=Paper=
{{Paper
|id=Vol-3290/short_paper5417
|storemode=property
|title=Measuring Rhythm Regularity in Verse: Entropy of Inter-Stress
Intervals
|pdfUrl=https://ceur-ws.org/Vol-3290/short_paper5417.pdf
|volume=Vol-3290
|authors=Artjoms Šeļa,Mikhail Gronas
|dblpUrl=https://dblp.org/rec/conf/chr/SelaG22
}}
==Measuring Rhythm Regularity in Verse: Entropy of Inter-Stress
Intervals==
https://ceur-ws.org/Vol-3290/short_paper5417.pdf
Measuring Rhythm Regularity in Verse: Entropy of
Inter-Stress Intervals
Artjoms Šeļa1,2,∗,† , Mikhail Gronas3,†
1
Institute of Polish Language (Polish Academy of Sciences), al. Mickiewicza 31, 31-120 Kraków
2
University of Tartu, Ülikooli 18, 50090 Tartu, Estonia
3
Dartmouth college, Hanover, NH 03755, USA
Abstract
Recognition of poetic meters is not a trivial task, since metrical labels are not a closed set of classes. Out-
side of classical meters, describing the metrical structure of a poem in a large corpus requires expertise
and a shared scienti昀椀c theory. In a situation when both components are lacking, alternative and contin-
uous measures of regularity can be envisioned. This paper focuses on poetic rhythm to propose a simple
entropy-based measure for poem regularity using counts of non-stressed intervals. The measure is val-
idated using subsets of a well-annotated Russian poetic corpus, prose, and quasi-poems (prose chopped
into lines). The regularity measure is able to detect a clear di昀昀erence between various organizational
principles of texts: average entropy rises when moving from accentual-syllabic meters to accentual vari-
ations to free verse and prose. Interval probabilities, when taken as a vector of features, also allow for
classi昀椀cation at the level of individual poems. This paper argues that distinguishing between meter as
a cultural idea and rhythm as an empirical sequence of sounds can lead to better understanding of form
recognition and prosodic annotation problems.
Keywords
rhythm, meter, poetry, regularity, entropy, diversity
1. Introduction
Identifying the meter of a poem is one of those tasks that is deceptively simple. The problem
lies not with methods: a wide array of successful solutions exist, ranging from rule-based [3, 1,
18] to probabilistic [16] to deep learning [17, 8]. The problem, as o昀琀en happens, is conceptual:
metrical forms are treated as a closed set of classes, when in fact they are not; far from it. There
is much more variation in organizational principles than common iambic or trochaic patterns.
Not having a matching label for some unusual arrangement of stressed and unstressed syllables
in a poem does not make that poem non-regular, or even non-metrical. And, indeed, quite o昀琀en
we do not have labels.
Here are some numbers from well-annotated, large poetic corpora that are indispensable in
today’s work. Only 2% of lines in the Russian corpus do not conform to any of the 昀椀ve classical
CHR 2022: Computational Humanities Research Conference, December 12 – 14, 2022, Antwerp, Belgium
∗
Corresponding author.
†
These authors contributed equally.
£ artjoms.sela@ijp.pan.pl (A. Šeļa); mikhail.gronas@dartmouth.edu (M. Gronas)
ȉ 0000-0002-2272-2077 (A. Šeļa)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
231
meters (iamb, trochee, dactyl, anapest, amphibrach); for Czech this number grows to 14%, in
the Dutch song collection it is 15%, and 昀椀nally the German corpus has an incredible rate of
68% ‘unrecognized’ lines (out of 170,000 in total).1 This is not simply a failure of recognition
systems—even if you suppose there is some noise. This is a problem of domain expertise and
levels of variation in modern verse forms. Germanic versi昀椀cation systems, for example, stem
from alliterative tonic verse and widely employ meters that are not based on stable, recurring
units of rhythm (metrical feet) [6]. With enough domain expertise and a shared taxonomy
(that stems from shared theory), all poems in a corpus, in principle, could be described with a
meaningful metrical label.2 That is how the Russian poetic corpus is described now [7].
Needless to say, ‘enough domain expertise’ and ‘shared theory’ are luxuries. More o昀琀en
than not, we will not have enough resources for the former nor enough scholarly consensus
for the latter. Semi-annotated, theory-agnostic and unstructured data is the primary reality of
computational work today. That is why parallel approaches—that are not based on labels—for
describing metrical and rhythmic features of verse might be considered. This paper proposes
a simple way to measure rhythm regularity as one continuous value based on measures from
information theory and ecological diversity.
