RegardingMeter and in the LEO TREITLER

SHE rhythmicimpulse in music is a quality directlyappre- hended,and its projectionis a mainaspect of theperformer's art. But when we conceptualizeabout rhythm,we tend to thinkof it as a functionof timewhich we expressmainly in termsof duration and succession.Explaining rhythm through temporal concepts, plac- ing it under control in that sense as a compositionalfactor, and devisinga notationto signifyit are all achievementsof the practice and theoryof musicin the twelfthand thirteenthcenturies. During that period,duration came to be apprehendedthrough a systemof proportionalmeasurement, and the successionof notes assumed patternsthat depended on two kinds of configuration at the same time: (1) groupsoriented with respectto accents,and (2) the backgroundarticulation of time in equal intervals;in short, the configurationsof rhythmand meter.It is a historyof the trans- formationof a performancepractice into a compositionalone, with the attendantprovision of a notationalsystem as the medium of transmissionfrom composer to performer;and of the ultimately successfulexplanation of thesethings in the preceptsof a theory. The control of rhythmand meterentailed their coordination withother compositional factors, particularly melodic phrasingand harmonicand contrapuntalorganization. The historyof rhythmand meterin that time is thereforeonly an aspect of musical develop- mentsin generaland it can be well understoodonly in thatlight.

This essay was completed while I was a fellow at the Humanities Research Centre of the Australian National University.I should like to express my gratitude to the Centre and its director,Professor Ian Donaldson, for the opportunityof working there.

524

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The coordination of time- and pitch-elementsproduced a new level of complexity, and the development of an explicit rhythmic notation served the consequent need for an invariable transmission. This outlines a simultaneous and fundamental change in the nature of the music and the relations of its transmission: a change toward the production of complex and fixed musical entities, signified by notated scores that provided performerswith relatively unambiguous instructions. It was one of the major revolutions in the history of Western music. The basic claim here, made against two prevailing views in the modern literature, is that the music of the twelfth and thirteenth centuries was accentual. It directly opposes the view - developed most fullyby William Waite - that ars antiqua rhythmwas derived from the quantitative meters of classical ;1 and it contradicts indirectly the view of Carl Dahlhaus that the modern rhythmicsys- tem based upon meter and emerged only in the sixteenth and seventeenth centuries as a result of transformationsin mensural rhythm. He characterizes mensural rhythm as "Zeitmessend" in that rhythmicconfigurations are determined most prominently by the measure and proportion of durations and less so by their group- ing with respect to accents.2I would put it, rather,that the accentual basis of rhythmwas established in the ars antiqua, but receded into the background with the development of the more subtle time-meas- uring rhythmfrom the fourteenthcentury on. How that occurred, and what the shiftingrelations were between accent and duration during the and Renaissance, are questions for furtherstudy. My task here will be to argue for the claim regarding the nature of rhythmin the twelfthand thirteenthcenturies. In both practice and theory, the rhythmic conception of that time was manifestedmost prominentlyas a set of stereotypedrhyth- mic patterns called "modes," hence the system itself is referred to in the modern literature as "modal rhythm." It was expounded in manuals writtenabout the second half of the thirteenthcentury and transmittedin practice through repertorycollections of which the earliest surviving ones were written down during the same half century- some fiftyto seventy-fiveyears after the practice had been

1 The Rhythm of Twelfth CenturyPolyphony (New Haven, 1954). 2 "Zur Taktlehre des Michael Praetorius," Die Musikforschung,XVII (1964), 162 ff.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 526 The Musical Quarterly established.The repertoriesinvolved are the polyphonicsettings of liturgicalchant () and the polyphonicconductus and motet compositionsof the School of Notre Dame in Paris.

I The basic notionin modal rhythmis the measuringout of musi- cal timethrough the regulation of long and shortdurations ("longa" and "brevis,"to be identifiedas L and B). In the earliestexplana- tion (De musicamensurabili by Johnof Garland,ca. 1250)3the ratio of L to B is normallyas two time units to one. Those basic dura- tions were paced out in repeatingpatterns according to a number of standardmodels or modes of rhythmicmovement. Usually, six rhythmicmodes are identifiedin the treatisesin the followingorder (the descriptionis takenfrom the treatiseof John of Garland): The firstmode proceedsby an L, a B, and anotherL, and continuesthus indefinitely. The second,conversely, by a B, an L, and anotherB. The thirdby an L and twoB's and anotherL. The fourthby twoB's, an L, and twoB's. The fifthentirely by L's. The sixthentirely by B's. The basic configurationin each patternis the (L-B in the firstmode, B-L in the second, L-B-B in the third,B-B-L in the fourth,L-L in the fifth,B-B-B in the sixth).Modes 1, 2, and 6 are called "measurable"because theyinvolve only the "correct"dura- tions (B of one time unit and L of two time units). These are the building blocksof the systemin the earliestconceptions. Modes 3, 4, and 5 are "beyondmeasure" because theyinvolve durations that are beyondthe measureof the "correct"values of the B and L (a B of two time units,an L of three).John describes the L of three time units as the sum of a correctL and B, whereasin the later explanationsby (ca. 1280), it is a "perfect"L and the durationalstandard for all the modes (therewill be more to sayabout thisdifference later).4

8Ed. Erich Reimer as Vols. X and XI of the Beihefte zum Archiv fiir Musik- wissenschaft(Wiesbaden, 1972). 4 ,ed. G. Reany and A. Gilles, Corpus scriptorummusica, XVIII (1974), American Institute of Musicology. Trans. Oliver Strunk in Source

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That the descriptionof modes 1-4carries through in each case to the firstelement of the followingfoot reflects the concept of ordo. An ordo is a melodicsegment or phrasein one voice comprisingone or more successivefeet of a mode uninterruptedby rests.The theo- ristsdistinguished between perfect and imperfectordines, according to whetherthe phraseends with the firstelement of the footor not, respectively.To speak of the second perfectordo of the firstmode, for example,would be to speak of a phrasecomprising two feetof the first-modepattern, ending with the long of a thirdfoot followed by a rest.Since "perfect"is synonymouswith "complete"and "im- perfect"with "incomplete," we learn fromthis classification scheme thatthere was a normfor ending phrases on the beginningof a foot - that is that melodywas understoodnormally to move fromthe beginningof one foot to the beginningof another. In Franco's terminology,that would be fromthe beginningof one perfectionto the beginningof another.When this conceptionis consideredto- getherwith otherssoon to be discussed,it will be seen that under- lyingthe concept of ordo is a conceptionof melodymoving from downbeatto downbeatin a triplemeter. The conceptsof the footand the ordo are twofundamental char- acteristicsof the modal systemthat were for a time in opposition, a situationthat created much difficulty.On the one hand, therewas the idea thatall rhythmicpatterns were built up of the basic dura- tionsL and B; on the other,that the perfection,whatever its dura- tional patterns,was the basis of rhythmicorganization, and that musicmoved from the beginningof one perfectionto the beginning of another.Musical timeis measuredin one conceptionby sequences of the basic durationalelements laid end to end, in the other by higher-orderdurations articulated in patternsof lower-orderones. The term"mode" fora standardrhythmic pattern denotes quite literallyboth the sense of manner(a termthat occursregularly in the treatises)and that of norm.Manner reflectsthe qualitative as- pect of the conception;the modes are distinguishedas qualities of rhythmicmovement.

Readings in Music History (New York, 1950). In Chap. V, Franco writes: "The per- fect long is called first and principal, for in it all the others are included, to it also all the others are reducible." The time span of three beats Franco calls a "per- fection." "Three tempora, whether under one accent or under several, constitute a perfection" (Chap. V).

