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Kirkman’s Ladies, A Combinatorial Design

In: Looking at Numbers

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  • Tom Johnson

  • Franck Jedrzejewski

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.

Suggested Citation

  • Tom Johnson & Franck Jedrzejewski, 2014. "Kirkman’s Ladies, A Combinatorial Design," Springer Books, in: Looking at Numbers, edition 127, chapter 0, pages 37-55, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0554-4_4
    DOI: 10.1007/978-3-0348-0554-4_4
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