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Hz to Cent Converter

Calculate the interval in cents between any two frequencies using cents = 1200 × log₂(f₂ / f₁). Auto-identifies the closest just or equal-tempered interval (5:4 major 3rd, 3:2 perfect 5th, etc.), shows frequency ratio, and includes A/B audio comparison.

Input — Two Frequencies

Hz
Hz
Common Interval Pairs

Result

Cents Interval (f₁ → f₂)
cents
Closest Musical Interval
Frequency Ratio (f₂ / f₁)
f₁ Nearest Note (A4 = 440 standard)
f₂ Nearest Note (A4 = 440 standard)
Formula
cents = 1200 × log₂(f₂ / f₁)
ratio = f₂ / f₁

Just vs Equal-Tempered Interval Reference

Interval12-TET (¢)Just (¢)Just ratioDifference (¢)
Unison001:10
Minor 2nd (semitone)100111.7316:15+11.73
Major 2nd200203.919:8+3.91
Minor 3rd300315.646:5+15.64
Major 3rd400386.315:4−13.69
Perfect 4th500498.044:3−1.96
Tritone600590.22 / 609.7845:32 / 64:45−9.78 / +9.78
Perfect 5th700701.963:2+1.96
Minor 6th800813.698:5+13.69
Major 6th900884.365:3−15.64
Minor 7th1000996.0916:9−3.91
Major 7th11001088.2715:8−11.73
Octave120012002:10

About Cents & Frequency Intervals

The cent is a logarithmic measure of musical interval: cents = 1200 × log₂(f₂ / f₁). There are exactly 1,200 cents per octave, 100 cents per equal-tempered semitone, and the cent applies the same way at any base frequency — going from 100 Hz to 100.58 Hz is the same "musical distance" (10 cents) as going from 1,000 Hz to 1,005.78 Hz.

Why two-frequency intervals matter

Pure tuning intervals (just intonation) use simple integer ratios: 3:2 = perfect 5th, 5:4 = major 3rd, 6:5 = minor 3rd. These ratios produce maximally consonant sounds because the overtones align. Equal temperament (12-TET) tempers all intervals to a uniform semitone of exactly 100 cents — convenient for keyboards but slightly "wrong" compared to just intervals (a 12-TET major 3rd is 13.69 cents flat of the just 5:4 version).

Practical use cases

Choir directors use cents to analyse pitch drift across phrases. Studio engineers use it to tune samples and loops to a target. Microtonal composers use it to specify experimental scales (e.g., 24-TET quarter-tones, 19-TET, Bohlen-Pierce). Researchers use it to study cultural tuning traditions — gamelan, maqam, raga systems all use non-12-TET intervals best described in cents.

Interval names beyond an octave

For cents values above 1,200, this tool reduces them to a single-octave interval class plus the octave count. So 1,902 cents = "Just perfect 5th + 1 octave" (a "twelfth"). 2,400 cents = "Octave + 1 octave" = two-octave doubling.

Frequently Asked Questions

How do I calculate cents between two frequencies?
Use the formula cents = 1200 × log₂(f₂ / f₁). For example, 440 Hz to 660 Hz: log₂(660/440) = log₂(1.5) = 0.585, × 1200 = 701.96 cents (a just perfect 5th — exactly 3:2 ratio). For 440 to 880 (an octave): log₂(2) × 1200 = 1200 cents exactly.
Why is 50 Hz to 60 Hz mains hum a "just minor 3rd"?
60 / 50 = 6/5 = 1.2 — that's exactly the just intonation minor 3rd ratio. The cents calculation gives 1200 × log₂(1.2) = 315.64 cents, which is exactly the just minor 3rd. So in countries with both 50 Hz and 60 Hz grids, the mains hum across borders forms a perfectly-tuned just minor 3rd interval.
Is the cents value positive or negative?
When f₂ > f₁ (going up), the cents value is positive. When f₂ < f₁ (going down), it's negative. The tool labels descending intervals as "(descending)". For example, 880 Hz → 440 Hz is −1200 cents (one octave descending).
What's the difference between a "just" and "12-TET" interval?
Just intervals use simple integer frequency ratios (3:2, 5:4, 6:5, 9:8, etc.) which produce maximally pure-sounding consonances. 12-TET (12-tone equal temperament) divides the octave into 12 mathematically equal semitones (each 100 cents), trading slight harmonic impurity for the ability to play in any key without retuning. Most just intervals differ from their 12-TET equivalents by 2–16 cents.
Can I use this for pitch drift analysis?
Yes — measure the frequency at two points in time (start and end of a sustained note, or before and after a recording session) and put them in as f₁ and f₂. The cents value tells you how much pitch shifted. Vocal performances naturally drift ±10 cents; piano tuning shifts ~3–5 cents per year; reed instruments warm up about 10–20 cents in the first minutes of play.
What's the Pythagorean comma?
It's the small interval (~23.46 cents) that "leftover" when you stack 12 perfect 5ths and compare to 7 octaves. (3/2)¹² = 129.746, while 2⁷ = 128. The ratio is 531441/524288 = 1.01364, which in cents is 23.46. This is why equal temperament has to "compromise" — you can't stack pure intervals and end up at pure octaves simultaneously.