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Mathematics of Piano Tuning

Eric Bynum
Organization: Wolfram Research, Inc.
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Piano Tuning Different systems of tuning musical instruments (namely keyboard instruments) have been developed since the time of Pythogoras. Each system has its own characteristic benefits and shortcomings. This notebook explores the mathematical backgrounds of four major systems of tuning, and includes many sound examples to give the reader/listener a sense of how the mathematics affects each system. The notebook PianoTuning.nb is the same as the notebook PianoTuningShort.nb except that the sound examples in PianoTuning.nb are fully evaluated. By evaluating the examples in PianoTuningShort.nb the notebook PianoTuning.nb will be created. PianoTuningShort.nb is a smaller file and therefore downloads faster; however, the pre-evaluated sound examples in PianoTuning.nb allow the user to play them without having to wait to generate them through evaluation.

*Arts and Humanities > Music
*Engineering > Acoustical Engineering

Tuning, Music, Chromatic Semitone, Diatonic Semitone, scales
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PianoTuning.nb (2 MB) - Mathematica Notebook [for Mathematica 4.0]
PianoTuningShort.nb (276.7 KB) - Mathematica Notebook