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As fornorm, it was not intendedthat the six modes should liter- ally exhaust all rhythmicpossibilities but ratherthat, as concrete modelswith several possibilities for variation and substitution,they would sufficeto providethe basis forthe range of possibilities. Never- thelesssome theorists,evidently not satisfiedwith these provisions, specifiedadditional modes as modelsfor exceptional cases. This fact suggeststhat the modesshould be regardedas crystallizationsout of a flexiblerhythmic practice. Franco reflects the oppositetendency of the laterthirteenth century to shiftthe emphasisaway fromthe dis- tinctnessof the modes and towardtheir commensurabilityon the basis of the three-beat L - the perfection- from which he wrote theycould all be derived.That amountedultimately to an explana- tion of rhythmicpatterns in the contextof what we would call measuresrather than modes. And it correspondsto a tendencyin the music of the late thirteenthcentury - especiallythe motets- to break down the sharp distinctionsbetween modes and simplyto composein triplemeter. Modal rhythmarose in the contextof polyphonicmusic, and earliestof all in the contextof organum.From the beginning,it was in theservice of the sound ideal thatinformed the principlesof poly- phony:the maintenanceof a prevailingconsonant sonority over and above thecontrasting of consonance and dissonance.With a rhythmic conceptionin which the centralphenomenon is the alternationof long and shortdurations, that sound ideal translatedeasily into the principlethat the long durationsshould in the main be consonant, and thatany dissonanceshould be short- somewhatlike the inten- tion of our idea of passingdissonance. This is the waysome manuals explained it. In what reads like an instructionto performerswho sang the upper voice in a two-partmelismatic organum, John of Garland wrote,"Everything that meets with anotheraccording to thevirtue of consonance is to be long."5 Franco put the matterin a characteristicallydifferent way: in theevent that a long note in theupper voice of an organumthreatens to makea dissonancewith the tenor, it is not to be made short;rather the tenoris eitherto move momentarilyto a consonanttone or be- come silent for the duration of the note.6 This providesfor the integrityof the rhythmand phrasestructure of the melody,while

5 Chap. XIII. 6 Chap. XIV.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 529 still satisfyingthe demand for consonance.Evidently that integrity had a greatervalue forFranco than forJohn, and perhapswe may conclude thathis attitudeis the more modernin that he wishesto leave such mattersas rhythmand phrase structureless open to the discretionof theperformer. The associationin the treatiseof Johnof Garland betweencon- sonanceand duration,while understandablein view of the priority of theconsonance principle, created problems. For in the alternation of consonanceand dissonance,it is consonancethat is the goal; con- sonance displacesdissonance, dissonance prepares consonance. This dynamicaspect of the consonanceconcept --which afterall is in the natureof things- is apparentin the language of the theorists. Thus, Franco: "Immediatelybefore a concordany imperfectdiscord soundswell." And AnonymousIV (ca. 1280,but afterFranco): "[Of two simultaneities]the finalone mustalways be consonant."'With the associationof consonanceand duration,the quality of arrival transfersto the L, which createsthe confusionbetween accent and durationthat flawedthe explanationsof John and his conservative followers.For in musical reality,the resolutionof a dissonanceby a consonance,in the absence of any contrarycues, itselfdefines an accent,whether the durationof the consonantnote is long or short. Francorealigned the association in a waythat resolved the confusion: "In all modesconsonances are alwaysto be used at the beginningof the perfection,whether this beginning be a long,a breve,or a semi- breve."8As he sayselsewhere, the perfectionis markedby an accent (although he does not make it explicit,everything points to the presumptionthat the accent is borne by the beginningof the per- fection).9Franco's preceptreinforces the sense of the beginningof the perfectionas a point of arrivalthat was alreadyimplicit in the conceptof ordo. Now thissecond of Franco'sformulations of the consonancerule refersto ,not organum.And fordiscant John of Garland also had a differentrule: "All odd-numberednotes should be consonant withone another."'0In effect,the rule applies to the firstelement of 7 Anonymous IV, Part III in Der Musiktraktatdes Anonymus4, ed. Fritz Reckow, Beihefte zum Archiv fiir Musikwissenschaft,IV and V (Wiesbaden, 1967), 75, 1.4; Franco, Chap. XI. 8 Chap. XI. 9 Chap. V. 10 Chap. XI.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 530 The Musical Quarterly everyfoot (in the thirdmode, the two B's are countedas one forthis purpose).John's theory is thusequivalent to Franco's.But since his theoryin generalexcludes the concept of the perfection,his explana- tion,here as elsewhere,is circumlocutional.Both formulations,how- ever, have the result that the demand for a prevailingconsonant sonorityis to be satisfiedby the principle that downbeats- the beginningsof the perfectionor the foot- jointlyconstitute a chain of consonancesequidistant in time and therebycreate a temporal hierarchy.Today we call such hierarchicalorganization meter, but the dependenceof rhythm,harmony, and counterpointon it then was essentiallythe same as now. The opposing statementsof John and Franco concerningthe control of consonance in both organum and discant again point to two fundamentallydifferent conceptions about the basis of rhyth- mic organizationwhich we have mentionedvery briefly: the simple alternationof long and shortdurations in a flatchain and the hierar- chicalorganization of timethrough musical meter. It is thedifference betweenthe filling-inof unarticulatedtime with fixeddurations of one and two beats,strung out accordingto traditionalpatterns, and the groupingof notes withinthe invariableunits in which time is divided.In the firstcase rhythmis a matterof the orderof material elements,the durations.In the second it is the creationof formor order within the successionof equal durations,the perfectionsor measures. A directinsight into the contrastbetween the two conceptionsis affordedby the correspondingexplanations about the two varieties of L's (thosewith two and threebeats). For Johnof Garlandthe two- beat long is the correctand true componentof rhythmicpatterns. The three-beatL is not a trueduration but a compositeof thecorrect L and B. For Franco the L that is measured"under one accent by threetime units" is the perfectlong. The two-beatL is a derivative, an "imperfect"L, a resultof thereduction of a perfectL by a follow- ing B. The perfectL is the commoncurrency of conversionfor all modes. In the alternationbetween consonance and dissonance,the consonanceis to fall at the beginningof the perfection.Considered together,these precepts of Franco'scan mean only thatrhythm for him was based on the perfection,that is on whatcorresponds to the modern three-beatmeasure.

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We can broaden the context for a moment in order to gain per- spective on this differencebetween John and Franco. The conception of the B as a "short time" (tempus breve) or simply as "a time" (tempus) satisfiesthe requirement for a minimum that is the reference unit for the formulation of all durational rela- tionships. From that vantage point the perfect L is a compound, as John has it. But Franco, while he transmitsthe brevis concept, wishes at the same time to present the perfectL as a primaryquantity. For he recognizes its essential role in the rhythmicsystem and its notation. The perfection is the referenceunit for all the modes; and it is the primary division of time into perfectionsthat is the basis for deter- mining the durations of L's and B's (i.e. it is the premise for the operation of alteration and imperfection). Johannes de Muris, in the Ars novae musicae (ca. 1300) resolved the ambiguity by making the minim the unit of referenceand giving all note levels from the B upward the perfectand imperfectforms." Presumably that was made possible by the shift of prevailing note values from L's and B's to B's and semibreves,and by the end of a rhythmicpractice characterized by modes. From this theoretical van- tage point, we can mark the conclusion of the period of modal rhythmby these changes. The two conceptions regarding modal rhythmwere mixed in the theoryof the thirteenthcentury, and that seems to have been respon- sible for much of the disagreement and internal inconsistencythat has made the theory as a whole so difficultto clarify. Looking only at the beginning and the outcome in the theory, it is tempting to trace a development from the conception based on quantity to that based on perfection. But that would be quite misleading, for the quantitative conception dominates some of the later treatises (e.g. that of Anonymous IV). Holding all the treatises in view, it is not a development that we see but a struggle with difficultand contra- dictory ideas in an effortto present coherent explanations and in- structions. The nature of the notational systemtransmitted in the practical and theoretical sources of the thirteenthcentury follows from two essential conditions of modal rhythm. First, modal rhythmis men-

