Semitone calculator: cents, ratio and speed

There are 100 cents in a semitone. A whole tone is 200 cents and an octave is 1200. This semitone calculator turns a shift in semitones into a frequency ratio (2 to the power of semitones ÷ 12), a playback-speed change in percent and the shifted frequency in Hz, so +7 semitones reads as ×1.498, +49.8% and 440 → 659.26 Hz. Enter a shift above, or use the tables below for the common conversions.

The second panel counts the semitone distance between two keys, and the third converts a pitch shift into a new tempo for samples played without time-stretch. Everything on this page is equal temperament, which is what tuners, DAWs and samplers use by default.

Cents to semitones (and back)

Cents to semitones: divide by 100. Semitones to cents: multiply by 100. The scale is logarithmic, so every cent is the same frequency ratio (2 to the power of 1 ÷ 1200, about 1.000578). That is why 50 cents is always a quarter tone and 1200 cents is always an octave, whatever note you start on.

Worked example: a tuner reads −30 cents. That is 0.3 semitone flat, a ratio of 0.9828, or 1.7% low. Correct it with +30 cents of fine tune in the sampler, or by moving the sample 0.3 semitone up. 440 Hz against a 442 Hz reference is 7.9 cents, which is the gap between a 440 piano and a 442 orchestra.

Semitones to frequency ratio and percent (±1 to ±12)

Pitch up multiplies the frequency by 2 to the power of n ÷ 12; pitch down divides by it. The percent column is also the playback-speed change on tape, vinyl or a sampler without time-stretch. Up a semitone is +5.95% but down a semitone is only −5.61%, because the ratios are reciprocals, not mirror images. The last column shows what A4 at 440 Hz becomes.

To look up the frequency of any note before you shift it, use the note to frequency calculator; to check a played note against 440 Hz, use the online tuner.

Hz to semitones: the formula

Two frequencies are a fixed number of semitones apart no matter how high or low they sit, so the conversion uses a logarithm of the ratio, not the difference in Hz.

Two more: 440 Hz to 523.25 Hz is 12 × log2(1.1892) = exactly 3 semitones (A4 to C5). 220 Hz to 440 Hz is log2(2) × 12 = 12 semitones, one octave, and the same is true for 55 → 110 Hz even though the Hz difference is eight times smaller. Going the other way, a bass note at 55 Hz shifted +7 semitones lands on 55 × 1.4983 = 82.41 Hz, the low E on a guitar.

Playback speed and pitch: tape, vinyl, samplers

When pitch and tempo are locked (varispeed tape, a turntable pitch fader, a sampler with time-stretch off), speed and pitch change by the same ratio. Speed +25% is +3.86 semitones; slowing to 90% speed is −1.82 semitones; half speed is exactly −12. Tempo follows the same ratio: 120 BPM at +3 semitones becomes 142.7 BPM, and matching 111 BPM to 129 BPM takes +2.6 semitones. The sample calculator above does both directions.

Modern time-stretch and pitch-shift algorithms decouple the two, so a −3 semitone shift with stretch on leaves the tempo alone. For the same math starting from a tempo change in percent, use the tape / vari-speed calculator; to change a file's speed in the browser, the audio speed changer. Once you have the new BPM, the song length calculator gives bars and minutes at that tempo and the delay & reverb time calculator gives delay times to match.

Transposing to a new key

Key-to-key moves are counted in semitones too, and the key panel above picks the shortest path. C to E♭ is +3 up or −9 down; because every 12 semitones is an octave, a sampler set to −9 lands on the same note name an octave lower. Identify the key of a sample or vocal with the song key finder and its tempo with the BPM detector, then transpose. Large shifts on vocals and acoustic instruments usually show artifacts, so if the shortest path is more than a few semitones, consider the nearest key that works instead.

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