pedagogy by no means continues the emphasis on fourths and fifths. It permits thirds and sixths not only within phrases, but sometimes also as initial sounds.

Postea primam vocem organi id est inceptionem ponat cum cantu vel inferius in diapason vel superius, vel in eadem vel in quinta vel in quarta. aliquando et in tertia vel sexta. In secunda autem vel septima voce a cantu nunquam erit organum, quia EGGEBRECHT and ZAMINER, p. 159. Roman letters in the Latin text indicate deviations from the corresponding Ad organum faciendum passage; those in the translation are mine. EGGEBRECHT and ZAMINER, p. 160. The redactor also retains the sentence calling for affinity of organal pitches with cantus notes, but it appears not as an integral part of the exposition but as an isolated statement toward the end, unrelated to the substance of the teaching. 45 This is the formula Organum est vox sequens precedentem sub celeritate diatessaron vel diapente.. ., EGGEBRECHT and ZAMINER, p. 187. 43


67

male sonat. Medias autem voces. inter primam et ultimas duas preelectas. ponat in quinta vel quarta vel tertia vel sexta, sed frequentius in quarta vel in quinta, quia pulcrius ona at.^^ (Afterwards [i. e, after choosing the copula] put the first organal pitch, that is, the inception, with the cantus either an octave below or above, either in unison or at the fifth or the fourth, sometimes also at the third or the sixth. But the organum will never be a second or a seventh from the cantus because this sounds bad. Put the medial pitches-those between the inception and the chosen last two [copula]-at the fifth, the fourth, the third, or the sixth, but more frequently at the fourth or the fifth, because this sounds more beautiful.) From the theoretical point of view, the remarkable feature of this passage is not the acceptance of thirds and sixths in organum but the reasons adduced for the choice of intervals. Seconds and sevenths are excluded from the ranks of initial sounds not on theoretical grounds (their proportions are too complex, they are not symphoniae) but on aesthetic grounds : they sound bad. Fourths and fifths are more frequent within phrases not because they are inherently organal, not because they are symphoniae, but because they sound very beautiful. Lacking any formal criterion by which to set fourths, fifths, thirds and sixths apart as a group from other intervals or to make a subdivision within this group, the writer resorts to sensory perception and aesthetic opinion: this sounds bad, this sounds beautiful. He does not attempt to explain this reaction in generalized terms, as, for instance, in terms of perceived blending of pitches, an idea readily accessible in Boethius. The verdict stands as an empirical statement of fact. The lack of polernic suggests that no challenge was anticipated, although in the context of treatises now survivingsuch an aesthetic argument appears quite special.

Lack of secure dating for those organum treatises that are certainly postGuidonian makes it impossible to fix a chronology for the process during which the original concept of organum became alienated from practice and the theoretical foundations on which it rested were rendered obsolete. Even if the treatises could be set in reliable chronological order, uncertainties in provenance would prevent any claim that the process spread uniformly through Europe during a defined period of time. An inquiry such as this is forced, then, to proceed by landmarks, plotting a course by those surviving works that epitomize certain stages of thought, while making no claim that the stages were either linear or orderly in sequence. We do not know, for example, whether in strict chronology the Montpellier treatise preceded or followed John of Afflighem's De Musica (dated c. 1100-1121),47 EGGEBRECHT and ZAMINER, p. 187. De Musica cum Tonario, ed. J . SMITS VAN WAESBERGHE, Corpus Scriptorum de Musica 1 (Rome 1950), p. 26. Hereafter cited as De Musica. "

68

5. Fuller: Theoretical Foundations of Early Organum T h e o y

but conceptually John's treatise represents a new stage in thinking about organum. This new stage is most readily distinguished by abandonment of that definition of organum which is the hallmark of post-Guidonian theory: organum est vox sequens precedentem . . . John of Afflighem initiates his discussion with this definition of his subject : Est ergo diaphonia congrua vocum dissonantia, quae ad minus per duos cantantes agitur, ita scilicet ut altero rectum modulationem tenente, alter per alienos sonos apte circueat, et in singulis respirationibus ambo in eadem voce vel per diapason conveniant. Qui canendi modus vulgariter organum dicitur, eo quod vox humana apte dissonans similitudinem exprimat instrumenti quod organum v o c a t ~ r . ~ ~ (Diaphony is then an agreeable separate-sounding of pitchesllines which is performed by at least two singers, so that with one holding to the given melody, the other roams appropriately around other sounds, and within a single breath, both come together on the same pitch or at the octave. This manner of singing is commonly called organum, because the human voice, in suitably sounding-separate, expresses a similarity to that instrument which is called the organ.) Several familiar elements are recognizable, but the emphasis has shifted drastically. Like the Ad organum faciendum theorist, John acknowledges two names for polyphony, diaphonia and organum. Like his, John's initial definition is in two parts, a statement of the meaning of one of the names, followed by a description of copula. John chooses, however, to start with the name diaphonia, not with organum. As a result, his presentation of what polyphony is stresses its duality of sound, the concept inherent in the name diaphonia. The second part of his statement is not conceptual but descriptive. It tells what happens in diaphony: one voice circles around the given melody until the end of a breath (phrase), where both concur on unison or octave. Specific intervals plainly are not central to John's concept of polyphony, as they are to the Ad organum faciendum theorist's concept of what is called organumldiaphonia. Even in his description of the phenomenon, John contents himself with referring vaguely to "other sounds" produced by the second voice, offering no comment on any constraints governing them.49 Moreover, John does not conceive the two liames for polyphony to be distinct and complementary, each conveying a different conceptual aspect of the phenomenon. He rather presents them as synonymous, an action that prevents him from remaining faithful to the traditional sense of the name organum. John relays the standard definition of the name diaphonia and adopts it as his chief name for polyphony because he can accept the separateness of voices denoted in that name. But he nowhere alludes to organum as that which consists in fourths and fifths. He dismisses the name as merely the common parlance: diaphonia is

De Musica, Chapter XXIII, p. 157. The entire treatise is translated in BABB (cited note 8), p. 101-187. The unusual choice of words merits attention: alienos sonos rather than alienas vores. The other singer produces not just different pitches, the traditional language in which organa1 activity is described, but different sounds, a word choice that stresses the sonorities resulting from interaction with the principal voice.