11 See the translationin Strunk,op. cit.,especially the table on p. 177.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 532 The Musical Quarterly sural, that is it entails the measurementof time. Indeed the term "" traditionallyreferred to "measureby length,circumference, size, quantity."12The modernconventional characterization of the theoristsof modal rhythmas "premensuralists"is quite misleading and should be abandoned.Second, the modal systemis proportional, that is the durationsof notes are regulatedthrough fixed propor- tions (2:1, 3: 1). In view of thesecharacteristics, it is the optimalfunction of the notationvis-a-vis rhythm to indicateto the singerthe arrangement of L's and B's that he is to follow,and whethereach L and B is "correct" (two and one beat[s],respectively) or "beyond measure" (threeand twobeat[s], respectively). We mustsay "optimal" because, takingthe notated Notre Dame sourcesas a whole,much of the time the notationsets up a generalrhythmic type, but leaves a more or less wide range of details for the singerto settle in performance. Indeed a fulldescription of thatsystem must present it as functioning throughthe collaborationof composer,notator, and performer,with variableand uncertainboundaries for the role of each. The significationof relative duration relied on a number of general principlesof which the followingare the most important forthis discussion. 1. In the notation of melismaticmusic, the successionof the L's and B's was indicatedby standardsuccessions of notationalfigures. The followingarrangements (see p. 533) representthe six modal patterns,summarized from the presentationof John of Garland.13 (In each case, the reader should comparethe patternwith the cor- respondingdescription on p. 526.) 2. The relativevalues of the L's and B's (whether"correct" or "be- yond measure")were to be determined,according to John'spropos- als, by the note's contextamong other L's and B's, followingthese rules: all notesare "correct"except an L precedingan L (threebeats) and thesecond of twoB's standingbetween two L's (two beats) both instancesof whichare "beyondmeasure."'4 On reflection,it will be seen thatthese rules can be deducedfrom the modal ligaturepatterns.

12 Charles Jones, "Carolingian Aesthetics:Why Modular Verse?" Viator/Medieval 6r Renaissance Studies, Vol. VI (Berkeleyand Los Angeles, 1975). 13 Chap. IV. 14 Chap. I.

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First: ?I Second:N IN

Third: r IRIN Fourth: NNI4 1I Fifth:IK Sixth: NA lor N

There is a clear driftthroughout the thirteenthcentury away fr-omreliance on contextualindications and towardgreater reliance on the shapes of the figures.Compare Franco's ligature rules to John's:binary ligatures are B-L; thosewith three or morenotes are B at the beginning,L at the end, and all notes in betweenare B; withoutpropriety (reversal of the normal presenceor absence of a stem)the firstnote is L; withoutperfection (reversal in the position of the last note in the ligature)the last note is B.15This gives the values forall notesindividually and independently,regardless of the contextof ligatures,and of thecontext of L's and B's withinligatures. In the theory,the change is neatly captured by the contrast betweenthese formulations of the relationshipsbetween the modes and the notationalfigures. Johln of Garland: "A figureis a represen- tation of a sound accordingto its mode." Franco of Cologne: "A figureis a representationof a sound arrangedin some mode. From this,it followsthat the figuresought to indicatethe mode and not, as somehave maintained,the contrary.""1 It requiressome effortto understandthe radical natureof what was effectedin the realmof notationduring the thirteenthcentury. And despite the differencebetween John of Garland and Franco of Cologne,the basic notionwas thereat the beginningof the theo- retical tradition.John wrotethis curioussentence: "All simple fig- 15 Chap. VII. 16 John,Chap. II; Franco, Chap. IV.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 534 The Musical Quarterly ures are valued accordingto theirnames, whether they are withtext or not."17That is, the graphicfigures designated "L," "B," etc.,rep- resentthe durationsthat have been assignedto those designations - two beats,one beat, etc. Statingit still more directly,written fig- ures representdurations. The formin whichJohn expressed this is characteristicof his reasoningstyle, but thathe should feel obliged to say it at all suggestsa consciousnessabout the noveltyof the idea. It was indeed novel when he proposedit; we do not see it put into practicefor another generation. But it was the basic notion behind mensuralnotation.

In orderto focusnow on the performer'srole in relationto the systemof rhythmand its notation,we shall considertwo shortpas- sageswhose notation falls more or less shortof the ideal of mensural- ly unambiguoussignification. The objectivewill be to definethe limitsof the informationthat is transmittedthrough the notation, to identifythe range of choicesopen to the performerand the sorts of considerationsthat would have guided his choices,and to gain an impressionof the kind of competencethat a rhythmicperform- ance fromsuch notationmight have entailed.We want a sense of the kind of notationthat it was, and of the sortof act thatperform- ing fromit was.

Example 1, from London, British Library, Harleian 978.

- 9!%C i--_me=- M: - I II III IV

1 2 3 4 5 6 7 8 9 0 1 3 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Example 1 is the openingpassage (phrases I-III) of a well-known Englishdance in a notationof the late thirteenthcentury. Taking just the lowervoice in I, thereis no standardligature pattern that is immediatelyapparent. The principalclue is the pitch repetition at the outset,which suggestsa blocked ternaryligature and hence - considering the following binary ligature (2) - a first-modepat- tern.The stemdescending from the thirdnote representsa passing

17Chap. VI.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 535 tone with the durationof a B. That reduceswhat would have been an L at the end of the initial ternarygroup (1) to a B. Assuming a first-modepattern, ligature 2 begins B, but the second note is uncertain,since ligature3 breaksthe modal pattern.Of the possible readingsof a ternaryligature, two are plausible here: L-B-L and B-B-L (all "correct").If L-B-L, then the last note of ligature2 is a three-beatL; if B-B-L then the last note of ligature2 is B. Why? For the firstcase, John of Garland could have cited the rule "L precedingL is beyond measure" (i.e., threebeats). The performer would not have rationalizedthat way. He would have starteda first- mode patterngoing in his ear, and he would have knownmusically thatL's are stressedand fall at the beginningof the perfection.To have ligature3 begina new perfection,he mustsustain the last note of ligature2 for threebeats - he mustlet it fillthe precedingper- fection.But if ligature3 begins B, then the last note of ligature2 must be B also. The rationalein this case is that the normal L at the end of ligature2 is replaced by two B's, the last of ligature2 and the firstof ligature3. But the musical impulse will again be more direct:one wantsthe finalnote of ligature3, an L, to fall on the stressedinitial position of the next perfection,for therestarts a rhythmicreprise of the beginning (through ligature 5). The choicescome down to twoversions of the phrase,each musi- cally and notationallyplausible (see Exx. 2a and 2b). Since the piece is clearlybuilt of parallel phrasesof identical lengths,and since the upper voice in phrasesIII and IV cannot be performed at all in the time of six perfectionsas is version2b, that versionis substantiallyruled out.

Example2 (seeEx. 1,lower voice, phrases I and II) a. F T U - 7-

1(6) 2(7) 3(8) 4(9) 5(10)

Phrase II of Example 1 repeats phrase I, and the performance of phrase III will be affectedby decisions made about phrases I and II. The phrase (lower voice, still) will begin in the firstmode. Figure

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13, by analogywith figure3, will begin L-B, but its finalnote will depend on the readingof figure14. Once again, thatwill be either L-B-L- in whichcase figure13 ends with a three-beatL (Ex. 3a) - or B-B-L - in which case figure 13 ends B (Ex. 3b).

Example3. (see Ex. 1, lowervoice, phrases m &IV) Sila.

I ~ I I II J II 12 13 14 15 A b.

