About the Music Interval Calculator
This interval calculator names the distance between any two notes the way music theory does — "major third", "augmented fourth", "minor tenth" — rather than just counting semitones. Type two notes with optional accidentals and octave numbers (for example C4 and E♭5, or F# and C) and it returns the interval name and abbreviation, the number of semitones and cents, the inversion, the equal-tempered frequency ratio and the nearest just-intonation ratio.
It is built for theory students checking homework, ear-training practice, composers voicing chords and anyone confused about why C to G♯ is an augmented fifth but C to A♭ is a minor sixth. Both letters and accidentals matter: the interval number comes from counting letter names, and the quality from the exact number of semitones.
Notes without an octave number are taken to be in octave 4 (the octave of middle C). If the second note is lower than the first, the interval is reported as descending.
How to use the music interval calculator
- 1Type the first (usually lower) note, e.g. C4.
- 2Type the second note, e.g. A♭4 — use b for flat and # for sharp.
- 3Read the interval name, abbreviation and semitone count.
- 4Use the inversion and ratio to check harmony or tuning work.
Formula and method
The interval number comes from counting letter names from the lower note to the upper note inclusive: C to E is C-D-E, a third, whatever the accidentals. The quality compares the actual semitone count with the reference size for that number: unisons, fourths, fifths and octaves are "perfect" at 0, 5, 7 and 12 semitones; seconds, thirds, sixths and sevenths are "major" at 2, 4, 9 and 11. One semitone smaller makes a major interval minor (or a perfect one diminished); one larger makes either augmented.
Inverting an interval moves the lower note up an octave: the numbers add to 9 and major↔minor, augmented↔diminished, perfect stays perfect (a major third inverts to a minor sixth). Cents are 100 per equal-tempered semitone and the frequency ratio is 2^(semitones/12).
- P, M, m
- Perfect, major, minor
- A, d
- Augmented, diminished
- cents
- 1200 × log₂(frequency ratio); 100 per semitone
Worked examples
C4 to E4
C-D-E spans three letters, so it is a third; four semitones is the major size. Turned upside down (E up to C) it becomes a minor sixth, and the two add to 9.
C4 to G♯4 vs C4 to A♭4
G♯ and A♭ sound the same, but C to G♯ spans five letters (a fifth) one semitone larger than perfect, so it is an augmented fifth. C to A♭ would be a minor sixth.
Compound and descending: G4 down to B♭2
From B♭2 up to G4 is 13 letter names (an octave plus a sixth) and 21 semitones, i.e. a major sixth plus an octave = major thirteenth. Its simple inversion is a minor third.
The tritone F to B
F up to B is a fourth with six semitones — one more than perfect — so it is an augmented fourth (the tritone). Its ratio is √2 ≈ 1.4142 and it inverts to a diminished fifth.
Frequently asked questions
How do you name a musical interval?+
Count the letter names from the bottom note to the top note, including both, to get the number (C to F = 4th). Then count semitones to get the quality: perfect, major, minor, augmented or diminished compared with the reference size.
How many semitones are in each interval?+
Minor 2nd 1, major 2nd 2, minor 3rd 3, major 3rd 4, perfect 4th 5, tritone 6, perfect 5th 7, minor 6th 8, major 6th 9, minor 7th 10, major 7th 11, octave 12.
What is an interval inversion?+
Inverting an interval puts the lower note an octave higher. The interval numbers always add up to 9 (3rd ↔ 6th, 2nd ↔ 7th, 4th ↔ 5th) and qualities flip: major ↔ minor, augmented ↔ diminished, perfect stays perfect.
Why is C to D♯ an augmented second and not a minor third?+
Both span three semitones, but C to D♯ uses two letter names (C, D), making it a second, while C to E♭ uses three (C, D, E), making it a minor third. The spelling reflects the harmonic function.
What is a compound interval?+
An interval larger than an octave, such as a ninth (octave + 2nd), tenth (octave + 3rd) or twelfth (octave + 5th). It keeps the quality of its simple counterpart: a major ninth is an octave plus a major second.