Major 13th
maj13
0 - 4 - 7 - 11 - 14 - 21Major11 + major 13th
About Major 13th
A major thirteenth chord is a major ninth with a thirteenth on top — in C that is C, E, G, B, D and A, written Cmaj13. Six notes, none of which fight each other, which makes it the largest chord in common use that can simply be played as written.
Notes and formula
The formula is 1 – 3 – 5 – 7 – 9 – 13, or 0 – 4 – 7 – 11 – 14 – 21 in semitones. The eleventh is skipped deliberately: it is the one degree that would collide with the third.
That omission is what the symbol means. A thirteenth chord in practice never contains a natural eleventh over a major third, and writing maj13 is a way of asking for everything except it.
How to play it
On guitar the standard form is x32435, sounding C–E–B–D–A. The fifth is dropped, which loses nothing, and the shape sits comfortably at the third fret.
On piano the usual voicing puts C in the left hand and E–B–D–A in the right — third, seventh, ninth, thirteenth, in that order. Adding the fifth back makes the chord heavier and no clearer.
How it sounds
Full and completely at rest. Everything that could pull has been left out: no tritone, no semitone clash, nothing but consonances stacked six deep. It is the most luxurious way to say that a piece has ended.
The thirteenth is the same pitch class as the sixth, and that is audible — the chord carries some of the settled quality of a sixth chord alongside the shimmer of the major seventh.
Where you hear it
As the final chord of jazz arrangements, where a plain major seventh would sound thin after a full band has been playing. As a tonic in bossa nova and city pop, and as the last chord of a great many big-band charts.
Guitarists in soul and R&B use it as a standing tonic: the shape rings, and the added sixth keeps a long-held chord from sounding static.
Major thirteenth against sixth and against dominant thirteenth
C6 is C–E–G–A: a triad plus a sixth, no seventh. Cmaj13 has the seventh and the ninth as well. C13 has a flattened seventh and is a dominant that resolves.
The same A appears in all three and means something different in each: an added colour in the sixth chord, the top of a stack in the major thirteenth, and one of the notes that softens the pull in the dominant.
Scales that contain it
Ionian and Lydian both fit. Lydian is the safer choice for a melody, because it raises the fourth degree — the note the chord deliberately excludes — and removes the temptation to play it.
The major pentatonic contains every chord tone except the seventh, which is why it sits so easily over this chord and why so many solos over a maj13 stay inside five notes.
Frequently asked questions
What notes are in a Cmaj13 chord?
C, E, G, B, D and A. The fifth is usually dropped in practice, giving C–E–B–D–A, which is what x32435 sounds on guitar.
Why is there no eleventh in a thirteenth chord?
Because it would clash with the third. A natural eleventh sits a semitone above a major third, so thirteenth chords skip it unless it is raised.
What is the difference between C6 and Cmaj13?
The seventh and the ninth. C6 is four notes with no seventh; Cmaj13 adds the major seventh and the ninth beneath the same top note.