Cents ↔ frequency ratio
Convert frequency ratios to cents and semitones, measure intervals, and compare just intervals with equal temperament.
cents
semitones
octaves
Interval between two frequencies
Hz
Hz
- Interval from 1 to 2
- 7.85142cents
- Beat frequency
- 2Hz
Just intervals compared with equal temperament
| Interval | Just ratio | Just (cents) | Equal (cents) | Difference |
|---|---|---|---|---|
| Unison | 1:1 | 0.00 | 0 | 0.00 |
| Minor second | 16:15 | 111.73 | 100 | -11.73 |
| Major second | 9:8 | 203.91 | 200 | -3.91 |
| Minor third | 6:5 | 315.64 | 300 | -15.64 |
| Major third | 5:4 | 386.31 | 400 | 13.69 |
| Perfect fourth | 4:3 | 498.04 | 500 | 1.96 |
| Tritone | 45:32 | 590.22 | 600 | 9.78 |
| Perfect fifth | 3:2 | 701.96 | 700 | -1.96 |
| Minor sixth | 8:5 | 813.69 | 800 | -13.69 |
| Major sixth | 5:3 | 884.36 | 900 | 15.64 |
| Minor seventh | 9:5 | 1017.60 | 1000 | -17.60 |
| Major seventh | 15:8 | 1088.27 | 1100 | 11.73 |
| Octave | 2:1 | 1200.00 | 1200 | 0.00 |
How it works
One octave is 1200 cents and an equal-tempered semitone is 100 cents. Just intervals use small whole-number ratios; a just fifth (3:2) is about 2 cents wider than the tempered one, a just major third (5:4) about 14 cents narrower.
Formulas
- cents = 1200 · log₂(f₂ / f₁)
- ratio = 2^(cents / 1200)
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