OneTaskBy Tim King · Updated
Pitch Shift Calculator
Semitones to Frequency Ratio, Speed and Tempo
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How the Pitch Shift Calculator works
This pitch shift calculator converts a shift in semitones and cents into the frequency ratio behind it, the new frequency of a note, and the speed and tempo change a recording takes on when it is resampled to that pitch rather than pitch-shifted.
How the pitch shift calculator works
In equal temperament each semitone multiplies the frequency by the twelfth root of two, about 1.05946. The formula is ratio = 2^(semitones ÷ 12), with cents counted as hundredths of a semitone. A pitch shifter changes the pitch by that ratio and keeps the length. Resampling changes the speed by the same ratio, so the length divides by it and the tempo multiplies by it.
First example. A shift of +3 semitones is a ratio of 1.189207. A4 at 440 Hz becomes 523.25 Hz, which is C5. Resampled, a 120 BPM track speeds up 18.921% to 142.7 BPM and plays in 84.09% of the time.
Second example. A shift of −2 semitones and −50 cents is −2.5 semitones, a ratio of 0.865537. Middle C at 261.63 Hz drops to 226.45 Hz, and a 100 BPM track resampled to that pitch slows to 86.55 BPM.
How many semitones is an octave? Twelve. A shift of +12 doubles the frequency and −12 halves it, so resampling an octave up plays at double speed in half the time.
Shifts of a few semitones sound natural on most material. Larger shifts on voices sound thin or cartoonish unless the pitch shifter preserves formants.
Frequency ratio, resampled speed change, A4 frequency and tempo from 120 BPM for each semitone shift
| Semitones | Ratio | Speed if resampled | A4 (440 Hz) becomes | Tempo from 120 BPM |
|---|---|---|---|---|
| -12 | 0.5 | -50% | 220 Hz | 60 |
| -11 | 0.52973 | -47.03% | 233.08 Hz | 63.57 |
| -10 | 0.56123 | -43.88% | 246.94 Hz | 67.35 |
| -9 | 0.5946 | -40.54% | 261.63 Hz | 71.35 |
| -8 | 0.62996 | -37% | 277.18 Hz | 75.6 |
| -7 | 0.66742 | -33.26% | 293.66 Hz | 80.09 |
| -6 | 0.70711 | -29.29% | 311.13 Hz | 84.85 |
| -5 | 0.74915 | -25.08% | 329.63 Hz | 89.9 |
| -4 | 0.7937 | -20.63% | 349.23 Hz | 95.24 |
| -3 | 0.8409 | -15.91% | 369.99 Hz | 100.91 |
| -2 | 0.8909 | -10.91% | 392 Hz | 106.91 |
| -1 | 0.94387 | -5.61% | 415.3 Hz | 113.26 |
| 0 | 1 | +0% | 440 Hz | 120 |
| +1 | 1.05946 | +5.95% | 466.16 Hz | 127.14 |
| +2 | 1.12246 | +12.25% | 493.88 Hz | 134.7 |
| +3 | 1.18921 | +18.92% | 523.25 Hz | 142.7 |
| +4 | 1.25992 | +25.99% | 554.37 Hz | 151.19 |
| +5 | 1.33484 | +33.48% | 587.33 Hz | 160.18 |
| +6 | 1.41421 | +41.42% | 622.25 Hz | 169.71 |
| +7 | 1.49831 | +49.83% | 659.26 Hz | 179.8 |
| +8 | 1.5874 | +58.74% | 698.46 Hz | 190.49 |
| +9 | 1.68179 | +68.18% | 739.99 Hz | 201.82 |
| +10 | 1.7818 | +78.18% | 783.99 Hz | 213.82 |
| +11 | 1.88775 | +88.77% | 830.61 Hz | 226.53 |
| +12 | 2 | +100% | 880 Hz | 240 |
FAQ
How do I convert semitones to a frequency ratio?
Raise 2 to the power of the semitones divided by 12. Five semitones is 2^(5 ÷ 12) = 1.3348, so the frequency rises by about 33.5%. Negative semitones give a ratio below one.
What is a cent in music?
A cent is one hundredth of an equal-tempered semitone, so an octave has 1,200 cents. Most listeners notice differences of about 5 to 10 cents between two notes played one after the other.
How much faster does a song play one semitone up?
About 5.95% faster when it is resampled, because the ratio for one semitone is 1.05946. A 120 BPM song becomes 127.14 BPM, and a four-minute song lasts about 3 minutes 46.5 seconds.
What is the difference between pitch shifting and resampling?
Pitch shifting changes the pitch and keeps the length and tempo. Resampling or varispeed, like speeding up a tape, changes pitch, length and tempo together by the same ratio.
Why are some shifts given as a ratio instead of semitones?
Samplers, granular plug-ins and code often take a playback rate rather than musical units. The ratio from this calculator is the value to enter, such as 1.5 for a perfect fifth in just tuning.
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