Compound intervals
Intervals larger than an octave, how they're named and why they're the key to the 9, 11 and 13 tensions.
Advanced
Content under musical review. It may contain inaccuracies.
Loading…
Intervals larger than an octave, how they're named and why they're the key to the 9, 11 and 13 tensions.
Advanced
A compound interval is wider than an octave. It's a simple interval with one or more octaves added: a ninth is a second plus an octave, a tenth a third plus an octave. On the guitar, with six strings covering more than two octaves, you use them all the time even if you don't name them.
A major second, then the same pair of notes spread out as a major ninth. The colour is similar, but the ninth sounds much more open:
A major third against a major tenth:
To reduce a compound interval to a simple one, subtract 7 from the number: ninth → second, tenth → third, eleventh → fourth, twelfth → fifth, thirteenth → sixth. The quality doesn't change.
| Compound | Half steps | Equals | Typical use |
|---|---|---|---|
| minor ninth | 13 | minor second + octave | G7♭9 |
| major ninth | 14 | major second + octave | Cadd9, C9 |
| major tenth | 16 | major third + octave | open voicings |
| perfect eleventh | 17 | perfect fourth + octave | Am11 |
| perfect twelfth | 19 | perfect fifth + octave | the 7th-fret harmonic |
| major thirteenth | 21 | major sixth + octave | G13 |
On the fretboard the ninth sits where the second does, just an octave higher:
String 6, Fret 8: C3 · 1 · Root
Measure the distance from C3 to D4 and compare it with C4 to D4:
Measure a second and a ninthThen play these two chords and find the ninth in each:
In chord symbols, numbers above 7 mark tensions: notes stacked above the seventh. C9 has a root, third, fifth, minor seventh and major ninth. The difference between "add9" and "9" is the seventh: Cadd9 doesn't have one.
Why not call the ninth a "second"? Because the name tells you where the note is expected. A second next to the root makes a tight clash; a ninth, an octave higher, sounds like a bright colour. On the guitar this decides the voicing: a ninth placed on the high strings, far from the bass, sounds clear; on the low strings it can get muddy.
Tenths are very guitar-friendly: a bass note on the sixth or fifth string and a note on the third or second string. Try a line of parallel tenths in C major with the bass on the fifth string (frets 3, 5, 7) and the top note on the second string (frets 5, 6, 8). Two notes, and it already sounds full.
Picking & articulationString skippingSkip a string with the pick without losing accuracy or letting unwanted strings ring.Not every tension suits every chord. Over a major chord, the perfect eleventh forms a minor ninth against the third and is usually avoided, hence Cmaj7♯11. Over a dominant, altered ninths and thirteenths (b9, #9, b13) create the typical jazz tensions. Levine treats them in relation to each chord's scale.
A compound interval is inverted through its simple form: a major ninth reduces to a major second and inverts to a minor seventh.