The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped.
Cmaj13 is C, E, G, B, D and A — Cmaj9 with the thirteenth on top, and the eleventh left out.
It sounds full and wide open. Six notes into four fingers means something goes: keep the third, the seventh and the thirteenth.

| C | E | G | B | D | A |
|---|---|---|---|---|---|
| 1 | 3 | 5 | 7 | 9 | 13 |
Tonic — the major sound with most of the scale showing.
Also written CM13, CΔ13 or C major 13. The same chord either way; which spelling you meet depends on who wrote the chart.
The same operation one voice further down: the third voice from the top falls an octave and becomes the bass.
That leaves a bigger hole under the top three notes, so a string gets skipped: the muted string in the middle is the shape, not a mistake.
Cmaj13 has 9 of them, on strings 6-4-3-2 and strings 5-3-2-1, from open position up to the 12th — every inversion the chord has: C in the bass, E in the bass, B in the bass and A in the bass. The one to learn first is the A shape at the nut.
5 of them sit on strings 5-3-2-1, so you can run the inversions up one set without changing strings — which is the whole reason to learn them as a family rather than as separate grips.
Start with x32201 — no barre and 1 open string. 1 of the 7 shapes here sits in open position. 4 of the 7 need a barre. Together they cover the neck from the 1st fret to the 15th.
| Frets | Where | Bass | Top | Hand |
|---|---|---|---|---|
| x32201 | open position | C, root position | F | 1 open string |
| x33455 | 3rd fret | C, root position | A | all fretted |
| 877787 | 7th fret | C, root position | B | barred |
| 8-8-9-9-10-8 | 8th fret | C, root position | C | barred |
| x-12-10-10-12-12 | 10th fret | A, 13th in the bass | E | barred |
| x-15-12-14-12-12 | 12th fret | C, root position | E | barred |
| x-15-14-14-12-12 | 12th fret | C, root position | E | all fretted |
The same notes rebuilt from scratch give 2 shell, 13 drop 2, 25 rootless and 6 open string voicings, each on its own page.
Tensions. A shell of Cmaj13, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (F#).
How you get to it. The turn that lands on Cmaj13 is Dm7 to G7 — the ii and the V of C — and G7 shares its third and seventh with Dm7, so the hand barely moves between them.
In which keys. Every note of Cmaj13 belongs to C major (the I, the tonic), E minor (the ♭VI), G major (the IV, the subdominant) and A minor (the ♭III).
Every note of Cmaj13 is in C major and C lydian.
Change one note of Cmaj13 and you have Cmaj9 (drop the sixth), Cmaj11 (the sixth becomes a fourth), C69 (drop the major seventh) or C13 (the major seventh becomes a flat seventh).
Cmaj13 is a major chord — root, major third, fifth. Major chords on every root.
On Cmaj13’s sound and use this page follows Ted Pease & Ken Pullig, Modern Jazz Voicings (Berklee Press, 2001). The shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.