Malcolm Hayward

Applications of a Connectionist Model of Poetic Meter

to Problems in Generative Metrics

Meter is one of the most distinctive formal features of English verse. Yet theoretical approaches to metrical analysis have proved problematical for a number of reasons. Traditional metrics, based upon scansion systems derived from Latin forms, is strong and flexible in its ability to describe individual units of a line, but fails to describe well the dynamics of the line as a whole and the lexical and syntactic structures which underlie that line. Moreover, traditional metrics does not address the general issue of metricality: most lines of poetry show some variation from metrical norms through the substitution of irregular units (such as a trochee opening an iambic line). When do such variations, which are permissible in individual units, render the line as a whole unmetrical? Generative metrics does address these issues by analyzing underlying lexical and syntactic structures and formulating rules to describe allowable and unallowable metrical transgressions. In this way, the theory defines metricality, distinguishing between lines which are metrical and those which are not. This approach has had some success, and yet counter-examples, lines which are unmetrical by its analysis but are found to be used by poets, have proved somewhat intractable.

Generative metrics is not, moreover, well adapted to describing verse in its actual performance. While generative metrics does account for some of the factors that affect the metrical rhythm of a line of poetry, such as lexical stress and the syntactic structure of a textual unit, it does not have a place for other features which may impact on the amount of stress that a syllable receives in performance, such as rhyme, alliteration, repetition, and the reader's interpretation of the significance of the word in the poem. Any or all of these features may affect the speaker's decision to give a certain prominence to the word, a prominence which will be realized in performance by stress. Moreover, since stress is measured in comparison to adjacent units, the amount of stress given to one unit will affect other units in its immediate environment. One reader of Keats's line, 'My heart aches, and a drowsy numbness pains' may stress 'heart', rather than 'aches'; this will affect the amount of stress given to 'aches'. But that in turn will affect the stress upon 'and', and so on throughout the line. Clearly such decisions are made upon the basis of interpretation rather than the following of metrical rules, whether those rules are defined by traditional or generative metrics.

In order to address these issues, I developed a connectionist model of poetic meter (Hayward 1991) which shows how linguistic and other features of a line of English iambic pentameter poetry interact and are resolved into a 'delivery instance', in Jakobson's (1960) terminology. This paper extends the analysis to a more detailed study of the relationship between the connectionist model and generative metrics. I compare the results each achieves in measuring a basic concept of metricality: how to distinguish whether a line is metrical or not. An analysis of specific lines by both generative and connectionist methods is provided. I also apply the connectionist model to several standard problems in metrical theory, promotion and bracketing. Because generative metrics takes account of the underlying syntactic and lexical structures of a line, promotion and bracketing are well accounted for by generative metrics. An adequate system of metrical analysis must be able to account for these qualities.

Briefly, the connectionist model of poetic meter is based upon the parallel distributed processing (PDP) models of McClelland and Rumelhart (1988). In a PDP model, information processing does not occur in a simple, linear fashion. Rather, units in a system are seen as connecting to and interacting with other units. The activation of any one unit tends to activate or suppress the activation of other connected units. This activation spreads throughout the system as each unit is affected by those units to which it is connected. The amount of activation a unit receives from other units will depend upon the initial activation of the other units (which might be received from an external input) and the strength and type of the connection between the units. The process of spreading activation continues through a number of cycles until a rather steady state is reached. At this point, the information available has been processed and a decision has been made as to the way that information might be used.

