Minor 13th chords
The Minor 13th (m13) chord is in theory a seven-note chord, but is played with one or more notes omitted on the guitar. The sound character of the 13th minor is a little dissonant – the 13th note is outside the relevant minor scale – and therefore it's not always a fitting substitute for minor 7th and minor 9th. Instead it's functionally is closer to that of a dim and aug chords, often used as an in-between chord.
There are different many different versions of this chord possible on the guitar, but it's common to exclude one or more of the following: the fifth, the seventh, ninth and eleventh.
m13 (movable shape)
The first shape has the root on the 5th string. The fifth, the ninth and the eleventh are omitted.
The alternative shape is played with the root on the 6th string, for Am13 the short notation is 575575. The ninth and the eleventh are omitted.
Minor 13th with flats and sharps
Additional chords in this category:
C sharp / D flat m13: X4X456
D sharp / E flat m13: X6X678
F sharp / G flat m13: 242242
G sharp / A flat m13: 464464
A sharp / B flat m13: X1X123
Open minor 13 chords
The F#m13 is more correct written as F#m13/E. The keys that have been left out has no good options for being played in open position.
The minor thirteenth is built with the formula 1-b3-5-b7-9-11-13 (root, minor 3rd, perfect 5th, minor 7th, major 9th, perfect 11th and major 13th).
Chord constructionCm13 x - C - x - Bb - Eb - A
Dm13 x - D - x - C - F - B
Em13 x - E - x - D - G - C#
Fm13 x - F - x - Eb - Ab - D
Gm13 x - G - x - F - Bb - E
Am13 x - A - x - G - C - F#
Bm13 x - B - x - A - D - G#
Guitar versions of the chord
Notes in chordCm13 C - Eb - G - Bb - D - F - A
Dm13 D - F - A - C - E - G - B
Em13 E - G - B - D - F# - A - C#
Fm13 F - Ab - C - Eb - G - Bb - D
Gm13 G - Bb - D - F - A - C - E
Am13 A - C - E - G - B - D - F#
Bm13 B - D - F# - A - C# - E - G#
The intervals are 1 – b3 – 5 – b7 – 9 - 11 - 13
Examples of progressions including minor 13th:
Am13 - Em9 - Gmaj7
Bm13 - E11 - Amaj13
The second progression is thought to be used in a jazz context.
Minor 13th chords work as ii, but not as iii and vi chords (atonal). So, for example, in C major key, Dm13 is an (diatonic) options. This circumstances is the reason for this chord category being quite seldom used.