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In Douglas Adams' The Hitchhiker's Guide to Galaxy, a supercomputer, asked to calculate the answer to 'life, the universe and everything' comes out with the rather enigmatic 'forty-two', and nobody quite understands what it means.
Trying to calculate the answer to 'versification, feet and everything' instead has two main advantages: you can do it with an elderly 8086, and the answer is 'twelve', which, you'll admit, is a much friendlier number.
Ah, and by the way, you have this page to explain why.

Stress patterns and binary numbers

In a paragraph of the last chapter of this guide, you can see that stress patterns stick to one's mind and can alone form the skeleton of a poetic composition. With the name 'stress pattern' of a line, we simply mean a representation of it in terms of which syllables carry a stress and which don't (in the remainder, we will indicate a syllable with S if it carries a stress, and with U otherwise). I.e., take the famous Hamlet line:

To be or not to be: that is the question

It has a total of eleven syllables and when you read it, you probably put the pressure on both occurrences of 'be', on 'is' and on 'question'; this would make the stress pattern of the line USUUUSUSUSU; this line actually lends itself to several ways of reading; let's try with Macbeth instead:

Tomorrow, and tomorrow and tomorrow

Here no sensible man would doubt that the pressure falls on the second O of each 'tomorrow', and the stress pattern is therefore, obviously USUUUSUUUSU. Let's go on:

Creeps in this petty pace from day to day
To the last syllable of recorded time

Here the two lines have the patterns SUUSUSUSUS (which, incidentally, is not an iambic pentameter) and UUUSUUUSUS (which forces us to eat up the -ble in 'syllable' to be in the meter). I am sure the Reader has, at this point, got the idea, and might try to apply it to something clearer than Shakespeare; later in this page, you'll get to know why Shakespeare (or anybody else) has such a problem sticking to iambic verses.
The paragraph above should become clearer to those reading on; however, it has been extensively criticised by a group of old-school prosodists, and it perhaps calls for some further elaboration.Their main objection of these gentlemen seems to be that 'last' (in the third verse) should be stressed as well, thus creating an UUSSU(U)UUSUS pattern. They also dig out the usual hogwash about 'allowed variations' to the basic iambic pentameter structures; I shan't respond to this particular objection, since I have already dealt with the subject below and elsewhere, but the one about scansion is trickier and worth an answer. Consider, therefore, the UUSSU(U)UUSUS pattern; if the verse were a pentameter, then the second feet would be a spondee, a foot that, even some old-school prosodists admit this much, doesn't exist in English. The verse is, therefore, not a pentameter, certainly not an iambic pentameter, something that, most sensible people would think, should be made of iambs.
However, as I say later on, I don't consider a valid pattern one in which two stresses follow each other, simply because such an occurrence is impossible to read without pausing. If 'last' were stressed, there would be a caesura between it and 'syllable'; verses split this way (or rather, couplets joined this way) are common both in Scandinavian and Romance languages, but they are supposed to be alien to classical English verse. In conclusion, the point of the old-school prosodists is one only: that whatever Shakespeare writes is, by definition, an iambic pentameter. I would be ready to accept it if Ol' Will had invented, defined or even ever mentioned the term, which he did not. I should, however, conclude this parenthesis with a warning: some of the rather gentlemen who started the argument are apparently in the trade of creating more old-fashioned prosodists–in other words, they are teachers. Should the Reader be a student in search of something original to say in his latest essay, he should consider that he is about to take arms against a sea of troubles, and that his opposition is hardly likely to end anything.

Resuming our main thread, it should be obvious to anyone familiar with mathematics that stress patterns can be associated to binary numbers, which makes it easier to count how many possible stress patterns fit in the definition of a type of verse. But before we do anything of the sort, we ought to state some rules.

Valid and distinct patterns

We will assume, based on common usage in verse, and on what said in the versification chapter, the validity of the following:
  1. Only stress patterns occurring before the last stressed vowel will be counted as distinct. E.g., the stress pattern USUUUSUSUSU ('To be or not to be: that is the question') shall be considered to be functionally identical to USUUUSUSUS ('To be or not to be: that is the quest') and to USUUUSUSUSUU ('To be or not to be: that is the quandary').
  2. No two consecutive syllables can be stressed; in symbols, no SS will ever occur inside a valid pattern.
  3. No four consecutive syllables can be unstressed; in symbols, no UUUU will ever occur inside a valid pattern.
If you look at real examples, you'll find these rules to be very reasonable: poets generally use verses regardless of the fact that their endings are masculine, feminine or triple, and they generally avoid having two accents in a row (it spoils the flow) or too many syllables without a phonetic pressure (it spoils the rhythm).

