THEOREM OF THE DAY: The Generalised Hexachord Theorem

Theorem

Suppose that $S$ is a subset of the set of pitch classes comprising $\mathbb{Z}_n$, with $n$ even, and $|S| = s$; then the interval class vectors of $S$ and its complement $\mathbb{Z}_n \setminus S$ differ componentwise by $|n - 2s|$, except for the last component, for which the difference is $|n/2 - s|$.

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