49


69

Instead of saying what organum i s , he takes refuge in vulgariter etymology: people call it organum because the sound in performance resembles the instrument called the organ. Plausible as this sounds, it rests on no continuous tradition within treatises on music. Indeed, John seems to be the first music theorist to advance it. In choosing an etymological mode of explanation, he masks what the concept organum originally meant as applied to polyphony. It is not difficult to surmise why John took this tack. From specimens of music from the early 12th century, we have good reason to believe that the polyphony he knew was by no means strictly based on fourths and fifths but commonly included other intervals. John, like other theorists of his day, confronted a pronounced discrepancy between received doctrine about organum and actuality of practice.'' This discrepancy not only caused linguistic adjustment-so that old names were stripped of their former conceptual meaning-but also forced a quest for new theoretical principles to support the pedagogy of the new practice. John's response to this situation reveals considerable imagination. One of the special, and rather puzzling, features of John's chapter on diaphony is a long passage on motus vocum or types of melodic motion. This begins right after the passage just quoted and, in its context, seems something of a non sequitur, despite John's promise that the subject will be useful to subsequent precepts. Sed antequam organizandi praecepta demus, de motibus vocum, quorum consideratio ad hoc negotium utilis est, pauca perstringere v01umus.~~ (But before we give the precepts of performing organum, we wish to touch upon a few matters about motus vocum, consideration of which is useful to this subject.) The discussion commences with the observation that melodic motion can either ascend or descend, and that a succession of two intervals-or two motus vocum-can either link two similar motus (both ascending, both descending) or two different ones (one ascending, one descending or vice versa). Pursuing this subject with pedantic delight in classification, John enumerates many sorts of possible relationships between motus vocum: one may have more notes than the adjacent one, as when a neume of two notes is followed by one of three; a second motus may start on a higher pitch than the preceeding one, or on a lower one, and so on. A musical example also illustrates how the motus vocum of a melody (its individual intervals) is affected by the mode in which it appears. All this may seem rather distant from the topic of polyphony, and John reinforces this impression, for with an apologetic reference to his compendious insertion and a curt "Let us return to diaphony" he abruptly closes this subject and proceeds to precepts. H . H.Eggebrecht considers diaphonia to be the theoretical, conceptual term, organum to be the practical, performance-oriented word ("Diaphonia vulgariter organum", in: Bericht iiber den Siebenten lnternationalen Musikwissenschaftlichen Kongress [Cologne 19581, p. 9?-97). Reckow has already questioned that interpretation, calling attention to the considerable theoretical weight given organum in earlier treatises ( o p . cit., note 6 , especially p. 134-5). The evidence provided b y surviving documents does not support Eggebrecht's suggested reading of the passage. 5' A s has already been mentioned, the offshootsand revisions o f Ad organum faciendum display some internal contradictions between the practice they teach and the theoretical doctrines they transmit. 52 De Musica, p. 157.

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Whereas the observations on motus vocum are presented as hard fact, the precepts for diaphony are highly qualified by the observation that different people practice diaphony differently. In contrast to most earlier organum theorists (Guido excepted), John professes to present not authoritative instructions but an account of what some people do-suggestions rather than firm rules. His precepts are few: 1) If the cantus rises, then the organum should descend, and vice versa. This, John says, is simply the easiest practice. He makes no attempt to justify it as principle but takes the attitude of pedagogue, not theorist. Historically, John seems to have been the first to enunciate this rule, which becomes standard for later discant teaching. 2) If the cantus is in a low register, the organum should seek the region an octave above; if high, the organum should dwell in the octave below; if in the middle (about mese is the way John puts it), the organum should meet it in unison. This corollary to the first precept functions to ensure registral balance in the piece, and to promote rule 3). 3) Octave and unison conjunctions should be intermixed, but unisons should be the more frequent. 4) The singer of organum may match groups of several notes (a double or triple motus vocum) to single intervals (or simple motus vocum) or may in any way conglobare-roughly, crowd in a bunch of notes.53 This set of precepts has obvious limitations. It offers no help to anyone seeking guidance on the kinds of intervals to form between parts, on how to begin a phrase, on how to continue or end a phrase. Except for a passing remark early in the chapter that organum is made from consonantiae (which he means in the Guidonian sense, see Chapter VIII), John mentions nothing about sonorities produced between the parts save for unison and octave at phrase endings.54 His attention falls on generalities of voice leading, registral balance, and rhythmic disparity between the voices (i.e. more notes in one than in the other). Even these receive little emphasis compared with the space granted motus vocum. Two questions that demand attention are a) whence comes the idea of motus vocum and b) why does John of Afflighem introduce this subject in a chapter on organum? The first is easily answered. John's passage on motus vocum stems directly from Chapter XVI of the Micrologus. In Guidols treatise, the concept motus vocum provides a means for systematic discourse about melodic motion in a single line. Guido does not invoke this concept in his chapters on organum, it belongs to the theory of chant. No known treatise prior to ~ o h n ' sassociates motus vocum in any way with organum. The answer to the second question is not so easily rendered. Viewed historically, John's incorporation of motus vocum within organum theory seems aberrant. It is neither prompted by earlier tradition nor echoed by later writers. Viewed contextually, the topic is not well integrated within the substance of the organum 53

De Musica, p. 159-161. This is mentioned not in the list of precepts but in the opening definition of diaphonia.


