Editing Metric modulation (section)

{{Short description|Musical technique}}
[[File:Metric modulation Bach.png|thumb|upright=1.4|Simplest form of metric modulation, unmarked ({{music|sixteenth note}} = {{music|eighthnote}}), in a piece by J.S. Bach. Slow introduction followed by an allegro traditionally taken at double the speed. Sixteenth notes in the old tempo prepare for eighth notes in the new tempo.{{sfn|Weisberg|1996|loc=51–52}} [[File:Metric modulation Bach.mid|thumb|Without repeat]]]]

In [[music]], '''metric modulation''' is a change in [[Pulse (music)|pulse]] rate ([[tempo]]) and/or pulse grouping ([[Metre (music)|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 ([[Metre (music)|metre]]) to another, wherein a [[note value]] from the first is made equivalent to a note value in the second, like a pivot or [[Bridge (music)|bridge]]. The term "[[modulation (music)|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{{sfn|Goldman|1951}} while reviewing the Cello Sonata of [[Elliott Carter]], who prefers to call it '''tempo modulation'''.{{sfn|Schiff|1998|loc=23}} Another synonymous term is '''proportional tempi'''.{{sfn|Mead|2007|loc=65}}

{{quote|A technique in which a rhythmic pattern is superposed on another, heterometrically, and then supersedes it and becomes the basic metre. Usually, such time signatures are [[coprime integers|mutually prime]], e.g., {{time signature|4|4}} and {{time signature|3|8}}, and so have no [[common divisor]]s. Thus the change of the basic metre decisively alters the numerical content of the [[beat (music)|beat]], but the [[lowest common denominator|minimal denominator]] ({{time signature|1|8}} when {{time signature|4|4}} changes to {{time signature|3|8}}; {{time signature|1|16}} when, e.g., {{time signature|5|8}} changes to {{time signature|7|16}}, etc.) remains constant in duration.{{sfn|Slonimsky|2000}}}}