The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped.
Abmaj13 is Ab, C, Eb, G, Bb and F — Abmaj9 with the thirteenth on top, and the eleventh left out.
It sounds full and wide open. Everything the major scale offers except the eleventh, which is left out because it fights the third.
Tonic — the major sound with most of the scale showing.

| Ab | C | Eb | G | Bb | F |
|---|---|---|---|---|---|
| 1 | 3 | 5 | 7 | 9 | 13 |
Also written AbM13, AbΔ13 or Ab 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.
Abmaj13 has 9 of them, on strings 6-4-3-2 and strings 5-3-2-1, from open position up to the 13th — every inversion the chord has: Ab in the bass, C in the bass, G in the bass and F in the bass. The one to learn first is the G shape at the nut.
5 of them sit on strings 6-4-3-2, 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.
Six notes and four fingers, so something has to go. Keep C and G (they fix the quality) and F and Bb (what the symbol is about). Let Eb and Ab go, in that order — a perfect fifth says nothing the root has not, and in a band the bass has the root.
Play Abmaj13 as a shell — root, third and seventh — and the spare string takes the #11 (D).
All 6 common shapes as fret numbers, lowest string first. Hover or tap one to see it drawn.
How you get to it. The turn that lands on Abmaj13 is Bbm7 to Eb7 — the ii and the V of Ab — and Eb7 shares its third and seventh with Bbm7, so the hand barely moves between them.
In which keys. Every note of Abmaj13 belongs to C minor (the ♭VI), Eb major (the IV, the subdominant), F minor (the ♭III) and Ab major (the I, the tonic).
Every note of Abmaj13 is in Ab major and Ab lydian.
Change one note of Abmaj13 and you have Abmaj9 (drop the thirteenth), Abmaj11 (the thirteenth becomes the eleventh), Ab69 (drop the major seventh) or Ab13 (the major seventh becomes the flat seventh).
Abmaj13 is a major chord — root, major third, fifth. Major 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.