BEATTIMING
Varispeed calculator

Pitch shift and tempo

Calculate the frequency ratio, speed change and resulting BPM when varispeed shifts pitch by semitones.

Varispeed tempo134.695 BPM+12.246% speed · 1.122462× ratio
Frequency ratio1.122462×
Speed change+12.246%
Inverse speed factor89.090%
Cents200

This relationship applies when pitch and speed are linked. Pitch-preserving processing can change one without changing the other.

Formula

How pitch and tempo change with varispeed

Equal-tempered pitch changes use a ratio of two raised to the number of semitones divided by 12. In linked varispeed playback, the same ratio changes frequency, playback speed and BPM together.

speed ratio = 2 ^ (semitones ÷ 12)

  1. 01

    Positive semitones increase both pitch and tempo in linked varispeed processing.

  2. 02

    Negative semitones lower pitch and slow the resulting tempo.

  3. 03

    Pitch-preserving time stretch changes tempo without following this varispeed relationship.

Worked example

Example: shifting 120 BPM by one octave

Raising linked varispeed by 12 semitones gives a ratio of 2, so 120 BPM becomes 240 BPM. Lowering it by 12 semitones gives a ratio of 0.5, so 120 BPM becomes 60 BPM.

Good to know

Assumptions and limits

  • Pitch and speed are linked, as with tape-style varispeed or resampling.
  • The calculation uses 12-tone equal temperament.
  • Pitch-preserving time stretch and formant controls do not follow this relationship.
Quick answers

Frequently asked questions

What happens when I pitch up one octave?

An octave is 12 semitones, so linked varispeed doubles the speed and BPM.

Why does my pitch shifter not change BPM?

Modern pitch shifters can preserve duration. This calculator describes linked pitch-and-speed or varispeed changes.

How many percent is one semitone?

One equal-tempered semitone has a frequency and speed ratio of approximately 1.05946, or a 5.946% increase.