Pitch & Intervals

Compound Interval

Definition

A compound interval is an interval wider than an octave, such as a 9th (an octave plus a 2nd) or a 10th (an octave plus a 3rd). It keeps the quality of the simple interval inside it.

A compound interval is any interval wider than an octave. Intervals up to an octave are simple; stretch one by an octave and it becomes compound. C4 up to D5 is a 9th: an octave (C4–C5) plus a 2nd (C5–D5).

Three one-bar treble-clef examples of three half notes each: C4 and D5, C4 and E5, C4 and G5, each as the lower note, the upper note, then both together. — Three compound intervals above C4, each shown in one bar: the lower note, the upper note, then both together. C4–D5 is a major 9th (an octave plus a major 2nd), C4–E5 a major 10th, and C4–G5 a perfect 12th.

Naming compound intervals

Count the letters from bottom to top, including both, just as for simple intervals. C4–D5 passes through C D E F G A B C D, nine letters: a 9th. To switch between compound and simple names, add or subtract 7, not 8, because the note at the octave is counted twice:

9th = 2nd + 7 (C4–D5)
10th = 3rd + 7 (C4–E5)
11th = 4th + 7 (C4–F5)
12th = 5th + 7 (C4–G5)
13th = 6th + 7 (C4–A5)
15th = a double octave (C4–C6)

The quality carries over unchanged: C4–E5 is a major 10th because C–E is a major 3rd, and C4–G5 is a perfect 12th. In half steps, add 12: a major 10th is 4 + 12 = 16 half steps.

E4 is a major 3rd above C4 (4 half steps). E5, one octave higher, is a major 10th above C4 (16 half steps): the same letters, stretched by an octave.

Compound or simple?

In harmony, compound intervals usually act like their simple versions. A 10th between the bass and the melody works like a 3rd, and the chord is still the same chord, so analysts often reduce compound intervals to simple ones ("the melody is a 3rd above the bass" even when it is an octave and a 3rd). Pianists meet 10ths constantly as wide left-hand stretches in stride and ballad accompaniments.

Chord symbols are the exception. In jazz and pop, 9, 11 and 13 name notes stacked above the seventh of an extended chord: C9 is C–E–G–B♭–D. To add the D without the seventh, the symbol is Cadd9 (see added-tone chord).

Inverting compound intervals

To invert a compound interval, reduce it to its simple form first: a major 10th behaves like a major 3rd and inverts to a minor 6th (see interval inversion).

Practice both skills with Inverting intervals & compound intervals.

Common questions

What is a compound interval?

An interval wider than an octave. It is named by counting letters as usual (C4–E5 is a 10th), and it has the same quality as the simple interval inside it: a major 3rd stretched by an octave is a major 10th.

Why do you subtract 7, not 8, to simplify a compound interval?

Because the note at the octave is counted twice: it is the 8th of the first count and the 1st of the next. A 10th is an octave (8) plus a 3rd (3) minus the shared note: 8 + 3 − 1 = 10. So 10 − 7 = 3.