With all the experimenting we see happening in "[i carry your heart with me(i carry it in]," it's no shock that Cummings would opt for free verse over the traditional sonnet. At the same time, though, he uses literary devices like parallelism, anaphora, and the occasional trochee that make it sound ultra-lyrical without the fancy form and meter. And that's not to mention all the parentheses that turn the whole idea of poetic form on its head. In a way, then, Cummings creates his own form and meter that doesn't play by the old rules.
The rhythm we hear in the poem is largely determined by the syntactical patterns Cummings uses. What the heck does that mean? Well, instead of using end rhymes and specific metrical feet to fit a particular kind of form (like the Romantics), he uses the arrangement (syntax) of his words to create rhythmic patterns. For example, the anaphora we see in the repetition of the "here is the" clause in lines 10-11 creates a familiar rhythm without sticking to a particular meter. In lines 5-7 we have another familiar rhythm with the pattern we hear in "i fear no fate" and then "i want no world." We can definitely hear and see Cummings's use of syntax hard at work in those clauses.
Similarly, in line 3 we have more trochees (which are two-syllable pairings with the emphasis on the first syllable: DUM-da). They can be found in the "i go, you go" clause. But again, Cummings isn't looking to pin the line down to a specific meter. He's way too modern for that. Lines 8-9 also have some parallelism, with that similar sounding "and […] whatever" syntactical arrangement that gives the lines that lyrical, song-like vibe.
Finally, Cummings's use of enjambment is super-modern, but also adds to the poem's lyrical quality. Each line flows into the next without any interruption from punctuation. In fact, the entire first stanza comes to us without any stops or pauses. And by the third stanza, the speaker's description of the "tree called life" is a constant flow of thought that's stressed even more by all those "of the" clauses. Even if we hit a set of parentheses, we still sense the flow of thought, since each parenthetical clause is squished into the adjacent word. So, just like everything else, Cummings is even giving the use of enjambment his own modern spin. We're telling you, there's nothing stopping this guy from shaking things up.