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Cents

A cent is a unit of measurement between two frequencies. An equally tempered semitone (the interval between two adjacent piano keys) spans 100 cents by definition. An octave spans twelve semitones and therefore 1200 cents.


ETDs use cents to calculate the inharmonicity of a given piano. Cents will be used as a metric to determine the quality of an interval for testing purposes.


If one knows the frequencies a and b of two notes, the number of cents measuring the interval from a to b may be calculated by the following formula:


n = 1200 * log2(b/a)


Likewise, if one knows a note a and the number n of cents in the interval from a to b, then b may be calculated by:


b = a * 2(n/1200)

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