Roethke is a real rhythm master and he wrote many poems following strict forms. Despite the fact that "Elegy for Jane" is written in free verse, his ability to subtly manipulate sound and tempo is part of what gives this poem the hypnotic feeling it has when you hear it read aloud.
Roethke employed repetition to get the sound he was after. Check out the first word in lines 2-4: "And," "And," "And." This repetition gives the first stanza a kind of incantatory feel—almost like someone saying a prayer. It also mirrors how we remember things: that kind of and then, and then, and then structure of how one memory leads to the next. This section of the poem sounds like the way memories materialize.
Her song trembling the twigs and small branches.
The shade sang with her;
The leaves, their whispers turned to kissing
You can really hear how those repeated sounds tie everything together in a subtle, musical way (musical as in awareness of sound, not Broadway). This mirrors how everything in nature is connected. All those different natural elements out there are all part of one big interconnected system that all works together. It's a bit like the way that the speaker's love of Jane seems to connect him to his love of nature. Having all those similar sounds ties the poem's words together in much the same way.