Major 13th chords
The Major 13th chord is most common in jazz and can function as a substitution chord to, for example, major 7th and major 9th.
The shape presented is movable and is all you need to remember. There are, of course, other versions as well, which can be seen below.
Major 13th with flats and sharps
Additional chords in this category:
C sharp / D flat maj13: 9 X 10 10 11 X
D sharp / E flat maj13: 11 X 12 12 13 X
F sharp / G flat maj13: 2X334X
G sharp / A flat maj13: 4X556X
A sharp / B flat maj13: 6X778X
The 13th chord is built with the formula 1-3-5-7-9-(11)-13 (root, major 3rd, perfect 5th, major 7th, major 9th, perfect 11th and major 13th). The 11th is mentioned in the formula, but is usually excluded.
Chord constructionCmaj13 C -x - B - E - A - x
Dmaj13 D -x - C# - F# - B - x
Emaj13 E -x - D# - G# - C# - x
Fmaj13 F -x - E - A - D - x
Gmaj13 G -x - F# - B - E - x
Amaj13 A -x - G# - C# - F# - x
Bmaj13 B -x - A# - D# - G# - x
Guitar versions of the chord
Notes in chordCmaj13 C - E - G - B - D - A
Dmaj13 D - F# - A - C# - E - B
Emaj13 E - G# - B - D# - F# - A
Fmaj13 F - A - C - E - G - B
Gmaj13 G - B - D - F# - A - C
Amaj13 A - C# - E - G# - B - D
Bmaj13 B - D# - F# - A# - C# - E
The intervals are 1 - 3 - 5 - 7 - 9 - 13
It is possible to include the first strings as well, by bar the two highest strings by the little finger. Notice the similarity with the 13 dominant chord shape.
Progressions including this chord type:
Dm7 - G9 - Cmaj13
Am7 - Fmaj9 - Cmaj13
A11 - Cmaj9 - Gmaj13
D6/9 - C6/9 - Gmaj13
Major 13th chords work as I and IV, but not as V chords (atonal). So, for example, in C major key, Cmaj13 and Fmaj13 are viable (diatonic) options.
Major 13th chord in open position
Here are additional shapes in open position for this chord category:
Alternative chord shape
It is handy to have a second shape to use when the situation calls for it.
Major 13th with the root on 5th string:
An easier shape for major 13th with the root on the 5th string is X35455 (Cmaj13), similar to one of the major 7th shapes. A third way is X3X455 (Cmaj13), with the 5th omitted as well.
Back to chord types