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Section 33.7 Transposition (T\(\text{}_{n}\))

Transposition is an operation performed as T\(\text{}_{n}\), where n is the number of semitones up a set is transposed. For example, [1, 2, 4, 6] at T\(\text{}_{4}\) is [5, 6, 8, 10].

When working in a modulo 12 system, remember that numbers larger than 12 have to be reduced to a number smaller than 12 by subtracting 12 from the larger number. For example, 6, 8, 10, 11 at T\(\text{}_{9}\) would result in 15, 17, 18, 20, which, after subtracting 12 from each number, results in 3, 5, 6, 8.

Pitch classes: 6 8 10 11
at T\(\text{}_{9}\): + 9 9 9 9
Result: 15 17 18 20
Make numbers modulo 12: 12 12 12 12
Result: 3 5 6 8
Table 33.7.1.