History and mathematics

Back in the good old days of the Lai, when long poems were written syllabically, it was usually in octasyllables. This was true for French (see, e.g., Jean Renard) and English (see, e.g. 'The Owl and the Nightingale'); in Italian and Provençal archaic narrative poems were made of even shorter lines, but these languages developed more complex verses more rapidly. Now, let us apply the rules above to the octasyllable, and see how many possible stress patterns we obtain. One could easily do that by hand, but the Present Author being a bit of a geek, he wrote a specific program to do it; the result of the count is 13: should you be in doubt, you can go and check for yourself.
Now, keeping this number in mind, we can consider the different development in different languages. Italian developed the endecasillabo, which is actually a collective name for two verses, the e. a minore and the e. a majore, which are always used together. Let's apply the program again, and count the possible stress patterns for both types: it turns out there are six for each (diffident people can verify it), total 12.
The two numbers are suspiciously similar; let's apply the same program to the Gallic decasyllable: amazingly enough, the stress patterns are, again, 12.
If we could do the same for all common types of verse, we would have pretty much proven our point. Unfortunately, poetry is not a particularly rigorous science: where it is widespread and of good quality, which seldom happens, it tends to fall into rational habits, otherwise, it is subject to the whims of noblemen with too much time on their hands, who write tomes and tomes of nonsensical poetry and become classics: do the names 'Charles d'Orleans' and 'Alfred, lord Tennyson' ring a bell?
Keeping this in mind, let's apply the program to the iambic pentameter and to the alexandrine; the counts are far away, from the Holy Twelve and from each other: 8 and 24 patterns respectively.
Is it over? Not quite. The first thing you ought to do is re-read the definition of alexandrine. We have a silly one, 'an iambic hexameter with a cesura in the middle': if this definition were correct, and if we consider that 'iambic' simply means 'not having stresses on odd-positioned syllables', we would find out that the possible stress patterns are not 24 but drum rolls 13. The definition is not true, but it is fully possible that some poets adopted it anyhow. The Present Author would very much like to see how the matter stands in the original 'Alexandre', but has failed to find a copy so far.
However, if one looks up the actual definition (the one provided by this guide, of course) of 'alexandrine', he'll presently find that this verse is just a collage of two verses of six metrical syllables each. Never the ones to be swayed by the presence (or absence) of line breaks, we can now take into account the number of stress patterns of a verse of six metrical syllables, which is rather scant: 6.
Still not convinced? You might want to consider another myth of English literature, namely the Skeltonic verse. The so-called 'light of English poetry' did not actually invent any verse form: he merely used a mix of verses of four, five and six metrical syllables, usually with a purposefully cranky and stinted flow; the avid reader can find an example of this in The Tunnyng of Elynour Rummyng. Now, if we sum up the verse patterns corresponding to the three metrical lengths employed in this (and many other) poems, we find: Quod erat demonstrandum.
Of course, the Number Twelve is not limited to Southern Europe's own syllabic verse. It can be easily applied to alliterative verse; consider for example the archaic fornyrðislag, from which we have demonstrated the Anglo-Saxon alliterative verse descends: if each verse carries two stresses and we consider the rules above to be still valid, we find that the possible stress patterns are still, believe it or not, 12.
On the same line goes this analysis of the metres of Eilífr Goðrúnarson's 'Þórsdrápa': 14 types of patterns are identified (a further one occurs only once, most likely by mistake).

How to get away with defective verses

Now, this takes more mathematics--in fact it takes so much mathematics I shan't even try to show where the numbers come from, but one can demonstrate that, if one has twelve possible stress patterns and a poem of fourteen lines, the average number of stress patterns he actually uses is 8.45; by writing at random there is also an almost 32% chance that he will use six, or less, patterns. What does this mean? Something absolutely simple: that if one writes a poem in iambic pentameters and purposefully uses all the eight stress patterns, he will sound more or less as if he wrote a poem, say, in endecasillabi and used the patterns at random. In other words he will get away with it! Even alexandrines can work: if one uses all the six patterns available (which is almost certain, having to write 28 of them), an ear trained to poems will assume that the sonnet simply belongs to the 'poorest' 32%.
If you consider, i.e., the success of the alexandrine in France, you'll notice that it is parallel to that of the sonnet: XVI century ballades are generally in octasyllables or decasyllable, whereas the moment of true glory of the alexandrine came with the Symbolism, which incidentally uses a cartload of other metres as well.
Of course this trick won't work for longer forms: a play or an elegy are far too extensive to keep disguising the scarcity of patterns; but do playwrights actually write blank verse? Jacobean playwrights like Webster are known to screw the form up to incredible levels, but the generation preceding them, namely the Elizabethian ones, are generally credited with sticking to it. This point of view is, however, merely wishful. The Shakespeare example above, in which the alleged bard of Avon stresses the first syllable ('creeps') was chosen because of its notoriety, not out of malice. If you pick at random among his verse, you will presently find that there is a metric irregularity every fourth line or so. If the Reader prefers Marlowe (the Present Author does), here is the beginning of Doctor Faustus' first monologue:

