Mathematical models of musical scales

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The work is permeated with a sense of artistic and historical realities. The index has entries for 78 composers, 24 mathematicians who have written about music, and 63 other music theorists. A 23-page survey of the history of pitch-class systems in Western polyphony is integrated with a 70-page section of music examples with explanatory captions. A brilliant appendix on “Pythagoreanism and Euler's theory” outlines the history of the idea that numerical ratios are the essence of harmony and of some other, related ideas (e. g., that only certain numbers are involved).