Music Theory for the 21st-Century Classroom

Transposition is an operation performed as T${}_n$, where n is the number of semitones up a set is transposed. For example, [1, 2, 4, 6] at T${}_4$ 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${}_9$ would result in 15, 17, 19, 20, which, after subtracting 12 from each number, results in 3, 5, 7, 8.