How Dominant Chords are Built?
When building a dominant chord, you generally stack thirds on top of each other and give a name to this chord related to the number of steps from the root note to the highest :
A triad is formed with a root (1), a third (3) and perfect fifth (5).
Adding a third to this triad gives a dominant 7 chord (1, 3, 5, b7).
Adding another third to a dom7 chord gives a dominant ninth chord (9).
Just add another third and you get a dominant eleventh chord (11) and a last third gives you finally a dominant thirteenth chord (13).
| Major triad |
1 |
3 |
5 |
|
|
|
|
| Cmaj |
C |
E |
G |
|
|
|
|
| Dominant 7th chord |
1 |
3 |
5 |
b7 |
|
|
|
| C7 |
C |
E |
G |
Bb |
|
|
|
| Dominant 9th chord |
1 |
3 |
5 |
b7 |
9 |
|
|
| C9 |
C |
E |
G |
Bb |
D |
|
|
| Dominant 11th |
1 |
3 |
5 |
b7 |
9 |
11 |
|
| C11 |
C |
E |
G |
Bb |
D |
F |
|
| Dominant 13th |
1 |
3 |
5 |
b7 |
9 |
11 |
13 |
| C13 |
C |
E |
G |
Bb |
D |
F |
A |
In this stack of tones (the 13th chord), the interval 3-11 (E-F for C major) is considered as dissonant so generally the 11 is omitted to avoid this dissonance.
It is better not to skip the third nor the 7th, since this would spoil the color of the 13th chord.
The 5th can be skipped, it is not the most interesting and important note in this chord.
The root (1), when played by the bass player or the pianist can be omitted.
So to play a dominant 13 chord on the guitar, a normal voicing would be 1-3-b7-13. However, the 9th could possibly be added.
Difference between 6th and 13th chord
That is a frequently asked question indeed, it is important to differentiate between 3 and 13 chords.
Generally a 13 chord refers to a dominant chord that contain an added 6 in the upper structure, in other word a 13.
Whereas a 6 chord is a major triad with a supplementary sixth (6).
Example with C6 and C13 :
C6 is a four-note chord built with C E G A respectively root, third, fifth and sixth.

C13 is a seven-note chord built with C (root), E (third), G (fifth), Bb (minor seventh), D (ninth), F (eleventh) and A (thirteenth).
