Cent

What it means

The cent is a logarithmic unit used to measure the size of musical intervals. In twelve-tone equal temperament, a semitone equals exactly 100 cents, and an octave therefore equals 1200 cents. The unit divides the octave into 1200 equal steps, regardless of whether an interval is based on a simple frequency ratio, as in just intonation, or not.

The cent system was developed in the nineteenth century by the British phonetician Alexander J. Ellis, to make tuning systems from different cultures and periods comparable without relying on complicated frequency ratios.

Musical use

Cents are used above all to describe small deviations from equal temperament, such as how far a historical tuning system, a non-Western scale, or an instrument's intonation departs from today's common standard. Cent values are also used when tuning instruments and in electronic tuners, to make the fine deviation of a pitch from its target frequency visible.

The cent should be distinguished from a frequency ratio: a frequency ratio such as 3:2 (a perfect fifth) works multiplicatively, whereas cent values simply add, because the unit is defined logarithmically. This makes it easy to add or subtract intervals, which simplifies comparing different tuning systems.

Performance practice

Use a tuner with a cent display to see how far a pitch you play departs from equal temperament, not just whether it is sharp or flat. Especially on instruments with free intonation, such as strings or winds, knowing typical cent deviations helps you tune deliberately pure or deliberately characterful, rather than blindly following the display.