In music transposition is moving a note or collection of notes (or pitches) 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 and modulation.
For instance, the notes, C-E-G, transposed up a major third become E-G#-B.
Diatonic transposition is transposition according to diatonic intervals. It may be thought of as strict transposition, as above, that is then altered to conform to the diatonic scale.
For instance, the notes above, C-E-G, tranposed up a third become E-G-B.
Transpositional equivalency is the concept that intervals and chords are the same or similar 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:
or
For pitch class transposition by an pitch class interval:
(Rahn, John. Basic Atonal Theory)
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