Additive rhythm and divisive rhythm
In music, additive and divisive are terms used to distinguish two types of both rhythm and meter.
A divisive (or, alternately, multiplicative) rhythm is a rhythm in which a larger period of time is divided into smaller rhythmic units or, conversely, some integer unit is regularly multiplied into larger, equal units; this can be contrasted with additive rhythm, in which larger periods of time are constructed by concatenating (joining end to end) a series of units into larger units of unequal length, such as a 5
8 meter produced by the regular alternation of 2
8 and 3
8 (London 2001, §I.8). When applied to meters, the terms "perfect" and "imperfect" are sometimes used as the equivalents of "divisive" and "additive", respectively (Read 1969, 150).
For example, 4 may be evenly divided by 2 (4 ÷ 2 = 2) or reached through repeatedly adding 2 (2 + 2 = 4), while 5 is only evenly divisible by 5 and 1 (5 ÷ 2 = 2 1⁄2; 5 ÷ 3 = 1 2⁄3) and may be reached by repeatedly adding 2 or 3 (2 + 2 = 4, 2 + 3 = 5; 3 + 3 = 6); thus 4
8 is divisive while 5
8 is additive.
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