Beyond the octave
An octave is eight notes wide, so an interval wider than that is a compound interval: one simple interval plus an octave. From C up to the D above the next C is a 9th: a 2nd (C to D) with an octave added.
The rule: add or subtract 7
The quality never changes: a major 9th is a major 2nd plus an octave (14 half steps); a perfect 12th is a perfect 5th plus an octave (19 half steps).
Why chords use them
Chords are stacks of thirds: root, 3rd, 5th, 7th, then the 9th, 11th and 13th. These are compound numbers because they stack above the seventh. A 9th chord's extra note is the same letter as the 2nd, but it is placed high above the chord, so it adds colour without crowding the root. See the 9th chords and altered chords.
How to practise
- Warm-up: major and perfect compound intervals on white keys.
- Working set: adds minor intervals.
- Heavy lift: every root and every quality.
Make sure your simple intervals are solid first with the interval builder.
Frequently asked questions
What is a compound interval?
Any interval larger than an octave. A 9th is an octave plus a 2nd, a 10th an octave plus a 3rd, and so on. They have the same quality as their simple partner: a major 9th is a major 2nd plus an octave.
How do I find the simple interval of a compound one?
Subtract 7 from the number (9 − 7 = 2, 13 − 7 = 6). Keep the quality: a minor 10th is a minor 3rd plus an octave.
Why does a 9th chord have a 9 and not a 2?
Because the note sits above the seventh in the stack of thirds, more than an octave above the root. Played in that position it is a 9th; it is the same pitch class as the 2nd.
Is a 9th the same as a 2nd?
They are the same note name, one octave apart. In harmony the difference matters: a Csus2 has D close to C, while a C9 has D high above the chord.
What is a 14th?
A 14th is two octaves minus a step: a 7th plus an octave. It is rare; the double octave (15th) is the usual bigger step.