metric modulation

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:

$\frac{new\ tempo}{old\ tempo} = \frac{number\ of\ pivot\ note\ values\ in\ old\ measure}{number\ of\ pivot\ note\ values\ in\ new\ measure}$

(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:

$\frac{x}{84} = \frac{3}{2}, x = 126$

(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.

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