Dmaj13 — D major thirteenth chord

A major seventh chord with the ninth and the thirteenth added. The eleventh is normally left out because it clashes with the major third.

1 = D
3 = F#
5 = A
7 = C#
9 = E
13 = B

Symbol: Dmaj13
Root: D
Quality: Major thirteenth
Family: extended
Notes: D F# A C# E B
Degree formula: 1 3 5 7 9 13
Semitones from the root: 0 2 4 7 9 11
Distinct pitch classes: 6
Interval structure: Stacked from the root: 4 semitones, 3 semitones, 4 semitones, 3 semitones, 7 semitones
Notation: Written maj13. A tonic chord in jazz voicing; in practice the fifth is often dropped so the seventh and thirteenth can sit close together.
Key: D · D major / B minor key signature

Dmaj13 chord fingering chart, six strings, frets marked — Dmaj13 — fingering chart Diagram: Will Chan

Formula

The chord tones in order from the root, with the interval each one forms above it.

Degree	Note	Semitones	Interval from the root
1	D	0	Perfect unison
3	F#	4	Major third
5	A	7	Perfect fifth
7	C#	11	Major seventh
9	E	2	Major second
13	B	9	Major sixth

Inversions

An inversion is the same set of notes with a different one in the bass. The last column gives the distance of each note above the bass note, in semitones.

Inversion	Bass note	Degree in the bass	Notes above the bass	Semitones above the bass
root position	D	1	D – F# – A – C# – E – B	0 4 7 11 2 9
first inversion	F#	3	F# – A – C# – E – B – D	0 3 7 10 5 8
second inversion	A	5	A – C# – E – B – D – F#	0 4 7 2 5 9
third inversion	C#	7	C# – E – B – D – F# – A	0 3 10 1 5 8
fourth inversion	E	9	E – B – D – F# – A – C#	0 7 10 2 5 9
fifth inversion	B	13	B – D – F# – A – C# – E	0 3 7 10 2 5

Playable voicings

These shapes were found by searching the fretboard of a standard-tuned guitar (E A D G B E) rather than copied from a chord book. The search allows every string to sound or to be muted, rejects any shape with a muted string between two sounding strings, rejects any shape whose fretted notes span more than four frets (a five-fret window), requires every chord tone to be present, and then sorts what remains with root-position shapes first and the most compact, lowest shapes next. The shapes shown are the first six of that ordering; other orderings are possible at the same frets.

#	Shape (low string first)	Notes	Degrees	Bass	Span (frets)	Sounding strings
1	10-9-9-9-10-9 (6→1)	D F# B E A C#	1 3 13 9 5 7	D	1	6
2	10-12-11-11-12-12 (6→1)	D A C# F# B E	1 5 7 3 13 9	D	2	6
3	10-7-7-6-7-7 (6→1)	D E A C# F# B	1 9 5 7 3 13	D	4	6
4	10-7-9-11-10-9 (6→1)	D E B F# A C#	1 9 13 3 5 7	D	4	6
5	10-7-11-11-10-7 (6→1)	D E C# F# A B	1 9 7 3 5 13	D	4	6
6	10-9-11-9-10-7 (6→1)	D F# C# E A B	1 3 7 9 5 13	D	4	6

Shape numbers run from the lowest string to the highest, so the left-hand number is the sixth string (low E) in standard tuning. Multiple shapes are listed because a chord can be voiced several ways, and because a lower position is not always the better sounding one.

Related chords and scales

KeyEverything in Dscale, chords and neck map for this root
ScaleD majorthe scale this chord comes from
ChordDmaj9the major ninth it extends
ChordDthe triad underneath it
ChordD7the seventh chord on this root

Everything in D · All chords

KeyKey of DD E F# G A B C# · D major / B minor
ScaleD major7 notes · 1 2 3 4 5 6 7
ChordDmaj9 — Major ninth1 9 3 5 7 · D E F# A C#
ChordD — Major1 3 5 · D F# A
ChordD7 — Dominant seventh1 3 5 b7 · D F# A C
ChordD11 — Dominant eleventh1 9 3 11 5 b7 · D E F# G A C
ChordD13 — Dominant thirteenth1 9 3 5 13 b7 · D E F# A B C
ChordD9 — Dominant ninth1 9 3 5 b7 · D E F# A C

Everything in this key: D · Chords · Theory Atlas