Cent to Hz Converter
Apply a cents offset to any reference frequency using the formula f = f₀ × 2^(cents/1200). Compare just intonation vs equal temperament with 13 interval presets, switch reference tunings (440 / 432 / 415 Hz), and A/B audio playback for direct ear comparison.
Input
Result
Just Intonation vs Equal Temperament Intervals
| Interval | 12-TET (¢) | Just (¢) | Just Ratio | Difference (¢) |
|---|---|---|---|---|
| Unison | 0 | 0 | 1:1 | 0 |
| Minor 2nd (semitone) | 100 | 111.73 | 16:15 | +11.73 |
| Major 2nd | 200 | 203.91 | 9:8 | +3.91 |
| Minor 3rd | 300 | 315.64 | 6:5 | +15.64 |
| Major 3rd | 400 | 386.31 | 5:4 | −13.69 |
| Perfect 4th | 500 | 498.04 | 4:3 | −1.96 |
| Tritone | 600 | 590.22 / 609.78 | 45:32 / 64:45 | −9.78 / +9.78 |
| Perfect 5th | 700 | 701.96 | 3:2 | +1.96 |
| Minor 6th | 800 | 813.69 | 8:5 | +13.69 |
| Major 6th | 900 | 884.36 | 5:3 | −15.64 |
| Minor 7th | 1000 | 996.09 | 16:9 | −3.91 |
| Major 7th | 1100 | 1088.27 | 15:8 | −11.73 |
| Octave | 1200 | 1200 | 2:1 | 0 |
About Cents, Microtuning & Just Intonation
A cent is 1/100th of an equal-tempered semitone, so 1,200 cents fit in an octave. Cents are a logarithmic unit — the same number of cents represents the same musical interval at any base frequency. This cent to Hz converter takes a reference frequency f₀ and applies a cents offset to compute the resulting frequency using f = f₀ × 2^(cents/1200), making it useful as both a cents-to-frequency calculator and an interval cents calculator for comparing tuning systems. To go the other direction — measuring the cents interval between two known frequencies — use the Hz to cents converter.
Why this matters: 12-TET vs just intonation
Equal temperament (12-TET) divides the octave into 12 mathematically equal semitones — convenient for keyboard instruments but not perfectly aligned with the simple integer-ratio frequencies that produce maximally consonant chords. Just intonation uses ratios like 3:2 (perfect fifth) or 5:4 (major third) directly from the harmonic series. The result: 12-TET intervals are slightly "off" by anywhere from 2 to 16 cents compared to just intervals. When two notes are played together, this misalignment produces audible beat frequencies — periodic amplitude fluctuations whose rate equals the Hz difference between the two pitches. Most listeners don't hear the beats at typical ensemble tempos; trained ears and tuners can. Historically, meantone temperament (c. 1500–1800) was a compromise that kept thirds nearly pure at the cost of extremely impure fifths in remote keys.
Microtones and small commas
The Pythagorean comma (23.46 ¢) and syntonic comma (21.51 ¢) are tiny intervals that arise when you stack pure intervals. Stacking 12 just perfect fifths overshoots 7 octaves by exactly one Pythagorean comma — the fundamental impossibility that 12-TET works around by narrowing each fifth by about 2 cents. Microtonal composers use cents to specify pitches that fall between standard semitones, and many explore equal divisions of the octave (EDO) beyond 12: 19-EDO offers better minor thirds, 31-EDO approximates just intonation more closely, and 53-EDO provides near-perfect Pythagorean and just intervals.
Practical use cases
Studio engineers use this microtuning calculator to detune a track (e.g., shift a sample by +7 cents for harmonic richness through chorus-style thickening). Choral conductors use it to analyse vocal intonation and determine whether singers are drifting toward just intonation on major chords. Microtonal composers use it to define non-Western or experimental scales — for example, Arabic maqam uses quarter-tones (50 ¢ intervals), which fall exactly between equal-tempered semitones. Synthesizer programmers use it for fine pitch correction of layered patches, and DAW users apply cents offsets in pitch-correction plugins like Auto-Tune or Melodyne to shift recordings to a reference pitch. To verify where a result note sits in the full chromatic scale, cross-reference with the note to Hz converter.
How to convert cents to Hz: a worked example
The formula is f = f₀ × 2^(cents / 1200), where f₀ is your starting frequency and the exponent scales the ratio logarithmically. Here is a step-by-step conversion: start with A4 at 440 Hz and apply a +702 cents offset (the equal-tempered perfect fifth). Step 1 — divide the cents offset by 1200: 702 / 1200 = 0.585. Step 2 — raise 2 to that power: 2^0.585 = 1.4983. Step 3 — multiply by the reference: 440 × 1.4983 = 659.3 Hz, which is E5. The just-intonation perfect fifth uses the ratio 3:2 = 1.5000, giving 440 × 1.5 = 660.0 Hz — a difference of 0.7 Hz, or about 1.96 cents, which produces a slow, barely-audible beat between the two pitches.
Two common reference values to check your work: adding 100 cents to any frequency raises it by exactly one equal-tempered semitone (multiplier 1.05946), and adding 1200 cents always doubles the frequency (multiplier 2.000, a perfect octave). You can verify any result against the full note grid in the equal temperament chart, or reverse the calculation — measure the cents gap between two known frequencies — with the Hz to cents converter.