Pitch Shift Semitones to Frequency

Pitch shift in semitones to frequency: formula and example

In equal temperament, moving a frequency by n semitones works out to f_new = f_old · 2^(n/12). Push 440 Hz up 5 semitones (a perfect fourth) and you multiply by roughly 1.3348, landing near 587.33 Hz (D5). An octave up, which is 12 semitons, doubles the frequency; drop 12 and it halves. A negative n lowers the pitch.

Applications

Every modern DAW (Pro Tools, Logic, Ableton) runs this formula under the hood when it pitch-shifts, usually through PSOLA or phase-vocoder algorithms. Antares Auto-Tune and Celemony Melodyne lean on semitone-based shifts to correct vocals. Producers nudge samples up or down a few semitones to match a song's key, harmonizers spin off parallel voices, and DJs key-match tracks so a mix flows without a jarring clash. Hardware pitch shifters like the Eventide H3000 are built right on top of this exponential relationship.

FAQ

Why does pitch-shifting audio change tempo? Plain resampling ties the two together. Modern phase-vocoder algorithms break that link, so you can shift the pitch without speeding the audio up.

How far can I shift before it sounds artificial? Vocals tend to hold up to about ±3-4 semitons before the formants start sounding chipmunked. Instruments take more abuse.

What about non-integer semitones? A shift of 7.5 semitons is perfectly valid, which comes in handy for micro-tuning or matching a recording that sits slightly off pitch.

Why 2^(n/12)? Equal temperament splits the octave (a 2:1 ratio) into 12 logarithmic steps of equal size, which makes each semitone the 12th root of 2.