11 12 13 14 15 AIV

16 17 18 19 This time both versionsare of the same length,but the differ- ence in the performanceof figures13 and 14 emergesin the rest at the end of phraseIII (B or L). That means thatneither version can be conclusivelyeliminated. But now if we take phrasesIII and IV as a pair (IV is transcribedwithout comment in Ex. 3, since there seem to be no questionsabout it), we note that theywork as ante- cedent-consequent,and thatthey will workbetter that way if phrase III is performedwith a feminineending (Ex. 3a) as comparedwith the masculineending of phraseIV (Ex. 3b). The readingof figures 13 and 14 is influenced,then, by a higher-ordermusical judgment. In interpretingthis notation,the performeris not simplyread- ing the individual figuresfor the durationsthey signify. A rhyth- mic performanceresults from the jugglingof fourdifferent kinds of configurationat once: the underlyingL-B-L pattern,the isochronous perfectionwith stressed initial position,the variable patternsof the L's and B's withinligattires, and the variablevalues of the L's and B's accordingto their juxtapositionswith one another. The per- formermust then control his interpretationsfrom the viewpoint of thelarger phrase organizations that they yield. These decisionswere no doubt quite spontaneous;hypotheses suggestedby the notationwere instantlyreinforced or contradicted throughcues providedby melodic and harmonicfactors. Plausible solutions fell into place and unlikely ones were eliminated.Of course once the performerhad made his way through the piece (or probably even once he had heard it), its performance became set,

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 537 that is stereotyped,and not to be forgotten.But then he would no longerhave been "reading"the notation.If he referredto it at all in subsequentperformance, it would have been onlyto remindhim of whathe alreadyknew. Notation of thissort must then have func- tioned in two differentways vis-A-visthe performance:as a set of cues that served the performeras points of departurein working out a performanceand as a mnemonic.Neither corresponds to the ordinarymodern sense of "reading." We can quicklygain a sense of how naturaland spontaneousa processthe performanceof such a piece as is shown in Example 1 would have been, if we consideras an analogoussituation the reci- tation of some simple English verse. The followingrhyme should be spokenaloud: Ride a cockhorse to BanburyCross To seea finelady upon a whitehorse; Ringson herfingers and bellson hertoes, Andshe shall have music wherever she goes. Usually the followingstress pattern will be markedin the per- formanceof thisverse (X designatesan accentedsyllable, O an un- accentedone, - designatesa pause in place of a syllablebut of the sameduration that is requiredfor a syllable): XOOX-OXOOX- OXOOXOOXOOX-- XOOXOOXOOX- OXOOXOOXOOX--

There is no consistentpattern in the numberof syllablesto the line, and while both dactylicand iambic movementcan be heard, thereis no consistentpoetic meter. There are two controllingfactors for the performance.Each line has four stresses,and the time in- tervalbetween stresses is alwaysthe same. This is so betweenlines as well as withinthem. In that time interval,there may be one or two unstressedsyllables, or none. (The dashes in the schemaabove show that the time betweenstresses is always the same, regardless of thenumber of unstressedsyllables.) We maysay that this duration has threepositions. The firstis alwaysoccupied by a stressedsylla- ble; the secondmay be occupiedby an unstressedsyllable, or it may be vacant; if it is occupied, the third position is also occupied by an

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unstressedsyllable; the second may be vacant and the thirdoccu- pied but not vice versa; the unstressedsyllables with which lines 2 and 4 begin are actuallyin the thirdposition of the last group of the precedingline. The timetaken for each syllableis a function of the numberof unstressedsyllables between stresses. Without the slightestreflection, the performerwill take care to observe the stressesand preservethe timeinterval (three "beats") betweenthem, adjusting for the variable number of unstressedsyllables. Where twostresses follow one anotherdirectly, the firststress is "sustained" for three beats ( J. ).Where there is one unstressedsyllable, the X-- performanceis J wherethere are two,the durationis evenly X-O, divided ( ; ). The firstof these principlescorresponds to the XOO mensuralrule thatan L beforean L is perfect;the second corresponds to the imperfectionprinciple (again, in English there is nothing correspondingto the alteration principle); and the third corre- ponds to the fractiomodi principle.Again the descriptionseems rathercomplex for what is essentiallya spontaneousand simple process.The readerwho leafsthrough Mother Goose will findagain and again thathis performancerests on his graspof two factors:the number of stressesin the line, and the constanttime intervalbe- tween stressesinto which he must fitthe unstressedsyllables (the numberwill varybetween 0 and 1 or 0 and 2, dependingon the metricalscheme). The parallel with modal rhythmis clear. The constanttime intervalis the perfection,and the regularlyrecurring stressesare the accentsat the beginningsof perfections.As for the numberof stressesin the line, the performermust make a projec- tion of the length of the phrase,based on his perceptionof the higher-orderform, and that,too, will be a factorin his workingout of the lower-ordermetrical organization. Then he proceeds,utilizing whateverdetailed cues thenotation provides.18 Example 4, a passagefrom an organumof the oldestlayer of the S. 18 This discussion has profited from the writings of Morris Halle and J. will be Keyser on prosody. Expositions of their theory and further bibliography K. found in the following: Halle, "On Meter and Prosody," in M. Bierwisch and Basis Heidolph, Progress in Linguistics (The Hague, 1970); Keyser, "The Linguistic in of English Prosody," in S. Schane and D. Reibel, eds., Modern Studies English XXX (Englewood Cliffs,N.J., 1969); Keyser,"Old English Prosody," College English, (1969).

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Magnus liber,offers another useful ground for reconstructing such a process.(The example followsFritz Reckow,19 although the analysis is somewhatdifferent from his.) In Example 4a, the passageis shown as it is notatedin threeNotre Dame sources.In Example4b, thesame passage is shownwith the ligaturesresolved for easy comparisonof melodic contours.Taking only the pitchesinto account,there is an obvious articulationin two phrases,A and B, relatedas antecedent and consequent.That mightsuggest to the singer a performance in whichthe twophrases are of thesame lengthand wherethe paral- lels and contrastbetween the firstfive notes of the two phrasesare broughtout. The versionof W1, with parallel notationfor those fivenotes, is easilyinterpreted that way (Exx. 4c and 4d). The two transcriptionsdiffer only with respect to the decision about the length (the numberof stresses)of the firstphrase. There seemsno obviousway to choosebetween them. In the versionof F, the phrasesare not given parallel notations. The explicitL figuresare the linchpinsfor working out the rhythm

Example4, Alleluia,Pascha nostrum a. W1, folio 32 recto

A B F, folio 109 recto

A B W2, folio 72 recto

A B Tenor

b . A B

n -o i II m -J w

% -

mi ., I, r I I I FL Ia l I1 I i l I j

19 Op. cit., Part II, p. 79.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 540 The MusicalQuarterly of the firstphrase. Everything else fallsinto place around them(Ex. 4e). The interpretationof the second phrasedepends on a decision about the lengthof the phrase- in particular,whether or not it is to matchthe firstin length.In W2, by means of anotherexplicit L figure,the two phrasesare given parallel openings.That rather forcesa secondphrase the equal in lengthof thefirst (Ex. 4f).

. A I -k II_ B

or

irn d I IRF _6

A I 1, . II I I I i

The point of all this is that the notationof the example does suggesta modal performance.But the performerwould not have read it off;he would have had to work out a performanceon the basis of the kindsof principlesand decisionsI have suggested.Some alternativeswere equivocal. The later sourcestend to reduce that by means of a greaterexplicitness in the notation.But, so faras we know, theirchoices have no necessarymusical priorityover others theymight have made. That is,there are no internalmusical grounds (in thenondurational aspects of themusic) forchoosing from among transcriptions4c, d, e, and f. This means thatthe rhythmicaspect is not highlyintegrated with other aspects. Later, in the discussion of Example 7, we shall see how such choices can be forcedby the nondurationalaspects.20

II How did this flexiblerhythmic practice and its pragmaticno- tation become a systemabout which one could writea theory?It has generallybeen held thatthe modeswere differentiated in stages, and thatearliest of all therewas a kind of first-moderhythm alone. Walter Odington (ca. 1300) wrote,"With the earliestpolyphon-

20 My interpretationof modal notation has much in common with Anton Maria Michalitschke's conception of "Modalschrift,"presented in his very interestingbook, Theorie des Modus (Regensburg,1923).

