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.
Common intervals reference table
| Semitones | Interval name | ET ratio | Cents | Just ratio |
|---|---|---|---|---|
| 0 | Perfect unison | 1.0000 | 0 | 1:1 |
| 1 | Minor 2nd | 1.0595 | 100 | 16:15 |
| 2 | Major 2nd | 1.1225 | 200 | 9:8 |
| 3 | Minor 3rd | 1.1892 | 300 | 6:5 |
| 4 | Major 3rd | 1.2599 | 400 | 5:4 |
| 5 | Perfect 4th | 1.3348 | 500 | 4:3 |
| 7 | Perfect 5th | 1.4983 | 700 | 3:2 |
| 9 | Major 6th | 1.6818 | 900 | 5:3 |
| 12 | Octave | 2.0000 | 1200 | 2:1 |
Worked examples
Transposing a concert pitch. Concert A is 440 Hz. A perfect fifth up (7 semitones) gives 440 × 2^(7/12) ≈ 659.26 Hz, the note E5. A minor third down (-3 semitones) gives 440 × 2^(-3/12) ≈ 369.99 Hz, the note F#4/Gb4.
Finding the frequency for a synth pitch. You want to tune an oscillator a tritone (6 semitones) above C3 (130.81 Hz). The ratio is 2^(6/12) = √2 ≈ 1.4142, giving 130.81 × 1.4142 ≈ 185.00 Hz — F#3.
Equal temperament vs just tuning. A perfect fifth in equal temperament has a ratio of approximately 1.4983, while just tuning gives exactly 3:2 = 1.5. The difference is about 2 cents — barely audible in isolation, but noticeable in slow-moving chord music, which is why some orchestras and choirs tune by ear to just intervals rather than to a fixed tempered pitch.
Uses for audio developers and producers
This calculator is useful when you need to pitch-shift audio programmatically, design synthesiser intervals, detune an oscillator by a precise number of cents for chorus or beating effects, or match a sample to a different key. Enter a negative cent value (converted to semitones as cents/100) to detune downward. Everything runs in your browser and nothing is uploaded.