Multiplication (music)

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This article is about multiplication in music; for multiplication in mathematics see multiplication.

In music and musical set theory, multiplication modulo 12 is a basic operation which may be performed on pitch or pitch class sets. Dealing with all twelve tones, or a tone row, there are only a few numbers which one may multiply a row by and still end up with twelve tones. Taking the prime or unaltered form as P₀, multiplication is indicated by Mx, x being the multiplicator:

[Mx(y) = xy ]

As with the other compound operations multiplication is carried out and then transposition. P₀ = M1₀, I₀ = M11₀, M7₀ = I(M5₀). Thus, for the untransposed form of all:

M1 M5 M7 M11
M5 M1 M11 M7
M7 M11 M1 M5
M11 M7 M5 M1

Even numbers remain unchanged under M7 and all odd numbers become transposed by a tritone.

The chromatic scale may be mapped onto the circle of fourths with M5, and the circle of fifths with M7.

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