Transposition (music)
In music transposition refers to the process, or operation, of moving a collection of notes (pitches or pitch classes) up or down in pitch by a constant interval.
The shifting of a melody, a harmonic progression or an entire musical piece to another key, while maintaining the same tone structure, i.e. the same succession of whole tones and semitones and remaining melodic intervals.
For example, one might transpose an entire piece of music into another key. Similarly, one might transpose a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch.
The transposition of a set A by n semitones is designated by Tn(A), representing the addition (mod 12) of an integer n to each of the pitch class integers of the set A. Thus the set (A) consisting of 0–1–2 transposed by 5 semitones is 5–6–7 (T5(A)) since 0 + 5 = 5, 1 + 5 = 6, and 2 + 5 = 7.
There are two different kinds of transposition, depending on whether one is measuring intervals according to the chromatic scale or some other scale. In chromatic transposition one shifts every pitch in a collection of notes by a fixed number of semitones. For instance, if one transposes the pitches C4–E4–G4 upwards by four semitones, one obtains the pitches E4–G♯4–B4. In scalar transposition one shifts every pitch in a collection by a fixed number of scale steps relative to some scale. For example, if one transposes the pitches C4–E4–G4 up by two steps relative to the familiar C major scale, one obtains the pitches E4–G4–B4. If one transposes the same pitches up by two steps relative to the F major scale, one obtains instead E4–G4–B♭4. Scalar transposition is sometimes called diatonic transposition, but this term can be misleading, as it suggests transposition with respect to a diatonic scale. However, scalar transposition can occur with respect to any type of scale, not just the diatonic.
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