arom time structure in the music of central africa

7/27/2019 AROM Time Structure in the Music of Central Africa

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Leonardo

Time Structure in the Music of Central Africa: Periodicity, Meter, Rhythm andPolyrhythmicsAuthor(s): Simha AromSource: Leonardo, Vol. 22, No. 1, Art and the New Biology: Biological Forms and Patterns(1989), pp. 91-99Published by: The MIT PressStable URL: http://www.jstor.org/stable/1575146 .

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T i m e Structure i n t h e M u s i c o fC e n t r a l A f r i c a : Periodicity, M e te r ,Rhythm a n d Polyrhythmics

Simha Arom

7IITe purpose of this article is to describe theprinciples underlying rhythm and polyrhythmics in CentralAfrican traditional music. Given the complexity of the sub-ject, it will be convenient to divide this discussion into fourparts: the first will describe the basic features of rhythm inCentral Africa, the second will deal with the temporal or-ganization that provides the governing framework, and thethird and fourth will take up the aim of this organization,namely, the production of rhythmic events and polyrhyth-mic structures.Before proceeding, I must distinguish between (1)rhythm as it appears in music in which relativized pitchesgive rise to a scalar system, i.e. any melodic music, and(2) rhythm appearing in a context where melody no longercomes into play and one encounters pure rhythm. Here, Iam concerned with the latter case.Pure rhythm maybe based on accentuation, on tone coloralternation or on contrasting durations. In Africa, as else-where, rhythm is produced by musical instruments (mostlyof the idiophonic or membranophonic types), but also byparts of the human body, e.g. by tapping one's foot on theground or clapping one's hands.

BASIC FEATURESIf one listens closely to a percussion group from CentralAfrica,one can perceive the basic rhythmic features that pre-vail in this region:*Steady, regular motion with no accellerandos, rallentan-dos or rubatos: Central African music is measured and

comprised of strictlyproportional durations.*The predominance of repetitive, uninterrupted formu-lae, in which similar material reappears at regular inter-vals, is evidence of strict periodicity.*The formulae one hears are not perfectly identical; therepetitive systemallowsfor a certain degree of variation.*The simultaneously performed instrumental parts donot give the impression of being ordered vertically, oneabove the other, but rather of being placed diagonally,according to a principle of crossing, or interweaving, ofindividual rhythms.*Central African music does not use a temporal refer-ence matrix based on the regular alternation of an ac-cented sound with one or more unaccented sounds.Consequently, it uses neither the notion of 'measure'nor the strong beat involved in this notion.For the listener, the interweaving of accents and tonecolors, together with the absence of a reference system ofregular accentuation, creates a feeling of uncertainty and of

? 1989 SASTPergamon resspic.PrintednGreatBritain.0024-094X/89 3.00+0.00

ambiguity regarding how thesubdivision of the period is per-ceived. This feeling can be com-pared to what one might feel ona train if one thought one hadcaught the rhythm of the 'click-ety-clack' but suddenly noticedan offsetting of the periodicrepetition: whatone had taken asa 'strong beat' marking the be-ginning of a new temporal cyclenow sounds like a 'weak beat'and vice versa. Something simi-lar happens when one listens forsome time to the binary cycle ofthe 'tick-tock' of a clock: thestress feature, which is first at-tributed to the 'tick' (TICK-tock), suddenly shifts onto the'tock' (TOCK-tick).The ambiguity is even greater

ABSTRACT

RhythmnCentralfricanmusics based nastrictlyeriodicstructure.he eriodsinternallyr-ganizedn wo evels:y hepulseand y heminimalperationalvalues. hythmonsistsn he m-positionfcyclicigures-withrwithoutariations-onnunderlyingperiod. hythmiciguresanbede-fined ya set offiveeatures:mark, urations,orphology,metricitynd tructure.he omi-nanthythmiceaturenCentralAfricas a contrametricelationshipto thepulse,whichreates nantag-onismetweenherhythmicalevents nd heiremporalrame-work.olyrhythmicusic esultsfromhe nteractionf woormoresuperposedhythmicigures, hichmay aryndimensionsuthave e-riodstandingn impleatios,nditsdominanteaturesthe nterweav-ingofaccents,one olors nd/orattacksf he imultaneouslyer-formedigures. his ives ise oaconflictetweenhythmndrhythm,hichscoupled ithheantagonismetweenhythmndmeterharacterizingach ndividualfigure.Manyf hephenomenadescribedn hispaperre urrentover much iderrea f sub-Saharanfrica.

in the case of a ternary period. Thus, an unaccented figurewith two sounds of equal value and a rest of the same dura-tion can be perceived in three different ways:

In none of the three cases, however, has the articulation ofthe periodic cycle been changed in any way. The onlychange is in one's perception, in the Gestalt extracted bythe mind from invariant data. Byitsveryregularity,an acous-tic form will create this feeling of uncertainty and allow itselfto be organized perceptually in different ways.

