Music Interval Calculator (interval name, semitones and inversion)

Understanding the music interval calculator — concept and principle

This calculator names the interval between two notes, such as a minor sixth or a perfect fifth, and gives the number of semitones, the simple interval, the inversion and the equal-tempered frequency ratio. Students use it for ear training and theory homework; composers and arrangers use it to check spelling.

Count letters, then semitones: with the default inputs the result is Minor sixth (m6) (inverts to a major third).

How it is calculated

Interval number = letter names counted from the lower note to the upper, both included (D up to B = D E F G A B = a sixth).
Semitones = difference in pitch.
Quality compares the semitones with the major scale on the lower note: unison, 4th, 5th and octave are perfect when they match; 2nd, 3rd, 6th and 7th are major when they match and minor when one semitone smaller. One more than perfect or major is augmented; one less than perfect or minor is diminished.
Inversion: numbers add up to 9; major ↔ minor, augmented ↔ diminished, perfect stays perfect.
Frequency ratio = 2^(semitones ÷ 12).

The principle

An interval has two parts: how many letter steps it spans and how many semitones it contains. The letter count gives the number, so C to E and C to E♭ are both thirds. The semitone count decides the quality, so C to E (4 semitones) is a major third and C to E♭ (3) a minor third. Keeping both parts lets each note keep its proper spelling. In equal temperament every semitone multiplies frequency by 2^(1/12), which gives the frequency ratio.

Worked example

Default inputs: D4 to B♭4.

Letters D E F G A B = 6, a sixth.
Semitones: D4 to B♭4 = 8.
The major sixth above D is B (9 semitones); B♭ is one less, so the quality is Minor (m): m6.
Inversion: 9 − 6 = 3, minor → major: M3.
Frequency ratio = 2^(8/12) = 1.587; second note is higher; no octaves added (0).

Each point is the calculator re-run with only “Second note octave” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Second note octave	Interval
1	M17
2	M10
3	M3
4	m6
5	m13
6	m20
8	m34

How to read the result

The interval name tells you both the size and how it should be written. Enharmonic intervals sound the same but are named differently: D to B♭ is a minor sixth, while D to A♯ (also 8 semitones) is an augmented fifth. The inversion is useful when you think of the same pair of notes upside down, for instance in harmony or voice leading.

Common mistakes

Counting only the steps between the notes and forgetting to include both ends.
Naming the interval from semitones alone.
Using "minor" for fourths and fifths, which are perfect, augmented or diminished.
Forgetting that a ninth is an octave plus a second.

Keep in mind: The frequency ratio assumes equal temperament. Just intonation and other tuning systems use slightly different ratios.

Frequently asked questions

What interval is D to B♭?

A minor sixth, 8 semitones.

What is the inversion of a minor sixth?

A major third.

Why are fourths and fifths called perfect?

They match the major scale on the lower note and have no major or minor forms; changed by a semitone they become augmented or diminished.

Sources: S. Kostka, D. Payne & B. Almén, Tonal Harmony, 8th ed. (McGraw-Hill, 2018), ch. 1 (intervals)

Checked 9 Nov 2026. Interval number and quality (perfect, major, minor, augmented, diminished), compound intervals and inversion — standard music theory as taught in common-practice harmony textbooks; equal-temperament ratio 2^(n/12).

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