Transposition & Inversion

T_n and I^u_v operations on pitch-class sets — Tsao, Ch. 4–5

Musical Space

Input Set

Clear

Comma-separated (0,1,4,6), space-separated (0 1 4 6), or unseparated (0146 / 014A)

Transposition T_n

n = 0

T₀(S) =

--

Inversion I^u_v

u = 0

v = 0

I⁰₀(S) =

--

▶ Show full orbits under all T_n and I^u_v

Each row shows the image of the input set under each operation. Green = current T_n; purple = current I^u_v.

T_n orbit

I^u_v orbit (fixing u = 0)

Based on Ming Tsao, Abstract Musical Intervals (2007), Ch. 4–5.  |  Hex notation: A = 10, B = 11.