This calculator moves a base frequency up or down by a number of semitones and returns the exact target pitch, the equal-temperament ratio, the size in cents, and the interval name with its just-intonation ratio for comparison. It is for musicians, tuners and audio developers.
How it works
In 12-tone equal temperament each semitone multiplies frequency by the twelfth root of two, so an interval of n semitones has a frequency ratio of:
ratio = 2^(n / 12) · target = base × ratio · cents = n × 100
The interval is named by reducing the semitone count within one octave (n mod 12) and looking it up — 0 unison, 7 perfect fifth, 12 octave — alongside its pure just-intonation ratio (e.g. 3:2 for a fifth). Negative semitones transpose downward.
Example
Starting from A4 = 440 Hz and going up a perfect fifth (7 semitones):
ratio = 2^(7/12) ≈ 1.4983; target = 440 × 1.4983 ≈ 659.26 Hz (E5); size = 700 cents; just ratio 3:2.
| Semitones | Interval | ET ratio | Cents |
|---|---|---|---|
| 0 | Perfect unison | 1.0000 | 0 |
| 4 | Major 3rd | 1.2599 | 400 |
| 7 | Perfect 5th | 1.4983 | 700 |
| 12 | Octave | 2.0000 | 1200 |
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