I7 - ♭VIImaj7
This vamp is by far the heaviest hitter of all the basic two-chord Mixolydian vamps. If you’re at a rock jam, and you ask the guitar player to start a song, a lot of times this is what they’ll do.
Why does it work so well? Partly because the ♭VIImaj7 is unique to Mixolydian among the common major modes; that is, Ionian and Lydian don’t have it. And so building a chord on it is a clear way to announce “we’re in Mixolydian”. In fact, the I7 and ♭VIImaj7 combined contain all 7 notes of Mixolydian.
Another reason is that the ♭VIImaj7 has no avoid notes — that is, it has a 9th, ♯11, and 13th all within Mixolydian. So this gives you a dial on how harmonically dense and lush you want this chord to be. It can be just a triad, ♭VII — in fact, this is what most rock contexts use by default — or you can stack extensions: add9, 6/9, maj79♯11, etc.
The ♭VIImaj7 is the brighter variant of v7, which we’ll get to in the next lesson.
I7 - ii7
The ii7 is closely related to ♭VIImaj7 — it's essentially the upper extensions of that chord (a ♭VIImaj9 without the root), which is why I’m covering it here.
As a vamp, I7 - ii7 is pretty rare. Why? A big reason is because of what Mixolydian’s characteristic ♭7 does to each of these chords. Over ii7, the ♭7 is an avoid note. And if voiced over the I, it makes the vamp actively unstable: your ear gets pulled toward the relative Aeolian mode. That is: in Mixolydian, the relative minor isn't on the vi7 like it is in Ionian — it's on the ii7. So when I say the vamp pulls toward the relative Aeolian, I mean the I7-ii7 starts sounding like it wants the ii to be the tonic.
And as triads, a I - ii vamp isn’t distinctly Mixolydian, it’s shared with Ionian. And Ionian is much better at using its version of this vamp, which is Imaj7 - ii7.
Subjectively, when I play this vamp, it has some rising energy, but it’s not quite dramatic enough to be actually dramatic. I see the ii7 being used on the way to somewhere more than I see it in vamps.