Essential Shell Chord Types
Here are the most important 3-note voicings used in jazz music categorized by types.
These four essential types are:
Major 7 (1 - 3 - 7)
Minor 7 (1 - b3 - b7)
Dominant 7 (1 - 3 - b7)
Diminished 7 (1- b3 - bb7) which can also be seen as a minor 6 chord (1 - b3 - 6)
Major 6 (1 - 3 - 6).
In all the ways, the fifth is not played to make the sound of the chord less fat and to economize a finger that can be used to enrich the chord with a most interested tone as the 13, 9 etc.
Notice that it is important note to confuse 3-note shell voicings with triad chords.
Triad chords are also made of three notes but they don't have seventh.
Major Seventh Chords (Maj7)
The three shapes below show how to play 3-note major 7 chords on guitar with root note on the 6th, 5th and 4th string.

Minor Seventh Chords (min7)
Here are the three voicing shapes to play minor 7 chords.

Dominant Seventh Chords (7)
Dom7 shell voicings are built with root (1), minor third (b3) and minor seventh (b7).

Diminished Seventh (dim7) and Minor 6 Chords (min6)
Diminished seventh 3-note chord positions are the same as minor 6. Indeed, the bb7 is the same as the sixth. They share the same root and the same b3.


Major Sixth Chords (Maj6)
In comparison with minor sixth chords, major sixth chords have a major third.
