loading . . . ###### As presented at “New Perspectives on Alliteration in Poetry and Cultural History”, University of East Anglia, 1 September 2025
## 1. Introduction
What’s the purpose of alliteration in modern poetry? The oldest answer I could find to that question is from 1902. Talking about Shakespeare’s sonnets, Thomas R. Price said, “As the result of the caesura was to cut the verse into two halves, he felt, like older poets, the need of linking the two parts by most ingenious harmonies of sound.” (Price) I like this: As poetic structures got longer and more complex, poets needed a technique to keep the listener’s ears connected to what they were doing. So they reached back into the history of English, where alliteration linked two halves of a longline, and gave it a new job: jumping across a caesura wherever one might show up. Or in a rhymed poem, alliteration can pole-vault line endings, connecting verses orthogonally to the rhythmic structure. In a sense, it might even form a separate melody, like a baroque concerto over the continuo, or a jazz solo over the rhythm section.
If this is truly what’s happening, it will take some proving. This is going to be harder to hear than the structures of formal verse. It’s just at the limit of what I can hear. Well, when confronted with a phenomenon that’s just beyond sensory perception, physicists immediately start thinking of a way to augment our senses with some sort of technology. And that’s exactly what I did.
As Paul Deane argued this morning, and as Dennis Wilson Wise demonstrated by collecting 400 pages of it (Wise), the language is currently experiencing a revival of alliterative verse. Are modern alliterative poets using it for the same function? Is this a recreation of the old forms, or are they doing something new? I can’t think of anything more 21st Century than to apply natural-language processing to that question. A caution, though, from Richard Bailey in 1971: “some of the questions of greatest concern to critics are amenable to mathematical treatment. Yet work of this kind is historically troubled by literary fatuity or statistical ineptness…”. (Bailey) I’ll have to be careful.
## 2. History
Literary scholars have been extracting everything they can from Shakespeare for a few hundred years, including detailed maps of which sounds are used where in his sonnets. They found all sorts of interesting things, like Price’s observation.
Around 1939, B.F. Skinner (the famous psychologist and rat-tormentor) decided that their scholarly claims were nice, but they needed quantitative validation, and he began with Shakespeare’s alliteration.(Skinner) He identified the positions of common letters at the start of stressed syllables, tested them according to a binomial distribution of the expected frequency of repetition, and concluded that you could produce a similar distribution “by drawing words out of a hat.” I have tremendous respect for anyone with the perseverance to do a binomial regression by hand, but unfortunately Skinner began from some flawed premises. He was immediately smacked down in the literature for (a) not understanding how alliteration is defined and (b) ignoring the fact that alliteration has an ancient tradition in English verse and poets have said they’re using alliteration for centuries. His antagonists, such as Elizabeth Jackson (Jackson) and Ulrich Goldsmith (Goldsmith), used the old qualitative methods, augmented by knowing that alliteration resides mostly in nouns and verbs and never in function words, and combinations of consonants aren’t the same as a consonant in isolation, to set the record straight, and there it lay for a few decades.
In the 1970s, digital computation became cheap enough that a new generation of non-poets was inspired to turn computers loose on the question of poetic alliteration. (Leavitt), (Greenberg) They created a variety of clever algorithms to do simple statistical tests and make contour maps of sound density of a selection of poems. They were hampered a bit, though, by the unavailability of a large corpus of phonetically-coded digital texts and, once again, their unfamiliarity with the traditions of alliterative verse. Their algorithms tended to zero in on very simple structures and miss some features that would jump out immediately at a human reader. As a result, when they ranked poems by the importance of alliteration within them, they would get odd results. For example, Ezra Pound’s translation of “The Seafarer”, (Pound) which explicitly echoes Old English alliterative patterns, comes out in the middle of the pack. Jay Leavitt et al. in particular knew this wasn’t working well, because their papers provide several different algorithms that give different results, and the reader is invited to choose among them. (Machine-learning researchers do this, today.)