PERIODICITYAperiod is a temporal loop based on "the recurrence of simi-lar events at similar intervals"[1]. All Central African musi-cal manifestations are based on a principle of periodicity.Levelsof OrganizationThe period provides a temporal framework for rhythmicevents. It is always composed of whole numbers, generallyeven ones (2, 4, 6, 8, 12, etc.), i.e. divisible bytwo. This meansSimha Arom (ethnomusicologist), Laboratoire de Langues et Civilisations a TraditionOrale, Centre National de la Recherche Scientifique (C.N.R.S.), 44 rue de l'AmiralMouchez, 75014 Paris, France.Received 16 March 1988.

LEONARDO, Vol. 22, No. 1, pp. 91-99, 1989 91


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A A A A

I IFig. 1. The macro-period (at the bottom) provides the sole point of junction that iscommon to all the superposed periods shown above it.that the period has a symmetricalstructure, which can be measured bythe pulse.The pulse is an isochronal standard,which is used by Central African cul-tures as the unit of reference for themeasurement of musical time. It pro-vides a series of regular referencepoints for ordering rhythmic events.In polyrhythmic music, the pulse is thecommon regulator of temporal or-ganization for all the parts. It is thusthe basic unit of time according towhich all durations are defined. InCentral Africa, however, the pulse israrely materialized. While it is alwayspossible to give it the concrete form ofhandclaps, it is nevertheless moreoften implicit, i.e. underlying.The pulse can be subdivided inthree different ways: he subdivision isbinary when the pulse splits into twoor four equal parts; it is ternarywhenthe pulse splits into three (or rarelysix) equal parts; and it is compositewhen the pulse splits into five equalpartsbya combination of the two pre-ceding (binaryand ternary) types.Thesmallest operational value equals theshortest relevant duration, in com-parison to which all the other dura-tions are multiples. The period thuswill equal the total number of thesevalues, e.g. a period of 12 pulses willhave 36 operational values if the divi-sion is ternary,and 24 (or 48) if the di-vision is binary.The importance of how the pulse issubdivided for understanding rhyth-mic organization in CentralAfricawillbecome apparent later. Metricallyspeaking, the period is thus twice sub-divided, into the pulse and into itsoperational values. It is important tonote the absence in this organizationof an intermediate level between theperiod and the pulse, consisting of aregular accent scheme, known as the'measure' in Western music, with acharacteristic strong beat. Since thereis no such phenomenon in the music

of the majority of the peoples of Cen-tral Africa, the time-units that theperiod comprises are all of equalvalue.On Diversityof PeriodicitiesThe foregoing discussion concernsthe metric organization of the periodas a temporal frameworkfor rhythmicevents. In African music, however, it iscommon for several rhythmic eventsto take place simultaneously: this iswhat is known aspolyrhythmics, whichwill be discussed later. For the timebeing, it need only be remarked that,in a polyrhythmic context, the super-posed rhythmic figures are of varyingdimensions but stand in simple ratios,such as 2:1, 3:1, 3:2, 4:2 and multiplesthereof. As far asmetrics is concerned,this means that different periodicforms will also be superposed. It there-fore will be necessary, hereafter, to usethe term 'period' in the plural, or, tobe more precise, to speak of 'peri-odicities', and to introduce two newterms: 'amplification' and 'macro-period'.By amplification, I mean the proce-dure by which the rhythmic materialof a period is developed sporadicallyover a number of periods, which is amultiple (generally the double ortriple) of that period. Thus, a periodof four pulses can be transformed fora few loops into a cycle of 8, 12 or,more rarely, 16 pulses.By macro-period, I mean the cycleresulting from the superposition ofperiods of different dimensions, all ofwhich are smaller than the dimensionof the macro-period. Such is the casewith two or more periods in a 2:3and/or 3:4 ratio. The macro-periodthen provides the sole point of junc-tion that is common to all the super-posed periods (Fig. 1).A few words on tempo are requiredbefore concluding this section, fortempo is the unavoidable concomitantof the pulse as the basic structural ele-

ment of all periodicity, i.e. insofar as itprovides the determining standard oftemporal reference.Tempo is the expression of theinner motion (or speed) of a piece ofmusic. That the motion of Central Af-rican music is extremely regular hasbeen shown by comparing severalrecordings, made over a period of 7years, of identical pieces played bythesame musicians. Metronomic meas-urements showed that, in all cases, thedifferences in tempo from one per-formance to the next were negligible,even when several years had inter-vened [2]. Thus, for a given piecewhere a quarter note is taken as themetronomic reference unit, the tem-po will not varymore than from 148 to156 oscillations per minute.These observations confirm the re-markable intuition of Andre Souris,who, more than 20 years ago, wrote:"One may assume that in civilizationsthat lack writingsystems, the tempo ofhighly structured music can be orallytransmittedwith the highest degree ofaccuracy" [3]. They also corroboratethe more recent observations of DavidEpstein, who describes the strikinghuman abilityto conserve a time stan-dard in a sort of organic memory like"a highly accurate biological clockmechanism" [4]; this seems to de-scribe exactly what happens.

