Definition
A simple interval is contained within the octave (from unison to the 8th). A compound interval exceeds the octave: 9th, 10th, 11th, 12th, 13th, 14th, 15th (double octave) and beyond. Every compound interval is a simple one plus one or more octaves and keeps the same quality (major, minor, perfect, augmented, diminished).
Conversion rule: compound = simple + 7 (not +8, because the arrival note of the octave is counted twice). So 2nd + octave = 9th, 3rd + octave = 10th, 3rd + two octaves = 17th.
Complete table
| Compound | Simple | Semitones (standard quality) | Example from C4 |
|---|---|---|---|
| Minor 9th | Minor 2nd | 13 | C4–Db5 |
| Major 9th | Major 2nd | 14 | C4–D5 |
| Augmented 9th | Augmented 2nd | 15 | C4–D#5 |
| Minor 10th | Minor 3rd | 15 | C4–Eb5 |
| Major 10th | Major 3rd | 16 | C4–E5 |
| Perfect 11th | Perfect 4th | 17 | C4–F5 |
| Augmented 11th | Augmented 4th | 18 | C4–F#5 |
| Perfect 12th | Perfect 5th | 19 | C4–G5 |
| Minor 13th | Minor 6th | 20 | C4–Ab5 |
| Major 13th | Major 6th | 21 | C4–A5 |
| Minor 14th | Minor 7th | 22 | C4–Bb5 |
| Major 14th | Major 7th | 23 | C4–B5 |
| Perfect 15th | 8th | 24 | C4–C6 |
Note: the augmented 9th and the minor 10th have the same number of semitones but different names (enharmony): in C7#9 the note is D# (augmented 9th), not Eb.
Why compound names are used
- In chord symbols: 9, 11, 13 indicate tensions above the seventh chord. C9 is not “C with some random D” but a seventh chord with a 9th. An “add2” and an “add9” contain the same pitch class; the first suggests a close voicing (D next to C), the second a D above the chord.
- In figured bass and counterpoint: the 9th (a dissonance that resolves to the 8th, 9–8 suspension) is distinguished from the 2nd (which resolves to the unison or the 3rd).
- In the harmonic series: the intervals from the fundamental are compound: the 3rd harmonic is a 12th, the 5th a major 17th (two octaves + a third), the 7th roughly a minor 21st (two octaves + a flat minor seventh).
Compound intervals and register: the “low interval limit”
Close intervals in the low register become muddy because the harmonics of the two sounds clash within the same critical band of the ear. The Berklee tables (low interval limits) indicate, roughly: a major third no lower than about Bb2, a minor third no lower than about C3, a perfect fifth usable down to about Bb1, a minor ninth no lower than about E2. The values vary a little between texts, but the principle is clear: in the low register spread out (5th, 8th, 10th), in the high register you can close up. This is why classical piano voicing is “octave or fifth in the bass, thirds and sevenths above”, and why the 10th (C–E an octave higher) is the typical left-hand interval in stride and ballads.
Inversion of compound intervals
To invert a compound interval, first reduce it to a simple one: the major 10th becomes a major 3rd, whose inversion is the minor 6th. The sum of the simple intervals' inversions = 9.
Examples in songs
- The melody of “Somewhere Over the Rainbow” (Harold Arlen) starts with an octave leap; many film themes use leaps of a 9th and 10th to give momentum.
- The left hand of stride piano (Fats Waller, Art Tatum) alternates bass and chord and often uses open 10ths in the low register.
- The “Hendrix chord” (E7#9, in “Purple Haze”) contains the G as the augmented 9th, above the G# of the third.
Exercise for the producer
- On a pad in C major, play C3–E3–G3 and then C2–G2–E3: compare the clarity of the bass. Repeat in a mix with kick and bass.
- Write a progression with the bass in octaves and the right hand playing 10ths and 13ths: listen to the openness.
- Train your ear: sing C and then D an octave higher (major 9th); do the same with 10ths and 12ths.
Related topics
Intervals and their inversions; Ninth chords; Extensions and tensions; Voicing: close, open, drop 2, shell; The harmonic series.