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In music transposition is moving a note or collection of notes up or down in pitch by a constant interval. This could be tranposing a piece of music into another key, transposing a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch. See also Transposing instrument. Transpositional equivalency is the concept that intervals and chords are the same when transposed. It is similar to enharmonic equivalency and octave equivalency. Transpositional equivalency is generally supposed by most music theory in that chords which may be transposed onto one another share something in common. However, taking them to be identical or near-identical is only assumed in musical set theory.
Using integer notation and modulo 12, to tranpose a pitch x by n semitones:
- <math>T^p_n (x) = x+n<math>
or
- <math>T^p_n (x) \rightarrow x+n<math>
For pitch class transposition by an pitch class interval:
- <math>T_n (x) = x+n\ (mod 12)<math>
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