Abstract

The theory of musical scales involves mathematical ratios, harmonic resonators, beats, and human perception and provides an interesting application of the physics of waves and sound. We first review the history and physics of musical scales, with an emphasis on four historically important scales: twelve-tone equal temperament, Pythagorean, quarter-comma meantone, and Ptolemaic just intonation. We then present an easy way for students and teachers to directly experience the qualities of different scales using MIDI synthesis.

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