RHYTHMICORGANIZATIONHaving discussed the metric aspects ofthe various levels of periodicity, i.e. itsfunction as a framework of temporalreference, I will now turn to the rhyth-mic organization of the period, i.e.how rhythmic events are distributedwithin this framework, or, to be moreprecise, how they are divided and ar-ranged into cells and configurations,and what principles underlie these ar-rangements. Thus, from now on, I willbe dealing with rhythmic figures.The ConstituentFeaturesofRhythmicFiguresA rhythmic figure can be defined byaset of features that fall into differentcategories or orders. There are fivesuch orders: mark, durations, mor-phology, metricity and structure. Theorders are organized so that each con-tains no more than one feature. Thisis to saythat a feature belongs solely toone order and that a set of five featuresis necessary and sufficient to describe

92 Arom,Time Structure in the Music of Central Africa


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any rhythmic figure from the region Iam discussing.Mark. The mark is the basic toolused to segment any rhythmic se-quence. If a sequence of percussionsis to be accounted a rhythmic figure,at least one of its constituents must bemarked. There are three kinds ofmarks-accentuation, tone color al-ternation and contrasting durations-one of which will be used to breakdown figures into their constituentparts: cells and configurations. A se-quence of at least two sounds is re-quired for a cell or a configuration toexist. In other words, a single isolatedpercussion may never be treated as aconstituent unit of a rhythmic figure.In accentuation, segmentation isbased on the recurrence of accents,i.e. on the time interval separating twoaccented sounds within the same fig-ure (Fig. 2). Clearly, if there is onlyone accent, the figure containing itcannot be split into parts. In such acase, one must look for one of theother marks.

Segmentation of unaccented fig-ures maybe based on marking bytonecolor alternation. Cells and configura-tions here are bounded by the recur-rence of at least one sound with a tonecolor differing from that of the pre-ceding sound. When a figure containsonly one sound with a different tonecolor, another mark must be sought;for only when at least two sounds aredifferent in tone color from the otherscan it be said that change of tone coloris used as a mark.When there is no accent and theconstituent sounds of a rhythmicfigure are not distinguished by tonecolor contrast, the alternation of dura-tions-i.e. contrasting durations, thesimilarityand/or difference of valuesand their arrangements-providesthe sole basis for segmentation.Durations. The durations compris-ing a rhythmic figure may be equal orunequal. At first glance, this remarkmayseem trivial;yet, for the importantand still often obscure problem ofmaking a precise distinction betweenmeter and rhythm, it is not without sig-nificance. Thus, a sequence of equalunaccented values with no tone colordifferentiation, such as the sequenceillustrated in Fig. 3a, is in fact a metriccontinuum, but it lacks one of the twoindispensable attributes for it to beconsidered rhythmic. It would firsthave to be marked, either by accents(Fig. 3b) or by tone color differentia-tion (Fig. 3c).

I I : J n m m\ a A c A d /

J - mna b ^ aX

r m n n . n a nm\ a b aa c I

Fig. 2. In accentuation, segmentation is based on the recurrence of accents, i.e. on thetime interval separating two accented sounds within the same figure.

iJJJ 1 : i i

Fig. 3. A sequence of equal unaccented values with no tone color differentiation (a) is ametric continuum,but to be considered valuesrhythmict wod haveoe coloremarked by ccent(a) is ametric continuum, but to be considered rhythmic it would have to be marked by accents(b) or by tone color differentiation (c).

Morphology. The form of a rhyth-mic figure is determined by the con-figurations and cells that it comprises.These figures may be classified as uni-tary,uniform or multiform.A figure is unitary when it containsonly one configuration; in such cases,there is no distinction between celland figure (Fig. 4a). A figure is uni-form when it is based on the repetitionof an identical cell or configuration,whose position nevertheless varieswith respect to the pulse each time itrecurs (Fig. 4b). A figure is multiformwhen it contains twoor more differentconfigurations (Fig. 4c).Metricity. There are five features bywhich the relationship of any rhyth-mic figure to the pulse can be defined.This relationship can be commetric orcontrametric [5]. Both these typescanbe either regular or irregular; how-ever, the metricity also can be mixed.A figure is commetrically arrangedwhen the accents, changes of tonecolor or (failing these) the attackstend to coincide with the pulse. Com-metricityis regular if all the accents, ormore than half of the tone colorchanges or attacks, coincide with thepulse, and if no sound produced off-beat overlaps the following pulse (Fig.5a). It is irregular whenever a stressedsound is off-beat, and/or whenever

