Ab Major 13th (Abmaj13)
Also written as G# Major 13th (G# and Ab are the same key).
Notes in Ab Major 13th
Inversions
Same notes as Ab Major 13th, with a different chord tone as the lowest note. Useful for smoother movement between chords instead of jumping around the keyboard.
Root position
G# in the bass
1st inversion
B# in the bass (Abmaj13/B#)
2nd inversion
D# in the bass (Abmaj13/D#)
3rd inversion
G in the bass (Abmaj13/G)
4th inversion
A# in the bass (Abmaj13/A#)
5th inversion
C# in the bass (Abmaj13/C#)
6th inversion
E# in the bass (Abmaj13/E#)
Open voicings
A close-position chord like Ab Major 13th can sound cluttered in the middle of the keyboard. Jazz players open it up by dropping one note down an octave, spreading the same notes wider without changing the chord.
Drop 2
G# on the bottom
Drop 3
G# on the bottom
Press G#, B#, D#, G, A#, C# and E# together on the keyboard and you're playing Ab Major 13th.
A major ninth chord stretched all the way to the thirteenth, rich and expansive on paper though almost always voiced with several notes left out in practice. What survives keeps the warm, settled character of a major ninth chord with an even fuller top end.