Cents and semitones are the universal language of tuning. This tool measures the interval between any two pitches, reporting the frequency ratio, the number of equal-tempered semitones, and the precise value in cents, plus the nearest named interval.
How it works
Pitch perception is logarithmic: doubling the frequency always sounds like the
same interval, an octave. So intervals are measured on a log scale. The
octave is divided into 1200 cents, and the conversion from a frequency ratio
is:
cents = 1200 x log2(f2 / f1)Semitones are simply cents divided by 100, since there are 100 cents in each
of the twelve equal-tempered semitones:
semitones = cents / 100 = 12 x log2(f2 / f1)Worked example
For f1 = 440 Hz (concert A) and f2 = 660 Hz:
- Ratio =
660 / 440 = 1.5 - Cents =
1200 x log2(1.5) = 701.96cents - Semitones =
7.02
That is a perfect fifth — 660 Hz is very close to the just-intonation fifth
above A, just under the 700-cent equal-tempered fifth by about 2 cents.
Reference intervals
| Interval | Equal-tempered cents | Semitones |
|---|---|---|
| Unison | 0 | 0 |
| Minor third | 300 | 3 |
| Major third | 400 | 4 |
| Perfect fifth | 700 | 7 |
| Octave | 1200 | 12 |
Why cents instead of hertz?
Two instruments both tuned to A at 440 Hz have a 0-cent difference. But if one drifts 10 Hz flat to 430 Hz, that sounds very different in the middle of a chord. Expressing that deviation in hertz is misleading for perception because the musical significance of a frequency difference depends on where you are in the pitch range: 10 Hz means a lot at 440 Hz but almost nothing at 4400 Hz.
Cents solve this by measuring intervals on the same logarithmic scale the ear uses. A 10-cent deviation at 440 Hz produces the same mistuned sound as a 10-cent deviation at any other pitch. This is why plugin manufacturers, tuners, and pitch analysers universally use cents for deviation readout.
Practical uses for this calculator
Pitch-shift planning — if you want to pitch-shift a vocal sample up by a major third, you need 400 cents. Many DAW pitch-shifters accept cents directly, so enter the source and target frequency here to confirm the exact value.
Tuning analysis — record a held note and measure its fundamental against the intended pitch. The cent deviation tells you how sharp or flat the instrument is. A professional in-tune instrument typically sits within ±5 cents of the target pitch.
Microtonality — quarter-tone music uses 50-cent intervals; 19-TET uses approximately 63-cent steps. Enter any two frequencies to confirm whether an interval matches a target microtonal division.
Equal temperament vs. just intonation — the pure major third has a ratio of 5/4, which is approximately 386 cents. Equal temperament places it at 400 cents, 14 cents wider. This is audible in sustained chords, which is why some styles (barbershop, choral music) tune by ear to the just intervals rather than equal temperament.
Tips and notes
- A negative cent value means the second frequency is lower than the first; the tool handles either order.
- Use the cent figure directly when detuning an oscillator or planning a pitch-shift — most plugins accept cents as a parameter.
- For just-intonation work, compare your measured cents against the pure ratios
(fifth
701.96, major third386.31) to see how far equal temperament strays. All calculations run locally in your browser.