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Octaves on a piano are not tuned pure. Because of inharmonicity, the higher partials of a single piano string are slightly sharper than theory would predict. Ideal harmonic series above 100Hz: 100 200 300 400 etc Actual harmonic series above 100Hz (approximation): 100 200.05 300.2 400.6 The higher the partial; the sharper the pitch. Shorter piano ...

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