Transposition (music)

Musicians who play transposing instruments sometimes have to do this (for example when encountering an unusual transposition, such as clarinet in C), as well as singers' accompanists, since singers sometimes request a different key than the one printed in the music to better fit their vocal range (although many, but not all, songs are printed in editions for high, medium, and low voice).

There are three basic techniques for teaching sight transposition: interval, clef, and numbers.

A performer using this method may calculate each note individually, or group notes together (e.g. "a descending chromatic passage starting on F" might become a "descending chromatic passage starting on A" in the target key).

Clef transposition is routinely taught (among other places) in Belgium and France.

Transposing by numbers means, one determines the scale degree of the written note (e.g. first, fourth, fifth, etc.)

The performer then plays the corresponding scale degree of the target chord.

In many musical contexts, transpositionally equivalent chords are thought to be similar.

Using integer notation and modulo 12, to transpose a pitch x by n semitones: or For pitch class transposition by a pitch class interval: [2] Milton Babbitt defined the "transformation" of transposition within the twelve-tone technique as follows: By applying the transposition operator (T) to a [twelve-tone] set we will mean that every p of the set P is mapped homomorphically (with regard to order) into a T(p) of the set T(P) according to the following operation: where to is any integer 0–11 inclusive, where, of course, the to remains fixed for a given transposition.