Extensions: 9, 11, 13 – free music theory course

Keep stacking thirds above the seventh and you get the ninth, the eleventh and the thirteenth. On C: C – E – G – B♭ – D – F – A. These are the extensions (or “tensions”). Notice they are scale notes 2, 4 and 6, an octave higher: 9 = 2 + 7, 11 = 4 + 7, 13 = 6 + 7.

What the symbols say

C9 = C7 + 9: C E G B♭ D. An extension number implies the seventh (minor unless “maj” is written).
Cmaj9 = C E G B D. Cm9 = C E♭ G B♭ D.
Cm11 = C E♭ G B♭ D F: gorgeous on minor chords.
C13 = C7 + 13 (A), usually with the 9th; the 11th is left out.
Cadd9, by contrast, has no seventh.

Altered tensions

On a dominant seventh chord you can alter the extensions to increase tension: ♭9, ♯9, ♯11, ♭13. C7♯9 (C E B♭ D♯) is the famous “Hendrix chord”, rubbing a major third against a minor one; C7♭9 is dark and dramatic.

M:4/4
L:1/2
%%staves {RH LH}
V:RH clef=treble
V:LH clef=bass
K:C
[V:RH] "Cmaj9"[EGBd]2 | "C9"[E_Bd]2 | "C13"[EAd]2 | "C7#9"[E_B^d]2 |]
[V:LH] C,2 | C,2 | [C,_B,]2 | C,2 |]

You don't play everything!

A full thirteenth chord has seven notes: impossible to play cleanly and frankly muddy. You choose:

Keep the third and the seventh: they define the chord's colour.
Drop the fifth first (unless it is altered): it adds almost nothing.
Drop the root if a bass player or your left hand already has it.
Add one or two extensions, at the top of the chord.

The “avoid note”: the natural 11th (F) on a major or dominant chord (C–E) forms a minor ninth with the third E: it grates. Replace it with the ♯11 (F♯), the Lydian colour, or drop the third (sus chord). On a minor chord, by contrast, the natural 11th sounds lovely.

Practice: play the root in the left hand and the third, seventh and ninth in the right (e.g. Dm9: D | F C E). This simple gesture instantly sounds “jazz” or “soul”.