Kirkman’s Ladies, A Combinatorial Design

Tom Johnson () and Franck Jedrzejewski ()

Chapter Chapter 4 in Looking at Numbers, 2014, pp 37-55 from Springer

Abstract: 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.

Keywords: Triple System; Parallel Class; Combinatorial Design; Steiner Triple System; Steiner System (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0554-4_4

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DOI: 10.1007/978-3-0348-0554-4_4

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