Then there was another lull until the 21st Century, when natural-language processing and digital archives of verse became available. Text-to-speech systems could finally reproduce the patterns of stressed syllables and their associated phonemes in a way that matches how humans hear poetry. These spoken-equivalent texts get tested with graph theory, time-series analysis, and geolocation. I’m a particular fan of a group called “Plotting Poetry” dedicated to pushing the boundaries of “mechanically-enhanced reading”. But I haven’t seen modern statistics applied to alliteration yet, and that’s where I’m going to go.
## 3. Method
Figure 1. Analytical process.
The Carnegie-Mellon University has put on line an open-source English dictionary for the text-to-speech step.(Rudnicky) Open source is important, because poets don’t use the same kind of English that telephone-answering robots use, so every new poem I investigate requires a few words to be added to the dictionary. I also needed to tweak the database to account for the convention that not all words participate in alliteration, so words like “the” and “she” and “if” don’t have a stressed syllable. The next step is a Perl program to read the poem and throw out everything except the sound at the beginning of the stressed syllables. (This role was played by two young women in Skinner’s work.) These sounds, the skeleton if you will of the audible part of the poem, are fed to a notebook in the R statistical software. A function in R counts, for each sound, the number of non-alliterating stresses that come before the next occurrence of the same sound, generates histograms of intervals, and compares them to the theoretical distribution we should get if the choice of sounds were truly random.
Figure 2. Intervals in strict Old English form
For the most-alliterative end of the bench, I chose J.R.R. Tolkien’s “Song of the Mounds of Mundburg”(Tolkien, _Poems_ 1235), which he said in Letter 187 was “the strictest form of Anglo-Saxon verse”. (Tolkien, _Letters_) The spike in the left figure is what the rules require: 0 means two consecutive stresses alliterate; 1 means the half-line skipped one syllable. So that’s what the left-hand side of these histograms means: a high bar means a lot of old-school alliteration.
Figure 3. Intervals in Wikipedia sample
The graph in Figure 3 might be unexpected, though. As we’d expect, it’s a lot more spread out and there’s no distinctive spike. Its maximum is 2 however, and zero is the second most-common interval. English speakers like to alliterate even when there’s no poetic intent at all.
### 4. Experiments
Now that we’ve got the machinery built, we can conduct experiments. The frequency of letters in English, etaoin shrdlu, is not the same as the frequency of alliterative sounds: all the vowels are lumped together; “T” gets split into T and TH; “S” gets split apart into S, SH, ST, and SK. When we get done, there are 28 possible things on which to alliterate. But the chance of getting an alliterating syllable on the next stress isn’t 1/28th – English speakers love to alliterate, so the best-fit chance is closer to 1 in 6.
#### 4.1. Inside you there are three Beowulves
Figure 4. Frequency graphs of three Beowulf poems.
Here are the first 200 lines of “Beowulf” translated by Seamus Heaney (Heaney), the same very freely translated by Maria Dahvana Headley (Headley), and “The Lay of Beowulf” by Tolkien (Tolkien, Poems 815). The red line I’ve put on the histograms is the best-fit parameter to a negative-binomial model of “K” in the Wikipedia selection. Headley, on the left, makes heavy use of alliteration but she’s not being poetic about it. She’s more like cramming alliterating words together for fun. You can see that the normally-expected intervals between consonants of 3-8 stressed syllables has been depleted after each alliteration binge.
Heaney, in the middle, looks pretty random. This is close to the reference line, and wherever there’s a peak, there’s a valley next to it. Tolkien’s “Lay” on the right doesn’t really have alliteration beyond the typical English rate, but since it’s a lay, every stanza ends with the word “Heorot”. The poem is in iambic tetrameter, so the end repetition causes the bump up at 15. The bump up at 8 is also not very alliterative, because that happens every time an H-syllable appears in the middle of a stanza. It breaks the 15 into two halves. So now we know what the right-hand side of those histograms means: it’s where large-scale poetic forms can make an appearance.
