Regarding Meter and Rhythm in the "Ars Antiqua"

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RegardingM etera nd Rhythm
in the Ars
Antiqua
LEO TREITLER
SHE rhythmici mpulse in music is a quality directlya ppre-
hended,a nd its projectionis a maina specto f thep erformer's
art. But when we conceptualizea bout rhythmw, e tend to thinko f
it as a functiono f timew hichw e expressm ainlyi n termso f duration
and successionE. xplainingr hythmth rought emporalc oncepts,p lac-
ing it under control in that sense as a compositionalf actor,a nd
devisinga notationt o signifyit are all achievementos f the practice
and theoryo f musici n the twelfthan d thirteentche nturies.
During that period,d urationc ame to be apprehendedt hrough
a systemo f proportionalm easurementa,n d the successiono f notes
assumed patternst hat depended on two kinds of configuration
at the same time: (1) groupso rientedw ith respectt o accents,a nd
(2) the backgrounda rticulationo f time in equal intervals;i n short,
the configurationosf rhythman d meter.I t is a historyo f the trans-
formationo f a performancper acticei nto a compositionalo ne, with
the attendantp rovisiono f a notationals ystema s the medium of
transmissionf romc omposert o performera; nd of the ultimately
successfuel xplanationo f theset hingsi n the preceptso f a theory.
The control of rhythma nd metere ntailed their coordination
witho therc ompositionalf actorsp, articularlym elodic phrasinga nd
harmonica nd contrapuntaol rganizationT. he historyo f rhythman d
meteri n that time is thereforeo nly an aspect of musical develop-
mentsi n generala nd it can be well understoodo nly in thatl ight.
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,P rofessorI an Donaldson, for the opportunityo f working there.
524
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Meter and Rhythmi n the Ars Antiqua 525
The coordination of time- and pitch-elementsp roduced 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 performersw ith 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 fullyb y William Waite - that ars antiqua rhythmw as derived
from the quantitative meters of classical prosody;1 and it contradicts
indirectly the view of Carl Dahlhaus that the modern rhythmics ys-
tem based upon meter and accent emerged only in the sixteenth and
seventeenth centuries as a result of transformationsi n mensural
rhythm. He characterizes mensural rhythm as "Zeitmessend" in
that rhythmicc onfigurationsa re 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,t hat the accentual
basis of rhythmw as established in the ars antiqua, but receded into
the background with the development of the more subtle time-meas-
uring rhythmf rom the fourteenthc entury on. How that occurred,
and what the shiftingr elations were between accent and duration
during the ars nova and Renaissance, are questions for furthers tudy.
My task here will be to argue for the claim regarding the nature of
rhythmi n the twelftha nd thirteenthc enturies.
In both practice and theory, the rhythmic conception of that
time was manifestedm ost prominentlya s a set of stereotypedr hyth-
mic patterns called "modes," hence the system itself is referred to
in the modern literature as "modal rhythm." It was expounded in
manuals writtena bout the second half of the thirteenthc enturya nd
transmittedi n practice through repertoryc ollections of which the
earliest surviving ones were written down during the same half
century- some fiftyt o seventy-fivye ears after the practice had been
1 The Rhythm of Twelfth CenturyP olyphony (New Haven, 1954).
2 "Zur Taktlehre des Michael Praetorius," Die Musikforschung,X VII (1964),
162 ff.
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526 The Musical Quarterly
establishedT. he repertorieisn volveda re the polyphonics ettingso f
liturgicalc hant( organum)a nd the polyphonicc onductusa nd motet
compositionos f the School of Notre Dame in Paris.
I
The basic notioni n modal rhythmis the measuringo ut of musi-
cal timet hrought her egulationo f long and shortd urations( "longa"
and "brevis,"t o be identifieda s L and B). In the earlieste xplana-
tion (De musicam ensurabilbi y Johno f Garland,c a. 1250)3t he ratio
of L to B is normallya s two time units to one. Those basic dura-
tions were paced out in repeatingp atternsa ccordingt o a number
of standardm odels or modes of rhythmicm ovement.U sually, six
rhythmimc odesa re identifiedin the treatisesin the followingo rder
(the descriptionis takenf romt he treatiseo f John of Garland):
The firsmt ode proceedsb ya n L, a B, and anotherL ,
and continuest husi ndefinitely.
