Perfect intervals are the unison, the perfect 4th, the perfect 5th and the octave: the most stable and consonant intervals in music. A perfect 5th spans seven semitones, a perfect 4th spans five, and the octave spans twelve, and they are called perfect because they sound so pure.
What are perfect intervals?
Perfect intervals are the unison, the perfect 4th, the perfect 5th and the octave, and they are called perfect because they are the most stable and consonant intervals in music. When two notes a perfect 5th apart sound together, their sound waves line up neatly, and the ear hears a pure, open, almost hollow sound with no tension at all. The perfect 4th and the octave behave the same way, and the unison, two notes of the same pitch, is the most perfect of all. The reason for this stability is acoustic: the perfect intervals correspond to the simplest ratios in the harmonic series. An octave is a 2:1 frequency ratio, a perfect 5th is 3:2, and a perfect 4th is 4:3, and those simple ratios are what the ear recognises as pure. The major and minor intervals have more complex ratios, which is why they sound less settled. This acoustic fact is also why perfect intervals are the skeleton of harmony: the root and the 5th of every chord form a perfect 5th, and the root and the octave frame every scale.
How perfect intervals work
The four perfect intervals have fixed sizes that never change. The unison is zero semitones, two notes of the same pitch. The perfect 4th is five semitones. The perfect 5th is seven semitones. The octave is twelve semitones. If you narrow a perfect interval by one semitone it becomes diminished, and if you widen it by one semitone it becomes augmented: C to F is a perfect 4th at five semitones, C to F# is an augmented 4th at six, and C to Fb is a diminished 4th at four. There is no major or minor version of a perfect interval, and calling one major or minor is a mistake. Perfect intervals are also the intervals that invert into each other. A perfect 5th up inverts to a perfect 4th down, and a perfect 4th up inverts to a perfect 5th down, because the two intervals add up to an octave: five semitones plus seven semitones is twelve. The octave inverts to a unison, and the unison inverts to an octave. That symmetry is useful when you are counting intervals downwards, because you can work out the ascending interval instead. The C major guitar chord is built on a perfect 5th, C to G, and the interval calculator measures any perfect interval from any root.
Worked example — perfect intervals above A. A to E is five letters, A, B, C, D, E, and seven semitones, so it is a perfect 5th. A to D is four letters and five semitones, a perfect 4th. A to A an octave higher is eight letters and twelve semitones, a perfect octave. Now narrow the 5th by one semitone: A to Eb, spelled D#, is six semitones, a diminished 5th, and the stable open sound collapses into the tense tritone. Widen it by one semitone instead: A to E# is eight semitones, an augmented 5th, and the chord becomes an augmented triad. The A major guitar chord and the A minor guitar chord both rely on the perfect 5th, A to E.
How to practise perfect intervals
Perfect intervals are the easiest to hear, because they sound so open and stable. Practise recognising them by their purity, not by counting.
- Play a perfect 5th on your instrument, then a major 3rd, and listen for the 5th sounding more open and hollow than the 3rd.
- Sing a perfect 4th above a root note, then a perfect 5th, and check yourself against the piano, aiming to feel the stability of each one.
- Play the open strings of a guitar in pairs, E to A, A to D, D to G, and name each interval: they are all perfect 4ths, five semitones apart.
- Practise the C major scale and notice that the 4th and 5th degrees, F and G, form perfect intervals above the root, while the other degrees form major intervals.
- Use the interval calculator to check any interval you think is perfect, and confirm that its size is 0, 5, 7 or 12 semitones.
Common mistakes
- Calling a 4th or 5th major or minor — Perfect intervals have no major or minor form. A 5th is perfect, diminished or augmented, and calling it major or minor is wrong and will confuse anyone you play with.
- Thinking the perfect 4th is always consonant — Against the bass note, a perfect 4th is treated as a dissonance in classical harmony, because it wants to resolve down to a 3rd. The 4th is perfect in size, but its function depends on where it sits in the chord.
- Confusing a diminished 5th with a perfect 5th — A diminished 5th spans six semitones, not seven, and it sounds tense and unstable, while a perfect 5th sounds open and settled. One semitone makes all the difference, so count carefully.
Quick reference
This table lists the four perfect intervals from two roots, C and G, so you can see that the semitone counts never change even though the note names do. The unison is the same note twice, the 4th is five semitones, the 5th is seven, and the octave is twelve, and those four numbers are worth memorising before anything else in interval theory.
| Perfect interval | From C | From G | Semitones |
|---|---|---|---|
| Unison | C – C | G – G | 0 |
| Perfect 4th | C – F | G – C | 5 |
| Perfect 5th | C – G | G – D | 7 |
| Octave | C – C | G – G | 12 |
Play the table on piano, first from C and then from G, and listen for the same open, stable quality in every row. When the four sizes feel automatic, try narrowing the 5th by one semitone to make a diminished 5th, and widening the 4th by one semitone to make an augmented 4th, and hear how quickly the perfection disappears.
Frequently asked questions
What are the perfect intervals?
The unison (0 semitones), the perfect 4th (5 semitones), the perfect 5th (7 semitones) and the octave (12 semitones). They are the most stable and consonant intervals in music, and they are called perfect because of their simple acoustic ratios.
Why are they called perfect?
Because their frequency ratios are the simplest in the harmonic series: 1:1 for the unison, 4:3 for the 4th, 3:2 for the 5th and 2:1 for the octave. Simple ratios sound pure to the ear, and musicians have called them perfect for centuries.
Can a perfect interval be major or minor?
No. Perfect intervals have no major or minor form. If a perfect interval is narrowed by a semitone it becomes diminished, and if it is widened by a semitone it becomes augmented.
What is the most important perfect interval?
The perfect 5th, because it is the interval between the root and the 5th of every chord, and between the tonic and the dominant of every key. It is the backbone of harmony, and the power chord is built from it alone.
Do perfect intervals invert to perfect intervals?
Yes. A perfect 5th up inverts to a perfect 4th down, and a perfect 4th up inverts to a perfect 5th down, because the two add up to an octave. The octave inverts to a unison, and the unison inverts to an octave.