In the connectionist model of meter, the units being processed are syllables in a line of iambic pentameter poetry. I have chosen to work with English iambic pentameter rhythm as it is the most common verse form in English poetry. The activation being measured represents the likelihood that a syllable will be stressed or, roughly speaking, the amount of stress that a syllable will receive in performance. A unit representing the metrical stress a syllable will receive is connected to five other units, representing intonation, lexical stress, prosodic features of the line, propositional features of the text base, and interpretive decisions by a reader. Each of these five may give an input to or tend to activate the stress achieved in the reading of the syllable; some of these units are interconnected with one another as well. If, for example, an interpretation of a poem hinges upon the importance of a particular word, I assume the reader will accord that word a greater prominence than it might otherwise receive. A reader might also choose to emphasize an alliterative effect in the line or a rhyme. To model these decisions, an initial input is given to the appropriate unit representing the syllable in question. In addition, the model builds in a bias towards stress on alternate syllables beginning with the second, because of the expectations of an iambic rhythm. There are also negative weights assigned to connections between adjacent units representing metrical stress on the assumption that stress on a syllable decreases the likelihood of stress on the following adjacent syllable. These negative connections and the bias towards stress on even numbered syllables push the stress pattern of the line towards an iambic rhythm.

Once inputs are assigned to the five sets of units connected to the units measuring stress, the metrical units, the computer measures the activation of each individual unit as it is affected by the activation by other units to which it is connected. Activation will be affected both by the initial inputs to the individual units and by the strengths of the connections between the units. As iambic pentameter has ten syllables per line and there are six units per syllable, there are a total of sixty units in the system. The measurement of activation of all sixty units represents one cycle. The model proceeds through a series of thirty cycles (by thirty cycles, a fairly steady state has been reached), measuring and updating the activation of stress for each of the units, arriving finally at a measure of the amount of stress assigned each metrical unit in a performance (for further specifics on the connectionist model of poetic meter see Hayward 1991).

For example, in Wordsworth's line, ''Twas Summer and the sun was mounted high', the syllable 'Sum-' receives a certain amount of stress in performance. Part of its stress comes from its position in the line--the bias towards stressing even numbered syllables in pentameter lines. Part also comes from its adjacency to weakly stressed syllables. Stress also comes from other factors, however: from the alliteration with 'sun', from a rising intonation at that point, from the lexical stress on the first syllable of the word 'Summer', from the function of the word in the sentence, and from the function of the word in the poem as a whole. The connectionist model measures the input of each of these elements to the syllable 'Sum-' and arrives at a decision as to the amount of stress the syllable will receive, measured as the activation of that syllable's stress.

One of the key issues for generative metrics is the ability to decide whether a line of poetry is metrical or not. In generative metrics, certain types of rule violations are permitted, such as the use of an unstressed syllable in a stressed position, while others are impermissible, such as a stress maximum (a stressed syllable in a weak position when surrounded by two unstressed syllables and not following a syntactic boundary). Distinction can then be drawn between metrical and unmetrical structures according to whether these basic rules are violated.

When the model is asked to scan lines which are not metrical, it produces readings which would, fairly clearly, not be produced under normal conditions, including violations of lexical or linguistic rules of stress or intonation. Because of the bias towards stress on even numbered syllables and the negative weights between adjacent units, the model attempts to 'read' a line as iambic, whether or not that passage was conceived as iambic. If the passage cannot be performed as an iambic line (which might include some variations of normal rhythm), then its unmetricality will show as a violation of basic linguistic rules governing stress. I use for my examples lines which have been explored by previous researchers.

Perhaps the best known example is Halle and Keyser's (1971) construction:

1. Ode to the West Wind, by Percy Bysshe Shelley.

This is unmetrical, according to Halle and Keyser, because the accent on 'Per-' represents a stress maximum in the weak position of syllable 7. Inputs for this line are provided to the model (i.e., the amount of stress available to each syllable due to intonation, lexical stress, prosody, grammatical function, and interpretation). The computer then measures the activation of each unit as it is influenced by other units. The stress activations below indicate a hypothesis for the likelihood for a syllable to be stressed, which is translated in performance to the amount of stress likely to be placed on a syllable (I have omitted the final unaccented '-ley' from the analysis). I have provided in parenthesis the activation achieved by each syllable after thirty cycles. The measurement is from no activation (0) to full activation (.9); the measures may be taken to indicate the relative amount of stress each syllable would be accorded:

1. Ode (.9) to (.6) the (.1) West (.9) Wind (.8), by (.6) Per- (.4) cy (.7) Bysshe (0) Shel- (.9)

The unmetricality appears in this production as an 'impossible' stress in syllable 8 (-cy), a violation of a lexical rule; syllable 8 shows a much stronger activation than syllable 7 (Per).