#### 4.2. A-LotR-ation
Figure 5. Last stanza of the poem.
Gimli’s song about Khazad-dum from _The Fellowship of the Ring_ (LR 2.04.188) is the poem that got me started. This all began with Corey Olsen’s talk at Mythmoot XI. The poem’s form is rhymed quatrains of iambic tetrameter, but some people see an irregular pattern of alliteration in it. Other people aren’t convinced, so out come the computer programs. Measuring the alliterative structure of a Tolkien poem is tough, though, because Tolkien used alliteration much more than your typical trafficker in text. If we feed the entire _Lord of the Rings_ to the program, zero is prominently above the curve. If we’re going to ask about “Khazad-dum”, we need to take this into account. If we compare Gimli‘s song to some random victorian tetrameters it might or might not look alliterative, but what happens if we compare it to the 300 words of prose that come right before it?
Figure 6. Frequency graphs for Gimli’s song and preceding prose.
Gimli’s song has a spike at 4 that might be important – 4 beats is the distance from the middle of one line to the next, which is what you’d see if alliteration was working vertically, tying lines together, but overall it’s much less alliterative than the prose section. It’s also less alliterative than the other dwarf song we get, “Far over the Misty Mountains Cold”. Now, an absence of tight alliteration goes along with the idea of tying large-scale structures together. If people are constantly hearing _ram-rum-ruf_ , it’s harder to hear an interleaved sparse alliteration, so a poet will want to exclude that. It’s possible that Tolkien was making what he thought of as a kind of blank verse, leaving out alliteration for poetic effect, just like the way a blank-verse poet avoids rhymes.
#### 4.3. Sparse Alliteration
Leaving out the close alliteration is a feature I’ve found in another genre. Here are four classic hip-hop songs, “C.R.E.A.M.” from the Wu-Tang Clan, “Express Yourself” from N.W.A., “Lose Yourself” from Eminem, and “Make Tracks” from US3. West Coast, East Coast, Detroit, and the U.K. The reference line in red is the same as before, scaled for the size of each sample. All of these songs have a deficit at 0, and 1. The Americans continue the deficit up to 4 or 5 syllables, but the Brits hit the curve at 3. I’m disappointed that US3 didn’t turn out to have a stronger Old English influence. That would have been fun, but numbers are merciless.
Figure 7. Frequency graphs for four hip-hop songs.
North Atlantic hip-hop basically doesn’t alliterate. It happens, but less often than standard English prose. Like Dwarves, rappers de-emphasize close alliteration. Their verses are short, dominated by rhymes crammed tightly together. There’s no need to bind together a long alexandrine or anything, so they don’t use alliteration for that purpose. Besides, when a rhyme comes every four or five syllables, it’s hard to alliterate on top of it without just saying the same word again. After Jacob Edmond’s talk this morning, highlighting repetition as a form of alliteration in Caribbean verse, I wonder if this might not be an explicit intention of the rap poets.
#### 4.4. Ranking poems by median interval
I’ve been saying the word “compare” a lot, but I haven’t given a direct standard yet. These histograms are important when we’re dealing with small sample sizes like a poem, but it’s hard to compare them directly. For that, we need a single metric. I propose to use the median of the distribution of intervals. Medians are good because they don’t depend on the exact value of long intervals that I’ve cut off of these histograms. And because my poet friends said they wanted a graph that showed how alliterative a poem is, this graph shows the inverse of the median.
Figure 8. Alliterative density of a set of poems.
This shows a sampling of verse that has already been identified as alliterative and some that isn’t. Paul Deane’s alliteration.net website has a great selection of poetry, some of which is more faithful to the Old English and Old Norse forms and some which is more modern and free-form. From this archive, I selected some poems that Paul has previously flagged if they’re faithful to an old form. Then I picked a few others that aren’t and a few non-alliterative Tolkien poems. The prose samples are in green and the rappers are in red. Last, in keeping with my conviction that literary theory should always be tested with literary experiments, I’ve included a poem by Rio Wulfmare, a fellow member on the “Forgotten Ground Regained” listserv, written precisely for the purpose of superposing an alliterative melody over metered rhymes.
