C major 13th chord

Cmaj13 chord for piano with keyboard diagram.
Explanation: The C major thirteenth is a six-note chord (the 11th, F in the case of Cmaj13, is normally excluded). For practical reasons the chord is normally played with omitted notes and/or inverted. It is often abbreviated as Cmaj13 (not to be confused with C13).
Omissions: Cmaj13(no5): C - E - B - D - A, Cmaj13(no9): C - E - G - B - A.
Theory: The C major thirteenth chord is constructed by extending the major eleventh chord with a major thirteenth note.

Cmaj13

Cm13 piano chord diagram
Notes: C - E - G - B - D - A

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Cmaj13 inversions and voicings

Cmaj13/B chord diagram
Notes: B - E - G - A - C
One of many possible inversions (Cmaj13/B with the 9th and the 11th omitted)

Cmaj13 chord voicing diagram
Notes: C - B - E - A
Two-hand voicing

C chord categories

C Cm C7 Cm7 Cmaj7 CmM7 C6 Cm6 C6/9 C5 C9 Cm9 Cmaj9 C11 Cm11 C13 Cm13 Cmaj13 Cadd C7-5 C7+5 Csus Cdim Cdim7 Cm7b5 Caug Caug7