less than half of all the sounds that areoff-beat overlap the following pulse(Fig. 5b).A rhythmic figure is contrametri-callyrelated to the pulse when accents,tone color changes or (failing these)the attacks occur predominantly off-beat. Contrametricity is regular whenthe marked element is invariablyfound in the same position withrespect to the pulse (Fig. 6a). Contra-metricity is irregular when the posi-tion of the marked element with re-spect to the pulse is not systematicallythe same (Fig. 6b).Structure. A rhythmic figure canhave a symmetric or asymmetric struc-ture (the latter of which can be eitherregular or irregular); however, on rareoccasions, it also can have a structurethat I will call 'indivisible'.A structure is symmetric when it canbe divided into two equal parts,starting from the position of at leasttwo of its accents, tone color alterna-tions or attacks (Fig. 7a). A structureis asymmetric when no such segmen-tation is possible, given the position ofthe accents, tone color alternation orattacks.

Asymmetry is regular when thecycle can be split on the same basisinto any number of equal parts otherthan two and multiples thereof

Arom,Time Structure in the Music of Central Africa 93


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aaccents ||: j :tonecolor :j - - :11durations ,,; 4F. J :

b L IaccentsIi:n J_:11

tone color I I I

\ a A a adurations L I

\ a A a A acaccents

tone color

: 1 1

bn n n

n m : n n r . n : \ \

II: J. 1I

I LI I Im jJ13a Ab!A c A d

I I I I I1a b /

\ a A b

Fig. 5. (a) Com-metricity is regularif all the accents,or more than halfof the tone colorchanges or attacks,coincide with thepulse and nosound producedoff-beat overlapsthe followingpulse. (b) Com-metricity is ir-regular whenever astressed sound isoff-beat and/orwhenever less thanhalf of all thesounds that are off-beat overlap thefollowing pulse.

(Fig. 7b). In Central Africa, regularasymmetry generally is based on therepetition, within the rhythmic figure,of a single cell or configuration, withits position with respect to the pulsebeing offset each time it recurs. Thisoffsetting is the result of a constantratio between two different arithmeticprogressions, one metric and theother rhythmic. This is precisely theprinciple of the hemiola (Fig. 7c).

Asymmetry is irregular when thefigure contains two or more configu-rations that cannot be divided intoequal parts (Fig. 7d).A particularform of asymmetrythatis frequently found in CentralAfrica isrhythmic oddity. This term applies toperiods for which an even number isobtained when the number of pulsesis divided by two. Figures under thisprinciple are so arranged that when-ever their rhythmic content is seg-mented as closely as possible to thecentral dividing point, the two result-ing parts will be composed of an oddnumber of minimal values. Thesefigures are always formed by irregu-larlyjuxtaposing binary and ternaryquantities. They thus give rise to sub-tle and complex rhythmic combina-tions. They respect a rule that mightbe called 'half - 1 / half + 1', as il-lustrated bythe following examples. Afigure of this kind with eight minimalvalues, i.e. which is a total of twobinarypulses, divides up as follows (Fig. 8a):

3/3.2=3/5=4-1/ 4+1.A figure contained in a period of 12operational values arranged into fourternary pulses can yield (Fig. 8b):

5/3.4 = 5/7 = 6- 1 /6 + 1;or (Fig. 8c):

3.2/3.2.2 = 5/7 = 6- 1 / 6 + 1.A four-pulse figure divided into 16minimal values presents the followingorganization (Fig. 8d):

3.2.2/2.3.2.2 = 7/9 = 8- 1 / 8 + 1.Finally, an eight-pulse cycle dividedinto 24 operational values yields thefollowing arrangement (Fig. 8e):

3.2.2.2.2/3.2.2.2.2.= 11/13=12-1 / 12 +1.But, as Fig. 8f shows, it can also be ar-ranged differently:

2.3.3.3/2.3.3.2.3=11/13=12-1 / 12 + 1.


durations I I I I I I I III: J. J J J. J. J. J J. 1l

\ a A b A c

Fig. 4. A figure is unitarywhen it contains only one configuration (a), uniform when it isbased on the repetition of an identical cell or configuration (b), or multiform when it con-tains two or more different configurations (c).


