As you can see, the third of the G scale is the only note that needs to be lowered to a Bb to get a C mixolydian scale.
Move the F up one fret to an F# to get a D mixolydian scale.
When you move from a V to a IV chord, things gets a bit more complex with two notes that change;
in this case the B becomes a Bb and the F# an F.
We’ll call this the inner logic of the mixolydian scales.
The third of the I chord wants to ‘resolve’ to the flat seventh of the IV chord.
And the flat seventh of the I chord wants to resolve to the third of the IV chord.
The same also works in a V to I chord progression.
We can make use of this inner logic in soloing and in playing chords.
Because the differences in the scales is so small, you often only have to move a pattern one fret down or up to get the corresponding pattern on another chord.
Change only one note to play the same riff over the IV chord.
In some cases, play exactly the same riff over I, IV and V; use only notes that those three scales have in common.
Note: other chords and more inner logic.
Inner logic also works with minor chords.
Every time you play a I – IV chord progression (or a V -I), you can use this theory.
In some cases, the third doesn’t have to resolve at all, because it’s already part of the chord you’re resolving to.
If you’re playing Am7 to D7 in a minor blues, the third of the Am7 is a C, which is also the flat seventh of the D7 chord.
This theory also works with the fifth and the ninth of a chord in these progressions.
The fifth of the I chord will want to resolve to the ninth of the IV chord and the ninth will want to resolve to the fifth.
And again, sometimes they are the same.