Cents in music — the logarithmic pitch unit
The reason a clip-on guitar tuner uses cents instead of hertz is not laziness. It is that human pitch perception is logarithmic, and cents are the unit that reflects that.
An octave is a doubling of frequency. A440 to A880. From there upwards, A880 to A1760, another octave, but now the same octave spans 880 Hz instead of 440. If tuners quoted hertz, the same 'in tune' precision would need ten times more resolution at the top of the piano as at the bottom. Cents fix this by dividing every octave into 1200 equal logarithmic parts.
The formula is short: cents = 1200 × log₂(f₂ / f₁). A frequency ratio of 2:1 is 1200 cents. A ratio of ¹²√2 (the equal-tempered semitone) is exactly 100 cents. A perfect fifth in just intonation is 3:2 = 702 cents, which is 2 cents sharper than the equal-tempered fifth of 700 cents. That two-cent difference is why choirs and string quartets sound sweeter than fixed-pitch instruments — they lean into the pure ratios.
What each amount actually sounds like
1 cent: below the threshold of detection for most people, even trained musicians. Only really matters when it accumulates across an ensemble.
5 cents: a good tuner considers this in tune. Solo string players hear it, most listeners do not.
10–15 cents: audibly out of tune on a sustained note. This is where beating starts against a reference pitch.
20 cents: obviously wrong. If your open D string is 20 cents flat, the guitar will sound cheap to anyone in the room.
50 cents: a quarter tone. The genuine 'between the keys' sound used in Middle Eastern and Balkan music.
100 cents: a semitone. F vs F♯.
Where cents show up in odd places
Piano tuners intentionally stretch the octaves — an actual concert grand has the top A tuned about 30 cents sharp of A7's mathematical frequency, because the physical strings have inharmonic overtones that the ear compensates for. Straight equal temperament sounds flat at the top and sharp at the bottom on a real piano.
Software instruments in DAWs let you detune samples in cents to layer them. Two identical piano samples with one shifted by ±7 cents sounds like a chorused, richer piano. Any more and it sounds broken.
Historical temperaments — meantone, Werckmeister, Kirnberger — are all described by tables of cent deviations from equal temperament for each of the twelve notes. Baroque tuning is a table of cents.
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FAQ
Why not just use hertz?+
Because pitch perception is logarithmic — the interval from 100 to 200 Hz sounds the same size as 400 to 800 Hz. Cents match this; hertz do not.
How many cents does a wind instrument bend?+
A saxophone's embouchure can nudge the pitch ±30 cents without effort. Trombones cover an entire octave in a single slide — 1200 cents of continuous glissando.
This article was written by The Turbo Unit Converter engineering desk (Applied metrology & engineering units) and last reviewed on 2026-07-20 against NIST SP 811 and the BIPM SI Brochure. Read our full editorial policy.