Settle thy studies, Faustus, and begin
To sound the depth of that thou wilt profess;
Having commenced, be a divine in show,
Yet level at the end of every art,
And live and die in Aristotle's works.
Sweet Analytics 'tis thou has ravished me:
Bene disserere est finis logicis.
Is, to dispute well, Logic's chiefest end?
 SUUSUSUSUS
USUSUSUSUS
SUUSUUUSUS
USUUUSUSUS
USUSUUUSUS
SUUS[U]USUSUS
SUUSUUUSUSUU
UUUSUSUSUS

Half the verses in this monologue fragment are not proper iambic pentameters; furthermore they all break the same rule, one which Marlowe almost never respects, that forbidding stresses on the very first vowel of the verse. This slackening of the rules of iambic pentameter, which is very common in Elizabethian verse, can be accounted for by the same program employed before: if one does so, he finds that the original eight possible stress patterns of the iambic pentameter become 11; the most curious part of this analysis is that one of the verses in the monologue above is in Latin, and still respects the warped pentameter pattern.
Of course, if you read Ben Johnson, you will find far more irregular pentameters, but does someone hearing "The Alchemist" actually recognise it as verse? Not likely, and the fact that Johnson wrote a number of his plays in prose should say something to you. And another thing the reader should consider is that one cannot only get away with defective patterns: with some skill, he can get away with overabundant ones as well. All one needs to do is build a 'skeleton' of regular verses and throw in little variations; the reader will probably have some problems memorising the irregular lines, but the overall effect can be poetic anyway. An illustration of this technique is Eliot's Waste Land, and in particular the last chapter, which begins with an impressive display of Elizabethian pentameters:

After the torchlight red on sweaty faces
After the frosty silence in the gardens
After the agony in stony places
 The shouting and the crying
Prison and palace and reverberation
 Of thunder of spring over distant mountains
He who was living is now dead
We who were living are now dying
With a little patience


Am I imagining things, or some of the lines of this poem, the ones in red in particular, are much easier to remember?

The meaning of it all

Twelve is not a remarkable number in poetry (and in the cabala) only: it is also the number of frequencies (excluding octaves) used in music. In layman terms: there are only twelve notes. But has it always been like that? No: until the second half of the 18th century, there were many more, e.g. a C sharp was not the same as a D flat. The way of writing classical music was different as well: it was controlled by a set of rules called tonal harmony (which survives, in a very simplified form, in modern rock and pop) which ensured that one never used too many of these notes at once. In order to do so, it divides the notes in sets called major and minor keys (or tonalities, hence the name); one can pass from a key to another only if they are close to each other (and therefore contain a large number of common notes), and with very strict rules in order to inure the ear of the listener to the change.
It is interesting that in a minor key one can use (following opportune rules) 10 of these notes, and introduce at least a couple more as the beginning of a change in key: now, since a theme (in layman terms, a sort of melody) is generally built over two "half themes" belonging to two adjacent keys, the theoretical choice of notes one could use in it is, chillingly enough, about 12. The actual number of different notes one normally uses is, however, something like 8. Do these numbers ring a bell? With the introduction of the 'tempered scale', the one which only has twelve notes, tonal harmony started declining. Its rules, which were very clear in the 17th become increasingly more blurred, and the most ferociously enforced ones turned to be those who ensured variety, rather than those which were meant to prevent chaos. The epilogue of the situation was the creation of dodecaphonic (twelve-tone) harmony, which imposes that every melody must contain all twelve notes (hence the name).
Where is the connection? Most likely, in the human brain: we owe to a branch of psychology called cognitive science the discovery of the phonological loop. It is extremely interesting because it is one of the very few psychological processes which yield reproducible numeric results. The phonological loop is a short term memory in which we can store, for example, numbers that somebody tells us; research shows that the amount of 'items' one can retain in this loop is 7 plus or minus 2. This demonstrates that there are universal constants in human memory, and it is at least reasonable to imagine that the binary stress patterns (or the frequencies) available for the immediate enjoyment of poetry (or of music) might be constrained by similar limitations. The last thing we can do, before this abstruse work is concluded, and its readers can decide whether it deserves contumely or plagiarism, is consider the experimental range of the result: if the average number of items kept in the phonological loop is 7 but the range is 5 to 9, assuming that patterns memory works the same way with an average of 12 would give us an 8 to 15 range; this works somehow: an 8 stress patterns range corresponds to something in between a six- and a seven-metrical syllable verse, and both are very common in archaic and popular poetry, albeit, in all honesty, they are lacking in the first place I looked for them, namely in nursery rhymes, which don't seem to have a metrical order whatsoever.Perhaps recognition of stress patterns is something we develop later in life: the Present Writer became fond of poetry when he was well over 18, in spite of constant exposure to it through all his childhood. An analysis of the most sophisticated pieces of the most sophisticated troubadours might help establish the higher limit (in Arnaut Daniel's L'Aur'Amara there are 16), but again the 'skeleton' effect might be misleading. As soon as more certain results are available, this page shall be the first to know.

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