maj13

Maj13 is a type of extended chord used in various styles, especially jazz. It is built on a major seventh chord and adds the ninth, eleventh, and thirteenth extensions. In theory, a maj13 chord contains the notes 1-3-5-7-9-11-13 relative to the root, but practical voicings often omit one or more tones to suit voice-leading and the instrument being used.

In C, a full maj13 would be C E G B D F A. Because the natural 11th (F) can clash with the major third (E), many common voicings omit the 11th or replace it with a sharp 11th (F#) for color, resulting in variants such as C E B D A (no F) or C E B D F A (with 11 retained). Guitar and piano players commonly omit the 5th as well, producing compact voicings like Cmaj7(9,13) or Cmaj9(13).

Notation and equivalents. The chord may be written as maj13, Δ13, or maj7(9,13). Some contexts distinguish maj13 from maj7(9,11,13) by indicating the 11th is omitted or altered. In jazz practice, maj13 often serves as a tonal color on the tonic (I) or as a colorive substitution over predominant chords, contributing a lush, expansive sound to cadences or progressions.

Voice-leading and function. The 9th (and 13th) commonly resolve toward chord tones in the next harmony, while the 11th is treated cautiously due to potential dissonance with the third. Overall, maj13 provides a rich extension palette while retaining the stability of a major seventh chord.