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 541 iststhe L was worthtwo timeunits... but later on it was brought to perfectionso as to contain three."That would rule 6ut modes 3, 4, and 5 for the early period,and Odington indirectly?confirms that: "The perfectL had its originsin these [the thirdand fourth] modes."21 In the two-partorganum of the Notre Dame school,wherever thereis a run of clear modal notation,it showsmainly first mode, and in laterrepertories in which all the modes are representedthe passagesin firstmode outweighthose in the othermodes. First-mode runs with passing tones and sustainedperfect L's can suggestthe fifthand sixthmodes respectively, but extendedpassages in B's and perfectL's occur mainlyas upper voices and tenors,respectively, in clausulae and motetsof the-Perotinperiod and after. Againstthe conclusion about the firstmode as the earliestin use, Gordon Andersonhas presentednew evidence of a predominance of second-modepatterns in eArlymonophonic that have been transmittedin mensuralnotation.22 But to speak of either:first or second mode as the earliest,and to representthe subsequenthistory as one in which the remaining modes are graduallyput into place, is to presupposea systemwith a priortheoretical existence. That is, to speak of a mode is to implya systemof modes.It is perhapssimpler and morerealistic to represent the initial situationas one in which the rhythmicnorm involved theregular alternation of single L and B notes,with the longs broken up by passing and accessorytones, and with the movementocca- sionallyslowed down by perfectL's. Out of thatgeneral and variable rhythmictype, particular modal patternsmight have become stereo- typedthrough practice and systematizedin the theory.John of Gar- land presentsthe secondmode as a reversalof the firstmode - that is he relatesthem as a small system- and the lateststate of the evi- dence is at least consistentwith the idea that theymay have crystal- lized at the same time.The conceptof fractiomodi is at least con- sistentwith the idea that the sixthmode may have crystallized'out of the first-secondmode type(i.e. by givingpassing and neighboring notes a primarystatus). That there is not a counterpartin the treatisesfor interruptionsby perfectL's is at least consistentwith

21 Speculatione musices,Coussemaker, Scriptores, I. 22 "The Rhythm of the Monophonic Conductus in the Florence Manuscript as Indicated in Parallel Sources in ," in JAMS, XXXI (1978), 480-89.

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Odington'sclaim thatthe perfect L derivesfrom the thirdand fourth modes.23In view of the relativescarcity of fourth-modepatterns in the music, that mode should perhaps be understoodas an artifice createdfor the sake of the systemas a reversalof the thirdmode (it is describedas such in the treatiseof AnonymousVII, ca. 1250), on themodel of the first-second mode relation. All such reasoningis speculationthat is not subject to confirma- tion. But whateverits exact details,it all bearson the hypothesisof a gradualsystematization of a flexiblerhythmic practice. There is, however,an idea verymuch taken forgranted in the modernliterature on thissubject that entails instead the assumption of an a priorisystem. It is the associationof the modes with poetic meters(first mode with trochaicmeter, second with iambic, etc.). The underlyingassumption, whether or not it is made explicit,is that the modal systemwas inventedon the model of the classical theoryof metrics- thatis thatmodal practicewas theory-induced.24 Perhaps the associationsmade in the modern literaturebetween modes and metersare oftenmade innocentlyand do not reflecta commitmentto that proposition.But questionsabout the relation betweenmusical rhythmand poetic meterare fundamentalto the problemabout thenature and historyof the modal system.It will be important,therefore, to considerthe reasons for believing that modal rhythmis based on metricsand to considerwhether they stand up. In 1199 - probably the year of Perotin's four-partorganum Sederunt principes - the Parisian grammarian Alexander de Villa- Dei described,in his Doctrinale,the principalmeters of quantitative versein a systemof six "modes."25Here are the namesof the modes in the order of his presentationand the quantitiesof the syllables in a footof each mode. (A shortsyllable has a value of one timeunit in his presentation,a long one has twicethat.) : long-short-short : long-long : long-short 23 The term "extensio modi," which has become a commonplace in the modern literature,is an invention of Willi Apel in The Notation of Polyphonic Music 900- 1600 (Cambridge, Mass., 1942). Such confoundingof medieval and modern terminol- ogy obscures the medieval conception and is betteravoided. 24 See especially William Waite, op. cit. 25 See Rudolf Flotzinger, "Zur Frage der Modalrhythmikals Antike-Rezeption," AfM, XXIX (1972).

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Anapest: short-short-long : short-short-short : short-long This expositionfollows the long traditionof the ars metrica. Metricshad to do with the measurementof syllable durationsor quantitiesand of the proportionsobtaining between them and with the standardpatterns of syllablequantities in versetypes. The tra- ditiongoes back to classicaltimes, and persistedinto the late Middle Ages,when in practicepoetic meter had long since become a matter ofaccentual rather than durational pattern. That the traditionnever- thelesscontinued indicates something important about its place and utilityin the systemof knowledge.The ars metricawas not simply a bodyof doctrineutilized by poets;rather it concernednumber and proportionin general,and poetic metermight be consideredas a concretemedium for its exposition.But metricsprovided the con- ceptual frameworkfor the discussionof numberand proportionin otherconnections as well. It supplied the "philosophicalpart," as a writerof the time expressedit, of the "lawful art of adjustingthis music in suitable proportions."26Once the attentionof music theo- ristswas focusedon the measurementand proportionsof durations, the terminologyand conceptsof metricswere at hand fortheir use, and especiallyfor their explanations. Villa-Dei's treatiseshows they wereavailable in Paris around 1200. A directassociation between rhythmic modes and poetic meters was drawnexplicitly only once, by WalterOdington, who noted the correspondencebetween the six rhythmicmodes of music and the correspondingmeters listed by Villa-Dei and suggestedthat the formerwould be suitablefor setting written in the latter. But thereis an oldertradition for the idea thatthe ancient meters could provide practical models for the rhythmicperformance of music. It is the testimonyfrom the ninth throughthe eleventh centuriesabout the performanceof plainchant according to the ancient poetic meters.This passage by Guido of Arezzo (eleventh century)is typical: The similaritybetween chants and metersis by no meansa smallone, sincethe correspondsto the foot,and the phrase to the verse. And, as is natural,

26 "Introductionto Music," ascribedin Coussemaker,Scriptores, I, to John of Garland.

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 544 The Musical Quarterly thisneume proceeds in dactylicmeter, this one in spondaic,and thatone in iambic;and one seesthe phrase to be now in tetrameter,now a pentameter,or sometimesas if it werean hexameter.[Micrologus, Chap. XV]

The tradition goes back to the great cultural leader of the Caro- lingian court, Alcuin, and seems to disappear in the eleventh cen- tury. On the basis of the evidence that has been very brieflytouched upon here, a strong circumstantialcase can be (and has been) made for the proposition that from the eighth century on, at least, the ancient meters provided a concrete basis for the rhythmicperform- ance of music, and that in the twelfthand thirteenthcenturies an independent system of musical -hythm, with its own notation and theory,was created throughthe direct adaptation of classical prosody. But there are reasons for circumspectnessabout this proposition. First, whatever the actual rhythmicpractices in the performance of plainchant were to which the medieval writers refer, they must have been forgottenby the twelfthcentury, for the writers of the eleventh centurywere already lamenting their passing. Furthermore, John of Garland, in his treatise De Musica mensurabili, concern- ing measured music, contrasts that genre with musica plana, from which we have our expression "plainsong." The contrast is between both and monody and measured and unmeasured (or even); that is, by his own testimony John was not building his theoryon plainchant practice. Second, it is important not to interpret the testimony about plainchant performance too literally. It leaves us completely unen- lightened about how the ancient meters would have related to the phrase structure and formulaic structure of the melodies, to the ligature formationsin the writtentransmission, to the tones of func- tional importance in the melodies (the finalis, the recitation tone), and to the declamation of the nonmetrical texts of the chants. We can well imagine artful performancesof plainchant in which some tones are drawn out, others are sung quickly, and thereby living configurationsare formed. The musical sources are in support of such an idea. And it is readily understandable that such an art would have been prized and therefore lamented when it was no longer cultivated. When it came to describing such a practice in writing, it is equally understandable that it would have been assimilated into

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 545 the doctrineabout the systemof durationsthat was taughtby theo- rists- and thatwas the traditionalformat of discussionabout dura- tionsand proportions. Plainchant is for Guido the practicalmedium of music. It is pleasingto the mind,hence it mustbe susceptibleof rationaltreat- ment, for the mind operates by reason. Differencein duration is one of the aspectsof plainchantthat must be open to rational ap- prehension,and the appropriatediscipline is metrics.To speak rationallyof long and shortdurations is to speak of these in terms of proportions.We cannot conclude fromGuido's expositionthat therewas a traditionof plainchantperformance according to the classicalmeters and thatthat tradition was absorbedinto the system of modal rhythm.We can howeversee in it a desire to conceive durationas discrete,measurable, and relatablethrough the propor- tions.That desireis apparentagain in the thirteenthand fourteenth centuries,when it was giventhe necessaryphilosophical implements for the productionof a theoryand notation,chiefly under the new Aristotelianinfluence in Paris.27But then the theorydid not rely on metrics. That the explanationsof the modal systembear the conceptual stampof the traditionof metricsis undeniable.Perhaps that reflects the effortsof those theoriststo derive legitimacyfrom the domain of the trivium.But metrictheory did not providean adequate theo- reticalframework for modal rhythm,for it offeredno way of taking into account factorsother than durationthat contribute to the ex- perience of rhythmin music: stressaccent, tonic accent,rhythmic grouping,phrase organization (sequences, antecedent-consequent, etc.), tonal prioritiesand polarities,consonance and dissonance, and contrapuntalrelations between voices in polyphony.These fac- torswere forcedon the attentionof musiciansby polyphonicprac- tice and by other developmentsof musical style. The systemof rhythmwas a productof theirefforts to bring themunder control. The principlesof modal rhythmare older than the systemof rhyth- mic modes; forthat matter there is reallynothing so veryanachro- nistic about the fact that it was only Walter Odington who sug- gesteda directassociation between the modes and the ancientmeters. That was strictlya rationalization,long afterthe fact.

