Name for a set of clauses that can be split into sentences multiple ways

Question

I'm a big fan of music with clever lyrics, and there's a particular bit of wordplay that I've come across in several songs and I've always wondered if it has a specific name. As the title says, it's when a set of clauses can make sentences multiple ways. In songs, it's usually that the rhythm splits what is being said into several distinct pieces, and those pieces can associate a few ways.

This is easiest to explain with an example. In the lyrics of Injection, by Rise Against, there are these lines:

Pull this plug
Let me breathe
On my own
I'm finally free

This could be interpreted as

Pull this plug, let me breathe. On my own I'm finally free.

but it could also be

Pull this plug. Let me breathe on my own. I'm finally free.

Is there a name for this? The closest I can think of is a garden path sentence, but that's not quite it - in a garden path sentence, one of the two implementations is wrong (or at least humorous), whereas in this, either is valid - when I've come across it in music it's often the juxtaposition between the two interpretations that is interesting or thought-provoking.

Answer 1

The classical rhetorical term closest to the phenomenon you describe is asyndeton, ‘not connected’, that is, a chain of words, clauses, or phrases without the use of conjunctions or other function words. While semantic ambiguity may not be a primary goal of this literary device, it can be part of the design:

"Asyndeton can also create ironic juxtapositions that invite readers into collaborative relationships with writers: because there are no explicit connections between phrases and clauses, readers must supply them to reconstruct the writer's intent. . . .
(Chris Holcomb and M. Jimmie Killingsworth, Performing Prose: The Study and Practice of Style in Composition. SIU Press, 2010)

In a song, melody and phrasing need not imitate that of speech, so that the listener is not certain how phrases and clauses relate to one another. This could make the song more directly evocative of emotional states rather than, say, narrating a description of events or states that result in those feelings.