Halle and Keyser also analyze the following line by Keats as unmetrical, for the same reason:

2. How many bards gild the lapses of time.

Again, there is a stress maximum in syllable 7, (lap-). The model produces the following pattern of activation:

2. How (.5) man- (.8) y (.2) bards (.9) gild (.9) the (.1) lap- (.9) ses (.6) of (.1) time (.9).

In this case the model produces a performance which is readable without violation of any linguistic rules; the line is thus accepted as metrical. Halle and Keyser attempt to explain Keats's rule violation by suggesting Keats is trying to 'caricature metrically the sense of the line' (185). Yet as Attridge (1982) points out, that reading is unconvincing and the line should be accepted as metrical--thus rejecting the principle of the stress maximum as a sole criterion for metricality.

The value of the connectionist model in measuring metricality can be seen in its application to several other examples analyzed by Attridge following the lines of Chisholm's (1977) modification of Magnuson and Ryder's (1970, 1971) earlier work (see Attridge, 43-46). Attridge points out that lines 3 and 4 are acceptable:

3. He struck at the tall cook with heavy blows.

4. The weeping man fell to his knees in pain.

However, according to Attridge, lines 5 and 6 are unmetrical because of the occurrence of a stressed syllable in a weak position that is not at the beginning of a new phrase:

5. He struck the amazed cook with heavy blows.

6. They sent the huge man to his knees in pain.

The problem lies with the accented '-mazed' in 5 and 'man' in 6. The model 'correctly' identifies examples 3 and 4 as metrical, with the following patterns of activation.

3. He (.5) struck (.9) at (0) the (.5) tall (.8) cook (.9) with (0) heav- (.9) y (0) blows (.9).

The only difficulty in this reading results from a rather heavy stress on syllable 4 (the). Line 4 reads as follows:

4. The (0) weep- (.9) ing (.4) man (.9) fell (.9) to (.6) his (.3) knees (.8) in (.5) pain (.8).

Again, despite a somewhat strong accent on syllable 6 (to) the line is performable with the stress as described.

The model also rejects line 6 as unmetrical:

6. They (.8) sent (.8) the (.1) huge (.8) man (.7) to (.8) his (0) knees (.9) in (0) pain (.9).

Here the rendering of accent in syllable 6 (to) would be highly unlikely in speaking as it violates normal intonation patterns.

Line 5, however, is accepted as metrical:

5. He (.6) struck (.9) the (.3) a- (.5) mazed (.8) cook (.9) with (0) heav- (.9) y (0) blows (.9).

The model proposes a reading of the section in question, 'the amazed cook', as a series of increasing stresses (.3 .5 .8 .9) which preserves a normal iambic rhythm. The stress pattern as indicated above, thus, provides a way of reading this line which is at once natural, in that it observes regular lexical and linguistic features, and metrical, in that it falls into a regular iambic rhythm.

The connectionist model of performance thus creates a distinction between metrical and unmetrical lines not according to a rule-based system but by describing what happens if a speaker attempts to read the line in an iambic rhythm. If the line can be read with the basic force of the rhythm at work (the bias towards alternate syllable stress and the negative weighting between units) without disrupting the linguistic features of the text, then the line may be said to be metrical, with regards to an iambic rhythm. If not, the line is unmetrical.

The model also handles well a number of features which affect metricality. One such is promotion, in which a non-stressed syllable is accorded a beat by virtue of its place between two other non-stressed syllables. Attridge's example is the following:

7. This thought is as a death, which cannot choose.

The phrase in question, 'is as a', calls for 'as', normally an unstressed syllable, to be promoted to a stress. The model reads the line as follows:

7. This (0) thought (.9) is (.4) as (.8) a (0) death (.9), which (0) can- (.9) not (.6) choose (.9).

Clearly 'as' has been promoted to a stressed position in the line. Attridge points out, however, that 'if either of the two outer syllables is given extra weight, the meter itself is not threatened; it is shifted towards the different, more complex formation of pairing' (250). In the model this occurs by an increase in the amount of input given to the word 'is' as a proposition in the line and in the intonation--as it might be if the line were to contradict some such question as 'Is this thought indeed like a death?' With new and stronger input for the intonation and the propositional importance of the word 'is', the model produces this reading:

7. This (0) thought (.9) is (.8) as (.6) a (0) death (.9), which (0) can- (.9) not (.5) choose (.9).

The stress has been shifted forward to 'is', without disturbing the basic metricality of the line.

