The band sits on a single 7th chord (1⁷) forever — funk, soul, a jam.
Mixolydian — it IS the sound of a dominant chord — SCL·03
drop in the blues scale for grit; the ♭3→3 slur is the whole vocabulary SCL·02
A lone 7th chord has no leading tone, so play like it — the ♭7 is home base, not a note to resolve. Mixolydian = major with that one flat.