The first thing to see is that when we rank the more-or-less poetic samples by density, they fall into natural groupings. At the bottom we have the Old English forms. Just above them are the Middle and Modern English poetic forms, with our Norse example mixed in because formal Old Norse poetry has other things going on besides the alliteration. Higher up are Tolkien’s non-alliterative poems. Prose is near the top, but not at it. The rappers have the lowest alliterative density. I spent quite a while looking around Ireland and anglophone Africa for writers who are unaffected by Anglo-Saxon traditions, without great success, but there was one right under my nose all along. The West-African/Celtic fusion from which American pop music sprang turns out to be the counterweight to Anglo-Saxon poetics.
A ranking that makes intuitive sense is further than my 20th-century predecessors in feeding poems to computers usually get. Their rankings are all mixed together, and they’ll often have something like Vachel Lindsay’s “The Congo” at the top.
The second thing to notice is that there’s not a clean break between poems that alliterate and those that don’t, with one exception: none of these poems has a median of 3 or 4 syllables, which would put them between .25 and .33 on the graph.
Figure 9. Frequency graph for “Children of Dusk”.
“Children of Dusk”, our literary experiment, is sitting between the old-school alliterative poems and the modern revival poems. Mr. Wulfmare set out with the intention of writing a two-level poem that exactly matches the melody-plus-continuo hypothesis. On its graph we can see more structure than most poems show: The usual spike at zero & 1 that says we’re in Old English alliteration, but then there’s a deficit at 2 and a spike at 3, a deficit at 5 and a spike at 6, and a deficit at 8 and a (tiny) spike at 9. Then we run up against the limits because we run out of poem.
#### 4.5. The “Main Sequence”
Here’s one last graph, of an unexpected result. I asked, How many of the possible alliterative sounds does a poem use? These samples are all pretty much the same length. There’s a general trend – the tighter the alliteration, the fewer consonants of the set of 28 get used by the text. The two outliers are Tolkien rhymed poems. It’s almost like alliteration is draining attention away from some other, less fortunate sound.
Figure 10. Scatter plot of sounds used vs alliterative interval.
## 5. Conclusion
In conclusion, this work has built upon a long tradition of numerical analysis of poetry. The tools we have now for language processing make it easy to investigate the distribution of alliteration within a poem, whether the poet has foregrounded it or not. This method is very simple; looking at histograms and picking out the median is as basic as you can get. I did some high-powered Bayesian analysis using Stan; it gave me better uncertainty estimates, but the story was the same. Apart from that, calibrating the baseline was the most statistically difficult part. Despite the lack of sophistication, the method can rank texts according to how they use alliteration, and the results seem correct: Different kinds of alliterative verse are stratified as we’d expect. Prose on one end, strict Old English on the other, middle-english in between Old and Modern. Spurious alliteration that comes from structural repetition in formal metered verse has a clear signal in the histogram, which resolves the weakest part of Skinner’s original treatment.
That horizontal bar graph was a surprise. I was expecting the analysis to show me that some poems are alliterative and some are not, but that’s not what came out. Instead, it shows that some poems are strict Old English, but those that aren’t have a lot of variety. Modern alliterative-revival verse lies on a continuum. We’re trying everything. With one exception – that gap at 3 or 4 syllables might present an opportunity. Maybe a hexametric expanded version of Old English longlines? I’ll leave that to a poet.
So what?
This is a method that works on small samples, where parametric statistics are overwhelmed by “noise” as scientists call it, or “technique” as poets think of it. The ideas are 50 years old; the difference here is that combining the statistics with natural-language processing, incorporating the rules of English stress, removes a lot of the noise that interfered with the letter-based methods a couple of generations ago.
