C13 is C, E, G, Bb, D and A — with the thirteenth added on top.
It sounds big and open. Big-band and gospel comping reach for it wherever a plain 7 would sound bare.
Dominant — the full V chord.
Play it instead of a m7♭5 a major third above this root, something else has the bass, since that chord is this one without its root.
Also written Cdom13 or C dominant 13.
In a jazz ii–V–I all three chords usually carry tensions: Gm9, C13, Fmaj9 rather than bare sevenths. The thirteenth is the ii’s ninth held over the barline, and it falls a step to the ninth of the I.
Listen for: The ii’s ninth holds as the V’s thirteenth, then falls a whole step to the ninth of the I. Underneath, the guide tones step down as usual.
In which keys. Every note of C13 belongs to D minor and F major.
Every note of C13 is in C mixolydian and C lydian dominant.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where C13 sits in it. Every scale.
Change one note of C13 and you have (the flat seventh becomes the major seventh), (drop the flat seventh), (drop the thirteenth) or (the thirteenth becomes the sharp eleventh).
C13 is a dominant chord — root, major third, fifth, minor seventh. Dominant seventh chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.