Dominant 13th
13
0 - 4 - 7 - 10 - 14 - 21Dom11 + major 13th
About Dominant 13th
A dominant thirteenth chord is a dominant ninth with a thirteenth on top — in C that is C, E, G, B♭, D and A, written C13. It is the standard full-size dominant of big-band and gospel writing: the tritone that makes it pull is still there, and everything above it is there to make the pull sound generous rather than harsh.
Notes and formula
The formula is 1 – 3 – 5 – ♭7 – 9 – 13, or 0 – 4 – 7 – 10 – 14 – 21 in semitones. The eleventh is skipped: over a major third it would clash, exactly as in the major thirteenth.
The thirteenth is a major sixth above the root, one whole tone below the flattened seventh. That proximity is deliberate — the two notes rub gently, and the friction is what gives the chord its warmth.
How to play it
On guitar the two standard forms are x–3–2–3–3–5 with the root on the fifth string and 8–x–8–9–10–x with the root on the sixth. Both drop notes; the second keeps only root, seventh, third and thirteenth, which is all the chord needs.
On piano the working voicing is C in the left hand and E–B♭–D–A in the right: third, seventh, ninth, thirteenth. Adding the fifth back is the commonest way to make a big chord sound smaller.
What it does
A dominant thirteenth resolves down a fifth like any dominant — C13 to F — and can be substituted for a plain C7 anywhere without changing the analysis. What changes is the texture.
It is also the chord that makes a dominant sit still. A plain seventh held for two bars begs to move; a thirteenth can be held for four because the upper notes give the ear something to listen to while the tritone waits.
Where you hear it
In big-band writing it is the default voicing for a dominant in the saxophone section. In gospel and soul it is the chord under the last line of a chorus, and in blues it turns up as the V chord of a jazz-inflected twelve-bar.
It is also the natural resting place of a 7sus4: hold the suspension, resolve the fourth to the third, and the thirteenth on top makes the arrival sound like an event.
Thirteenth against sixth and against the altered dominants
C6 is a resting chord with no seventh; C13 is a dominant that resolves. The A is the same note in both and does completely different work.
Alter the chord and it changes character rather than function: C13♭9 and C13♯11 keep the thirteenth and add bite, and all of them still go to F. The thirteenth is the mildest thing that can sit on top of a dominant.
Scales that contain it
Mixolydian fits without alteration and is the standard choice — its sixth degree is the chord's thirteenth and its fourth is the degree the chord leaves out.
Over a dominant that is about to resolve, players often switch to the altered scale for the last beat. That scale contains no natural thirteenth, which is exactly why the switch is audible.
Frequently asked questions
What notes are in a C13 chord?
C, E, G, B♭, D and A. Guitarists play it as x–3–2–3–3–5 or 8–x–8–9–10–x, both of which drop notes that carry no information.
Why is there no eleventh in a thirteenth chord?
It would sit a semitone above the major third. Dominant thirteenths skip the eleventh unless it is raised, which gives 13♯11.
What is the difference between C13 and C6?
The seventh. C6 is C–E–G–A and rests; C13 adds B♭ and D, contains a tritone, and resolves toward F.