The second,c onverselyb,y a B, an L, and anotherB .
The thirdb y an L and twoB 's and anotherL .
The fourthb y twoB 's, an L, and twoB 's.
The fifthen tirelyb yL 's.
The sixthe ntirelyb yB 's.
The basic configurationin each patterni s the foot (L-B in the
firstm ode, B-L in the second, L-B-B in the third,B -B-L in the
fourth,L -L in the fifthB, -B-B in the sixth).M odes 1, 2, and 6 are
called "measurable"b ecause theyi nvolve only the "correct"d ura-
tions (B of one time unit and L of two time units). These are the
building blockso f the systemi n the earliestc onceptions.M odes 3,
4, and 5 are "beyondm easure"b ecause theyi nvolved urationst hat
are beyondt he measureo f the "correct"v alues of the B and L (a
B of two time units,a n L of three).J ohnd escribest he L of three
time units as the sum of a correctL and B, whereasi n the later
explanationsb y Franco of Cologne (ca. 1280), it is a "perfect"L
and the durationals tandardf or all the modes (therew ill be more
to saya bout thisd ifferenclea ter).4
8E d. Erich Reimer as Vols. X and XI of the Beihefte zum Archiv fiir Musik-
wissenschaft( Wiesbaden, 1972).
4 Ars cantus mensurabilis,e d. G. Reany and A. Gilles, Corpus scriptorumm usica,
XVIII (1974), American Institute of Musicology. Trans. Oliver Strunk in Source
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Metera nd Rhythmin theA rsA ntiqua 527
That the descriptiono f modes 1-4c arriest hroughi n each case to
the firste lemento f the followingf ootr eflectst he concept of ordo.
An ordo is a melodics egmento r phrasei n one voice comprisingo ne
or more successivef eeto f a mode uninterruptedb y rests.T he theo-
ristsd istinguishedb etweenp erfecta nd imperfecot rdines,a ccording
to whethert he phrasee nds with the firste lemento f the footo r not,
respectivelyT. o speak of the second perfecto rdo of the firstm ode,
for example,w ould be to speak of a phrasec omprisingt wo feeto f
the first-modpea tterne, ndingw itht he long of a thirdf ootf ollowed
by a rest.S ince "perfect"i s synonymouws ith "complete"a nd "im-
perfect"w ith" incomplete,"w e learn fromt hisc lassificatiosnc heme
thatt herew as a normf ore ndingp hraseso n the beginningo f a foot
- that is that melodyw as understoodn ormallyt o move fromt he
beginningo f one foot to the beginningo f another. In Franco's
terminologyt,h atw ould be fromt he beginningo f one perfectiont o
the beginningo f another.W hen this conceptioni s consideredt o-
getherw ith otherss oon to be discussed,i t will be seen that under-
lyingt he concept of ordo is a conceptiono f melodym ovingf rom
downbeatt o downbeati n a triplem eter.
The conceptso f the foota nd the ordo are twof undamentacl har-
acteristicos f the modal systemt hat were for a time in opposition,
a situationt hatc reatedm uch difficultyO.n the one hand, therew as
the idea thata ll rhythmipc atternsw ere built up of the basic dura-
tionsL and B; on the other,t hatt he perfectionw, hateveri ts dura-
tional patterns,w as the basis of rhythmico rganization,a nd that
musicm ovedf romt he beginningo f one perfectionto the beginning
of another.M usical timei s measuredi n one conceptionb y sequences
of the basic durationale lementsl aid end to end, in the other by
higher-ordedru rationsa rticulatedi n patternso f lower-ordeorn es.
The term" mode" fora standardr hythmipc atternd enotesq uite
literallyb oth the sense of manner( a termt hat occursr egularlyi n
the treatisesa) nd that of norm.M anner reflectts he qualitative as-
pect of the conception;t he modes are distinguisheda s qualities of
rhythmimc ovement.