Conceptually, our approach focuses on rhythm alone and brackets the ‘meter’ (as an already
known template) out. We try to ask how regularly the rhythmical features are organized in
a text, to de昀椀ne a single scale that has highly regular iambs on one side, and irregular prose
on the other—with many more intermediate and heterogeneous cases in between. Similar at-
tempts to de昀椀ne one space for metrical forms have been made before [16], but su昀昀ered from
not distinguishing between the metricality and regularity of verse. At the same time, scholars
working with syllabic verse (mostly Romanic) o昀琀en looked in the same direction, because sim-
ilarly organized isosyllabic verse might have di昀昀erent rhythmic features across languages [4],
or authors [13].
Our reasoning here is informed by the so-called ‘Russian school’ of metrics that have es-
tablished a distinction between poetic meter and rhythm. In the classic formulation, meter
is a theoretical abstracted scheme, while rhythm is an empirical realization of (and deviation
from) that scheme in a given poem (with ‘wrong’ stresses, additional syllables, distribution of
word boundaries, etc.; for a brief English overview see Starostin & Pilshchikov [22]). Czech,
English, Russian and German literatures all had an idea of iambic meter by the 19th century,
but the meter’s rhythm was di昀昀erent everywhere: English iambs allowed the most freedom
and scheme transgressions (impossible in Czech and Russian); however, Slavic iambic meters
still had enough rhythmic variation compared to German that was the strictest in following
the iambic pattern (unstressed syllable followed by a stressed one) [23, 14]. Conversely, Span-
ish syllabic verse had strong iambic tendencies in its rhythm [4, 14], without having an iambic
meter in its cultural repertoire per se.
This fundamental distinction was taken further by Maksim Shapir [20], who suggested that
the relationship between meter and rhythm is dialectic, continuous, and non-hierarchical (in
the sense that rhythm is not an outcome of a meter). Meter is just a rhythm that is repeated
1
Numbers were provided by Petr Plecháč. For the detailed description of the mentioned corpora, see [19].
2
Even if the label is just ‘free verse’, ‘tonic verse’, or something more exotic like: ‘3-ictus line with maximum
inter-stress interval of 2 syllables and regular alternation of masculine and feminine clausulae’.
232
enough times and standardized in a tradition. For example, Russian folksongs allowed a re-
curring rhythmical sequence of 昀椀ve syllables with a strong preference for stress on position
3, ‘00100’ (o昀琀en as a hemistich in 10-syllable line). This rhythm was a mere tendency, until it
was recognized by poets and literati and parsed as metrical foot [2, 5]. It even received its early
name—‘reduplicated amphibrach’—despite being open to equally plausible scansions within an
already existing system: either as a trochaic ‘(1)0-10-0’ or anapestic ‘001-00’ meter.3 This is
how a ‘penton’ (piatislozhnik) was born in literary tradition for writing stylized folk-inspired
poetry—when one of the rhythmical possibilities in folksongs became a rule.
Conversely, a meter could be ‘rhythmicized’ by breaking expectations and inertia in a given
poem: actual rhythm can be so individual that it would not be possible to make a judgement
about a governing scheme. From this perspective, meter is more of a cultural phenomenon,
while rhythm is of prosodic nature. Meters, or measures, are crystallized technologies for the
organization of speech: it is possible for them to be written down in poetics manuals, taught in
schools, transmitted. They are (mis-)recognized by poets, debated, weaponized for ideological
reasons or completely deconstructed [11]. Rhythm is a source of cultural conventions and
a sub-product of linguistic a昀昀ordances. Here, we concentrate on information from the sub-
product alone, while tracing its relationship to culturally recognized meters using existing deep
annotations in the corpus of Russian poetry.
2. Materials and methods
The underlying idea of a regularity measurement is simple. Any systematic outside force—
like meter—that organizes speech prosody will leave its trace in the distribution of possible
unstressed intervals. By measuring the shape, or (un)evenness of these distributions we ac-
quire a proxy for rhythmical regularity. Ideal iambic meter allows only one type of unstressed
interval—one syllable. In practice, it frequently allows one, o昀琀en three; rarely 昀椀ve (pyrrhics
happen instead of fully 昀氀edged iamb feet). In prose (at least in most of it) there is no reason
to suspect systematic limitations on the allowed inter-stress interval. We can also think about
it as an inequality problem—meters are tyrannical forces that allow only a fraction of linguis-
tically possible intervals to dominate, while prosaic language has a more democratic (or just
disinterested) outlook on the distribution of the possible intervals.