A related issue is that of bracketing in polysyllables, as in Kiparksy's (1977) example of the unmetrical line:

8. Alabaster will not outlast this rhyme.

The third syllable (-bas-) is in a dominant node and should not be allowed in a weak position. The model correctly identifies this as unmetrical:

8. Al- (.9) a- (.6) bas- (.5) ter (.7) will (.5) not (.9) out- (.1) last (.9) this (0) rhyme (.9).

The weak stress on '-bas-' and the stronger stress on '-ter' violates rules of lexical stress. On the other hand, when lexical stress is inverted and there are no bracketing mismatches, the model allows those readings as metrical. For example, Kiparsky cites the line from Milton:

9. To the Garden of Bliss, thy seat prepar'd

The inversion is in 'Garden'. The model delivers the following reading of the stress in the line:

9. To (.6) the (.4) Gar- (.9) den (.5) of (.5) Bliss (.8), thy (0) seat (.9) pre- (.6) par'd (.9)

The reading accepts the stress on 'Gar-' in the third, normally weak, position, which prevents the stressing of 'den' in the fourth position. The model, then, is in accord with theories of generative metrics in its analysis of bracketing mismatches.

In conclusion, I have tried here to show how the connectionist model of poetic meter deals with the general issue of metricality and with two specific areas which affect metricality, promotion and bracketing mismatches. I have chosen for my examples well-known lines and constructions that have proved problematical to theorists. The model distinguishes between metrical and unmetrical lines as analyzed by theories of generative metrics. In addition, the model distinguishes metricality in lines which have eluded a full analysis. The strength of the model is in its built-in iambic connections which use not only syntactic, lexical, and metrical features, but also interpretation, the base structure of the text, and prosodic features. All these features do have a direct impact on the delivery of a line of poetry. A complete theory of meter must, therefore, take these into account. Only a computer analysis is able to manipulate such a large number of variables.

The model also offers a number of possibilities for future research, such as extended analysis of patterns characteristic of individual authors or periods. Because the model renders stress patterns in relatively fine, straightforward numerical gradients (there are ten possible levels of stress as compared to the two or three commonly found in other theories of scansion) statistical analysis of large units of poetry becomes possible. While this model does not provide interpretive statements about poetry based on its findings, it does hold promise for much more objective descriptions both of poetry and of the way it is rendered in performance.

References

Attridge, D. (1982), The Rhythms of English Poetry (London). Chisholm, D. (1977), 'Generative prosody and English verse', Poetics 6: 111-54.

Halle, M., and Keyser, S. J. (1971), English Stress: Its Form, Its Growth, and Its Role in Verse (New York).

Hayward, M. (1991), 'A Connectionist Model of Poetic Meter', Poetics 20: 303-17.

Jakobson, R. (1960), 'Closing Statement: Linguistics and Poetics', in Sebeok (1960), 350-77.

Kiparsky, P. (1977), 'The Rhythmic Structure of English Verse', Linguistic Inquiry 8: 189-247.

McClelland, J. L., and Rumelhart, D. E. (1988), Explorations in Parallel Distributed Processing: A Handbook of Models, Programs, and Exercises (Cambridge, Mass).

Magnusson, K., and Ryder, F. G. (1970), 'The Study of English Prosody: An Alternative Proposal', College English 33: 789-820.

Magnusson, K., and Ryder, F. G. (1971) 'Second Thoughts on English Prosody', College English 33: 198-216.

Sebeok, T. A. (1960) (ed.), Style in Language (Cambridge, Mass).