Enumeration in Musical Theory

Being a mathematician and a musician ( I play the flute) I found it very interesting to deal with Polya's counting theory in my Master's thesis. When reading about Polya's theory I came across an article, called "Enumeration in Music Theory" by D. L. Reiner. I took up his ideas and tried to enumerate some other "musical objects". At first I would like to generalize certain aspects of 12-tone music to n-tone music, where n is a positive integer. Then I will explain how to interpret intervals, chords, tone-rows, rhythms, motifs and tropes in n-tone music. Transposing, inversion and retrogradation are defined to be permutations on the sets of "musical objects". Polya's enumeration theory is the right tool to solve this problem. In the first chapter I will present a short survey of parts of Polya's counting theory. In the second chapter I will investigate serval "musical objects".

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