Metric modulation

In music, metric modulation is a change in pulse rate (tempo) and/or pulse grouping (subdivision) which is derived from a note value or grouping heard before the change. Examples of metric modulation may include changes in time signature across an unchanging tempo, but the concept applies more specifically to shifts from one time signature/tempo (meter) to another, wherein a note value from the first is made equivalent to a note value in the second, like a pivot or bridge. The term "modulation" invokes the analogous and more familiar term in analyses of tonal harmony, wherein a pitch or pitch interval serves as a bridge between two keys. In both terms, the pivoting value functions differently before and after the change, but sounds the same, and acts as an audible common element between them. Metric modulation was first described by Richard Franko Goldman (1951) while reviewing the Cello Sonata of Elliott Carter, who prefers to call it tempo modulation (Schiff 1998, 23). Another synonymous term is proportional tempi (Mead 2007, 65).

A technique in which a rhythmic pattern is superposed on another, heterometrically, and then supersedes it and becomes the basic meter. Usually, such time signatures are mutually prime, e.g., 4
4 and 3
8, and so have no common divisors. Thus the change of the basic meter decisively alters the numerical content of the beat, but the minimal denominator (1
8 when 4
4 changes to 3
8; 1
16 when, e.g., 5
8 changes to 7
16, etc.) remains constant in duration. (Nicolas Slonimsky 2000)

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