Acuity: A Metric for Enjambment
We know enjambment is an important means of rhythmic control in all verse, and vital in free verse; we know that enjambments have different "strengths"; but we have no definite way to measure and compare these strengths. I propose a measure tentatively called "acuity." ("Gradience"? One emphasizes the poet's act of cutting into the sentence with more or less vigor; the other emphasizes the reader's experience in traversing the enjambment.)
Determining acuity begins with a complete parsing of the sentence that contains the line-break. The tree diagrams, or equivalent labeled-bracketings, common in linguistic studies of syntax, provide a convenient basis. Here's an example from Radford, Transformational Grammar, pp. 53-54: "This boy must seem incredibly stupid to that girl."
[S [NP [D this] [N boy] ] [M must] [VP [V seem] [AP [ADV incredibly]
[A stupid] ] [PP [P to] [NP [D that] [N girl] ] ] ] ]
The words of this sentence, and the acuity of a possible line-break following each word:
To measure the acuity of a line-break following a word, we count opening brackets to the left of the word, subtract closing brackets to its left, and subtract the one or more closing brackets to its right preceding the next opening bracket (or non-bracket, non-punctuation text) if any. For "to" in the sample sentence the measure is 12 - 8 - 1 = 3; for "boy" it is 4 - 1 - 2 = 1; for "girl" it is 15 - 10 - 5 = 0. The proviso about non-bracket, non-punctuation text means that a line-break in the middle of a word ["in- / credibly"] has an acuity higher by one than a line-break at the end of the word.
Among many practical difficulties, one complication is that syntactical ambiguity, which is common, may allow the sentence to be parsed in more than a single way.
Since this metric cries out for a computer program that would catalogue the acuities of a poem's enjambments, a vital practical question is whether the state of the art has arrived at a point where completely parsing arbitrarily complex English sentence is possible. I don't know the answer; I'm trying to find out.
The next step is to recognize potential acuity. In the formulation above, the crucial qualification "uncompleted" suggests a separate characterization of enjambments based on whether each node to which the pre-line-break word belongs might or could be complete without damaging grammaticality. The relevance of this addition shows up most sharply in possible enjambments of "garden-path sentences":
The horse raced past the barn
The metric proposed so far assigns to the line-break after "barn" an acuity of 1. Intuitively speaking, it should be much higher, because the first line can so readily be parsed as complete. In general, the possible unfoldings of a sentence -- as opposed to and preceding the actual -- influence the felt sharpness of the line-break. When a poem begins with the line, "This is the time of year" (Bishop, "The Armadillo"), a potential acuity of 0 vies with what turns out to be the realized acuity of 1 or 2. In the sample sentence above, the same would be true of a break after "stupid."
Is it true, as it seems, that potential acuity can never be greater than realized acuity? It is not true semantically or pragmatically; the sentence's continuation can constitute less of a surprise than seemed promised. (This renders the line-break less interesting, and poets therefore avoid it. This makes examples difficult to find, though not to construct.) The question about measures of acuity is whether a similar syntactical anticlimax is possible.
As a first, sentence-level measure of the potential acuity of a line-break, we could hypothesize a period at the end of the line and seek a complete parse of the sentence as if it ended there. Extensions to lower levels of the parse tree might be complicated but should not require breaking different conceptual ground.
Potential acuity, however, is inevitably more difficult to specify deterministically than actual acuity. When the sentence and its complete (and unique) parse are given, actual acuities can be derived by simple counting of brackets. Hypothetical sentence terminations raise questions that are not strictly syntactical; in "This is the time of year," the semantics of "the" increases the probability that the sentence will continue so as to specify which time of year the sentence is undertaking to designate.