Individual Chord Shapes
Playing modal guitar is as much about harmony as it is about improvising melody with a mode.
From the Major Scale we construct seven modes. Each of these modes have a chord that is the tonic chord for the mode.
To put this into context, the tonic chord of the Major Scale is the Maj7 chord. The fourth mode of the Major Scale is the Lydian Mode, and this is a Maj7 chord also, with a difference - there is a #4th note available to play with this Maj7 chord, and this is referred to as the tonic chord of the Lydian Mode.
So now we have an idea of two modal chords. The tonic chord of the Major Scale is the Maj7 chord, and the tonic chord of the Lydian Mode is the Maj7 (#4) chord.
There are three minor modes, and each of these begins with a tonic chord of min7. How do we find the difference between the "sound" of these modal chords, if all three of them are min7?
Well, let's just keep it simple for now.
The Dorian min7 may also have a Major 6th note, and if it does, it is called a min13 chord.
The Aeolian min7 does not have a Major 6th note, it has a minor 6th note. In context of the sound of the chord, this minor 6th note is just a semitone above the 5th note of the chord, and sounds like an "augmented 5th" min7 chord. To name this, min7+5 is fairly adequate.
Both Dorian and Aeolian Modes have a natural 9th note, two semitones above the tonic, above the octave. So it is possible to play a min9 chord for the tonic chord of Dorian Mode and for the Aeolian Mode.
The Phrygian Mode has a b9 note, and also has a minor 6th note. So therefore we could define the "sound" of the Phrygian tonic chord as min7 (b9). This is not a chord that is played very often, it's just good to know.
Mixolydian Mode is also known as the Dominant 7th Scale, and logically enough, the tonic chord of the Mixolydian Mode is the Dom7 chord.
Locrian Mode has the min7b5 chord as the tonic chord. This could be grouped with the three minor modes, although the sound of the b5 note makes such a big difference to the sound of this mode, it is useful to describe it individually.
So there we have it, the seven Modal Chords. Two Maj7 chords, three min7 chords, a single Dom7 chord and a single min7b5 chord.
These chord types appear in a sequence, in each of the modes, and their placement in relation to the tonic note of the mode plays an important role in the sound and vibe of the mode.