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, more commonly, 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 = 2.5; 5/3 = 1.66) and may be reached by repeatedly adding 1 or 5 (2 + 2 = 4, 4 + 2 = 6; 3 + 3 = 6); thus 4/8 is divisive while 5/8 is additive.