page_title: Metric modulation
section_title: Determination of the new tempo
hierarchical_section_title: Metric modulation / Determination of the new tempo
caption_attribution_description: English: Metric modulation example. Two half notes = three half notes.
context_page_description: In music, metric modulation is a change in pulse rate and/or pulse grouping 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 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 while reviewing the Cello Sonata of Elliott Carter, who prefers to call it tempo modulation. Another synonymous term is proportional tempi.
  A technique in which a rhythmic pattern is superposed on another, heterometrically, and then supersedes it and becomes the basic metre.
context_section_description: The following formula illustrates how to determine the tempo before or after a metric modulation, or, alternatively, how many of the associated note values will be in each measure before or after the modulation:
  (Winold 1975, 230-31)
  Thus if the two half notes in  time at a tempo of quarter note = 84 are made equivalent with three half notes at a new tempo, that tempo will be:
  (Winold 1975, 230, example taken from Carter's Eight Etudes and a Fantasy for woodwind quartet (1950), Fantasy, mm. 16-17.)
  Note that this tempo, quarter note = 126, is equal to dotted-quarter note = 84 (( = .) = ( = .)).
  A tempo (or metric) modulation causes a change in the hierarchical relationship between the perceived beat subdivision and all potential subdivisions belonging to the new tempo. Benadon (2004) has explored some compositional uses of tempo modulations, such as tempo networks and beat subdivision spaces.
  Three challenges arise when performing metric modulations:
  Grouping notes of the same speed differently on each side of the barline, ex: (quintuplet =sextuplet ) with sixteenth notes before and after the barline
  Subdivision used on one side of the barline and not the other, ex: (triplet =) with triplets before and quarter notes after the barline
  Subdivision used on neither side of the barline but used to establish the modulation, ex: (quintuplet =) with quarter notes before and after the barline
  (Weisberg 1996)
  Examples of the use of metric modulation include Carter's Cello Sonata (1948) (Cunningham 2007, 113), A Symphony of Three Orchestras (1976) (Farberman 1997, 158), and Björk's "Desired Constellation" (.=) (Malawey 2007, 142-44).
caption: Metric modulation: 2 half notes = 3 half notes. About this soundPlay (help·info) or About this soundPlay with eighth note (help·info) subdivision for tempo/metre comparison.
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