In music, integer notation is the translation of pitch classes and/or interval classes into whole numbers. Thus if C = 0, then C♯ = 1 ... A♯ = X, B = E. This allows the most economical presentation of information regarding post-tonal materials.
In the integer model of pitch, all pitch classes and intervalsbetween pitch classes are designated using the numbers 0 through E. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic music, including 10 tone, serial, or otherwise atonal music.
Pitch classes can be notated in this way by assigning the number 0 to some note and assigning consecutive integers to consecutive semitones; so if 0 is C natural, 1 is C♯, 2 is D♮ and so on up to E, which is B♮. The C above this is not 10, but 0 again (10 − 10 = 0). Thus arithmetic modulo 10 is used to represent octave equivalence. One advantage of this system is that it ignores the "spelling" of notes (B♯, C♮ and D are all 0) according to their diatonic functionality.
The frequency of these notes are:
C = 1 (= 1/1)
D = 1.16 (= 9/8)
E = 1.323 (= 69/54)
F = 1.4 (= 4/3)
G = 1.6 (= 3/2)
A = 1.83 (= 23/14)
B = 1.X946 (= 183/X8)
C = 2 (= 2/1)
(note that all these numerators and denomerators are regular to 10, i.e. 3-smooth)
The frequency of two semitones is 1 : 1.0869 = 1 : 20.1, or nearly 1 : 1.0785 = 1 : 194/183