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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528 The Musical Quarterly
As forn orm,i t was not intendedt hatt he six modes should liter-
ally exhaust all rhythmicp ossibilitiesb ut rathert hat,a s concrete
modelsw iths everalp ossibilitiesf orv ariationa nd substitutiont,h ey
would sufficteo providet heb asis fort her angeo fp ossibilitiesN. ever-
thelesss ome theoristse,v identlyn ot satisfiedw ith these provisions,
specifieda dditionalm odesa s modelsf ore xceptionalc ases. This fact
suggestst hatt he modess hould be regardeda s crystallizationosu t of
a flexibler hythmipc ractice.F rancor eflecttsh e oppositet endencyo f
the latert hirteenthce nturyt o shiftt he emphasisa way fromt he dis-
tinctnesso f the modes and towardt heir commensurabilitoyn the
basis of the three-beat L - the perfection- from which he wrote
theyc ould all be derived.T hat amountedu ltimatelyt o an explana-
tion of rhythmicp atternsi n the contexto f what we would call
measuresr athert han modes. And it correspondst o a tendencyi n
the music of the late thirteenthce ntury- especiallyt he motets-
to break down the sharp distinctionbs etweenm odes and simplyt o
composei n triplem eter.
Modal rhythma rose in the contexto f polyphonicm usic, and
earliesto f all in the contexto f organum.F rom the beginning,it was
in thes erviceo f the sound ideal thati nformedt he principleso f poly-
phony:t he maintenanceo f a prevailingc onsonants onorityo ver and
above thec ontrastinogf c onsonancea nd dissonanceW. ith a rhythmic
conceptioni n which the centralp henomenoni s the alternationo f
long and shortd urations,t hats ound ideal translatede asilyi nto the
principlet hat the long durationss hould in the main be consonant,
and thata ny dissonances hould be short- somewhatl ike the inten-
tion of our idea of passingd issonanceT. his is the ways ome manuals
explained it. In what reads like an instructiont o performerws ho
sang the upper voice in a two-partm elismatico rganum,J ohn of
Garland wrote," Everythingt hat meets with anothera ccordingt o
thev irtueo fc onsonancei s to be long."5
Franco put the matteri n a characteristicalldyi fferenwt ay: in
thee ventt hata long note in theu pperv oiceo f an organumt hreatens
to makea dissonancew itht het enor,i t is not to be made short;r ather
the tenori s eithert o move momentarilyto a consonantt one or be-
come silent for the duration of the note.6 This providesf or the
integrityo f the rhythma nd phrases tructureo f the melody,w hile
5 Chap. XIII.
6 Chap. XIV.
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Metera nd Rhythmin theA rsA ntiqua 529
still satisfyingth e demand for consonance.E videntlyt hat integrity
had a greaterv alue forF ranco than forJ ohn,a nd perhapsw e may
conclude thath is attitudei s the more moderni n that he wishest o
leave such mattersa s rhythma nd phrase structurele ss open to the
discretiono f thep erformer.
The associationi n the treatiseo f Johno f Garland betweenc on-
sonancea nd duration,w hile understandablein view of the priority
of thec onsonancep rinciple,c reatedp roblemsF. or in the alternation
of consonancea nd dissonance,i t is consonancet hati s the goal; con-
sonance displacesd issonance,d issonancep reparesc onsonance.T his
dynamica spect of the consonancec oncept- -which aftera ll is in
the natureo f things- is apparenti n the language of the theorists.
Thus, Franco: "Immediatelyb eforea concorda ny imperfecdt iscord
soundsw ell." And AnonymousIV (ca. 1280,b ut afterF ranco): "[Of
two simultaneitiest]h e finalo ne musta lwaysb e consonant."'W ith
the associationo f consonancea nd duration,t he quality of arrival
transfertso the L, which createst he confusionb etweena ccent and
durationt hat flawedt he explanationso f John and his conservative
followersF. or in musical reality,t he resolutiono f a dissonanceb y
a consonance,i n the absence of any contraryc ues, itselfd efinesa n
accent,w hethert he durationo f the consonantn ote is long or short.
Francor ealignedt hea ssociationi n a wayt hatr esolvedt hec onfusion:
"In all modesc onsonancesa re alwayst o be used at the beginningo f
the perfectionw, hethert hisb eginningb e a long,a breve,o r a semi-
breve."8A s he sayse lsewheret, he perfectionis markedb y an accent
(although he does not make it explicit,e verythingp oints to the
presumptiont hat the accent is borne by the beginningo f the per-
fection).9F ranco's preceptr einforcets he sense of the beginningo f
the perfectiona s a point of arrivalt hatw as alreadyi mpliciti n the
concepto f ordo.
