I found some interesting (in my geeky sort of way) reading in a short essay, Self-similar syncopations: Fibonacci, L-systems, limericks and ragtime by Kevin Jones.
He draws some interesting parallels, but I feel that some of his observed relationships between the Fibonacci series, L-systems and limericks have more coincidence than anything else, particularly given the variation in the number of leading and trailing unstressed syllables in popular limericks. Kevin has chosen one particular form of limerick (iamb-anapest-anapest) as the archetypical limerick form and then sung its praises and noted the way it can be modeled with an L-system. His matching of the syllable counts to the Fibonacci series (which appear in so many other places in nature) seems to make sense of the world unless we look closer at his own selection process.
If he'd chosen one of the other very common limerick line forms (anapest-anapest-anapest, or amphibrach-amphibrach-amphibrach) his numbers wouldn't have worked out, and yet limericks written in those forms are just as catchy, just as "strangely appealing and intuitively 'natural'".
Let's take another example of an Edward Lear limerick.
There was a Young Lady whose bonnet,
Came untied when the birds sat upon it;
But she said, 'I don't care!
All the birds of the air
Make my Limerick seem like a Sonnet.
di dum di di dum di di dum di
di di dum di di dum di di dum di
di di dum di di dum
di di dum di di dum
di di dum di di dum di di dum di
This has 13 stressed syllables, 28 unstressed syllables (a total of 41), 9/10 syllables in the longer lines, and 6 in the shorter lines. By my count that's only 1 Fibonacci series number. Does that make the limerick sound unpalatable? Not at all! The deviation from perfect self-similarity in the lack of one unstressed syllable at the start of the first line doesn't hurt it at all. The change from 8 and 5 syllables per line to 10 and 6, has done nothing to make this limerick less appealing. It still has the regularity of meter, even when it lacks the magic of "special numbers".
Let's look at the claims Jones makes about ragtime music. The variety of syncopated rhythms in ragtime is such that I'd have to regard his Fibonacci match here as complete coincidence. The very catchy Pineapple Rag has groups of notes in patterns of 2,9,2,2 and 6. How much of a contortion is required here to fit an L-system? One of the best known Joplin rags, The Entertainer, is littered with patterns of 4s and 2s -- very un-Fib. There are patterns in the groupings but self-similarity across levels is a coincidence if it exists.
The essence of catchiness in music and rhythmic poetry is a balance of pattern and variation. There must be enough repetition of patterns to make your mind predict what will follow, and enough variation to entertain or surprise. By employing building blocks of pattern and variation at different scales or levels within a work (beat, phrase, theme, section) we produce something that is entertaining to the mind. Any self-similarity arises from applying our process of repetition+variation at different levels.
There are a lot of instances of "copying with errors" in nature, where a working pattern is repeated but with small variations. From the regularity of crystals (strongly patterned with very few defects or variations) to the variety of a forest (many trees of the same form but every one clearly unique), there is an abundance of examples of pattern+variation in nature. Is it an "inevitable reflection of nature" that causes us to find pattern+variation appealing in our entertainment, or is it mere coincidence? Unless we find alien intelligence from a universe where nature is predominately pattern-less, or dominated by patterns with almost no variation, we can never test that assertion. I think it's a long stretch to declare that our human preference for a balance of predictability and surprise arises from nature's collection of patterns. Nature's sheer variety of forms from the very regular to the unpredictable ensures that one can always find coincidental matches.
