Cent (music)

Octaves increase exponentially when measured on a linear frequency scale (Hz).

Octaves are equally spaced when measured on a logarithmic scale (cents).

The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, to check intonation, or to compare the sizes of comparable intervals in different tuning systems. For humans, a single cent is too small to be perceived between successive notes.

Cents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century.^[a] Ellis chose to base his measures on the hundredth part of a semitone, ¹²⁰⁰√2, at Robert Holford Macdowell Bosanquet's suggestion. Making extensive measurements of musical instruments from around the world, Ellis used cents to report and compare the scales employed,^[1] and further described and utilized the system in his 1875 edition of Hermann von Helmholtz's On the Sensations of Tone. It has become the standard method of representing and comparing musical pitches and intervals.^[2][3]

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