Now thiss econd of Franco'sf ormulationosf the consonancer ule
referst o discant,n ot organumA. nd ford iscantJ ohno f Garland also
had a differenrtu le: "All odd-numberedn otes should be consonant
witho ne another."'0I n effectt,h er ule applies to the firste lemento f
7 Anonymous IV, Part III in Der Musiktraktatd es Anonymus4 , ed. Fritz Reckow,
Beihefte zum Archiv fiir MusikwissenschaftI,V and V (Wiesbaden, 1967), 75, 1.4;
Franco, Chap. XI.
8 Chap. XI.
9 Chap. V.
10 Chap. XI.
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530 The Musical Quarterly
everyf oot( in the thirdm ode,t he two B's are counteda s one fort his
purpose).J ohn'st heoryi s thuse quivalentt o Franco's.B ut since his
theoryin generale xcludest hec oncepto f the perfectionh, is explana-
tion,h erea s elsewherei,s circumlocutionalB. oth formulationsh,o w-
ever, have the result that the demand for a prevailingc onsonant
sonorityi s to be satisfiedb y the principle that downbeats- the
beginningso f the perfectiono r the foot- jointlyc onstitutea chain
of consonancese quidistanti n time and therebyc reate a temporal
hierarchyT. oday we call such hierarchicalo rganizationm eter,b ut
the dependenceo f rhythmh, armonya, nd counterpointo n it then
was essentiallyth es ame as now.
The opposing statementso f John and Franco concerningt he
control of consonance in both organum and discant again point
to two fundamentalldyi fferencto nceptionsa bout the basis of rhyth-
mic organizationw hichw e have mentionedv eryb rieflyt: he simple
alternationo f long and shortd urationsi n a flatc hain and the hierar-
chicalo rganizationo f timet hroughm usicalm eter.I t is thed ifference
betweent he filling-inof unarticulatedt ime with fixedd urationso f
one and two beats,s trungo ut accordingt o traditionalp atternsa,n d
the groupingo f notes withint he invariableu nits in which time is
divided.I n the firstc ase rhythmis a mattero f the ordero f material
elements,t he durations.I n the second it is the creationo f formo r
order within the successiono f equal durations,t he perfectionos r
measures.
A directi nsighti nto the contrastb etweent he two conceptionsi s
affordedb y the correspondingex planationsa bout the two varieties
of L's (thosew itht wo and threeb eats).F or Johno f Garlandt he two-
beat long is the correcta nd true componento f rhythmicp atterns.
The three-beaLt is not a trued urationb ut a compositeo f thec orrect
L and B. For Franco the L that is measured" under one accent by
threet imeu nits"i s the perfectlo ng. The two-beatL is a derivative,
an "imperfectL" , a resulto f ther eductiono f a perfectL by a follow-
ing B. The perfectL is the commonc urrencyo f conversionf ora ll
modes. In the alternationb etweenc onsonancea nd dissonance,t he
consonancei s to fall at the beginningo f the perfectionC. onsidered
togethert, hesep receptso f Franco'sc an mean only thatr hythmf or
him was based on the perfectiont,h ati s on whatc orrespondts o the
modern three-beatm easure.
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Meter and Rhythm in the AirsA ntiqua 531
We can broaden the context for a moment in order to gain per-
spective on this differenceb etween John and Franco.
The conception of the B as a "short time" (tempus breve) or
simply as "a time" (tempus) satisfiest he 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 transmitst he brevis concept, wishes
at the same time to present the perfectL as a primaryq uantity. For
he recognizes its essential role in the rhythmics ystema nd its notation.
The perfection is the referenceu nit for all the modes; and it is the
primary division of time into perfectionst hat 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 referencea nd giving
all note levels from the B upward the perfecta nd imperfectf orms."
Presumably that was made possible by the shift of prevailing note
values from L's and B's to B's and semibreves,a nd by the end of a
rhythmicp ractice characterized by modes. From this theoretical van-
tage point, we can mark the conclusion of the period of modal
rhythmb y these changes.
The two conceptions regarding modal rhythmw ere mixed in the
theoryo f the thirteenthc entury,a nd that seems to have been respon-
sible for much of the disagreement and internal inconsistencyt hat
has made the theory as a whole so difficultt o 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 difficulta nd contra-
dictory ideas in an effortt o present coherent explanations and in-
structions.
