Measuring alliterative structure in a text

Hypothesis: the te-tum-te-tum of the iambics is just the rhythm section, and there’s a melody going on in the alliteration that’s much more varied and interesting. Olsen thought of a hip-hop singer over top of a mechanical rhythm track; I’d have said a baroque concerto over a continuo. The alliterative patterns aren’t rigid or repetitive enough that it’s easy to say for certain that Tolkien created the counter-structure intentionally.

We can confirm or refute the hypothesis if we look at the full distribution of sounds in the poem. First thing I did was tweak the program I wrote for finding Old English alliterative long lines. Out with the Sievers types; now I just want to flag the initial sounds of stressed syllables. Start at the beginning of a text. Count how many stressed syllables there are before I reach the next repetition of its sound. Then do the same for the second stressed syllable. Repeat until we run out of text.

To see what this distribution ought to look like for different kinds of texts, let’s take some easy examples. First, the least-poetic thing in the world: Choose 50 random sentences from the Simple English Wikipedia. (Drop sentences with numbers in them.) I got this from Goldhahn, et al., ¹ The histogram of intervals looks like this:

Fig. 1. Unpoetic intervals

This is a geometric distribution, more or less. If all stressed sounds were equally common in English, and people didn’t like the sound of alliteration, the distribution would be exactly geometric. But some letters are more common than others, so there are random peaks and valleys, and people like alliteration even when they’re not writing poems, so there’s a bit of a spike at zero. So far, so good. Let’s cut the graphs to hide the extreme outliers from now on — extremes tell us mostly about the length of the text, not so much about sounds.

Now let’s pin down the other end of the spectrum of possibility with the “Song of the Mounds of Mundberg”. Tolkien said in Letter 187 that it was “written in the strictest form of Anglo-Saxon alliterative verse.”² Old English long lines have alliteration patterns of either axay or aaax, so we’d expect the histogram of distance through the text to be heavily weighted at 0 and 1.  And so it is:

Fig. 2. Intervals in strict Old English form.

More than half of the time, an alliterating sound comes with the next or next-but-one syllable. This is a good benchmark for the low end of alliteration intervals.

Last, we’d like a statistic to compress the information. The median over all intervals in the poem is not sensitive to the extreme tails of the distribution, but catches how scrunched-up to the left everything is.

Comparing Poems and Prose

Let’s look at a variety of texts that span a range of unintentional and intentional alliteration. I am indebted to Paul Deane’s overview of alliterative verse for good examples of verse-forms I’m not so familiar with.

1. Wikipedia, as above. Tagged “wiki”.
2. “The Mounds of Mundburg”. Strict Old English, as above. Tagged “mundburg”.
3. Gimli’s Khazad-dum poem, where we started. Tagged “khazad”.
4. The section of prose right before Gimli’s poem, for comparison. Tagged “prose”.
5. “Far over the Misty Mountains cold” from The Hobbit. Thorin & Co. aren’t trying to alliterate, but you can’t avoid it when you’re talking about the Misty Mountains. This is what happens when Tolkien’s natural penchant for alliteration gets polished into verse. Tagged “mistymts”.
6. Legolas’s song about Nimrodel. Not trying to alliterate at all.
7. “Rosemary” by Andrew Frisardi. A modern adaptation of strict Old English verse form.
8. “Quest for Valhalla” by Robert Cuthbert. Using Old Norse form.
9. “Sea Change” by John Beaton. This is in a Middle English style of alliteration.
10. “Old English, New World“, by me. An attempt to reconcile modern Southeastern-US word order with Old English form. Tagged “shenandoah”.
11. “Do you hear me, Mere-Watcher?” by Laura Varnam. This is purely modern free verse, using alliteration to allude to Beowulf. ³ Tagged “merewatcher”.

The histograms in Fig. 3 give us a feel for what’s happening. “wiki” and “prose” seem to be the most spread out, as we’d expect.

Fig. 3. Interval histograms

Ranking the texts by median interval of sound similarity in Fig. 4, the prose texts are at the high end and the Old English are at the low end, as the metric was constructed to do.

This metric left the Old Norse patterns in the middle of the pack. “Valhalla” does have a strong presence of 0 and 1-syllable intervals, but it has a heavy presence of longer ones, too. Wrapping the alliteration around the end of a line⁴ moves it up the graph.

The most interesting thing about Fig. 4 is that it doesn’t have an obvious breakpoint between alliterative and non-alliterative verse. I was expecting a big gap, but the possible uses of alliteration form a continuum, visible even in this small sample.

Fig 4. Ranked text samples.

The histogram for a poem with a free-form alliterative “melody” should have a secondary peak in its histogram at some larger spacing than the 0-1 that come from strict alliteration. We see something like that in Varnam’s poem, which definitely has such a melody. It’s a short poem, only half the length of the other texts, so its histogram can have large fluctuations around the ideal form. “Sea Change” has two linked stanzas, the second of which occasionally harks back to the first with K and S sounds, which puts a small peak about 15.

Alas for Prof. Olsen’s idea, Gimli’s song has barely closer alliteration than prose texts do. Figure 3 almost has a secondary peak at 5, but it’s not significantly different from random fluctuation. Now, I’m not one to claim poetry should have statistical significance, but the prose section just before Gimli’s song has more of those peaks than the song does. If anything, this method of measuring suggests Tolkien removed alliteration to make the poem, as John Ruskin totally didn’t advise.

Technical Details

There are 28 sounds on which we can alliterate here, since we count all vowels as one class, C is either K or S, etc. I’ve added the sound “KH” to the set since we’re dealing with Dwarves.  Using the CMU notation, the sounds are “B” “CH” “D” “DH” “E” “F” “G” “HH” “JH” “K” “KH” “L” “M” “N” “NG” “P” “R” “S” “SH” “SK” “ST” “T” “TH” “V” “W” “Y” “Z” “ZH”.

The CMU pronouncing dictionary thinks “Shenandoah” is a four-syllable word with the accent on the “do”. John Denver probably deserves the blame for this geographical lapse. I overrode the dictionary entry to restore the name to its true dactylic nature. (The Boss said so.)

There are quite a few 2’s in the “Mundberg” graph that shouldn’t really be there. That’s because the intervening word is one that sometimes has a stress and sometimes doesn’t, and my program isn’t smart enough to tell which is which. This happens in all the texts. The extreme case is in “Mere-Watcher”: The last line of this poem is “So fucking what?” Under the usual rules, “so” would be unstressed. It’s stressed here, so I jumped into the program’s output and fixed it by hand to give it the proper weight. I imagine Seamus Heaney had the same problem, once.