71

chapter but appears to be something of a digression. John himself promotes this impression in characterizing the passage as "these things compendiously i n ~ e r t e d " One . ~ ~ might conclude that in its context the passage on motus vocum is a thoughtless blunder or fortuitous lapse in organization. I propose to argue that this is not the case, that John's appeal to motus vocum represents a reasoned and bold attempt to formulate a viable theoretical foundation for organum and its pedagogy. Contrary to appearances, John's discussion of motus vocum in the chapter on diaphony is not digressive. It is germane to his two most central precepts about organum. One is his first precept, that the voices should proceed in contrary motion. Motus vocum offers a way of coming to grips with the melodic motion of a given chant, a potential means of perceiving order in series of intervals, whether of similar motus or dissimilar motus. This done, the melodic movement of the organal voice will follow: a mirror image if it consistently counters the chant, a replication if it sometimes parallels the given melody. These two modes of relationship could themselves be categorized as types of motus vocurn. Through the language of motus vocum, judgment about voice-leading aspects of organum can be rendered not merely with reference to isolated moments but by appeal to more generalized patterns and principles. Although motus vocum provides no systematic control over sonorities, it does affect them, for as John states, the disposition of intervals in organum can be thought of as dependent upon the voice-leading. Cum enim organum per consonantias fiat, ipsarum autem constitutiones per motus vocum varientur, quod eorum insertio hoc in loco utilis sit, nulli dubium e ~ t . ~ ~ (Since organum is made by accepted intervals, and the arrangement of these is varied according to the motus vocum, there can be no doubt that their [the motus vocum] insertion in this place will be useful.) The apparatus of motus vocum also pertains directly to John's precept allowing more notes in the organum than in the cantus. It offers for the first time a concise technical way of talking about this phenomenon. John's statement that the organum may oppose a double or triple motus vocum to a single motus vocum in the cantus is far more direct and unambiguous than speaking of the organal voice multiplying its notes (Ad organum faciendurn) or breaking up its notes (Milan verse treatise).57 Even more significantly, it offers a potential means of subjecting combinations of motus vocum to rational control: two notes in the cantus to three in the organum a ratio of 3:2, two in the cantus to four in the organum, 2:1 or perhaps performed as 3 :1 plus 1:I, etc. Ultimately this could prove a useful pedagogical tool, a means for teaching how two voices with unequal numbers of notes can be fitted together appropriately. John does not work out these implications. His carefully adopted stance of relativism seems to prevent him from being very rigorous about any aspect of organum. But by pulling motus vocum out of the realm of chant (where Guido has "His ita compendiose insertis ad diaphoniam redeamus", De Musica, p. 159. De Musica, p. 157. 57 The ambiguity of language in the Milan Verse Treatise is such that scholars argue whether it really refers to additional notes in the organal voice, see EGGEBRECHT and ZAMINER, p. 133. 55

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it) and associating it with two primary aspects of polyphony-voice-leading and rhythmic relationship between the parts-he points the way toward a rational framework within which polyphony might be comprehended. As has already been observed, John cannot (or at any rate does not) uphold the doctrine that organumldiaphony possesses certain inherent sonic properties, specifically, intervals of fourth and fifth. Moreover, lacking a system of interval hierarchy-such as a theory of consonance and dissonance, something foreign to the theory of polyphony in and before his time-John of Afflighem finds no way of justifying the choice or prominence of some intervals in two-part music, the exclusion or relative rarity of others. Hence he ignores the issue, maintaining a strange silence on that aspect of polyphony-its sounds-most central to the theoretical tradition. Yet his chapter is not devoid of theoretical (as opposed to pedagogical) substance. Its chief topic in this vein is motus vocum. It is hard to escape the conclusion that John views motus vocum as the theoretical basis for the current practice, especially as it meshes so well with the chief precepts of his organum teaching. Since the old conceptual basis so fiercely defended by the Ad organum faciendum theorist will not do, he proposes a new one.58His solution, a response to the inadequacy of traditional concept, had multiple advantages. First of all, motus vocum was a known doctrine, promulgated by no less an authority than Guido of Arezzo. Second, it had the status of a universal. Motus vocum applies to chant as well as to polyphony, it is inherent to any melody or combination of melodies. (Indeed, the language is so generalized one could apply it to virtually any music : Bach, Webern. . . .) Finally, John's main concerns about polyphony-voiceleading, registral balance, rhythmic interplay between the parts-could all be dealt with in terms of motus vocum. Whether the existence of these concerns prompted John to adopt motus vocum as a theoretical framework, or whether John's interest in motus vocum as a means toward understanding contemporary polyphony led him to emphasize just those aspects most pliant to it, cannot be known. What is important for the history of a theory of polyphony is the process seen here of a theorist seeking out new doctrine to replace the old consensus which had become untenable. Such a process is familiar in the history of science and scientific theory. In his classic work, The Structure of Scientific Revolutions, Thomas Kuhn persuasively narrates how the failure of entrenched theories or matrices of thought to account for observed phenomena eventually precipitates a crisis state, or revolution, in which competing new theories are proposed, challenge the old, and vie for ~ u p r e m a c y Such . ~ ~ a state ceases only when a new theory broad enough to cover the contested domain and comprehensive enough to explain a certain range of phenomena achieves general recognition and dominance. In Kuhn's view, the theory of a subject develops not in progressive,

58 In doing this, he shows himself to be more persistent a theorist than Guido who makes no attempt to support

his teaching precepts with theoretical principle.

59 (Chicago 1970). Also published as volume 2, No. 2 of the International Encyclopaedia of Unified Science,

Foundations of the Unity of Science.


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incremental stages, but disjunctively, with expanses of relative stability sharply punctuated by periods of dislocation. Within organum theory, John of Afflighem's chapter on diaphony would seem to belong to a period of dislocation. John does not subscribe to the concept of organum asserted in the earliest treatises and endorsed in such post-Guidonian works as Ad organum faciendum and the Milan verse treatise. Rather, he adopts a new mode of explanation for diaphonylorganum, one which emphasizes direction and density of melodic motion and disregards sound quality. That this maneuver is not well executed is symptomatic of both the difficulty of the endeavor and the problem of elevating what is essentially a useful means of description to the status of a fundamental axiom. Kuhn's paradigm indeed predicts that most of the proposed solutions to a theoretical crisis will prove inadequate for one reason or another.

