Combinatorial Music Theory
Musical patterns may be investigated with the mathematical tools more commonly applied in science and engineering. For example, the cyclic autocorrelation of a musical scale describes its interval content. Fingering patterns on string instruments are embedded in a space with an unusual topology. Ideas from crystallography may be applied to the description of structure-preserving transformations of melodies. These phenomena are explored for the particularly common case of the twelve-note equally tempered scale.
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