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Rhythmic oddity works by a prin-ciple of enlargement based on the pro-gressive insertion of binary quantitiesin configurations bounded by ternaryquantities. This is apparent from theparadigmatic representation of itsfunctioning shown in Table 1. Thefigure illustrated in Fig. 8f (2.3.3.3/2.3.3.2.3) applies the same principle,but in reverse, for here ternary quan-tities are inserted in configurationsbounded by binary values.Finally, a structure is called indivis-ible when it contains only one dura-tion. This case, though extremely rare,can appear in a polyrhythmic context(Fig. 8g).Combination of ConstituentFeaturesA rhythmic figure, as mentioned, ismade up of a set of features. These fea-tures (17 in all) are distributed amongfive different orders. Since a featurecannot belong to more than oneorder, it follows that five features arenecessary and sufficient for the defini-tion of any rhythmic figure, as the fol-lowing examples will show.Figure 9a, which is taken from aBanda-Linda piece performed by thedrum called 'the husband', can be de-scribed as follows: it is marked by ac-cents, it is composed of unequal dura-tions and it is multiform andirregularly contrametric but sym-metric. Figure 9b, performed by thedrum called 'the mother', is super-posed on the preceding one. It has allthe same features as the 'husband's'figure but one: its structure is irregu-larly asymmetric.The next twofigures, which are em-ployed byeach of two double bells, sus-tain a repertory of Ngbaka songs ac-companied on the harp: The first ismarked by tone color alternation andhas unequal durations, its morphol-ogy is uniform, its metricity is mixedand its structure is symmetric (Fig. 9c).The second has the same mark andalso contains unequal durations; how-ever, its arrangement is multiform, itsmetricity is irregularly contrametricand its structure is irregularly asym-metric (Fig. 9d).Once one has established a list offeatures that characterize a rhythmicfigure, it becomes possible to set up atypology, for the recurrence of a set offeatures in different figures allowsthem all to be placed in a single cate-gory.

I would conclude this study of thevarious ways of organizing rhythmic

a

baccents

tone color

durationsII

I I L K Il. I_ j : _ 1 1s--11Fig. 6. (a) Contrametricity is regular when the marked element is invariably found in thesame position with respect to the pulse. (b) Contrametricity is irregular when the positionof the marked element with respect to the pulse is not systematically the same.material in Central Africa by sayingthat the dominant characteristic ofrhythm is a strong tendency towardscontrametricity, which gives rise to anunceasing conflict between the metricstructure of the period and the rhyth-mic events it contains.

POLYRHYTHMICSPolyrhythmics is the coherent super-position of two or more rhythmic fig-ures, each of which is arranged in sucha waythat the configurations compos-ing it (as defined by accentuation,tone color alternation or contrasting

durations) are inserted in those ofother figures, so as to create an effectof constant interweave. While all thesefigures have a common standard oftemporal reference, i.e. the pulse, theyare contained in periods of varyingdi-mensions, which nevertheless stand insimple ratios (1:2, 1:3, 2:3, 3:4) to oneanother.The various superposed configura-tions alwaysmove along in a fast tem-po. The result is a permanent state oftension deriving from the antagonismamong the different figures. This an-tagonism shows up simultaneously intwoways:I already remarked that each

Table 1. Paradigmaticrepresentationof the functioningof rhythmicoddity. Rhythmicddityworksbya principlef enlargement asedhereontheprogressivensertion f binary uantitiesnconfigurationsounded yter-naryquantities.Cycleof 8 minimalalues ] f3 2 .Cycleof 12 minimalalues F 2 2 . 2.Cycleof 16 minimalalues 3. 2. 2 F 2 . 2 . 2 .Cycleof 24 minimalalues 2 .2. 2 [32.2.2.2.2.

Arom,Time Structure in the Music of CentralAfrica 95

II:J |'11I: J J J J :11l. I I II : n n :11

t I l i IInLT j I ' n n r n 11

ls lv lo to1. w . . .W


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aaccents

tone color

duration

b

II:II:

caccents II:tone color I1duration II:

daccents I1:tone color

II:duration II:Fig. 7. (a) Astrufrom the positiolAsymmetry is regequal parts otherregular asymmetsingle cell or contime it recurs. Thmetic progressiothe figure contai

I I I I I I figure, taken individually, is in conflicti>^~~~~~~n~~~ -- -^^ nwith the temporal organization of thenJnn Jn 3' " J .|| period, i.e. its metric structure; how-L 8 s \ I ever, in a polyrhythmic context, theconflict between rhythmic elementsl|\ l|~| l| l| l| l| l and metric elements is conjoined withI i . i k . ^ another conflict, that between rhyth--J4 J. J l ) JiJ ~S . micelementsandrhythmic lements,12 1 12 ' specifically, between the content ofeach figure and that of all the others.

