Camping on I7

The I7 chord is a dominant seventh chord serving a tonic function (that is: it’s the home chord, the one you resolve to). If you know some music theory already this might be confusing. It’s because the word “dominant” conflates three different things: a chord shape, a gravitational pull toward home, and a local pull that can happen anywhere in the key. We’ll untangle those later. For now, just know that the I7 chord has the dominant shape, but it’s also home.

It’s a great tonic chord to vamp on because it’s a dominant chord. Meaning nearly every note is a chord extension. The only avoid notes are the 4 (diatonic) and the ♮7 (borrowed from Ionian). The diatonic chord extensions are a 9th and a 13th.

Your borrowed options are a ♭9, a ♯9, a ♯11, and a ♭13. An upshot of this is that chromatic passing tones work really well here (and in fact that’s a core part of the harmonic language of both bebop and New Orleans brass band music).

In practice, the I7 chord is played as a triad 80-90% of a time. I’ll still refer to it as a I7 chord, the voicing of the ♭7 is just likely to be subtle — in the melody, in a guitar riff, in the horn backgrounds, revealed through another chord, etc. When it is voiced in a chordal instrument, it adds a nice crunchy texture that’s idiomatic for rock jams, bluesy rock songs, and that kind of thing. The Beatles, for instance, like doing this in their bluesier songs.

A note about the iii7♭5 chord: it doesn’t really have its own distinct identity in Mixolydian. If you try to vamp I7 - iii7♭5, it won’t really sound like a vamp, it’ll sound like you’re just sitting on a I9 chord.