Our approach is summarized in Figure 1. Given a binary rhythmical annotation of an in-
dividual text, we extract all inter-stress intervals. We include in the notion of ’interval’ an
unstressed syllable that precedes the 昀椀rst instance of stress in a line (anacrusis), but we ex-
clude unstressed syllables that follow the last stressed syllable (clausula).4 The types (intervals
of particular lengths) are then counted and transformed to probabilities. To measure how ‘un-
even’ the resulting probability distribution is we use classic Shannon entropy. This measures
the uncertainty of a probability distribution and has two features that are useful for us: it
3
To be fair, both trochees and anapests were heavily employed as meters for imitation of folksongs—dactylic line
endings played an important role here.
4
Clausulae are dominantly regular in verse. However, the same pattern of line endings (that might depend on
the prosody of rhyming words) can be shared across poetic forms of very di昀昀erent organization (syllabic, tonic,
accentual-syllabic). Since the appearance of clausulae is an almost constant feature of traditional verse, counting
them will not add much to our task of di昀昀erentiating verse of di昀昀erent organization.
233
Figure 1: Summary of the method and two short examples. As expected, Whitman’s free verse in
Leaves of Grass has greater entropy of intervals than Milton’s iambic pentameter, even if the latter
has irregularities. The scansion was done by a native English speaker. It is open to debate, but a few
changes would not alter the overall picture.
grows with the number of the outcomes (i.e. possible interval types) and decreases when some
outcomes are more likely than others; a fair die will have a larger entropy compared to an
even slightly unfair die. In our case, lower entropy value will signal increased regularity, since
some intervals end up being much more likely than others (unfair). Entropy is widely used as
a diversity measure in ecology and is closely related to a family of measures that, to varying
degrees, capture richness (amount of types) and evenness (how some types are more probable
than others). To adopt a holistic approach to rhythm diversity, we also calculate Hill numbers
[9] for interval probabilities that summarize diversity information in one curve (cf. their recent
use to calculate surviving manuscript diversity by Kestemont et al. [10]).
To predict stressed syllables in a text, we use a pre-trained, bidirectional RNN model that
performed better than dictionary-based methods [15] and was further 昀椀ne-tuned for Russian
poetic prosody (‘ru-accent-poet’ Python module). This model has one important limitation: it
leaves all monosyllables unstressed. This will introduce noise to our measures, but we want
to demonstrate that high-accuracy performance is not necessary when dealing directly with
enough rhythmical features.
To determine if the entropy of inter-stress intervals is able to capture di昀昀erences in regularity
across di昀昀erent types of texts, we measure entropy at the level of individual texts that are
sampled from several di昀昀erently organized domains. Poetry comes from the Russian National
234
Corpus [7], prose from the collection of 19th c. narrative 昀椀ction [21].
• Classic meters Sample of 700 poems for each of the classic accentual-syllabic meters
(iamb, trochee, anapest, dactyl, amphibrach);
• Baseline prose Sample of 1000 paragraphs of Russian 19th century literary prose (2
paragraphs sampled from each of 500 texts);
• Chunked prose The calculated regularity of poetry, at least partly, emerges from di-
vision into lines that can arti昀椀cially cut mid-sentence and mid-unstressed intervals. To
emulate this behavior, we cut continuous prose into quasi-poems. For each chunk, its
line length in syllables and overall length in lines is determined randomly by drawing
values from the empirical distribution in the poetry corpus. In the end, our quasi-poems
closely resemble the average dimensions of actual poetry. We sample 1000 quasi-poems
(2 from each of 500 texts) ;
• Free verse Verse that is labeled ‘free’ in corpus annotations, and that should not be
governed by any surface-level prosodic pattern (700 poems);
• Accentual, 1-2 (A1-2) Poems that take an intermediate position between accentual and
accentual-syllabic verse by allowing variation of 1-2 syllables in inter-ictus intervals. A
meter also known as dolnik (700 poems);
• Accentual, 1-3 (A1-3). The same as A1-2, but allowing greater variation of 1-3 syllables.