I l l l e This can be seen from the two poly-|Jmn~ rJ m~ (~ r .n n |1w~ ~rhythmic formulae transcribed in Fig.J j3. ^. 3.:|| 10 6].I ~~~~~6116The first is taken from the agaterumo ritual music of the Banda-Lindal 1 I I I I | (Fig. 10a). Close observation of thisI|~ |I 1( I I~ i~ X~~ formula reveals the following:'* i I' J .' J. J J :11 * Itcontains wo evelsofperiodicity8 1 8 1 8 | in a ratio of 1:2; the figures pro-duced by the first two drums and3 1 33 3 3 | by thejingles establish a two-pulser I'- l | | e fT-T-a cycle, while the third drum has4m m pT Tli only one pulse.lI4~~~ ~~4 l 4 l '~*n the drum parts, the pulse isdivided into five minimal values|3 3 3 |3 | arranged in binary and ternaryquantities, while in the jingles4*-J- I~~~J J49~~4J ^J, ~||part, its division is perfectly bi-I*1 4 |nary. * The four superposed figures use|3 3 3 3 |two different marks: the first two3;3| X i|drum parts have no accents orJJ.' ~ ' : tone color change whatsoever, butl [ 4 I 4 1 are marked by attacks, while thethird drum and jingles parts aremarked by accents.I I| | I I3 *The rhythms herefore are inter-I,j?T]I , , ,woven on two levels at the same1 6 5 15 i time: first, the two unaccentedparts, one with the other, andthen the parts marked by accents,

l| I~~~~~ l ii | I ~ while the formula as a whole as-, I l I I I i Isociates these two forms of inter-J~ J J.3 J . L-J.J J ,,11weave.7I 1 1 I * There is one simultaneous percus-sion by all three drums; their partsl|I~~~ l(~~~~ g~ ~therefore are partially inter-[ [[ woven.4! J J11 *Since thejingles figure is based on3 1 3 2 I a binary division of the pulse, it fol-

lows that its accent does not coin-cide with any of the drum-partcture is symmetric when it can be divided into two equal parts, starting percussions: it therefore is com-n of at least two of its accents, tone color alternations or attacks. (b) pletely interwoven with them.,ularwhen the cycle can be split on the same basis into any number of * The figure performed by the firstr han two and multiples thereof. (c) The principle of the hemiola: drum regularly adjoins two fol-rygenerally is based on the repetition, within the rhythmic figure, of a lowed by three quantities, thusfiguration, with its position with respect to the pulse being offset each contrasting with the arrangementis offsetting is the result of a constant ratio between two different arith- r teof the accents of the third drum,ns, one metric and the other rhythmic. (d) Asymmetry is irregularwhen he cc s te r runs two or more configurations that cannot be divided into equal parts. which performs an equally regularsuccession of three followed bytwo quantities. Meanwhile, thesecond drum alternates these two

arrangements: each of the twopulses that make up its figure



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shows a different arrangement,the first being three plus two, andthe second, two plus three.The second formula is the poly-rhythmic support for a piece from thembenzeleance music repertoire of theAka pygmies (Fig. lOb). This formulahas four parts, which are distributedamong three drums and a pair of ironblades, which are struck together. Thefollowing observations can be made:* It contains three different periodi-cities: the figures performed bythe second drum and the blades

provide the longest period ofeight pulses; the first drum plays afigure based on four pulses, whilethe third plays the shortest, withonly one pulse.*The metal blades have neither ac-cents nor tone color change, un-like the three drums, which are allmarked by accents.*The accents of the second andthird drums are simultaneous;their parts are distinguished bytheir content.*The first drum playsan irregularlycontrametric hemiola-type figure;it stands in a 2:1 ratio with thefigure of the second drum, and ina 1:4 ratio with that of the third;its accents are partially nterwovenwith those of the other two drums.*Finally, the blades perform a fig-ure of the same dimensions as thatof the second drum; this figurestands in the same ratio to theparts of the first and third drumsas the figure of the second drum.As a result of the clear and pene-trating sound produced bythe twoblades striking against each other,some of the attacks, which are in-terwoven with the accents of theother parts, stand out sharplyfrom the whole.The degree of complexity of a poly-rhythmic piece is not a function of thenumber of parts alone. It can depend

equally, if not more, on the internalorganization of each one. Thus, themore ambiguity (contrametricity,asymmetry and, above all, rhythmicoddity) there is in the rhythmic con-tent of the superposed figures, themore complex the resulting poly-rhythmics will be.The following example provides aneloquent illustration of this fact. Thepolyrhythmic basis for the zoboko itualmusic of the Akas employs two figureswhose periodicity is identical. Thefirst, called mokongo Fig. lla), is per-formed by several crouching men,

a

3 121

b I I1 131 412

I 2) 21 3 1 2)2e

f

g

II: J J J J JJ. J J J J J :111 3 12 21 2 2 1 3 12 1 21 2 21 2 1>. , ) .- > -> >I I : F m m n m m n m1 2 1 3 1 3 1 3 1 2 3 1 3 21 3 1I I

Fig. 8. Rhythmic oddity: periods for which an even number is obtained when the numberof pulses is divided by two. (a) A figure of this kind with eight minimal values. (b, c)Figures contained in a period of 12 operational values arranged into four ternary pulses.(d) A four-pulse figure divided into 16 minimal values.(e, f) Eight-pulse cycles dividedinto 24 operational values. (g) An 'indivisible' structure, i.e. one containing only oneduration, can appear in a polyrhythmic context.

