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. In scalar transposition, every pitch in a collection is shifted up or down a fixed number of scale steps within some scale. The pitches remain in the same scale before and after the shift. This term covers both chromatic and diatonic transpositions as follows. Chromatic transposition is scalar transposition within the chromatic scale, implying that every pitch in a collection of notes is shifted by the same number of semitones. For instance, transposing the pitches C4–E4–G4 upward by four semitones, one obtains the pitches E4–G4–B4. Diatonic transposition is scalar transposition within a diatonic scale (the most common kind of scale, indicated by one of a few standard key signatures). For example, transposing the pitches C4–E4–G4 up two steps in the familiar C major scale gives the pitches E4–G4–B4. Transposing the same pitches up by two steps in the F major scale instead gives E4–G4–B4. There are two further kinds of transposition, by pitch interval or by pitch interval class, applied to pitches or pitch classes, respectively. Transposition may be applied to pitches or to pitch classes.