A meter known as taktovik (700 poems);
• Accentual (A). Pure accentual: inter-ictus intervals are not under any regulation, the
only measure is the tendency for a constant number of strong positions in a line (700
poems).
Intuitively, all these forms should be positioned at di昀昀erent parts of the scale of regularity.
We can expect that the regularity of Classic meters > A1-2 > A1-3 > A > Free verse (Chun-
ked prose) > Baseline prose. This is what we set out to test using the per-poem distributions
of regularity measures.
3. Results
Figure 2 shows the distribution of entropy measures for individual texts in each category, ar-
ranged by median value. While the variance of observations is large, there is a clear increase
in average entropy (decrease in regularity) from accentual-syllabic (median around 1) to base-
line prose (median above 2). Hill numbers calculated for bootstrapped samples also show a
clear di昀昀erence in diversity pro昀椀les between prose, classical meters, and intermediate forms
(see Appendix B). Overall, this supports our expectation of how things should be arranged on
a regularity scale.
The interval distributions also reveal a shortcoming of this measure based only on inter-
stress intervals: pure accentual, free verse and chunked prose all show similar median regu-
larity. While for free verse and chunked prose this is not surprising, we know that accentual
verse has a governing principle and is regular, it is just that this regularity is not re昀氀ected in
the distribution of rhythmical patterns. Additionally, trochaic meters show unexpectedly large
235
Figure 2: Distribution of entropy measures per di昀昀erent corpus subsets, arranged by median value. Red
boxplots mark all classic accentual-syllabic meters, whiskers correspond to 95% confidence interval.
diversity of inter-stress intervals compared to all other accentual-syllabic meters. Partly this
is a natural outcome of the measurement: trochee allows even-length intervals from anacrusis
(unlike iamb), which can in昀氀ate entropy. However, it is important to note that Russian trochee
can allow more metrical freedom than other meters, because of its historical source in folk-
songs. The perceived irregularity of the source material became a stylistic marker for folksong
imitations that were o昀琀en rendered in trochaic meters.
There is an another potential problem with our observations—the length of the line. As
one might expect, it is hard to cram a long unstressed interval into a short line. To account
for this, we can formalize regularity di昀昀erences across categories by building a linear model
that estimates mean entropy for each group, conditioned on the average length of lines in a
poem (for more details, see Appendix C). Posterior predictions made for the global average
length across corpora are fully consistent with the observed trend. Based on this model, the
di昀昀erence that we are seeing does not come from di昀昀erence in length of lines.
It is also possible to use raw probabilities of individual poem intervals to perform recognition
of classic meters if every text is put in the same feature space. Figure 3 shows a UMAP [12]
projection of a subset of our data, with each point corresponding to a single poem. Even with
noisy, imperfect scansion, the potential for clustering is evident (�㕘-means clustering with �㕘 set
to the number of meters shows an Adjusted Rand Index of 0.6, suggesting a decent clustering
force at the scale of individual poems).
236
Figure 3: UMAP projection of interval data using 5000 texts. Each point corresponds to a single poem.
Prose and ‘Accentual,1-2’ were added for comparison. Adjusted Rand Index for �㕘-means clustering for
data on this plot plot is 0.41.
4. Discussion
Our entropy-based, continuous measure of rhythm regularity is able to adequately describe
di昀昀erences in verse organization at the level of individual poems. It is also independent from
language and versi昀椀cation system, and could be used to compare poetic forms across languages
and across meters—as long as the scansion is available. Of course the nature of this measure-
ment makes it more suitable for accentual-syllabic foot-based verse, as that style has the great-
est in昀氀uence on the distribution of allowed inter-stress intervals. As we have seen in Figure 2,
it is hard to distinguish pure accentual and free verse; purely syllabic poems will most likely
show a similar range of entropy values. To account for this, regularity measurement would
need to include both the regularity of stressed/strong positions (for tonic verse) and the regu-
larity of line lengths (for syllabic verse)—but introducing additional dimensions would make
comparisons on a single, continuous scale meaningless. There is little point in asking whether
tonic verse is ‘more regular’ than syllabic.