Fig.9. Fivefea- a I I Itures are neces- I Isary and suffi-

n n1cient orthe 4definition of any Irhythmicigure. b I I

c I

d I I Iz D l

dl l l

117M,6 l I,Arom,Time Structure in the Music of Central Africa 97


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I I I: C r: -Li- :V ;r KI I Ix 11, %I

I I > I- Li- l

J 138 I I1 1 . I> > I r I .-

Fig. 10. In a polyrhythmic context, the conflict between rhythmic elements and metric ele-ments is conjoined with the conflict between rhythmic elements and rhythmic elements,i.e. between the content of each figure and that of all the others, as seen in the polyrhyth-mic formulae transcribed: (a) from the aga terumo itual music of the Banda-Linda; (b)from the mbenzeleance music repertoire of the Aka pygmies.

who, in unison, strike hard woodensticks against a tree trunk lying on theground. The second, diketo(Fig. 1b),which also appears in the precedingexample, is performed by one person,who strikes two iron blades together.Before examining the wayin whichthese two figures are superposed, itwill be helpful to compare their re-spective constituent features. Mokongois marked by accents, and diketoby at-tacks.The durations in mokongo re allequal, while those in diketoare un-equal. Both have a multiform mor-phology, an irregularly contrametricrelationship to the pulse, and an asym-metric structure. However, mokongo'sasymmetry is regular, while diketo's sirregular.Of the five features, two are thesame and three are different. Bothfigures are based on the juxtapositionof binaryand ternaryquantities. Whileternary quantities appear in mokongoin the interval between single binaryunits, the opposite occurs in diketo,where binary quantities are insertedbetween the two isolated ternary ele-ments used in this figure. The inser-

tion of binary quantities to fill thespace between the two ternary units isprecisely what makes it possible to seg-ment this figure into two cells of 11and 13 values, respectively. Since theperiod has a total of 24 such values,diketo is not only irregularly asym-metric, it also obeys the rules of rhyth-mic oddity: 'half- 1 / half + 1'.Mokongoalso follows this rule, but,unlike diketo, ts asymmetryis regular.In fact, it can be divided into threeequal parts, each with eight minimalvalues:

3.3.2/3.2.3/3.3.2.Only two cells are used for these threesegments, one of them (3.3.2) occur-ring twice. But while the two occur-rences of this cell are identical as faras rhythm is concerned, this is not sowith respect to metricity, for the cellchanges its position in relation to thepulse (Fig. llc).If one superposes the two figures,one obtains the formula for the zoboko(Fig. lld). The polyrhythmic natureof this formula is based on the inter-weaving of certain mokongoaccents

with diketoattacks, to which the iso-chronal handclaps (which, in this par-ticular case, materialize the pulse) areadded.The period comprises eight pulses.Mokongohas nine accents; of these,three commetric ones coincide natu-rallywith the beat, while the other sixare irregularly contrametric. In the di-ketopart, five attacks are commetric;the other eight are irregularly con-trametric. However, mokongo'scom-metric accents do not all coincide withdiketo'scommetric attacks. A look atthe formula shows that the commetricaccents and attacks coincide onlytwice, on the first and third beats; else-where, they are interwoven.The interweaving of the quite dif-ferent sounds produced by these twoinstruments contrasts with the regu-larity of the beat; moreover, it confersa rhythmic function on the beats thatdo not coincide with a mokongo ccentor with a diketoattack, for the hand-claps that materialize them are them-selves interwoven with some mokongoaccents and diketo ttacks.The interac-tion of these three different kinds ofsound thus will be perceived as a poly-rhythmic entity of three interwovenparts from which one mokongo ccent,three diketo ttacks and two irregularlyspaced handclaps stand out separately(see Fig. 12a).These various percussions stand outfrom the continuum of the formula,which, let it be remembered, consistsof uninterrupted drumming of taps ofequal durations, interspersed with theirregularly spaced accents of mokongoand the irregularly asymmetric strik-ing of the iron blades.As for the remaining marks, besidesthe two percussions that are simulta-neous to the three parts, there are 11combined percussions: five commonto mokongo nd diketo, ne common tomokongo nd the handclaps, and threecommon to diketoand the handclaps.When one adds the six isolated percus-sions, one finds, for a cycle of 24 min-imal values, a total of 17 rhythmicevents, which make use of seven differ-ent combinations of three tone colors(Fig. 12b).In concluding, let me mention thatall these phenomena whose complex-ity I have just examined interact at atempo of J- = 144, which means thatthe entire cycle in which they takeplace lasts barely 4 seconds.


