An interval is the distance between two notes. It has two parts: a number, found by counting letter names (C up to E is C–D–E, a third), and a quality, found from the exact number of semitones (a third with 4 semitones is major, with 3 semitones minor). Perfect intervals – unisons, fourths, fifths and octaves – can be perfect, augmented or diminished; seconds, thirds, sixths and sevenths can be major, minor, augmented or diminished.
Because the number comes from the letters, two intervals can sound the same yet be named differently. F♯ up to B♭ spans four semitones like a major third, but its letters F–G–A–B make it a fourth – a diminished fourth. Such spellings matter in harmony and in reading music, which is why the calculator offers a “note names” mode. In “pitches” mode only the semitone count is used, as you would hear the interval.
You also get the size in tones and cents, the equal-tempered and just-intonation frequency ratios, the frequencies of both notes and the inversion of the interval (the interval that completes the octave).
How to use the Music Interval Calculator
- Interval between
- Note 1
- Octave of note 1
- Note 2
- Octave of note 2
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
In note-name modes the calculator counts the letter steps between the notes (plus octaves) and compares the semitone count with the major or perfect interval of that number to find the quality. In pitch mode the interval is named from the semitone count alone.
Worked example
F♯ to B♭: the letters F, G, A, B make a fourth. A perfect fourth from F♯ would be B (5 semitones), but B♭ is only 4 semitones above F♯, one less than perfect, so the interval is a diminished fourth (d4). It sounds like a major third: 400 cents, ratio 2^(4/12) = 1.2599. Its inversion is an augmented fifth (8 semitones).
Intervals within an octave
| Semitones | Short | Interval | Just ratio |
|---|---|---|---|
| 0 | P1 | Perfect unison | 1:1 |
| 1 | m2 | Minor second | 16:15 |
| 2 | M2 | Major second | 9:8 |
| 3 | m3 | Minor third | 6:5 |
| 4 | M3 | Major third | 5:4 |
| 5 | P4 | Perfect fourth | 4:3 |
| 6 | A4 / d5 | Tritone | 45:32 |
| 7 | P5 | Perfect fifth | 3:2 |
| 8 | m6 | Minor sixth | 8:5 |
| 9 | M6 | Major sixth | 5:3 |
| 10 | m7 | Minor seventh | 9:5 or 16:9 |
| 11 | M7 | Major seventh | 15:8 |
| 12 | P8 | Perfect octave | 2:1 |
Formula
Interval number = letter steps + 1 (C→E = 3rd)
Quality from semitones: P/M (reference) · m = M − 1 · A = P or M + 1 · d = P − 1 or m − 1
Cents = 100 × semitones · equal-tempered ratio = 2^(semitones ÷ 12)
Worked example
Inputs — Interval between: Note names – note 2 above note 1 (within an octave); Note 1: F♯; Note 2: B♭.
Results — Interval = Diminished fourth; Short name = d4; Semitones = 4; Tones (whole steps) = 2; Cents = 400; Equal-tempered frequency ratio = 1.25992.
Key terms
- Interval number
- The count of letter names from the lower to the upper note, both included.
- Interval quality
- Perfect, major, minor, augmented or diminished.
- Compound interval
- An interval wider than an octave.
- Inversion
- The interval obtained by moving the lower note up an octave; the two sum to 9 (number) and 12 (semitones).
- Cent
- 1/100 of a semitone.
Frequently asked questions
What interval is C to E?
A major third – three letter names (C, D, E) and four semitones.
What interval is F to C?
A perfect fifth (F, G, A, B, C = five letters, seven semitones).
What interval is A♯ to C?
A diminished third: three letters (A, B, C) but only two semitones.
What interval is F♯ to B♭?
A diminished fourth – it sounds like a major third (4 semitones) but spans four letter names.
How many semitones are in a perfect fifth?
Seven; the just ratio is 3:2 and the equal-tempered ratio 1.4983.
What is the inversion of a major third?
A minor sixth – the two add up to an octave (4 + 8 = 12 semitones), and major turns into minor.
What is a compound interval?
An interval larger than an octave, e.g. a major tenth = an octave plus a major third (16 semitones).