We are not rich enough in documents to tell how John's attempt to establish a stable theory for organum stacks up against others of the time, but we can surmise that his solution was a dead end. Except for one treatise that quotes both Guido and John so literally and extensively as to be little more than a conflation of the two, no extant works pick up on John's ideas about polyphony.60 So few documents on organum theory or pedagogy can be reliably assigned to the 12th century, one might even venture to claim that few teachers dared confront the subject. The situation is quite different for the 13th century. Suddenly treatises on polyphony proliferate. I would suggest that this is no accident and that the major factor in this change is the invention-or, if preferred, discovery-of theory which convincingly reestablished a legitimate foundation for organum and won acceptance within the community of those concerned with this aspect of music theory. Writing about polyphony in the 13th century can be broadly divided into discant treatises-short, usually anonymous, works chiefly concerned with lists of interval progressions-and treatises on musica mensurabilis-works associated with such figures as John of Garland, Franco of Cologne, Magister Lambert and the elusive Anonymous IV. We can leave aside the discant treatises : for the most part they are devoid of explicit theoretical s ~ b s t a n c eBut . ~ ~the treatises on musica mensurabilis, strongly theoretical in bias, are another matter. They bring us to the seminal thinker whose work becomes the basis for a new theoretical consensus: John of Garland. This man, who presumably taught at the University of Paris, seems to have been the first fully to articulate a new theoretical framework for polyphony, to formulate firm

"

This treatise is variously known as the Schneider anonymous or the London treatise. I call it the London/ Naples treatise after its two main sources. The Naples version is edited by GUIDO PANNAIN, Liber musicae. Un teorico anonimo del X1V secolo, in: RM127 (1920), p. 407-440. The London version appears in MARIUS SCHNEIDER, Geschichte der Mehrstimmigkeit (Berlin 1934-35; reprinted Tutzing 1969), p. 106-120. Even the Vatican organum treatise, one of the most ambitious of its type, begins by quoting out-moded formula, stripped of its essential reference to fourths and fifths: organum est cantus subsequens precedentem, quia cantor debet precedere organizator . . ., in: Der Vatikanische Organum-Traktat, edited F. ZAMINER (Tutzing 1959), p. 185.


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doctrines on the nature of contemporary polyphony to which pedagogy could appeal. John of Garland's theory is two-pronged. Its vital elements are a system of mensuration and a system of interval classification. John's very announcement of his subject unequivocally proclaims the centrality of mensuration to his frame of thought. Habito de ipsa plana musica, quae immensurabilis dicitur, nunc est praesens intentio de ipsa mensurabili, quae organum quantum ad nos appellatur, prout organum generaliter dicitur ad omnem mensurabilem m ~ s i c a m . ~ ~ (Having considered that plana musica which is called unmeasured, our attention is directed presently toward that measured music which is called organum according to us, insofar as the word organum is generally applied to all measured music.) Organum, then, is the general term for polyphony, b u t only insofar as polyphony is considered musica mensurabilis. This is a breath-taking shift in perspective. Whereas symphonic intervals were once t h e criteria by which organum was identified, now mensuration is the sine qua non of organum. Systematic temporal organization has replaced sound quality as the identifying feature of the genre. John of Garland's definition of discantus-the analogue to John of Afflighem's definition of diaphonia-continues this emphasis. Discantus est aliquorum diversorum cantuum sonantia secundum modum et secundum aequipollentis sui aeq~ipollentiam.~~ (Discant is the sounding of some diverse melodies according to mode and according to their equivalence in duration.) The only element common to this definition and John of Afflighemls is the notion of separate lines, and even this is expressed in different language.64But the idea of separate lines in itself receives less emphasis in John of Garland than the requirement that the melodies sound according to mode (by which he means rhythmic mode) and that they be equivalent (which I take in two senses: modal units themselves must be equivalent, so two units of mode 2 must accompany one of mode 3 if the two are combined, and they must be the same length or number of tempora overall, so they will end together). Whereas J o b of Afflighem calls his diaphonia a dissonantia or separate-sounding, John of Garland calls his discant a sonantia, plain sounding. The nature of the sound is not specified in this initial definition but is significantly qualified when John reiterates his definition of discant in Chapter XI with one addition: 65 lohannes de Garlandia: De Mensurabili Musica, Teil I , edited E. REIMER, Beihefie zurn Archiv fir Musikwissenschaft 10 (Wiesbaden 1972), p. 35. Hereafter cited as De Mensurabili Musica. " De Mensurabili Musica, p. 35. John of Afflighem uses the equivocal voces, which can be interpreted as either line or pitch, while John of Garland refers unambiguously to cantus, a line or melody. 62

65

The division into chapters is Reimer's.


75

Unde discantus est aliquorum diversorum cantuum sonantia secundum modum et secundum aequipollentis sui aequipollentiam per c ~ n c o r d a n t i a m . ~ ~ (Discant is the sounding of some diverse melodies according to mode and according to their equivalence in duration through consonance.) By this late point in the treatise, the reader knows exactly what consonance is, for the two sections immediately preceding this statement (Chapters IX and X) have exhaustively explored musical intervals. Even in these sections John does not sever intervals from the temporal dimension but commences :

Sequitur de consonantiis in eodem t e m p ~ r e . ~ ~ (There follows the topic of intervals in the same tempus.) The inference is that he speaks only of what we would call harmonic intervals. The properties he claims subsequently for intervals apply only insofar as their constituent pitches sound simultaneously at a moment in time, a regulated moment called a t e m p s . John postulates two broad categories of interval:

Consonantiarum quaedam dicuntur concordantiae, quaedam discord~ntiae.6~ (Some intervals are called consonances, some are called dissonances.) This distinction rests on the degree to which their constituent pitches blend, i. e. it rests most immediately on sense perception.

