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Additive rhythm is much used in folk music, especially in Africa and Eastern Europe, and has been standard in Western concert music since the beginning of this century. In music using non-additive rhythm, or ‘divisive rhythm’ (which is the most common form used in Western music) the rhythm is the product of binary or ternary divisions of a larger unit of time. (A waltz, for example, makes rhythmic patterns based on groups of three equal beats repeated regularly, with the main accent on the first beat; in ‘common time’, the main accent occurs on the first of every four equal divisions or beats.) In additive rhythm, by contrast, instead of large time-units being subdivided into regular beats, the beat, metre and melodic rhythm are all fashioned from multiples of the smallest unit.
One result of this aggregative procedure is that the beats need not be of equal length. In the Balkan regions in particular, rhythmic and metric patterns are often asymmetrical, comprising different combinations of binary and ternary multiples of a the basic small unit. In Bulgaria, for example, paidushka contains five basic units, with two stresses, in the ratio [2 + 3]; rachenitsa has seven units [2 + 2 + 3], and gankino khoro has eleven [2 + 2 + 3 + 2 + 2]. Combinations of these asymmetrical patterns also occur and are described as ‘additive metres’. A typical example of such a pattern might be a repeated sequence of fourteen units, functioning as an aggregate of two accented patterns of five and nine units [2 + 3] + [2 + 2 + 2 + 3].
The effect of additive rhythm on the ear is of a kind of organized anarchy, a rhythmic delirium. Folk players, trained in the method, find it easy to perform, but it can cause problems for classically-trained instrumentalists. In the Western concert tradition, therefore, additive-rhythm music is usually notated with constantly changing time signatures. A typical sequence of bars from the Danse sacrale which ends Stravinsky\'s The Rite of Spring, for example, has the time signatures [2/16 + 3/16 + 3/16 + 2/8 + 3/16 + 3/16 + 5/16 etc.]: that is, taking sixteenth-notes as the basic units for aggregation, a sequence of [2 + 3 + 3 + 4 + 3 + 5]. With practice, this kind of thing ceases to pose problems—and orchestras once had difficulty with the (non-additive, ‘divisive’) ‘waltz’ rhythms in Tchaikovsky\'s Sixth Symphony: a sequence of 5-beat bars instead of 3. KMcL SSt |
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