Playable, correctly spelled, and not how the chord is normally voiced. Right now this is the shapes that put a ninth, eleventh or thirteenth below the root.
Amaj13 is A, C#, E, G#, B and F# — Amaj9 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.

| A | C# | E | G# | B | F# |
|---|---|---|---|---|---|
| 1 | 3 | 5 | 7 | 9 | 13 |
Also written AM13, AΔ13 or A major 13. The same chord either way; which spelling you meet depends on who wrote the chart.
Six notes and four fingers, so something has to go. Keep C# and G# (they fix the quality) and F# and B (what the symbol is about). Let E and A go, in that order — a perfect fifth says nothing the root has not, and in a band the bass has the root.
Play Amaj13 as a shell — root, third and seventh — and the spare string takes the #11 (D#).
All 8 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 Amaj13 is Bm7 to E7 — the ii and the V of A — and E7 shares its third and seventh with Bm7, so the hand barely moves between them.
In which keys. Every note of Amaj13 belongs to C# minor (the ♭VI), E major (the IV, the subdominant), F# minor (the ♭III) and A major (the I, the tonic).
Every note of Amaj13 is in A major and A lydian.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where Amaj13 sits in it. Every scale.
Change one note of Amaj13 and you have Amaj9 (drop the thirteenth), Amaj11 (the thirteenth becomes the eleventh), A69 (drop the major seventh) or A13 (the major seventh becomes the flat seventh).
Amaj13 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.