Tempo and Pitch Calculator: BPM Change to Semitones

How does a tempo change become a pitch change?

Pitch moves by 12 × log₂ of the speed ratio, measured in semitones. Playing audio faster raises every frequency by the same ratio as the tempo. An octave, 12 semitones, is a doubling of frequency, so the logarithm turns the ratio into semitones.

semitones = 12 × log₂(new BPM ÷ original BPM) · cents = semitones × 100

One semitone equals a speed ratio of 1.0595, a 5.95% change. That is why a 6% tempo change sounds almost exactly one semitone higher. The reverse form multiplies the tempo by 2^{semitones ÷ 12}.

Varispeed vs time-stretching and key lock

Varispeed changes tempo and pitch together; time-stretching changes tempo alone. The calculator describes varispeed.

• Varispeed is what a turntable, tape machine or sampler does when it plays faster: the whole signal speeds up, so pitch rises with tempo.
• Time-stretching is digital processing that changes length without changing pitch. DAW warp and elastic audio modes use it.
• Key lock, also called master tempo on DJ players, applies time-stretching live so a track keeps its key while the pitch fader moves.

With key lock on, the semitone result is the pitch change you avoided; with it off, it is the pitch change you hear.

How to use both forms

1. Enter the two tempos

   Type the Original tempo (BPM) and New tempo (BPM), each from 20 to 300.

2. Read the four results

   Pitch change in semitones, Speed change in percent, the same shift In cents, and the Speed ratio of new ÷ original.

3. Or start from semitones

   Under Shift by semitones instead, enter an original tempo and a value from −24 to 24 semitones. Negative numbers lower the pitch.

4. Read the new tempo

   The sentence gives the BPM that varispeed produces for that shift.

Worked examples: tempo changes and their pitch shift

Small tempo nudges move pitch by fractions of a semitone. Each row is computed with the formula above.

Going from 120 up to 128 and back is not symmetric in percent (+6.67% versus −6.25%), but it is symmetric in semitones. For the percentage alone, the BPM percentage calculator also checks pitch-fader ranges.

Where the result matters

The number tells you whether a speed change will clash with the key. DJs mixing without key lock use it to judge whether two tracks stay in tune: a shift of 0.27 semitone (27 cents) is a slight detune, while a full semitone moves the song into a new key. The guide to BPM for DJs covers beatmatching in detail.

Producers use the reverse form to repitch a sample by whole semitones and learn the tempo it will play at. Pitching a 90 BPM break up 12 semitones doubles it to 180 BPM, the relationship the half and double tempo tool lists.

Limits

The calculator assumes equal temperament and pure varispeed. It does not process audio, detect the key of a track, or model the small artifacts of time-stretching algorithms. Results are rounded to two decimals for semitones and to whole cents.

Questions