In music a metric modulation is a change (modulation) 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. The term was invented to describe the practice of Elliott Carter, who prefers to call it tempo modulation.
The following formula illustrates how to determine the tempo before or after a metric modulation, or, alternately, how many of the associated note values will be in each measure before or after the modulation:
(DeLone et. al. (Eds.), 1975, chap. 3)
Thus if the two half notes in 4/4 time at a tempo of quarter note = 84 are made equivalent with three half notes at a new tempo, that tempo will be:
(ibid, example taken from Carter's Eight Etudes and a Fantasy for woodwind quartet (1950), Fantasy, mm. 16-17.)
References
DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ASIN 0130493465.
A sequence does not have to modulate; a modulating sequence is known as a rosalia.
Metricmodulation (known also as tempomodulation) is the most common, while timbral modulation (gradual changes in tone color), and spatial modulation (changing the location from which sound occurs) are also used.
Modulation may also occur from a single tonality to a polytonality, often by beginning with a duplicated tonic chord and modulating the chords in contrary motion until the desired polytonality is reached.
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