27 See the forthcomingessay of Max Haas on this subject in Forum musicologicum, II.

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The hypothesisthat modal rhythmwas imposedon music as a systemfrom without is inadequate. The alternativeis that it grew naturallyfrom within, and graduallybecame systematized.But in orderto feel comfortablewith thathypothesis, we ought to be able to see what it was about musical developmentsin generalthat en- couragedthis sort of rhythmic focus. A pair of exampleswill takeus quite farinto these style-historical matters.They are shownwithout any interpretationabout duration or bar lines in orderthat we maybe freeto considerthe other factors thatbear on theirrhythm and meter. Example 5 is a passage froma three-voicedliturgical organum of the Notre Dame school, presumablyfrom the time of Perotin, thatis circa 1200. Example 6 is a passage froma two-voicedversus containedin an Aquitanian manuscriptof the same period. (The manuscriptis associatedwith othersof Aquitanian provenancethat span the entire twelfthcentury or more and that constitutethe sourcesof what is knownas Saint Martial polyphony.)

Example5. GradualBenedicta. F, fb6. 29; W1f. 67

m, --Ir- I ~~~~~~~~~~~.- -l --

L I L I .. , l I L l [ I--..Ii L. _-- -. I L! A Ia ii m m AP -

I:IL1

(di) *W1

Example6. VersusOmnis curet homo, London, B.M. add.36881, f.2v

(pro -)1 L t i ca Kpo- 'I i F ti - ca. The greatsimilarity between the two examples,in view of the absenceof any directcontact between the repertoriesthey represent, allows us to see in them the featuresof a well-established,strong, and widespreadstyle. The followingcharacteristics are striking. 1. Melodic contourand phrasing.In both examples,each voice pro-

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ceeds as a sequentialrepetition of a six-notegroup that is articu- lated as twothree-note groups. 2. Contrapuntalrelationship between the voices, emphasizingthe articulationof two three-notegroups. In Example 5 thisamounts to an inversionalexchange of successivethree-note groups between the two voices. In Example 6 the three-notegroups in the two voicesare relatedalternately through simple inversionand retro- gradeinversion. 3. Diminutionof a diatonicstepwise descent to the tonic. Both ex- amples are strongcadential thrusts.In both, each of the succes- sive six-notegroups begins with a unison,and thoseunisons carry the passageby stepdown to the tonic.They constitutea structural frameworkfor the passageand would quite naturallyreceive the primaryaccent in each six-notegroup. 4. Sequential repetitionof a patternof sonorities.The mostsalient aspect of that in both examples is the repeatedexpansion from the unison to the fifthof whichit is the center.It gives each ex- ample theaspect of a triadicsonority shifting downward by steps. Of coursethese features are not independentof one another;they are rather the coordinatedaspects of a highlyorganized periodic form,governed by a singleidea. Disregardingfor the momentany direct clues about duration thatmay be furnishedby the notationof thesepassages, their metri- cal articulationis alreadydetermined to a high degreeby the non- durationalcharacteristics that have just been reviewed.There are twomain aspects: 1. The groupsof threenotes and twice threenotes are presumably isochronous- theymark equal time intervals.There is no direct proofof this,but there is no evidence for any othersort of in- terpretation,and it would be odd to proposeone. For any alter- nativewould distortthe patternsmade by the pitches. 2. All the musicalfactors emphasize a main groupingof twicethree notes. The choice is betweena main stresson the firstof every threeor the firstof everysix notes.The formerseems more likely because thereis no evidence in the notationor the theoryof a conceptof compound meter. These two factorsalone are sufficientto establish a meter, what- ever the durational patterns within three-notegroups may be. As in

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 548 The MusicalQuarterly tonalmusic, the articulationof musicaltime and the resultingmusi- cal structuresdo not simplyproceed from a pulseand its organization into measuresin the mannerof a preestablishedgrid. It is a function of the configurationscreated by the melodic, harmonic,and con- trapuntalactions of the music.The rhythmis generatedfrom with- in, not imposedfrom without. For the details of durationand the rhythmicgrouping within the metricalconfigurations, we may turn firstto the notation of Example 5. Given the repertoryand sourcesfrom which the passage is taken,an effortto read the notationas modal is appropriate.But the ligaturepattern does not correspondto any one of thosetaught by thetheorists. Chains of ternaryligatures occur in the notationof modes 3, 4, 5, and 6. We mayrule out mode 5, whichis strictlya tenorpattern. All of the othersare plausible,but each will assumesome deviation fromthe modal norm in the notation.There is no evidence for a uniquely correctchoice, and that itself is noteworthywhere the notationis so sharplyand consistentlypatterned. It puts in doubt the idea thatthe passageis built as a patternof fixeddurations. Its generatingidea must have been the larger form,and the rhythm would haveprojected that. With Example 6 we are in a similar situation.The rhythmic modes as such, and their notation,are highlyspecific and local phenomena.There is no pressingreason to look forjust those pat- ternsin the musicrepresented by Example 6, althoughthere is no reasonto rejectthem, either. The simplestreading would be one in whichall notesare givenequal durations:

But since the middle notes in the groupsof threefrequently come togetherin dissonantintervals, it would make senseto shortenthem. If we wishto do thatand to preservethe equality of durationamong three-notegroups, there are thesepossibilities: I i = m I II ' pr'r Again,there Prris no evidenceor'rPr' r for a uniquely correct choice, and indeed it is easy to hear one possibilityfading into another. Bruno Sthibleinsuggested the possibilityof a modal rendering of Limousine polyphony on the grounds of just such pitch group-

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 549 ings.28His actual focuswas as much on ligatureformations as pitch groupings,but chains of binaryor ternaryligatures that mightbe interpretedin the lightof modal notationare afterall reflectionsof pitchpatterns. Fritz Reckow developed this point with respect to the organumof the and establishedclearly the relevance of the pitch parameterof the music to the developmentof regular rhythmicpatterns.29 With Example 7 I shouldlike to carrythis kind of analysissomewhat further, for I believe that a reallysatisfactory accountof the natureand originsof modal rhythmrequires that we understandhow it servedto project the tonal, harmonic,and con- trapuntalrelations of the music in whose contextit arose (p. 550). The example is the Parisian organumduplum Judea et Iheru- salem,transcribed from the manuscriptsW1, F, and W2. The lower two staves in each systemcontain a reductionof the upper voice, designedto bringout its voice-leadingrelationships in termsof the elaborationof the principaltones consonant with the tenor.Those tones are writtenas half notes. Upward- and downward-directed stemsidentify the two registersin whichthe voice moves.Slurs indi- cate long-rangevoice-leading connections. Arabic numeralsidentify ordines,lower-case Roman numeralsidentify notational groups. The discussion here will concern in detail only the passage through phrase 5. The passage has a clear gross-structurecomprising the opening sonority,sustained ad libitum,and threephrases that I take to be eightperfections in lengtheach: 2, 3, and 4-5 (the thirdphrase comes out to eightperfections on the plausible suppositionthat 5 [includ- ing its rest]would have a durationof two perfections).This exem- plifiesthe associationof a clear modal microrhythmwith a balanced macrostructureof phrasesmatched in duration.(Reckow has drawn attentionto this associationin his discussionsof copula, but it ob- tains as well in symmetricalstructures of the kind shownhere. It is in general a mark of the establishmentof modal rhythmand its notationin organumduplum.) The organalvoice establishesitself in tworegisters at the outset, the octave(1) and the fifth(2) of the tenor'sf. Its action through6

28 "Modale Rhythmen im Saint-Martial-Repertoire?" in Festschrift Friedrich Blume (Kassel, 1963), 340-62. 29 Die Kopula. Akademie der Wissenschaftenund der Literatur (Mainz, Jg. 1972), Nr. 13.

