The 13th Chord expands the 11th chord with another tone and, hence the name, this tone is 13 steps from the root. A pianist could play this chord with seven tones, but the guitar is limited to six tones, and therefore, at least one tone is always excluded. The omitted tone, or the omitted tones, can vary depending on the chord shape.
The shape presented below is similar to the movable 9th chord. If you don't feel comfortable with the stretch, more shapes follows below.
Chord constructionC13 x - C - E - Bb - D - A
D13 x - D - F# - C - E - B
E13 x - E - G# - D - F# - C#
F13 x - F - A - Eb - G - D
G13 x - G - B - F - A - E
A13 x - A - C# - G - B - F#
B13 x - B - D# - A - C# - G#
Guitar versions of the chord
Notes in chordC13 C - E - G - Bb - D - F - A
D13 D - F# - A - C - E - G - B
E13 E - G# - B - D - F# - A - C#
F13 F - A - C - Eb - G - Bb - D
G13 G - B - D - F - A - C - E
A13 A - C# - E - G - B - D - F#
B13 B - D# - F# - A - C# - E - G#
The intervals are 1 - 3 - 5 - b7 - 9 - 11 - 13
Alternative chord shapes
Besides the chord pictures above there are more ways to play the 13th chord. On the pictures below you can see alternatives which also are movable.
With the root on the 6th string and muted 5th string:
Bass note left out for a funkier sound:
Since the root is on the sixth string, you use 3X345X to play G13 with the shape above. In this chord shape you will mute the second string with an adjacent finger. This chord can sound great with a single stroke as an outro, for example in a 12 bar blues (as a last stroke, in the last bar). (The similar shape 3X3455 is sometimes also referred to as G13, but is more correctly referred to as G13 6/9.)
These are two common voicings:
On the diagram to the left, the root is on the 2nd string and on the diagram to the right, the root is on the 1st string. Two examples written in short notations are E13: X5665X and F13: XX1231.
13th chord alterations
Alterations means that a note in the chord is altered, for example, a flattened fifth. Here is an example using C as root tone (the shape is movable).
In C13b9 the ninth flattened.