Hong Life CalculatorsUnderstanding the semitone calculator — concept and principle
This calculator moves a note up or down by any number of semitones and shows the resulting note, the frequency ratio, both frequencies, the shift in cents and octaves, and the playback-speed change that would give the same pitch shift. Musicians, producers and audio students use it for transposing, tuning and sample manipulation.
How it is calculated
- MIDI number m of the starting note (A4 = 69, middle C = 60).
- Starting frequency f = A4 reference × 2^((m − 69) ÷ 12).
- Ratio r = 2^(n ÷ 12) for a shift of n semitones; resulting frequency = f × r.
- Cents = n × 100; octaves = n ÷ 12.
- Playback-speed change for the same shift = (r − 1) × 100%.
- Fractional shifts are shown as the nearest note plus cents.
The principle
In twelve-tone equal temperament every semitone multiplies the frequency by the same factor, 2^(1/12) ≈ 1.05946, so twelve semitones exactly double it, one octave. A cent is a hundredth of a semitone, a convenient unit for small tuning differences. Playing a recording faster raises every frequency by the same ratio, so a speed change of (r − 1) × 100% gives the same pitch shift, which is why simple resampling also changes the tempo.
Worked example
Default inputs: A4, up 7 semitones, A4 = 440 Hz.
- Starting frequency = 440 Hz (A4 is MIDI 69).
- Ratio = 2^(7/12) = 1.49831.
- Result = MIDI 76 = E5, 440 × 1.49831 = 659.26 Hz.
- Cents = 700; octaves = 7 ÷ 12 = 0.583.
- Same shift by speed = (1.49831 − 1) × 100 = 49.8% faster.
| Octave (middle C = C4) | Resulting note |
|---|---|
| 1 | E2 |
| 2 | E3 |
| 3 | E4 |
| 4 | E5 |
| 5 | E6 |
| 6 | E7 |
| 8 | E9 |
How to read the result
Seven semitones is a perfect fifth; the equal-tempered ratio 1.498 is very close to the pure 3:2 used in just intonation, which is why fifths sound so stable. Use the cents figure to fine-tune instruments or pitch-correct audio. To shift pitch without changing tempo, use a pitch-shift tool rather than speed.
Common mistakes
- Adding frequencies instead of multiplying by the ratio.
- Mixing octave numbering systems (some software calls middle C "C3").
- Forgetting to change the A4 reference for orchestras tuned to 442 Hz or older music at 415 Hz.
- Treating a speed change as pitch-only.
Frequently asked questions
What is 7 semitones above A4?
E5, at about 659.26 Hz with A4 = 440 Hz.
How many cents are in a semitone?
100 cents.
How much faster must audio play to go up a semitone?
About 5.95% faster.
Sources: ISO 16:1975, Acoustics — Standard tuning frequency (A4 = 440 Hz) · MIDI Manufacturers Association, MIDI 1.0 Detailed Specification (note numbering, A4 = 69)