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Example7 1. 2. 3. Wi

Tenor *1 Ju-

Duplum reduction

4 54a. 6.

A ri m - r- V W2 M S _ _- - ,_- " "'- - Tenor-_._. .

Duplum 0

reductionFF0 j 7. 7a. I I8.9. - Am-r' I --- - Wi

F 77*1 M

W2 Ptb%'

Tenor

Duplum reductionI I I I I I I

can be understoodas double voice-leadingin those two registers, elaboratingthose two tones.The decisivefact of this interpretation is that the organalvoice movesby step withineach of the registers,

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 551 and movesby skip betweenthem. The essentiallines of motioncan be summarizedthus: in 1-3the duplum makesa linear descentfrom f' to c' in the upper register,and a linear descentfrom c' to f in the lowerregister. But in thesecond descent in 3 thef' is leftby skip, and that keeps it hanging,so to speak, as an upper ceiling that is re- claimed in 8-9. In 4-8 thereis a linear returnin the upper register fromc' to f',and in the lowerregister from f to c'. By virtueof these underlyinglines theentire passage from 1 to 9 attainsa unifiedstruc- ture of a higherorder. The movementof the Tenor is workedinto the total action,rather than being treatedas the a prioribase for a seriesof melismasin theupper voice. How thatis done is exemplified by thepreparation for the firstTenor motionto d. In 4 the tworegis- tersof the duplum are collapsedinto one on f,whence the motionis to a. In the circumstancesthat has the effectof two voicesmoving in unison. It is the strongestthrust in the duplum to thispoint, and it motivatesthe shiftin the Tenor voice at the precisemoment when it occurs. The Tenor's returnto f in 6 is again preparedby the duplum, somethingthat is best seen in the reduction.The lower "voice" prolongsa, consonantwith the Tenor's d, while the upper one prolongsc', whichis dissonantwith the Tenor's d but consonant withits comingf. That is confirmedwhen theupper "voice" repeats its figureagainst the Tenor's f in 7. The Tenor's move to f is moti- vated as the resolutionof the dissonantaltension in 6. Perhapswe oughtto considerthis sort of planningof the presentin view of the futureas a markof composed, as distinctfrom extemporized, music. Now we must focuson the progressionof the duplum melody fromanother point of view. It moves in two-and three-notedirec- tional unitsthat make the detailedcontours of the line, and thatco- incide withthe groupingof notesin ligatures.That is the notation, hence the rhythm,is an expressionof the melodiccontours. But it is an expressionof the voice-leading,as well. Thus in 2 the accented beginningsof the odd-numberedperfections are alwaysoccupied by thec; thatis wherethe dissonancesare mostconsistently resolved. In 3, wherethe main descent takes place, the stressed position of theodd- numberedperfections is occupied firstby f', then again by f', then by c', and finallyby f. I am proposing,with this interpretation,the followingreading of 3, in the more explicitnotation of W2: I .LL I I IJLJ rnLa

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All thisis to say thatthe principalnotes of the voice-leadingfall at the beginningsof alternateperfections. Rhythm and voice-leading reinforceone another as aspects of an integratedcompositional scheme. The transmissionof thispiece throughthe threesources is stable. The variantsthat occur are mainlynotational, and theycan be under- stoodin the lightof a clarificationof the essentialprocesses that have been observedto thispoint. In 3 the extrac' of F and W2 (i) makes foran easy continuationof the first-moderhythmic pattern. In W2 the binaria (ii) and the breve-long(iii) furtherclarify that pattern. In 4 the breve-longof W2 (iv) makesclear a second-moderhythmic pattern,and thefinal note withplica in F and W2 (v) in place of the binaria of W1 suggestsa reversalto ~ Pinstead of . That is con- sistentwith the tendencyto stressthe consonanttone. ,4 But it maybe that it simplymakes explicit what a performerwould have done in any case. That would be to suggestthat the notationof F and W2 is more prescriptivethan thatof W1. The clarificationsunder vi, vii, and viii are self-explanatory. In Examples4 and 7 we see the same kindsof changesthrough- out the sourcestoward a greaterexplicitness in the notation.The performerwas givenmore, and morespecific, cues. He could get his readingsmore directly, and his rangeof choiceswas narrowed.There is thisimportant difference: with Example 7 we can see the musical motivationfor this narrowingof the options.But the scribesof F, and especiallyW2, applied theirtechniques, and throughthem their attitudesabout the fixedstate of music and the role of notationin transmittingit, to theolder music (Ex. 4) as well as thenewer (Ex. 7.) We see twophenomena in theseexamples: the integrationof musical parametersin music representedby Example 7, creatinga pressure forexact transmission,and the habit of exact transmissionoperating independentlyas a phenomenonof notation,affecting also the writ- ing down of older musicfor which it was less essential.The musicof all stratais given a uniformredaction in the later sources,under assumptionsabout transmissionand performancethat are funda- mentallydifferent from those that prevailed during the early phase of the tradition. (This ratherreduces the appearance that these sources are sometimes said to have of "historical" collections, or as "anachronisms." For the notational clarifications presumably indi- cate that a performancewas intended, and that the tradition, there-

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fore,was still alive.) This situationis strikinglysimilar to that of the Frankishredaction of the Gregorianchant, in whichmusic that was originallya performer'sart in the makingas well as the render- ing, was graphicallyfixed on new principlesregarding transmission, therebyseparating the work from the performance.The modern scholar is obliged in both cases to read the musical scriptwith a versatileeye, penetratingthrough the fixedsurface to the fluidity of transmissionthat once obtained. One othermatter regarding the tendencytoward metrical phrase formationmust be taken into account,one which is ratherironic. We have alreadynoted that while the prosodythat was taughtin the ars metricaconcerned quantitative verse, it was accentualverse that poets had been composingand musicianssetting since Carolingian times. For the music, however,there is an essentialdifference. In quantitativeverse, the primaryconstraint on the line is the meter: the foot is definedas a particulararrangement of long and short syllables,and the lengthof the line is determinedby the number of feet.Because of the possibilitiesfor elision and substitution,two lines of dactylichexameter need not scan the same number of syl- lables. In accentualverse, the primaryconstraint on the line is the number of syllables,and the patternsof accentedand unaccented syllablesthrough which the poets ultimatelyimitated the ancient metersare articulationswithin isosyllabic lines. But it appears that whereaccented verse is concerned,isosyllabism has historicalpriority, and while stresswas a means of articulationfromi the beginning, stresspatterns became conventionallater.30 Here is an instructive examplefrom the tenth century:

O Roma n6bilis,/orbiset d6mina, cunctarum t'rbium/excellentissima, roseo mirtyruih/sanguinertbea, albis et virginui/liliiscAndida: salutemdicimus/tibi per 6mnia, te benedicimus;/salve per sa6cula.

The twelve-syllablelines are marked by an end rhymeand divided by a caesura afterthe sixthsyllable. Each half line rises to an accent on the antepenultimatesyllable and fallson the last two

30 Instructivereviews of thissubject are givenin Jonesop. cit.,and Dag Norberg, Introductiona l'dtude de la versificationlatine mddie'vale(Upsala, 1958).

