The singsong rapper began as an oddity. His new "psych rock" album feels representative of his career arc.

This week's Heat Check selects come largely from iconoclasts who have already zeroed in on their individual aesthetics: a singsong rap soulman, an alté sensation, a noise-rap radical and more.

The annual Music Midtown festival takes place this weekend. Through its 25 year history — it launched in 1994 — A-list acts like Coldplay, Pearl Jam,...