Compound intervals are named in 3rds from the 9th to the 13th.
All harmony can be expressed in chord notation. The biggest interval in chord notation is the diatonic 13th. Bigger intervals like "two octaves and a diatonic 6th" are in the study of transposition and voicing but not chordal harmony.
We support each compound interval with its preceding third. We support he 9th interval with a four note chord, the 11th interval with a five note chord, the 13th interval with a six note chord.
Cmaj7 = C E G B
Cmaj9 = C E G B D
Cmaj9#11 = C E G B D F#
Cmaj13#11 = C E G B D F# A
In practice it is not always possible to play every harmonic tone. This makes harmonic analysis devilishly interesting.
Some intervals are enharmonic. D# (the sharp 9th of C) and Eb (the minor 3rd of C) are enharmonic. Whether the harmonic interval is sharp 9th or minor 3rd depends on the surrounding intervals. The combined effect of all harmonic tones played together has more bearing on the nature of the harmony than the distance between the tones. We will see some chords in action in chapter 4.
|Minor 3rd||Sharp 9th|
|Diatonic 4th||Diatonic 11th|
|Flat 5th||Sharp 11th|
|Diatonic 6th, Diminished 7th||Diatonic 13th|