Concordantia dicitur esse, quando duae voces iunguntur in eodem tempore, ita quod una vox potest compati cum alia secundum a ~ d i t u m . 6 ~ (Consonance is said to be when two pitches are joined together in the same tempus so that one pitch can blend with the other according to the sense of hearing.) Discordantia dicitur esse, quando duae voces iunguntur in eodem tempore, ita quod secundum auditum una vox non potest compati cum a l i ~ . ~ O (Dissonance is said to be when two pitches are joined together in the same tempus so that according to the sense of hearing one pitch cannot blend with the other.) The degree of blending constitutes the criterion for further subdivision under each category. Consonances are of three kinds: perfect, imperfect, and intermediate. In perfect consonances, unison and octave, the degree of blending is so great that one pitch cannot be distinguished from the other. In imperfect consonances, major third and minor third, the two pitches can readily be distinguished from each other, but they still blend to such a degree that they can be characterized as consonance. The intermediate consonances stand partway between these poles. When heard, their elements sound more distinct than in octave or unison, but less distinct than pitches De Mensurabili Musica, p. 74-75. De Mensurabili Musica, p. 67. 68 De Mensurabili Musica, p. 67. Note that John keeps to the Guidonian sense of consonantia as interval. I translate his concordantialdiscordantia not with their cognates but with normal English usage, consonance/ dissonance. 69 De Mensurabili Musica, p. 67. De Mensurabili Musica, p. n. 67

76


constituting a third. Dissonances subdivide in parallel manner. According to their degree of not blending, John categorizes them as perfect (semitone, tritone and major seventh-these blend to the least degree), imperfect (major sixth and minor seventh-these blend to some degree, but not sufficiently to be called consonance), and intermediate (tone and minor sixth-these fall between the extremes of perfect and imperfect). As if conscious that the criterion of perceived blending is imprecise, and that in any case the phenomenon demands explanation, John of Garland immediately seeks firmer, mathematical grounds on which to support his theory of consonance and dissonance." He starts with the observation that the "best" consonance, the unison, results from equality, i. e. 1:1, and then reviews the ratios of all the consonances: octave 2:1, fifth 3:2, fourth 4:3, major third 81:64 (17 parts over 64), minor third 32:27 (5 parts over 27). From this impressive array of numbers, he derives a rule: Unde regula: quae magis procedunt ab aequalitate, et magis concordant in sono. Et quae minus appropinquant aequalitati, et minus concordant, ergo et magis discordant secundum a u d i t ~ m . ~ ~ (Whence the rule: those [intervals] which most proceed from equality also concord best in sound; and those which least approach equality are less concordant, hence are more dissonant to the sense of hearing.) The basis for degrees of dissonance is the same as that for consonance. The tritone is the most perfect dissonance because of its ratio of 729 :512 (or a remainder of 217 over 512). The tone at 9 :8 is last on the scale. As John is unconcerned that the tone, which passed as an intermediate dissonance according to the ear, (Chapter IX) emerges at the least dissonance according to number (Chapter X), we too will pass over this and other difficulties with this rationalization and will turn to John's strategy as a theorist.73 John of Garland explicates a system of modal rhythm in which time is regulated by standard modular patterns. This rests on convention. He also establishes a hierarchy of sounds-at-moments-in-time (tempus), broadly divided into consonances and dissonances. This rests in the nature of things. It is supported by naive sense perception on the one hand and by immutable relationships of number on the other. That is, John devises a theory that encompasses how music moves in time and De Mensurabili Musica, Chapter X, p. 72-74. De Mensurabili Musica, p. 73. 73 The series for consonances yields a coherent series if "departure from equality" is viewed as the relationship between the difference of the terms and the smaller of the terms. The result, expressed decimally and rounded off to the nearest hundredth is: 1, .5, 33, .27, .19. The series for dissonances is not coherent. Graphed, it would show a jagged line rather than a smoothly ascending or descending one. Starting with the tritone, it reads: .42, .05, 39, .58, .68, .77, .13. Carl Dahlhaus ingeniously explains John of Garland's first classification of dissonances according to patterns of resolution to perfect and intermediate consonances (Untersuchungen iiber die Entstehung der hannonischen Tonalitat, Saarbriicker Studien zur Musikwissenschaft 2 [Kassel-Basel19671, p. 7C-n). Although there is no trace of this kind of thinking in De Mensurabili Musica, Dahlhaus's explanation illustrates well how one might arrive at, or rationalize, John's classification. Franco of Cologne drops the threefold classification of dissonance, retaining only two categories, perfect and imperfect (Ars Cantus Mensurabilis, edited G. REANEY and A. GILLES, Corpus Scriptontin de Musica 18 [American Institute of Musicology 19741, p 67). 71

72


77

what sounds it makes within the modules of that time. In this respect he is eminently "modern": he has come to grips with both temporal and sonic dimensions of music. Moreover, John welds these two dimensions together in defining discant as a union of the two : the sound produced by melodies in rhythmic modes. This dual theoretical system provides a foundation for incisive pedagogy. In his teaching, John identifies three factors that must be considered when two voices of discant are taken together as an entity : mode, number, and concord or consonance. The two parts must match in mode and number, that is, they must be equivalent both in "measures" (mode) and in total temporal length of phrases (number). The two parts must also concord "in a required way" : Unde regula: omne, quod fit impari, debet concordari omni illi, quod fit in impari, si sit in primo vel secundo, et hoc in primo mod0 sive secundo vel t e ~ t i o . ~ ~ (Whence the rule : all odd-numbered pitches in one voice should concord with all odd-numbered pitches in the other voice in the first, second and third modes.) The purpose of this precept is to coordinate recurrent rhythmic patterns with stable sound quality by locating consonance at the beginnings of rhythmic units. Successive rhythmic modules will be articulated not only through reiterated L S-LiSlLrS L, L = long, S = durational patterns (e.g. L S L S L S L processed as r short) but also through coincidence of consonance with the beginning of each mpattern ( L S'L s"LS'~,x = consonance). Such coordination between stable Y Y Y Y sonority and the beginnings of units (routinely rendered as measures in modern transcriptions) leads easily to elevation of the stable initia to the status of downbeats, and to perception of the module length as a metric unit, independent of specific rhythmic divisions. When John comes to speak of organum style, organum in speciali, he explicates the relationship between rhythm/modular unit and sound quality in a significantly different manner than when discussing- discant. Whereas in discant consonances reinforce a standard rhythmic pattern which is coded in notation and generated quite independently of them, in organum style the consonances themselves govern the rhythmic interpretation. Longae et breves in organo tali mod0 dinoscuntur, scilicet per [concordantiam], per figuram, per paenultiman. Unde regula: omne id, quod accidit in aliquo secundum virtutem [concordantiarum], dicitur longum. . . . Alia regula: quidquid accipitur ante longam pausationem vel ante perfectam concordantiam dicitur esse 10ngum.'~ (Longs and breves in organum are distinguished in this way, that is, through [consonance], through the notational symbol, through the penultimate. Whence the rule: whatever sounds a consonance with something else is called a Long. ... Another rule : whatever preceeds a Long rest or a perfect consonance is said to be a Long.) 75

De Mensurabili Musica, p. 76. De Mensurabili Musica, p. 89.

