๐ต Cents (Pitch Interval) Calculator
Enter two frequencies to calculate the pitch interval between them in cents (a logarithmic unit dividing the octave into 1200 parts), or convert a cents value back into a frequency ratio. Useful for checking piano tuning or pitch adjustments on audio equipment.
How to use
- Choose "frequency to cents" or "cents to frequency ratio" mode.
- Enter two frequencies, or a cents value.
- The result is calculated automatically.
How the calculation works
Cents measure the size of an interval: an equal-tempered semitone is 100 cents and an octave is 1200 cents. This tool finds the difference between two frequencies in cents, or the frequency ratio for a number of cents. Cents = 1200 ร logโ(frequency 2 รท frequency 1) Frequency ratio = 2^(cents รท 1200) We hear pitch by ratio rather than by difference in hertz, so cents let you compare tuning at any pitch on the same scale, which is why they are used for tuning and comparing temperaments. If frequency 2 is lower than frequency 1, the result is negative.
Worked example
440 Hz โ 880 Hz: 1200 cents (one octave) 440 Hz โ 441 Hz: about 3.93 cents 440 Hz โ 442 Hz: about 7.85 cents 440 Hz โ 432 Hz: about โ31.77 cents 100 cents โ ratio about 1.05946 (an equal-tempered semitone) โ50 cents โ about 0.97153 (a quarter tone lower)
Things to be aware of
- Within ยฑ5 cents on a tuner, most listeners hear a note as in tune.
- A just major third (ratio 5:4) is about 386.3 cents, about 14 cents narrower than the equal-tempered major third (400 cents).
- Entering the same value for both frequencies gives 0 cents.
FAQ
What is a cent?
A logarithmic unit of pitch interval, defined so that an equal-tempered semitone is 100 cents and an octave is 1200 cents.
What formula does this use?
Cents = 1200 ร log2(f2/f1), the standard formula used in acoustics.
Why is an octave exactly 1200 cents?
An octave is a 2:1 frequency ratio, so 1200 ร log2(2/1) = 1200 ร 1 = 1200 cents.