>.. 15o

a

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SUMMARY ANDCONCLUSIONRhythm in Central African music isbased on a strictly periodic structure.The period is internally organized ontwo levels: by the pulse, a sequence ofequal standard units serving as tem-poral points of reference and exclud-ing a regular strong beat; and by theminimal operational values, which de-rive from the way the pulsation is sub-divided into binary or ternary (some-times binary and ternary) quantities.

Rhythm consists in the impositionof cyclic figures (with or without vari-ations) on an underlying period.Rhythmic figures can be defined by aset of features that fall into five orders:mark, durations, morphology, metric-ity and structure. The dominant rhyth-mic feature in Central Africa is a con-trametric relationship to the pulse,which creates a contrast between therhythmical events and their temporalframework. This relationship appearsin the form of regular and irregular(hemiola-type) contrametricity andrhythmic oddity.

Polyrhythmic music results fromthe interaction of two or more super-posed rhythmic figures, which mayvary in dimensions but have periodsstanding in simple ratios: 1:2, 1:3, 2:3,3:4 and multiples thereof. The domi-nant feature of polyrhythmic music isthe interweaving of the accents, tonecolors and/or attacks of the simulta-neously performed figures. This givesrise to a conflict between rhythm andrhythm, which is coupled with the an-tagonism between rhythm and metercharacterizing each individual figure.

Many of the phenomena describedin this paper are current over a muchwider area of sub-Saharan Africa. Therhythm of Central African traditionalmusic is remarkable in its ability to ob-tain such complex, subtle, varied andyet strictly coherent systems, with avery limited number of elements.Such systems are a lasting testimony tothe extraordinary ingenuity of theircreators and the contemporary cul-tures that carry the tradition.References and Notes1. Abraham A. Moles, "Informatique du rhy-thme", in 'Lesrythmes' Conferences presentees au Col-

a I I I I II I 1 1 I I

II : m m m m m m m

d : FI I I I I I I mI 1 I1 I I I I I*j j J j I > *IIFig. 11. The more ambiguity there is in the rhythmic content of the superposed figures,the more complex the resulting polyrhythmics will be.

mokongohandclapsdiketo

mokongo

I I I I I I I

cE1 I I I I Ia

* I. I. .1 1 I* Ihandclaps * I * I I I Idiketo * 0 1 ( * * I * 10b

'O

0Q 0I .1. 0

Fig. 12. (a) The superposition of the mokongoigure and the diketofigure yield the for-mula for the zoboko.The interaction of these figures combined with isochronal handclapswill be perceived as a polyrhythmic entity of three interwoven parts from which onemokongo ccent, three diketoattacks and two irregularly spaced handclaps stand outseparately. (b) Beside the two percussions that are simultaneous to the three parts, thereare 11 combined percussions. When one adds the six isolated percussions, one finds, fora cycle of 24 minimal values, a total of 17 rhythmic events, which make use of seven dif-ferent combinations of three tone colors.

loque sur les rythmesa Lyon en decembre1967, supple-ment No. 7 du Journalfranfais d'oto-rhino- laryngo-logie (Lyon: Editions Simer, 1968).2. Simha Arom, "The Use of Play-Back Tech-niques in the Study of Oral Polyphonies",Ethnomusicology 20, No. 3, 483-519 (1976).3. Andre Souris, "Tempo", in Encyclopedie de laMusique, Vol. 3 (Paris: Fasquelle, 1961) p. 787.4. David Epstein, "ACross-Cultural Study of Musi-cal Tempo", Communication presented at thesymposium Biological Aspects of Aesthetics, Werner-

Reimers-Stiftung, Bad-Homburg (Resume in6dit,1981).5. Mieczyslaw Kolinski, "A Cross-Cultural Ap-proach to Metro-Rhythmic Patterns", Ethnomusi-cology 17, No. 3, 495-506 (1973).6. The transcription of orally transmitted poly-rhythmic pieces is now possible owing to the de-velopment of a special recording method for fielduse, based on the application of 're-recording'techniques. Each constituent part of a polyrhyth-mic whole can thereby be isolated without beingdesynchronized with respect to the others. SeeArom [2].

I I I> I31 > 1 S 3 l.=160 I

arom time structure in the music of central africa

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