S . Fuller: Theoretical Foundations o f Early O r g a n u m Theory

78

This is an exact reversal of the relationship between sound-quality and duration asserted for discant. The very language reveals a sharp difference in conception. In discussing discant, John speaks precisely of odd-numbered notes and specific modal patterns-first, second, third. In discussing organum in speciali no regular pattern is even implied. Consonance is just one of three ways by which a long duration may be recognized. The duration follows from the fact of consonance, it is not independent of it (unless dictated by notational figure or penultimate position). The difference in the way John relates duration and consonance under the topics discant and organum in speciali is one among many compelling reasons for believing that the two species were quite distinct in rhythmic nature."j Abstract and universal as John's consonance/dissonance system is, it is nevertheless not totally immune to contextual factors. Position relative to certain degrees of consonance may to some extent influence disposition of intervals in discant and in organum and can even alter the interpretation of a sound.

Sciendum est, quod omnis discordantia ante perfectam concordantiam sive mediam aequipollet concordantiae mediae, et hoc proprie sumitur ante unisonum vel diapason. . . . Et improprie surnitur ante mediam. Sed multum invenitur in multis partibus organi, ut tonus ante diapente.. . . . . Et sciendum, quod nurnquam ponitur discordantia ante imperfectam concordantiam, nisi sit causa coloris sive pulchritudinis m ~ s i c a e . 7 ~ (Know that any dissonance before a perfect or intermediate consonance is the equivalent of an intermediate consonance, and this is properly assumed before unison or octave. . . . this is assumed improperly before intermediate [consonance, i. e. fourth or fifth], but is found often in many sections of organum, as a tone before a fifth. . . And know that a dissonance is never placed before an imperfect consonance, except for reasons of melodic pattern or the beauty of the music.) The prime theoretical interest of this statement lies in the startling notion that the classification of a sound quality is not immutable but can be modified by context. The import of John's claim is quite simply:

, Perfect Consonance

Dissonance before

\Intermediate

\ = Intermediate Consonance ConsonanceI

Any dissonance before a perfect consonance becomes "as" an intermediate consonance, hence could fall metrically on a position where consonance is required. Dissonance before an imperfect consonance never has theoretical justification, but may occur for ad hoc reasons : local melodic pattern or aesthetic choice. Dissonance See F. RECKOW, Das Organum, in: Gattungen der Musik in Einzeldarstellungen (Bern 1973), p. 434-496, and Der Musiktraktat des Anonymous 4, part 11, Beihefte z u m Archiv fur Musikwissenschaft 5 (Wiesbaden

76

1967).

De Mensurabili Musica, p. 74.


79

before the intermediate grade of consonance bothers John. He grants that it too becomes as an intermediate consonance, but improperly and especially in organum. Such a ~ossibletransformation might naturally confuse estimation of organum rhythm somewhat (especially if attempted without the guidance of an experienced performer). Consonances are to be performed as Longs, but if dissonances in certain contexts are to be considered as consonances, then they too must be rendered as Longs. In discant too, dissonance placement cannot serve unilaterally to resolve ambiguities of notation, for some dissonances can-even should-be ~erformedas Longs. John's sense of the propriety of dissonance before perfect consonance may well go back to an older tradition. His notion that a dissonance before octave or unison changes status to intermediate consonance resonates in a striking manner with the Ad organum faciendum statement allowing the voices to approach octave or unison "via any appropriate interval" when otherwise only fourths and fifths (John's intermediate consonances) are permitted." It would seem that John of Garland and John of Afflighemcould hardly be more opposite as theorists of polyphony. This is a fair estimation in terms of the theories they advance, but it does not hold for their preoccupations. Like John of Garland, John of Afflighem professes concern for rhythmic relationship between the parts, most overtly when dealing with a multiplicity of notes in the organa1 voice relative to the chant. The earlier John also perceives some relationship between harmonic sound and motion in time and links the generation and disposition of intervals to the melodic paths of the two lines, although he does not pursue the subject. His motus vocum is not, however, a tough enough theoretical tool to enable him to deal effectively with either temporal relationships between the parts or with the intervals that result from the coincidence of two motus v0cum.7~John of Garland forges a more effective theoretical instrument. He separates the temporal from the harmonic, orders each in a rational system and then fuses them in defining what discant is and in asserting all polyphony to be musica mensurabilis. The success of this solution is apparent in the degree to which it becomes the received doctrine of subsequent 13thcentury theory. Two observations should be made about John of Garland's solution to the problem of organum theory. First is that it is by no means flawless. In particular, it is geared to discant and is not especially suited to copula or organum. John himself reveals this.in the amount of space he devotes to discant relative to the other subspecies of organum: of 55 pages in the Reimer edition, only two take up organum style and copula, the other fifty-three all treat of discant. Moreover, John is considerably more direct and explicit about the nature of discant than about the nature of copula or organum. This is one reason why so much uncertainty has In the teaching of Ad organum faciendum, one can put any interval before the cadential union in place of a fourth or a fifth (which are otherwise obligatory within the phrase). In that of John of Garland, any interval before a unison or octave may be considered not merely as a consonance, but as an intermediateconsonance, i. e. fourth or fifth. 79 If John of Afflighem's theory has any progeny, it is the discant treatises that oppose to a single interval (motus vocum) in the cantus another interval in the discant that will render a fixed sequence of harmonic intervals, quite independent of context.