The nature of the notational systemt ransmittedi n the practical
and theoretical sources of the thirteenthc entury follows from two
essential conditions of modal rhythm. First, modal rhythmi s men-
11 See the translationi n Strunk,o p. cit.,e specially the table on p. 177.
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532 The Musical Quarterly
sural, that is it entails the measuremento f time. Indeed the term
"modus" traditionallrye ferredto "measureb y length,c ircumference,
size, quantity."12T he modernc onventionalc haracterizationof the
theoristso f modal rhythma s "premensuralistsi"s quite misleading
and should be abandoned.S econd,t he modal systemis proportional,
that is the durationso f notes are regulatedt hroughf ixed propor-
tions (2:1, 3: 1).
In view of thesec haracteristicist, is the optimalf unctiono f the
notationv is-a-virs hythmt o indicatet o the singert he arrangement
of L's and B's that he is to follow,a nd whethere ach L and B is
"correct" (two and one beat[s],r espectivelyo) r "beyond measure"
(threea nd twob eat[s],r espectivelyW). e musts ay" optimal"b ecause,
takingt hen otatedN otreD ame sourcesa s a whole,m uch of the time
the notations etsu p a generalr hythmitcy pe,b ut leaves a more or
less wide range of details for the singert o settle in performance.
Indeed a fulld escriptiono f thats ystemm ustp resentit as functioning
throught he collaborationo f composern, otator,a nd performerw, ith
variablea nd uncertainb oundariesf ort her ole of each.
The significationo f relative duration relied on a number of
general principleso f which the followinga re the most important
fort hisd iscussion.
1. In the notation of melismaticm usic, the successiono f the L's
and B's was indicatedb y standards uccessionso f notationalf igures.
The followinga rrangement(ss ee p. 533) representt he six modal
patternss, ummarizedf romt he presentationo f John of Garland.13
(In each case, the reader should comparet he patternw ith the cor-
respondingd escriptiono n p. 526.)
2. The relativev alues of the L's and B's (whether" correct"o r "be-
yond measure")w ere to be determineda,c cordingt o John'sp ropos-
als, by the note's contexta mong other L's and B's, followingt hese
rules: all notesa re "correct"e xcepta n L precedinga n L (threeb eats)
and thes econdo f twoB 's standingb etweent wo L's (two beats) both
instanceso f whicha re "beyondm easure."'4O n reflectioni,t will be
seen thatt heser ulesc an be deducedf romt hem odal ligaturep atterns.
12 Charles Jones, "Carolingian Aesthetics:W hy Modular Verse?" Viator/Medieval
6r Renaissance Studies, Vol. VI (Berkeleya nd Los Angeles, 1975).
13 Chap. IV.
14 Chap. I.
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Metera nd Rhythmin theA rsA ntiqua 533
First: ?I
SecondN: IN
Third: r IRIN
Fourth:
NNI4 1I
Fifth:IK
Sixth: NA lor N
There is a clear driftt hroughoutt he thirteenthce nturya way
fr-omre lianceo n contextuali ndicationsa nd towardg reaterr eliance
on the shapes of the figures.C ompare Franco's ligature rules to
John's:b inaryl igaturesa re B-L; thosew itht hreeo r moren otesa re
B at the beginning,L at the end, and all notes in betweena re B;
withoutp ropriety(r eversalo f the normal presenceo r absence of a
stem)t he firstn ote is L; withoutp erfection( reversali n the position
of the last note in the ligature)t he last note is B.15T his gives the
values fora ll notesi ndividuallya nd independentlyr,e gardlesso f the
contexto f ligaturesa,n d of thec ontexto f L's and B's withinl igatures.
In the theory,t he change is neatly captured by the contrast
betweent hesef ormulationosf the relationshipbs etweent he modes
and the notationalf iguresJ. ohlno f Garland: "A figurei s a represen-
tation of a sound accordingt o its mode." Franco of Cologne: "A
figurei s a representationof a sound arrangedi n some mode. From
this,i t followst hatt he figureso ught to indicatet he mode and not,
as someh ave maintainedt, hec ontrary.""1
It requiress ome effortto understandt he radical natureo f what
was effectedin the realmo f notationd uringt he thirteenthce ntury.
And despite the differencbe etweenJ ohn of Garland and Franco
of Cologne,t he basic notionw as therea t the beginningo f the theo-
retical traditionJ. ohn wrotet his curiouss entence:" All simple fig-
15 Chap. VII.
16 John,C hap. II; Franco, Chap. IV.
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