How many semitones are in an interval?

A minor third is 3 semitones, a major third 4, a perfect fifth 7 and an octave 12. The full table is on this page, alongside the frequency ratio each interval represents.

One hundredth of a semitone. Tuners and pitch plugins use cents for fine adjustment: five cents is a subtle detune, fifty cents is a quarter tone and clearly out of tune.

Why is the ratio not a whole number?

Equal temperament divides the octave into twelve equal multiplications rather than simple whole-number ratios, so each semitone multiplies frequency by the twelfth root of two — about 1.05946. Only the octave comes out exact at 2.

Does the octave matter?

For the interval name, no — an interval is the distance between pitches. For frequencies it does, which is why you can set the octave of the starting note.

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Semitone & Interval Calculator

Semitone distance, interval name, cents and the exact frequency ratio between any two notes.

Deterministic maths, calculated in your browser.

Notes

From note

Octave

Middle C is C4.

To note

Semitones up

Perfect 5th

Shortest distance

-5

Signed, within an octave

Cents

700

Frequency ratio

1.498307

Multiplier

261.63 Hz

Resulting pitch

392 Hz

G above

Interval reference

Semitones, interval names and ratios
Semitones	Interval	Ratio	Cents
0	Unison	1	0
1	Minor 2nd	1.05946	100
2	Major 2nd	1.12246	200
3	Minor 3rd	1.18921	300
4	Major 3rd	1.25992	400
5	Perfect 4th	1.33484	500
6	Tritone	1.41421	600
7	Perfect 5th	1.49831	700
8	Minor 6th	1.5874	800
9	Major 6th	1.68179	900
10	Minor 7th	1.7818	1000
11	Major 7th	1.88775	1100
12	Octave	2	1200

Interval names here are the common equal-tempered ones. Enharmonic spellings such as augmented fourth and diminished fifth are the same six semitones; which name is correct depends on the harmonic context, not the distance.

Detail

How this works

An interval is a distance measured in semitones, and in equal temperament each semitone multiplies frequency by 2^(1/12). Twelve semitones therefore double the frequency, which is why an octave is the one interval with a clean ratio.

Cents are the fine unit: one hundred per semitone. Pitch correction, tuning references and detuned layers all work in cents rather than semitones because the useful moves are far smaller than a fret.

FAQ

Frequently asked questions

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