Compound intervals

An interval wider than an octave is compound. One within an octave is simple.

Naming them

Keep counting letter names past eight.

Subtract seven from the compound number to get the simple one. A ninth minus seven is a second; an eleventh minus seven is a fourth. The quality is unchanged — a major ninth is a major second plus an octave.

When the distinction matters

Often it does not. In casual analysis a tenth is usually just called a third, because the two notes have the same harmonic relationship.

It matters in three places:

Chord symbols. The numbers in C9, Cm11 and C13 refer to compound intervals, and they carry an implication: a chord labelled with a ninth is normally understood to contain the seventh as well. C9 is C–E–G–B♭–D, not C–E–G–D. If you want the second without the seventh, you write Cadd9. See chord symbols.

Voicing. A major second between two notes clashes; the same two notes spread into a major ninth sounds open and modern. The spacing genuinely changes the effect, which is why jazz voicings so often move the tension note up an octave.

Counterpoint and part-writing. Rules about parallel motion and voice crossing depend on actual distance, not the reduced equivalent.

Beyond a thirteenth

There is nowhere to go. A fifteenth is two octaves, and every note is already accounted for: a thirteenth chord in principle contains all seven notes of the scale. In practice players drop notes — usually the fifth and often the eleventh — because seven notes at once is muddy.