Kirkman’s Ladies, A Combinatorial Design

Abstract

I found a surprising number of new musical patterns in formations as simple as the permutations, sums and subsets already discussed, and in the case of my “counting music”, even simpler ones, but I was always interested in finding new directions in all this. One new direction presented itself quite unexpectedly in 2003, when I heard a piece by a young Dutch composer, Samuel Vriezen. Using a scale of only 11 notes, Vriezen constructed 11 five-note chords in such a way that each chord had exactly two notes in common with each other chord. I asked the composer how he had ever found such a group of chords, and he told me it was not too complicated. He thought I could construct such a system myself, if I thought about it a bit.