Tap a key to set the first note
Interval: C4 → E4
Major third
3M4 semitones
From C4 to E4: Major third, 4 semitones
- Inversion
- Minor sixth
- Same sound
- Diminished fourth
- Size
- 400 cents · 5:4
- Consonance
- Imperfect consonance
How to name an interval
An interval has two parts, and each is counted separately: the number comes from the letters, the quality from the semitones.
- Count the letters, including both ends. C to E is C–D–E, three letters, so it is a third; C to A is six letters, a sixth. Accidentals do not change this: C to E♭ is still a third, and so is C to E♯.
- Count the semitones. C to E is four; C to E♭ is three. On a keyboard, every key — black or white — is one semitone from the next.
- Match the semitones to the number. Unisons, fourths, fifths and octaves are perfect when they have their usual size (0, 5, 7, 12 semitones). Seconds, thirds, sixths and sevenths are major at their larger size (2, 4, 9, 11) and minor one semitone smaller.
- Anything one semitone beyond those is augmented; one semitone short of perfect or minor is diminished. C to F♯ is a fourth by letters and six semitones, one more than perfect: an augmented fourth. C to G♭ is also six semitones, but a fifth by letters, one short of perfect: a diminished fifth.
Inversions
Move the lower note up an octave and the interval turns over: C up to E is a major third, E up to C is a minor sixth. The numbers of an interval and its inversion always add up to nine, and the qualities swap — major with minor, augmented with diminished, perfect with perfect.
That is why the calculator shows the inversion beside every result: an interval heard downward is usually easier to recognise as the inversion of one you know upward, and a chord voicing is often the inversion of the interval you expected.
Compound intervals
An interval larger than an octave is compound. Its name keeps counting letters — a tenth, an eleventh, a thirteenth — but its quality is that of the simple interval inside it: a major tenth is an octave plus a major third and sounds like one.
The calculator names compound intervals up to the fourteenth and states the simple form beside each. Past two octaves it says what a musician would say — two octaves and a fifth — rather than inventing a nineteenth.
A worked example
C4→A4·Major sixth
6M · 9 semitones · inversion: minor third
From C4 to A4. Letters: C, D, E, F, G, A — six, so it is a sixth. Semitones: C→C♯→D→D♯→E→F→F♯→G→G♯→A — nine. A sixth of nine semitones is major, so the interval is a major sixth, written 6M.
Turned over, A4 up to C5 is a minor third: six plus three is nine, and major has become minor. Respelled, C to B𝄫 has the same nine semitones but seven letters, which makes it a diminished seventh — the same sound, a different interval, and the reason the calculator asks for spellings rather than keys.
The simple intervals
Every interval within an octave, computed by the same code the calculator runs. Each name links to its reference page.
| Interval | Shorthand | Semitones | From C | Inversion |
|---|---|---|---|---|
| Unison | 1P | 0 | C – C | Unison |
| Augmented unison | 1A | 1 | C – C♯ | — |
| Diminished second | 2d | 0 | C – D𝄫 | Augmented seventh |
| Minor second | 2m | 1 | C – D♭ | Major seventh |
| Major second | 2M | 2 | C – D | Minor seventh |
| Augmented second | 2A | 3 | C – D♯ | Diminished seventh |
| Diminished third | 3d | 2 | C – E𝄫 | Augmented sixth |
| Minor third | 3m | 3 | C – E♭ | Major sixth |
| Major third | 3M | 4 | C – E | Minor sixth |
| Augmented third | 3A | 5 | C – E♯ | Diminished sixth |
| Diminished fourth | 4d | 4 | C – F♭ | Augmented fifth |
| Perfect fourth | 4P | 5 | C – F | Perfect fifth |
| Tritone | 4A | 6 | C – F♯ | Diminished fifth |
| Diminished fifth | 5d | 6 | C – G♭ | Tritone |
| Perfect fifth | 5P | 7 | C – G | Perfect fourth |
| Augmented fifth | 5A | 8 | C – G♯ | Diminished fourth |
| Diminished sixth | 6d | 7 | C – A𝄫 | Augmented third |
| Minor sixth | 6m | 8 | C – A♭ | Major third |
| Major sixth | 6M | 9 | C – A | Minor third |
| Augmented sixth | 6A | 10 | C – A♯ | Diminished third |
| Diminished seventh | 7d | 9 | C – B𝄫 | Augmented second |
| Minor seventh | 7m | 10 | C – B♭ | Major second |
| Major seventh | 7M | 11 | C – B | Minor second |
| Augmented seventh | 7A | 12 | C – B♯ | Diminished second |
| Octave | 8P | 12 | C – C | Unison |
| Diminished ninth | 9d | 12 | C – D𝄫 | Augmented seventh |
Questions
- How do you calculate the interval between two notes?
- Count the letter names from the first note to the second, including both, to get the number: C to G is C–D–E–F–G, a fifth. Then count the semitones to get the quality: C to G is seven, the usual size for a fifth, so it is a perfect fifth. The calculator does both counts and names the result.
- Why are C–F♯ and C–G♭ different intervals when they sound the same?
- Because the number is counted in letters. C to F♯ spans four letters and is an augmented fourth; C to G♭ spans five and is a diminished fifth. Both are six semitones, the tritone. Which one is written depends on the key and on where the note is going next, so the spelling carries information the sound alone does not.
- What is the inversion of an interval?
- The interval you get by moving the lower note up an octave, or the upper one down. A major third inverts to a minor sixth, a perfect fifth to a perfect fourth. The numbers add up to nine and the qualities swap, except perfect, which stays perfect.
- What is a compound interval?
- Any interval wider than an octave. A tenth is an octave plus a third, a twelfth an octave plus a fifth. Its quality is that of the simple interval inside it, so a major tenth is a major third with an octave added.
- Which intervals are consonant and which are dissonant?
- In the traditional classification, unisons, octaves, fourths and fifths are perfect consonances; thirds and sixths are imperfect consonances; seconds, sevenths and every augmented or diminished interval are dissonances. The perfect fourth is treated as a dissonance in some contexts, notably above the bass in strict counterpoint.
- How does the calculator handle a descending interval?
- If the second note is lower than the first, the interval is named from the lower note upward and marked as descending. E4 down to C4 is a major third, descending. In the from-a-note mode, choose the downward arrow and the calculator transposes down: a major third below C4 is A♭3, not A3.
- Why does the result sometimes show a double sharp or double flat?
- Because that is the correct spelling. A major third above E♯ is G𝄪: it must be some kind of G to be a third, and it needs two sharps to be four semitones away. The calculator keeps double accidentals, and only simplifies spellings that would need three, showing the strict spelling beside the simpler one.
- What are cents and the just ratio shown with an interval?
- Cents divide the octave into 1,200 equal parts, so an equal-tempered semitone is 100 cents and a major third is 400. The ratio is the frequency relation of the same interval in just intonation — 5:4 for a major third, 3:2 for a perfect fifth — which is where the equal-tempered version is tuned a little sharp or flat.