When I started my project of quantitative analysis of literature, my goal was to find ways that graphs and numbers and maps can increase readers’ enjoyment of whatever they’re reading. Now, the world contains quite a few nerds who are delighted just to see things in graphs, and for … us … this is already an interesting contribution. But it’s really just the first few steps. The more I’ve learned about Old English, the more I’ve come to see that its old music is still with us today. If Price is right, though they can be hard to see and hear, they’re what makes modern poetry possible. I hope to extend this method to find out how to alert readers when an ancient tradition is still alive and playing a new role in a modernized form.
The “Main Sequence” is intriguing: There’s no reason in principle that alliterative poems couldn’t use the same range of consonants as any other sample of similar size, but they don’t. Next up is to figure out if this is true in general, or just for the poems I happened to choose. It’s possibility that alliterative verse might be as much about the sounds poets omit, as about the ones they use. Richard Bailey stated in his 1971 review that “readers can’t hear the sounds that aren’t there.”(Bailey) It will be fun to put that to the test.
* * *
## Works Cited
Bailey, Richard W. “Statistics and the Sounds of Poetry.” _Poetics_ , vol. 1, no. 1, Jan. 1971, pp. 16–37. DOI.org (Crossref), https://doi.org/10.1016/0304-422X(71)90003-9.
Goldhahn, D., et al. “Building Large Monolingual Dictionaries at the Leipzig Corpora Collection: From 100 to 200 Languages.” _Proceedings of the 8th International Language Resources and Evaluation_ , 2012.
Goldsmith, Ulrich K. “Words out of a Hat? ‘Alliteration and Assonance in Shakespeare’s Sonnets.’” _The Journal of English and Germanic Philology_ , vol. 49, no. 1, 1950, pp. 33–48. JSTOR.
Greenberg, Nathan A. “Aspects of Alliteration: A Statistical Study.” _Latomus_ , vol. 39, no. 3, 1980, pp. 585–611.
Headley, Maria Dahvana. _Beowulf : A New Translation_. Farrar, Straus and Giroux, 2020.
Heaney, Seamus, editor. _Beowulf: A New Verse Translation_. 1st bilingual ed, Farrar, Straus, and Giroux, 2000.
Jackson, Elizabeth. “The Quantitative Measurement of Assonance and Alliteration in Swinburne.” _The American Journal of Psychology_ , vol. 55, no. 1, 1942, pp. 115–23, https://doi.org/10.2307/1417038. JSTOR.
Leavitt, Jay A. “On the Measurement of Alliteration in Poetry.” _Computers and the Humanities_ , vol. 10, no. 6, 1976, pp. 333–42.
Pound, Ezra. “The Seafarer.” The Poetry Foundation, https://www.poetryfoundation.org/poems/44917/the-seafarer. Accessed 16 June 2025.
Price, Thomas R. “The Technic of Shakespere’s Sonnets.” _Studies in Honor of Basil L. Gildersleeve_ , Johns Hopkins Press, 1902, pp. 363–75.
Rudnicky, Alex. CMU Pronouncing Dictionary. 0.7b, http://www.speech.cs.cmu.edu/cgi-bin/cmudict.
Skinner, B. F. “Alliteration in Shakespeare’s Sonnets: A Study in Literary Behavior.” _The Psychological Record_ , vol. 3, 1939, p. 185.
Tolkien, J. R. R. _The Collected Poems of J.R.R. Tolkien_. Edited by Christina Scull and Wayne G. Hammond, William Morrow, an imprint of HarperCollins Publishers, 2024.
—. _The Letters of J.R.R. Tolkien_. Edited by Humphrey Carpenter and Christopher Tolkien, Revised and Expanded edition, William Morrow, an imprint of HarperCollins Publishers, 2023.
Wise, Dennis Wilson, editor. _Speculative Poetry and the Modern Alliterative Revival: A Critical Anthology_. Fairleigh Dickinson University Press, 2024.
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### _Related_ https://www.idiosophy.com/2025/09/the-hunt-for-alliterative-melody/