We hope that this measure might be used for cross-linguistic comparisons, but its simplicity
makes it especially useful in unseen and unstructured data scenarios, where expert annotators
are unlikely to be available. This includes collections of self-published poetry, rap, and song
lyrics. The regularity scale can be also used to answer long-standing questions about tenden-
cies that are hard to see: e.g. whether all ‘free verse’ is completely free, or if some authors prefer
237
it with a bit of regularity (like micropolymetry)? We have seen that it is almost impossible to
distinguish free verse from quasi-poems that were cut from prose; however, these quasi-poems
have much more regulated line length per text, and, under certain conditions, visibly higher
average entropy than free verse (see Appendix C).
One of the key features of this regularity measure is that it does not depend at all on the art
of scansion. Imperfect, automated rhythmical annotation provides enough information both
for entropy scores to make sense, and for meters to form distinct clusters. This reminds us
that the rhythm of a poem as an empirical sequence of sounds is not equal to (and not always
dependent on) meter as a cultural idea. By distinguishing the two concepts, we can focus our
e昀昀orts on improving the rhythm annotation: deriving metrical labels is a parallel, and o昀琀en
much more costly, process.
Acknowledgments
AŠ was supported by the “Large-Scale Text Analysis and Methodological Foundations of Com-
putational Stylistics” project (SONATA-BIS 2017/26/E/HS2/01019). We are deeply grateful to
Benjamin Nagy and Petr Plecháč for their advice and discussion of the early dra昀琀s of the pa-
per. We also would like to thank two anonymous reviewers for their helpful and thoughtful
feedback.
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Figure 4: Hill numbers up to diversity order 4 for di昀昀erent corpus subsets.
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A. Code and data
The data pre-processing and analysis pipeline is openly available in a repository:
https://github.com/perechen/verse_regularity
B. Rhythm diversity, Hill numbers
Figure 4 displays the decay of Hill numbers (diversity curves) for corpus subsets up to diversity
order (�㕞) 4. �㕞 = 0 corresponds to the simple number of types; �㕞 = 1 to Shannon diversity (our
regularity measure); �㕞 = 2 to Simpson’s index. Higher positions on a curve signal higher
relative diversity. We see that classical meters have the least diversity of unstressed intervals,
followed by accentual variants and then followed by the highest, and distinct, curve for prose.
The only exception is the behavior of trochee that displays a diversity of intervals (a昀琀er �㕞 =
1) approaching accentual verse and quasi poems. Lines show average Hill numbers for 1000
bootstrapped subsets (100 texts in each run), shaded areas correspond to 95% interval.
240
C. Regularity and line length: posterior predictions
To formally model regularity di昀昀erence between corpus subsets given the relationship entropy
∼ line length, we build a Bayesian regression model using the ‘brms’ interface in R, where we
estimate the average entropy (�㕅) for each group of texts (�㔶), conditioned on poem’s average
line length in syllables (�㕆) within each group (interaction). We add a quadratic term for �㕆, since
the �㕅 ∼ �㕆 relationship di昀昀ers across meters and is not linear. We also log-transform �㕆 to have
better predictions in the presence of outliers. In ‘brms’ formula notation (modeling �㕅 using
normal distribution):
R ∼ C * (S + I(S^2))
The le昀琀 side of Figure 5 shows posterior predictions for 昀椀xed global average line length
(dotted lines on the right side plot). Since there is an interaction between each subset and
length, each prediction for each group uses its own scale. Estimates are consistent with the
empirically observed di昀昀erences in Figure 2, with one exception: quasi-poems at the average
corpus line length show greater average entropy than accentual and free verse. Note that while
some forms show a slight increase in entropy as line lengths increases, the relationship is not
clear in many cases, except for free verse and chunked prose that are unconstrained by metrical
regularities.
Additionally, we omit prose samples from modeling, because the division to lines was absent
from them, which means that ‘line length’ was just equal to the length of a paragraph (in
syllables). This would introduce unreasonable predictions for unobserved lengths, like iambic
poems with an average line length of, say 400 syllables (200-foot iamb! iambic diakosiameter!).
The right side of the Figure 5 already shows wide con昀椀dence intervals for extremely short and
extremely long lengths for which we don’t have many (if any) observations.
241
Figure 5: Le昀琀: posterior estimates (black) for corpus subsets superimposed on empirical data. Pre-
dictions are made for global average line length (9.4 syllables). Right: posterior relationships between
entropy and line length for each group. Vertical line marks the point that was used for predictions on
the le昀琀.
242