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 554 The MusicalQuarterly unstressedsyllables. Occasionally that rhythmspreads through the entireline, giving it a dactylicmovement (11. 3, 4, and 6). But it would be an analyticaldistortion and historicallymisleading to attri- bute a dactylicmeter to thepoem as a whole. The lines are not built of dactylicfeet, but of isosyllabichalf lines with parallel contours in whichthe play of accentedand unaccentedsyllables has a major role.83 In the time of the ars antiqua, however,consistent accentual meterswere a normal aspect of syllable-countingverse. And these were associatedwith such rhythmicpatterns as are found in the modes- thoughnot alwaysin the mostobvious ways.The ironyis that, while theoristsof the thirteenthcentury explained modal rhythmas chainsof durationsfollowing the model ofclassical meters, the historicalinfluence that poetic formhad on musical rhythm seemsin practiceto have been of just the oppositekind. For it seemsthat the periodicorganization of musical time,like the structuringof the poetic line, proceededfrom the largerarticu- lation to the smaller. The proportionalorganization of durations withinthe phrase,like the breakingdown of the line into accentual meters,followed the articulationof an overallphrase structure. The introductionof musical meterfollowed the concern for symmetri- cal forms. With this historical perspective,the hypothesisthat modal rhythmwas invented(as distinctfrom explained) on the model of the ancient metersbecomes even more doubtful. I have argued that a historicalunderstanding of the theoryof modal rhythmrequires us to see in it a tensionbetween an additive rhythmicconception based on quantityand an analyticalone based on perfections.What evidenceis thereabout the stanceof practical musicianson thisissue? We can concretizethe question- and make a finalapproach to the nature of modal rhythm- througha question that has been much discussedin the literature:does the B in the second-mode patternB-L-B-L-B fall on an upbeat, or on a downbeat, [ J) P1

31 For a view of prosody based on stresspositions rather than meter, the reader is referredto the studies of Halle and Keyser cited in n. 18, and also to Martin Halpern, "On the Two Chief Metrical Modes in English," Publications of the Modern Language Association,LXXVII (June, 1962) 177-86.

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l)P?From the quantitative point of view that is not a coherent IPquestion. The secondmode was conceivedas a chain of singleB and L durations,in that order.There is no upbeat or downbeat in a quantitativemeter, there are only patternsof duration.So Franco wrotethat if one replacesan L in the midstof a first-modepattern with a rest of the same duration,the line will continueafterwards as secondmode:

And if one replacesa B in the midstof a second-modepattern with a B rest,the line will continueafterwards as firstmode: JJJ)J J J J...32 Modern scholarshave beratedhim for this. They chargehim with confoundingaccent and durationand insistthat the case in question simplycontinues as firstmode with an upbeat.33But here Franco had in mind the idea of mode as a series of durations,to which "upbeats" and "downbeats"are not relevant.He was simplyfollow- ing the accepteddefinitions of the firstand secondmodes. That this idea was still so stronglyimpressed on the mind of Franco must make a strongimpression on us, for it showsthat not even he had crossedthe conceptualthreshold beyond which it becomes easy to think of rhythmin relation to metricalorganization; and indeed it is difficultto thinkof it in any otherway. He was not mistaken, he was just not writingfrom our musicalvantage point. Usually we will not be contentwith a descriptionof a durationalseries as a statementabout rhythm.Examples 8 and 9 demonstratethis point.

Example8 AMIL IB I-I a - roundthe cob- bench the mon chasedthe wea - sel. The wea- All bler's -key etc.

Example9. TheSinecure Policeman (Highland Real)

i etc. :

32 Chap. IX. as Friedrich Ludwig, AfM, V (1923) 290; Oliver Strunk,op. cit., p. 150, n. 13.

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From a strictlyquantitative point of view, Example 8 begins, clearlyenough, with a L-B-L pattern,in the manner of the first rhythmicmode. But therewill be a tendencyto hear a movement fromthe B into the L, at firstbecause of the underlyingmotion g-a-b,and thatwill be stronglyreinforced beginning with the upbeat to the thirdmeasure. The groupingB-L, with stresson the L, is largelyresponsible for the rhythmic character of thistune. (We note at once thatthis sort of figure-groundrelationship between the pat- ternsB-L and L-B-L is somethingwith which metrics cannot possibly be concerned.) Example 9 also groupsmainly B-L and withoutany ambiguity, but it has a fardifferent rhythmic character that principally concerns the dispositionof the B-L groups with respect to the measure- especiallythe downbeat.The stressis on the B. We should identify the B-L rhythmin Example 8 as iambic (it moves fromunaccent to accent) and the B-L in Example 9 as trochaic(it moves from accentto unaccent;because of the durationalrelationship it is some- times called "reversetrochaic" or "'scotchsnap"). This rhythmis reallythe mostunambiguously trochaic one, forin thereverse series is alwaysthe eventualtendency to hear the "; ?J [ J) shortnote moving,[thereinto the long; that is, to group short-long;short- long,short-long, rather than the otherway round. It is preciselythis conceptionof rhythmicgrouping in relationto the accentsof the (musical)meter that is lackingin the explanationsof the thirteenth century.But wasgthis kind of relationshipnot at all involvedin the composingand hearingof the thirteenthcentury? There is a way of gainingat leastan impressionabout that. Walter Odington,as has been noted,linked the rhythmicmodes directlyto the poeticmeters, enumerated by Villa-Dei.With iambic verse he associatedthe second mode, with trochaicthe first,which takes the conceptionof rhythmicmodes as durationalseries to its mostliteral extreme. But in 1xample 9 we saw thata second-mode patterncan be apprehendedas a trochaicrhythm, with accentedB and unaccentedL, and in Example 8 thata first-modepattern may, at least,be dominatedby an iambicrhythm. (This differenceis ap- parentin the notationsfor the two modes.The secondmode begins in binariesexpressing B-L, which defineperfections. The finalter- nary ligature of the second mode brings the end of a phrase down on the beginning of a perfection. In the first-modenotation, the

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions Meterand Rhythmin theArs Antiqua 557 binariesalso signifyB-L but because of the initial ternary,whose initialand finalnotes begin perfections, they overlap the perfections. The notationindicates not onlythe durationalpatterns but also the rhythmicgroupings - and does so somewhatbetter than our nota- tion, with its way of settingbar lines inside of rhythmicgroups.) Now if there,is anyconsistency about the accentualverse meters that are declaimed,say, as second mode in the music of the thirteenth century,that should give some indicationwhether or not the musi- cians followedOdington's recommendations. For this,we mustlook at the syllabicsettings of Latin verse (French accentuationis un- certain)written in unambiguousmensural notation so thatwe may read thedurations without regard to thetext.

Example10. Mo fol.366 motet(duplum only)

q) " _ L Iu - re tu - is lau - di - bus

Sv ,I I Be-ne - vo-lis men - ti - bus, etc.

In thirteenth-centurysources, second-mode pieces of thatdescrip- tion set trochaicverses with such consistencythat we may safelysay that the second mode is treatedas a trochaicrhythm, with accented B and unaccentedL (Ex. 10). With thisknowledge, we can see that Franco understoodand intendedexactly what he said in the passage cited above. For the textin his example of second mode is trochaic and declaimedthus:

O Ma-riamater dei.

This showsexactly that separation of functionbetween accent and duration which Franco made explicit with his formulationof the consonancerule fordiscant (the beginningof the perfectionis con- sonant,whether it is L or B). Accentand consonanceare attributesof the initialposition of theperfection, which coincides with the initial elementof the modal foot,and is the position on which phrases normallybegin and end. Withinthe perfection,any arrangementof L's and B's is possibleand the resultingrhythmic groupings may be

This content downloaded from 159.149.103.9 on Sat, 6 Apr 2013 18:42:52 PM All use subject to JSTOR Terms and Conditions 558 The MusicalQuarterly containedwithin the perfections - as in the trochaicsecond mode - or overlapthem - as in theiambic first mode. Odington'slinking of the firstmode with trochaicmeter is per- fectlysound froma nominalisticpoint of view- it followsdirectly fromthe definition of mode as a seriesof durations,and of firstmode as the seriesL-B-L-B . . . L. That it does not correspondto practice is a furtherindication that this practicewas not inventedout of theoreticaldeliberations, and that the theoryof that time cannot simplybe read as instructionsfor performance.

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