A compound interval is an interval larger than an octave, made by adding an octave to a simple interval: a 9th is a 2nd plus an octave, fourteen semitones for a major 9th, and an 11th is a 4th plus an octave, seventeen semitones. Compound intervals are named by adding seven to the simple interval's number.
What are compound intervals?
A compound interval is any interval larger than an octave. It is made by taking a simple interval, one within an octave, and adding an octave to it. A 9th is a 2nd plus an octave, an 10th is a 3rd plus an octave, an 11th is a 4th plus an octave, and a 13th is a 6th plus an octave. The naming rule is simple: add seven to the number of the simple interval, and add twelve to its semitone count. A major 2nd is two semitones, so a major 9th is fourteen semitones; a perfect 4th is five semitones, so a perfect 11th is seventeen semitones. Compound intervals matter because they are the language of extended chords. When a chord symbol says C9, the 9th is a compound interval: the D sits an octave above the root, not next to it. When it says C13, the 13th is a compound 6th, the A sitting an octave above the 6th degree. Understanding compound intervals means understanding why extended chords are spelled the way they are, and why the 9th, 11th and 13th are written as large numbers instead of as 2nds, 4ths and 6ths.
How compound intervals are calculated
To name a compound interval, subtract seven from the number to get the simple interval, and subtract twelve from the semitones to get the simple interval's size. A 13th minus seven is a 6th, so a major 13th is a major 6th plus an octave: nine semitones plus twelve is twenty-one. A minor 10th minus seven is a minor 3rd: three semitones plus twelve is fifteen. The quality never changes when you add an octave: a major interval stays major, a minor interval stays minor, and a perfect interval stays perfect, because the octave adds no new quality, only distance. The most common compound intervals are the 9th, 11th and 13th, because they are the extensions of chords. A major 9th is fourteen semitones, a minor 9th is thirteen. A perfect 11th is seventeen semitones, and an augmented 11th is eighteen. A major 13th is twenty-one semitones, and a minor 13th is twenty. Less common are the 10th, a compound 3rd, and the 12th, a compound 5th, which appear in piano voicings and in the analysis of wide melodies. The C9 guitar chord contains a major 9th, and the C13 guitar chord contains a major 13th.
Worked example — the 11th above G. Subtract seven from eleven to get four, so the 11th is a compound 4th. The perfect 4th above G is C, five semitones, so the perfect 11th above G is C an octave higher, seventeen semitones. In a G11 chord the notes are G, B, D, F, A and C, and the C is the 11th, sitting above the rest of the chord. Notice that the 11th, C, sits a semitone above the 3rd, B, which is why 11th chords usually leave the 3rd out. The G major scale shows the 4th degree, C, that the 11th is built from.
How to practise compound intervals
Practise compound intervals by reducing them to their simple form first, then adding the octave back, so the calculation becomes a habit.
- Name the simple interval inside each compound interval: a 9th is a 2nd, a 10th is a 3rd, an 11th is a 4th, a 12th is a 5th and a 13th is a 6th.
- Play a major 9th on the piano by playing the major 2nd and then the same note an octave higher, and listen for the same quality at a greater distance.
- Work out the compound intervals above C, from the 9th to the 15th, and write down the semitone count for each one.
- Build a C13 chord note by note, naming each extension as a compound interval: the 9th is a compound 2nd, the 11th is a compound 4th, the 13th is a compound 6th.
- Use the interval calculator to check the semitone count of any compound interval before you use it in a chord.
Common mistakes
- Adding seven to the semitones instead of twelve — A compound interval adds an octave, twelve semitones, not seven. A major 9th is fourteen semitones, two plus twelve, not nine semitones, which would be a major 6th.
- Calling a 9th a 2nd — A 9th and a 2nd sound the same pitch class, but they are different intervals with different functions. In a chord, the 9th sits above the octave and the 2nd sits below it, so the names are not interchangeable.
- Forgetting that the quality stays the same — Adding an octave never changes the quality: a minor 3rd becomes a minor 10th, not a major 10th. The quality comes from the simple interval, and the octave adds only distance.
Quick reference
This table lists the common compound intervals with the simple interval inside each one, so you can see the add-seven rule working down the rows. The 9th holds a 2nd, the 10th holds a 3rd, the 11th holds a 4th, and so on, and the semitone column is always the simple interval's size plus twelve.
| Compound interval | Simple interval | Semitones |
|---|---|---|
| Minor 9th | Minor 2nd | 13 |
| Major 9th | Major 2nd | 14 |
| Minor 10th | Minor 3rd | 15 |
| Major 10th | Major 3rd | 16 |
| Perfect 11th | Perfect 4th | 17 |
| Augmented 11th | Augmented 4th | 18 |
| Perfect 12th | Perfect 5th | 19 |
| Minor 13th | Minor 6th | 20 |
| Major 13th | Major 6th | 21 |
Memorise the table by working out each row yourself: subtract seven from the number, name the simple interval, and add twelve to its semitones. When you can do that without looking, try the same calculation for a compound interval above a root other than C, such as the major 9th above G, which is A, fourteen semitones up.
Frequently asked questions
What is a compound interval?
An interval larger than an octave, made by adding an octave to a simple interval. A 9th is a 2nd plus an octave, an 11th is a 4th plus an octave, and a 13th is a 6th plus an octave, with twelve semitones added to the simple interval's size.
How do you name a compound interval?
Add seven to the number of the simple interval and twelve to its semitone count. A major 2nd is two semitones, so a major 9th is fourteen semitones; a perfect 4th is five semitones, so a perfect 11th is seventeen semitones.
What is the difference between a 2nd and a 9th?
The distance: a 2nd sits within the octave, two semitones above the root for a major 2nd, while a 9th sits above the octave, fourteen semitones above the root for a major 9th. They are the same pitch class, but the 9th is an octave higher and functions as a chord extension.
Which compound intervals are most common?
The 9th, 11th and 13th, because they are the extensions of 7th chords. The 10th and 12th appear less often, mostly in piano voicings, and the 15th, a double octave, appears in the analysis of very wide melodies.
Does the quality change when you add an octave?
No. A major interval stays major, a minor interval stays minor, and a perfect interval stays perfect when you add an octave. The octave adds distance only, so the quality of a compound interval is always the quality of its simple form.