Cent

A measure for fine detail

The cent divides the equal-tempered semitone into a hundred equal parts. 100 cents equal a semitone, 1200 cents an octave. A tone is generally considered cleanly tuned when the deviation is smaller than ±5 cents. The limit of hearing lies at about 3 to 6 cents, depending on pitch, loudness and timbre; for tones sounding together, beats reveal even smaller differences. A tuner determines the fundamental frequency and shows how many cents the tone lies from the nearest target pitch.

Deviations in tuning

Equal temperament is a compromise. Twelve pure fifths miss seven octaves by the Pythagorean comma of 23.46 cents. In equal temperament this error is spread evenly, with the following deviations from just intonation:

The fifth is 2 cents too low, which nobody hears. The major third is 14 cents too high, which you do hear once you have paid attention to it. Ensembles with flexible pitch therefore play it lower. The individual values are in the article Equal, meantone, just: why your piano is slightly out of tune. A further example: the seventh partial lies about 31 cents lower than the tempered minor seventh. This is where the “blue seventh” of the blues comes from.

Cents and beating

If you turn one of two tuned strings up minimally, say by about five cents, the sound begins to pulse. That is the beating. It can be counted: two tones 2 Hz apart pulse twice per second. Piano tuners work with exactly this.

Common mistakes

• Trusting the tuner as the yardstick of purity: It measures against the equal-tempered grid. If you play the third 12 cents below the display in an ensemble, you are not tuning wrongly but purely.
• Confusing cents and hertz: Cents describe a ratio (interval), hertz the frequency.
• Tuning a piano to zero cents across all octaves: Piano strings are stiff, so a piano is tuned stretched. A piano with zero cents throughout sounds wrong.