Extended chords are created by stacking additional 3ʳᵈs above a seventh chord. These added notes are called extensions or tensions and include the 9, 11, and 13.
Ninth Chords
A ninth chord adds a 9ᵗʰ above a seventh chord. The table below shows how each ninth chord is derived by stacking one additional 3ʳᵈ above its corresponding seventh chord.
Quality Maj9th Min9th Dom9th
Intervals 1 - 3 - 5 - 7 - 9 1 - ♭3 - 5 - ♭7 - 9 1 - 3 - 5 - ♭7 - 9
Root C C-E-G-B-D C-E♭-G-B♭-D C-E-G-B♭-D
7th Chord + Third Maj7th + m3 Min7th + M3 Dom7 + M3
Eleventh Chords
An eleventh chord adds the 11ᵗʰ above the ninth.
Quality Maj9#11 Min9(11) Dom9#11
Intervals 1 - 3 - 5 - 7 - 9 - #11 1 - ♭3 - 5 - ♭7 - 9 - 11 1 - 3 - 5 - ♭7 - 9 - #11
Root C C-E-G-B-D-F# C-E♭-G-B♭-D-F C-E-G-B♭-D-F#
7th Chord + Third + Third Maj7th + m3 + M3 Min7th + M3 + m3 Dom7 + M3 + M3
Thirteenth Chords
A thirteenth chord adds the 13ᵗʰ above the eleventh.
Quality Maj13th Min13th Dom13th
Intervals 1 - 3 - 5 - 7 - 9 - 11 - 13 1 - ♭3 - 5 - ♭7 - 9 - 11 - 13 1 - 3 - 5 - ♭7 - 9 - 11 - 13
Root C C-E-G-B-D-F-A C-E♭-G-B♭-D-F-A C-E-G-B♭-D-F-A
7th Chord + Third + Third + Third Maj7th + m3 + m3 + M3 Min7th + M3 + m3 + M3 Dom7 + M3 + m3 + M3
Although the 9 and 11 are theoretically part of a thirteenth chord, they are often omitted in practical voicings to avoid a muddy sound.
Cmin13
A Cmin13 is built by adding the 9, 11, and 13 to a Cmin7 chord.
Formula:
1-♭3-5-♭7-9-11-13
In practice, guitar voicings commonly omit the 5 and often the 11, leaving compact voicings such as:
♭3-♭7-9-13
♭7-♭3-13-9
1-x-♭7-♭3-13
The table below shows related upper-structure chords that contain the same notes as Cmin13. For example, E♭Maj7(9♯11) contains the same notes as Cmin13 and can function as a substitute when C is supplied by the bass.
C major13♯11
A C maj13♯11 is a major seventh chord with the extensions 9, ♯11, and 13.
Formula:
1-3-5-7-9-♯11-13
Like the minor example above, several upper-structure chords share these same notes. The table below illustrates these relationships and common substitutions.