80


attended what copula is and whether organum purum is or is not subject to modal rhythm. John's failure to explain these things clearly is doubtless due, at least in part, to the fact that his theoretical construct, machined to discant, does not prove the most apt mode for handling organum or copula. The very way John frames his definitions of the three subspecies of organum in general reveals a pronounced difference in attitude. The definition of discant states the individual elements from which it takes its being : sound, mode, and equivalent lines. Copula is defined, in but the first of a series of thrusts, not as what it is but as what it is not : it is something "between discant and organum" (this before organum has been defined). Organum is presented as that which is performed in some modus non rectus, in distinction to the rectus modus of discant." The definitions of both copula and organum are thus contingent upon the concept of discant, rather than standing on their own. Considering the problems which later writers have had in dealing with rhythm in organum style (to mention only Anonymous IV), it appears increasingly likely that in collecting all organum generically under the rubric musica mensurabilis John of Garland sacrificed some degree of accuracy to the vision of a unified polyphonic theory. A second point to be noted about John of Garland's achievement is that it did not spring out of a vacuum. The Discantus positio vulgaris, which Jerome of Moravia called the "first positio . . . older than all the others,"81 anticipates two central ideas of John's conception: association of greater degrees of consonance with primary rhythmic position, and a fundamental dichotomy between consonance and dissonance. Although, as Fritz Reckow has observed, the Discantus positio vulgaris shows unmistakable signs of both conflation and later emendation in the state it has reached usjB2the rudimentary way in which these two particular ideas are presented makes it highly likely that they spring from a period prior to the codification of John's teaching. The language in which the Discantus positio vulgaris links sound quality with rhythmic position clearly parallels John's way of specifying locus through odd or even numerical order. Sciendum insuper, quod omnes notae impares, hae quae consonant, melius consonant, quae vero dissonant, minus dissonant quam pares. Unde si ascendat vel descendat de quinta in unisonum, per tertiam debet ascendere uel descendereaS3 (Know, moreover, that [in discant] . . . such of these odd-numbered notes that are consonant are more consonant than the even-numbered notes [that are consonant]. Those that are dissonant are less dissonant than the even-numbered notes [that are dissonant]. Whence, if one ascends or descends from a fifth to a unison, one ought to ascend or descend by a third.)

De Mensurabili Musica, p. 88-89. Hieronymous de Moravia 0. P. Tractatus de Musica, edited S. M . CSERBA, Freiburger Studien zur Musikwissenschaft 2. Reihe (Regensburg 1935), p. 194. Hereafter cited as CSERBA. F . RECKOW, Proprietas und perfectio, in: AM1 39 (1967), p. 137, note 81. CSERBA, p. 191. J . Knapp's English translation of the entire treatise appears in the Journal of Music Theory 6 (1962), p. 203-207. 80

"


81

There follow two very explicit examples describing voice-leading from an initial consonance through a second, less consonant, sound to a third consonance (Example 3). Example 3'* Example 3a

Example 3b

position

1

2

3

1

2

3

organum

c

a

F

f

e

c

cantus Hypothetical realization in rhythmic mode 1

Although the Discantus positio vulgaris is far from John of Garland's systematic categorization of consonance and dissonance, it does introduce the dichotomy. Rather than rigidly distinguishing which intervals are consonant and which dissonant, this treatise describes a continuum. Opposite ends of the continuum are precisely defined by the quality of specific sounds, while the intermediate stages are left vague.

Item consonantia est diversarum vocum in eodem sono vel in pluribus concordia. Inter concordantias autem tres sunt ceteris meliores, scilicet unisonus, diapente et diapason. Ceteri vero modi magis sunt dissonantiae quam consonantiae, tamen secundum magis et minus. Unde major videtur dissonantia in tono quam in aliquo alio m ~ d o . ~ ~ (Interval is the concord of different pitches in the same sound or in several. Among concords, three are better than the others, i, e, unison, fifth, and octave. The other intervals are more dissonant than consonant, but according to greater and lesser degrees. Whence the dissonance of a tone is greater than in any other interval.) While consonance and dissonance are invoked as qualities, there is no sense here of their existence as substantive categories. Judging from this early positio (and qualified by the degree to which it may have reached us in emended state), it would

"

CSERBA, p. 191. The author surely has modal rhythm in mind here, as in the paragraph directly preceding

he has asserted all discant notes to be measurable by recta longa and recta brevis, and the section quoted here

continues to deal with discant.

CSERBA, p. 190. Consonantia in this passage may have overtones beyond interval and toward consonance.

"


82

appear that John of Garland assimilated ideas that were in the air in early 13thcentury Paris, developed them more concretely and forged them into a coherent system. There is, in addition, a more venerable source-and authority-for one of John's tenets: the distinction between consonance and dissonance. This is the De institutione musica of Boethius. John's first formulation of the difference between consonance and dissonance, which identifies the ear as arbiter of this distinction, is closely modeled on Boethius.

Consonantia est acuti soni gravisque mixtura suaviter uniforrniterque auribus accidens. Dissonantia vero est duorum sonorum sibimet permixtorum ad aurem veniens aspera atque iniucunda percussio.s6 (Consonance is a mix of a higher sound with a lower one, reaching the ear smoothly and uniformly. Dissonance reaches the ear as the harsh and unpleasant coincidence of two intermixed sounds.) Both John and Boethius appeal first and foremost to the ear. Both place a premium on the quality of the resulting sound, the degree of blending or uniformity, though Boethius goes further in castigating dissonance as something unpleasant. John's subsequent eagerness to confirm aural judgment through number is also eminently Boethian. The wonder of it is that the Boethian distinction between consonance and dissonance lay so long unused by theorists of organum. Polyphonic theory prior to John-that which we possess-shows no trace of such thinking. Perhaps as long as organum as a concept clung to the symphoniae no such distinction was needed. Or, rather, the functional distinction was between the few intervals that were symphoniae and those that were not. With the erosion of this state of affairs, it became expedient-even urgent-to find some other mode of categorizing sounds. Just as John of Afflighem found in Guido of Arezzo a ready-made concept pertinent to relationships between two lines, so, conceivably, John of Garland perceived in Boethius a notion of sound quality ideally suited for exploitation. The success of his choice can be judged pragmatically by the hold consonance/dissonance theory has maintained within music theory since his time. Although, at least in some contemporary styles, dissonance has long since been considered "emancipated", the consonance/dissonance dichotomy holds its place as a central rudiment of our ~edagogy,engrained in the ears and minds of all who study music.

