Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top.
AmMaj9 is A, C, E, G# and B — AmMaj7 with the ninth added on top.
It sounds the same unease with more colour over it. The ninth softens the edge without resolving anything.

| A | C | E | G# | B |
|---|---|---|---|---|
| 1 | ♭3 | 5 | 7 | 9 |
Minor tonic — melodic minor, extended.
Also written AmM9, Am(maj9) or A-Δ9. The same chord either way; which spelling you meet depends on who wrote the chart.
Root, third and seventh. The third and seventh, the guide tones, are what make the chord major, minor or dominant, so the fifth can go: it says nothing the symbol needs.
Three notes means a spare string, which is the real point. Put a tension on it.
AmMaj9 has 3 of them, on the bottom four strings, the top four strings and the middle four strings, from the 3rd fret up to the 10th — all in one inversion, so the bass note never moves. The one to learn first is the A shape at the 3rd fret.
Start with x06504 — no barre and 2 open strings. 1 of the 8 shapes here sits in open position. 4 of the 8 need a barre. Together they cover the neck from the 3rd fret to the 15th.
| Frets | Where | Bass | Top | Hand |
|---|---|---|---|---|
| 53x454 | 3rd fret | A, root position | G# | all fretted |
| x06504 | open position | A, root position | G# | 2 open strings |
| 5364xx | 3rd fret | A, root position | B | all fretted |
| 576557 | 5th fret | A, root position | B | barred |
| x09998 | 8th fret | A, root position | C | barred |
| 777998 | 7th fret | B, 9th in the bass | C | barred |
| x-12-10-13-12-x | 10th fret | A, root position | B | all fretted |
| 12-15-14-13-12-12 | 12th fret | E, 2nd inversion | E | barred |
The same notes rebuilt from scratch give 7 drop 2, 5 drop 3, 14 rootless and 6 open string voicings, each on its own page.
Tensions. A shell of AmMaj9, root, third and seventh, leaves a string free, and the tones that belong over it are the 11 (D) and the 13 (F#).
How you get to it. The turn that lands on AmMaj9 is Bm7♭5 to E7♭9: the ii and the V of A minor, which is where a minor tonic is usually arrived at rather than simply begun on.
Every note of AmMaj9 is in A harmonic minor and A melodic minor.
Change one note of AmMaj9 and you have Amaj9 (the minor third becomes a major third), Am69 (the major seventh becomes a sixth), Am9 (the major seventh becomes a flat seventh), AmMaj7 (drop the ninth), AmMaj11 (add the fourth) or Amadd9 (drop the major seventh).
AmMaj9 is a minor chord — root, minor third, fifth. Minor chords on every root.
On AmMaj9’s sound and use this page follows Mark Levine, The Jazz Theory Book (Sher Music, 1995). 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.