The poem mimics the loose rhythm of blues music. All the even-numbered lines rhyme in sections 1, 2, and 3: line 2 rhymes with line 4, line 6 rhymes with line 8, and so on. And if you were listening to a poem being read aloud, you would hear that the rhymes occur at the big pauses; so you can read right through the lines until you hit a rhyme. The poet even drops the G's and D's at the ends of words just to bring out the rhyming sounds all the more.
Section 4 shakes things up, for sure, but the same repetitive rhymes are in play. The end of the lines in the first and fifth stanzas of the section all rhyme, giving the lines the bluesy punch they need. And of course the final couplet rhymes as well.
Once you pay attention to all these patterns, it's hard to ignore the fact that this poem sounds an awful lot like a song. And that's fitting, no? After all, the poem itself is about the power of song—it only makes sense that the poem would go for the same patterns that make blues songs so very relatable.