What are ninth, eleventh and thirteenth chords?
A triad stacks two thirds on its root, and a seventh chord stacks one more. Keep going and the next thirds land on the 9, the 11 and the 13. They are the 2nd, 4th and 6th of the scale, counted an octave higher: above C, the 9 is D, the 11 is F and the 13 is A. A ninth is an octave plus a second, the compound intervals of the Intervals entry. The stack ends at the 13, because the next third would be the root again.
The seventh is built into the number. A plain 9, 11 or 13 means a dominant chord, so C9 is C7 with a ninth: C–E–G–B♭–D. Cmaj9 is Cmaj7 with a ninth, and Cm9 is Cm7 with a ninth. You never write the 7 as well, because the 9 already says it is there.
Why is the eleventh usually left out?
On a major or dominant chord the 11 is F, a half step above the major third E. Played together they grind, and the F blurs the third. So an eleventh chord on a dominant usually drops the third, and a thirteenth chord skips the 11. Piakno writes them that way: C11 is C–G–B♭–D–F with no E, and C13 is C–E–G–B♭–D–A with no F. A chord with no third is neither major nor minor by itself.
A minor chord has E♭ instead, a whole step below F, so the clash goes. Cm11 keeps its third: C–E♭–G–B♭–D–F.
What are 6/9, add9 and the suspended sevenths?
Not every added note comes with a seventh. Cadd9 is a plain C triad with a D on top: C–E–G–D. It is not a C9, which has a B♭. C6/9 adds both the sixth and the ninth to the triad, C–E–G–A–D, and Cm6/9 does the same to a minor triad. With no B♭ in them, none of the three pulls toward F the way C9 does.
A suspended seventh swaps the third for the fourth. C7sus4 is C–F–G–B♭, and C9sus4 adds the D. With no E or E♭ the chord is neither major nor minor, and its F often falls to E when a C7 follows, though it does not have to.
Which notes does each symbol spell?
| Symbol | Name | Notes on C |
|---|---|---|
| C9 | dominant ninth | C E G B♭ D |
| Cmaj9 | major ninth | C E G B D |
| Cm9 | minor ninth | C E♭ G B♭ D |
| C11 | dominant eleventh (no third) | C G B♭ D F |
| Cm11 | minor eleventh | C E♭ G B♭ D F |
| C13 | dominant thirteenth (no eleventh) | C E G B♭ D A |
| C6/9 | six-nine | C E G A D |
| Cm6/9 | minor six-nine | C E♭ G A D |
| Cadd9 | add nine | C E G D |
| C7sus4 | seventh, suspended fourth | C F G B♭ |
| C9sus4 | ninth, suspended fourth | C F G B♭ D |
How do you play them on the piano?
You rarely play every note. The third and the seventh say what kind of chord it is, and the top notes give it colour. The fifth adds the least, so it goes first, and the root often moves to the left hand alone.