Scale (music) identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale. It is assumed that the scale is tuned using 12-tone equal temperament (so that, for instance, C is the same as D), and that the tonic is in the leftmost position. For example, the binary number 101011010101, equivalent to the decimal number 2773, would represent any major scale (such as C–D–E–F–G–A–B). This system includes scales from 100000000000 (2048) to 111111111111 (4095), providing a total of 2048 possible species, but only 351 unique scales containing from 1 to 12
Transposition (music) Thus the set ("A") consisting of 0–1–2 transposed by 5 semitones is 5–6–7 (T("A")) since , , and . 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 C–E–G upwards by four semitones, one obtains the pitches E–G–B. In scalar transposition one shifts every pitch in a collection by a fixed number of scale steps relative to some scale. For example,