Semitones Between Frequencies
Calculator
Results
- Interval (semitones)
- 7.01955
- Interval (octaves)
- 0.584962
- Frequency ratio
- 1.5
Music and audio results
| Interval (semitones) | 7.01955 |
| Interval (octaves) | 0.584962 |
| Frequency ratio | 1.5 |
formula-map diagram
- Interval (semitones)
- 7.01955
- Interval (octaves)
- 0.584962
- Frequency ratio
- 1.5
Musical and acoustic relationship
Formula
n = 12 × log₂(f₂ ÷ f₁)= 7.0195500086539
Note
This result is a simplified model: it applies the displayed standard formula to the values you entered, assuming twelve-tone equal temperament, a speed of sound of 343 m/s in dry air at 20 °C, an ideal free field with no reflections or air absorption, purely resistive speaker loads and Sabine's diffuse-field assumption. Real rooms, instruments, codecs and amplifiers depart from these idealisations, so measure with proper instruments for critical work.
More in Music and audio
See all →Frequently asked questions
What formula converts two frequencies into a semitone distance?+
The calculator uses n = 12 x log2(f2/f1), which measures how many equal-tempered semitone steps separate the two frequencies. The result can be fractional if the frequencies don't fall exactly on standard note pitches.
Why is the result sometimes not a whole number?+
A non-integer result means the two frequencies aren't a clean number of semitones apart, which happens with detuned instruments, synth sweeps, or measured audio rather than theoretical note values. A result like 3.18 semitones means the interval is a bit wider than a minor third.
Does the order of the two frequencies matter?+
Yes, the sign of the result indicates direction: a positive number means the second frequency is higher, a negative number means it's lower. The magnitude stays the same either way since it's a ratio-based logarithmic measure.
Why use semitones instead of just comparing frequencies in Hz directly?+
Pitch perception is logarithmic, not linear, so a 10 Hz difference sounds huge in the bass range but negligible in the treble range. Semitones express musical distance the way the ear actually hears it, which is why tuners and pitch-shifters use this unit instead of raw Hz differences.
How is this useful for tuning or pitch correction?+
Feeding in a measured frequency and a target frequency tells you exactly how many semitones (and hundredths of one) to shift a sample, oscillator, or instrument to bring it in tune. This is the same math behind auto-tune plugins and sampler pitch-shift controls.