Welcome to... "Micro-Lesson 270"
The mode of "A Mixolydian" comes from the major scale of "D Major." By starting a, "Major," scale from it's 5th degree, we create the Mixolydian mode. Since the 5th tone of the "D Major" scale is the "A" we can achieve the "A Mixolydian Mode" by playing the "D Major" from that "A" tone.
In the case of our Micro Lesson's groove, we are playing a common rhythm of eighth-notes using double-stops, (two-note chords). The first measure of our riff begins from an open 5th string "A" with the major 3rd on the 3rd string. A harmony of suspended 4th enters in the second measure from the "D Major" chord, bringing in the sounds of the Major chord to force a return back to the tonic chord of "A," in the 3rd measure.
The riff wraps up in measure four with the "G" Major chord entering along with an interesting sound of the "E Minor" arpeggio that pushes us back around once again to the "G Major" harmony on the last beat of "4." This allows the progression to loop or to end upon the "A Major" chord.
The riff is best performed either by "Hybrid Picking" or with the finger-picked method. This is important since there is a certain dynamic that occurs when the notes are pulled at with the fingers, rather than strummed with the guitar pick.
Take your time memorizing the parts and be sure to get the correct feel for the eighth-note rhythm groove. Enjoy!
Micro Lesson 270: "A Mixolydian" Classic-Rock Riff