VI This essay began with the claim that the word organum as understood in the 9th and loth centuries was not the equivalent of the modern word polyphony, but had a very specific technical sense which denoted certain sonic properties. Its companion, diaphonia, came closer to our polyphony but even its sense was somewhat 86

De institutione musica, edited G. FRIEDLEIN (Leipzig 1867, reprinted Frankfurt am Main 1966), Book I:8,

p. 195.


83

different-an emphasis on separateness rather than multiplicity of sound. Organum seems to have been the preferred, and more ordinary, term and is the one which survived (though with a shift in conceptual reference) into the 13th century. This thesis has repercussions for our understanding of organum theory and of the music itself. As long as organal intervals remained central to the practice of organum, theorists could defend choices of pitch in the organal voice by appeal to some solid theoretical premise : the privilege of symphonia, integrity of mode, the property of affinity. Neither these explanations nor the original concept of organum could withstand the increasing frequency of non-organa1 intervals in "organum" as practiced. This touched off a severe crisis in theory, one marked by incompatible melanges of old and new elements in some treatises, and by an original, but unsuccessful, projection of new theory in John of Afflighem's De Musica. The resolution of this crisis came with the acceptance of a notion promulgated by John of Garland that organum was to be understood as musica mensurabilis. This formulation should be understood as a response to a particular situation, one whose authority derives as much from its subsequent reception as from any inherent correctness. This is only to acknowledge evidence suggesting that this doctrine did not fit all polyphony of the time equally well. In particular, the musica mensurabilis formulation may have distorted how subsequent generations (to the present day) dealt with Notre Dame organum style and its rhythmic nature. It also appears that no surviving treatise on polyphonic theory prior to the Discantus positio vulgaris focuses on a dichotomy between consonant sounds and dissonant sounds, and that only with John of Garland is the distinction elaborated systematically. This bears not only upon the history of musical concepts but on practical aspects of the transcription of 12th-century polyphony. Most who have attempted this thorny task rely on a value system in which consonance is preferred over dissonance to justify both choices of voice alignment and rhythmic interpretation left unsettled in the scores as written. This can be pushed quite far, so that dissonance is systematically relegated to rhythmically weak positions, or so that modal rhythms are worked out principally on the basis of consonance/dissonance placement. I would argue that we can legitimately prefer symphoniae and unisons as prevailing sounds or as the structural underpinning of individual phrases, but that the theoretical evidence does not allow us to interpret the music so that particular intervals such as seconds are invariably made of short duration or, in a metric interpretation, put on weak beats. Even if statistically speaking some intervals are much more frequent than others or more frequently appear in certain positions (such as beginnings or ends of phrases), it does not follow that the less preferred intervals would always have been treated as subsidiary when they do appear. The original notation would seem to leave considerable flexibility in this matter. Comments such as John of Garland's assertion that dissonance before a perfect consonance becomes as intermediate consonance indicate that even in a considerably later period context was conceived to influence the interpretation, the very sense of a sound. The performance traditions of 12th-century polyphony are, in large part, lost to us, but this does not mean we

84

S . Fuller: Theoretical Foundations o f Early Organum Theory

should impose a certainty on our transcriptions of their scores by applying theoretical doctrine of the next century. From John of Afflighem's words-"different people practice organum differentlyu-and from the generality of his precepts, one would gather that the tradition he knew lacked hard and fast rules to control sonorities produced between the parts or to fix duration with respect to quality of sound. This study claims too that in Western medieval music theory a categorical and systematic distinction between consonance and dissonance lay dormant until the emergence of meter as a dominant trait of polyphonic music. Only when theorists of organum dwell on meter and patterned rhythms do they stress also a dichotomy in sounds between consonances and dissonances-and in that order, meter first, consonance/dissonance second. In John of Garland's influential formulation, the interaction between the two is most clearly fixed in that species of musica mensurabilis called discant. Here the rhythmic pattern or meter is precedent, in a chronological sense.87 It guides the appropriate placement of consonances and dissonances, requiring, in the main, consonance on the initial attack and on the oddnumbered positions (what we transcribe as beginnings of measures) thereafter. The interaction is quite different in the species organum. Here, as John explains it, rhythm and any emergent metric patterns are functions of consonance. The quality of sound between the voices is a determinate factor in deciding which durations will be long, which short. It is the interaction found in discant that is most suggestive for future developments (not surprisingly, since discant becomes the dominant mode of composition from the 13th century on). In tonal writing, for example, meter is a matrix that governs the proper disposition of consonances and dissonances and controls the sense, analytically speaking, of relationship among them. Leaping forward to the early 20th century, one finds concommitant with the "emancipation of the dissonance" a weakening of meter as a clear surface phenomenon. This may be coincidental, or the two ends of the spectrum-starting with the 13th century and ending with the 20th-may point to some fundamental connection between meter and classification of sound as pleasant or unpleasant, stable or unstable, that is central to the Western musical tradition. In any event, the contribution of John of Garland can hardly be overestimated for his role in elevating the Boethian distinction between consonance and dissonance to a prime tenet of polyphonic theory and in disseminating ~rincipleswhich were to regulate vertical combinations of simultaneous voces through the subsequent half-dozen centuries.

LEO TREITLER, in a recent article, maintains that the origins of modal rhythm must be considered in the context of melodic, contrapuntal, and harmonic relationships which it served to project (Regarding Meter and Rhythm in the Ars Antiqua, in: M Q 65 [1979],p. 524-558). I concur in that view; but in the realm of theory, once modal rhythms have been codified into a system, the rhythmic mode in discant is presented as primary, other elements as conforming to it.

early organum.pdf

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