A major 9 guitar chords

A - C# - E - G# - B

Amaj9 chords consist of the 1st, 3rd, 5th, 7th, and 9th notes of the A Major Scale.

Construction: root, major third, perfect fifth, major seventh, and ninth.
A Major Scale: A - B - C# - D - E - F# - G# - A - B
We need to extend the A Major Scale to accommodate the 9th note of the scale.
Chord: Amaj9 (AM9 or A∆9)
Formula: 1 - 3 - 5 - 7 - 9
Notes: A - C# - E - G# - B

Amaj9 (A ⃤ 9 ) - A major ninth (1-3-5-7-9)

Spelling: 1st(A), 3rd(C#), 5th(E), 7th(G#), 9th(B)

Chart Legend

Numbered Circles: number inside circle indicates which finger to use
X: Don't play string
White Numbered Circles: Optional Notes
X on string with optional note: if you omit the note, don't play string
Unmarked strings: Play open
Barre Line: One finger holds down multiple strings
R: Root Note

TAB: Numbers represent frets - not finger positions
Blank Strings: Do not Play
0: play string open

1st

Written: x02100
Notes: x-A-E-G#-B-E

 
TAB     
e |-0-|
B |-0-|
G |-1-|
D |-2-|
A |-0-|
E |---|

2nd

Written: 54645x
Notes: A-C#-G#-B-E-x

 
TAB     
e |---|
B |-5-|
G |-4-|
D |-6-|
A |-4-|
E |-5-|

3rd

Written: x-12-11-13-12-0
Notes: x-A-C#-G#-B-E

 
TAB     
e |-0--|
B |-12-|
G |-13-|
D |-11-|
A |-12-|
E |----|

↓ A major 9 guitar chords

Notes

A major 9th chord implies the preceding 1st, 3rd, 5th, 7th, before the added 9th.
This could also be written as an Amaj7 chord with an added 9th.
In the 1st position chord, the 3rd (C#) is omitted... this is a particular voicing of the major 9th chord. This could also be classed as a maj7sus2 chord, in this case Amaj7sus2. The chord formula is 1-2-5-7 = A-B-E-G# (notes in the first position). Amaj9 is almost identical to Amaj7sus2 except the 9th is played an octave lower (9 - 7 = 2), and the 3rd is omitted. This voicing is quite common with 9th chords.
You tend to find all types of 9th chords in alternative styles of music, especially jazz music where the use of extended chords and compound intervals are prevalent.
Standard keys using the A major 9 chord: A/F#m and E/C#m. Both sets of scales share the same notes, i.e., A Major and F# minor share the same notes, as do E major and C#minor (F#m is the relative minor of A major, and C#m is the relative minor of E major).
Amaj9 can therefore be used as a usable chord in any of the above chord progressions which means in this example, chords that utilize notes belonging to the A Major Scale (A-B-C#-D-E-F#-G#), and E Major Scale (E-F#-G#-A-B-C#-D#). Amaj9 meets the criteria (A - C# - E - G# - B)... this also includes the relative minor keys of F#m and C#m.

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