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The Mathematics of Musical Composition

Gresham College Lectures

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Translations and the Clock Arithmetic Property

Up through 12 semitones, we're going to think of as really not doing anything. The identity map and because of that, the kind of arithmetic we do in these translations is a bit like o'clock. Translations also satisfy this clock arithmetic property. Inversion is like reflection in a horizontal but where is your horizontal line? It does us.

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