HesapHanem

Cents Interval Calculator

Find the interval in cents between two pitches.

Result

19.56 ¢

How it is calculated

The interval from the first pitch to the second is cents = 1200 × log2(f2 / f1), where f1 and f2 are frequencies in hertz (both must be above zero, and any consistent unit gives the same ratio). The result is rounded to two decimals and carries a sign: positive when the second frequency is higher, negative when it is lower. An octave (ratio 2) gives 1200 cents, an equal-tempered semitone 100 cents, and a unison 0. Only the ratio matters, so 220 to 440 Hz and 440 to 880 Hz both give 1200.

Worked example

You tune a string to 445 Hz against a 440 Hz reference. The ratio is 445 / 440 = 1.011364. Its base-2 logarithm is 0.016302. Multiply by 1200: 0.016302 × 1200 = 19.56 ¢, which is about one fifth of a semitone sharp. Swapping the two inputs gives −19.56 ¢, the same distance in the opposite direction.

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Common mistakes

  • Putting the frequencies in the wrong order. Entering the reference pitch second flips the sign, so a sharp note reads as flat.
  • Subtracting frequencies to compare intervals. 440 to 450 Hz (about 39 ¢) is not the same interval as 880 to 890 Hz (about 19.6 ¢); only the ratio counts.
  • Entering note names or MIDI numbers. The fields take frequencies in Hz.
  • Expecting a result for zero or negative frequencies; both must be positive.
  • Confusing cents with semitones: 100 cents make one equal-tempered semitone, so 19.56 ¢ is far smaller than a semitone.

About this calculator

A cent is a logarithmic unit of musical pitch equal to 1/100 of an equal-tempered semitone, so an octave (a 2:1 frequency ratio) always spans exactly 1200 cents regardless of the actual frequencies involved. The interval between two frequencies is calculated as cents = 1200·log₂(f₂/f₁), which lets any pitch difference — however small — be measured on a single, uniform scale rather than in raw Hz, where the same musical interval corresponds to a different Hz gap at every octave.

Piano tuners and instrument technicians use cents to measure and correct tuning deviations with precision finer than the ear alone can judge, while ethnomusicologists use them to compare non-Western and microtonal scales (Indian shruti, Indonesian gamelan) against the Western equal-tempered system. Sound engineers, synthesizer designers, and music theory students also use cents when analyzing or building tuning systems, since it is the standard unit for describing pitch precision in acoustics.

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Comments (1)

  • Editorial team

    A good way to feel cents is to compare tuning systems. Enter 440 and 660 Hz, a pure 3:2 fifth, and you get 701.96 cents, about 2 cents wider than the 700 of equal temperament. Try 440 and 550 Hz, a pure 5:4 third, and it reads 386.31 cents against 400 in equal temperament. Which tuning or temperament are you comparing against, and what intervals do you check most often?

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