Shakespeare and Maths: Metre and Completeness

Shakespearian sonnets have a particular structure where each line of the poem contains ten syllables (due to the use of iambic pentameter). This is, one might think, because ten sounds 'complete' to some extent, like 4. For example

Love alters not with his brief hours and weeks

or

Which alters when its alteration finds

Is there any explanation in number theory to why the number 10 might seem complete to human minds and ears?

Or perhaps there is a mathematical explanation for why 10 is chosen for the number of syllables in the line?

Are there examples in nature where sets have a magnitude of 10 elements, or where the number 10 signifies some sort of totality, whether in a cycle or other abstract setting?

• To my Polish ear, iambic pentameter is simply unnatural. I do not enjoy Shakespear's sonnets for this very reason -- the number of syllables.
– Bartek
Commented Mar 11, 2014 at 20:29

The reason why iambic pentameter is common among Shakespeare and other English poets has nothing to do with the intrinsic properties of the number 10, but rather the properties of the English language. Given the number of syllables and emphasis of English words, iambic pentameter is a meter that's easy to put English words into. The Greeks and the Romans were more inclined to use other meters. The Greeks primarily used dactylic hexameter, because that was most convenient for the pattern of long and short syllables of Greek words. The Romans used dactylic hexameter as well in their epic poetry, not because the length of each syllable in Latin words were particularly suited to it, but just because they were imitating Greek poetry. A more natural meter for Latin is the hendecasyllabic meter, used in Latin love poetry.

In any case, when the English started writing poetry, they tried to write it in dactylic hexameter, but they found it too difficult and awkward to squeeze English words into the meter, so they switched over to iambic pentameter. (And they also switched what they based the poetic meter on from how long a syllable is to what syllable is emphasized, because the length of a syllable is less useful a concept in English.) It had nothing to do with a recognition of how "complete" 10 was.

• Would you say 10 sounds complete? Like 4?
– Alexander Giles
Commented Mar 11, 2014 at 20:06
• @AlexanderGiles No, I don't think that a series of ten sounds feels more inherently "complete" then some other number. A line of dacyllic hexameter in Latin or Greek sounds just as complete. Commented Mar 11, 2014 at 20:27
• so essentially there is no objective basis for the number 10. It just evolved out of other processes.
– Alexander Giles
Commented Mar 11, 2014 at 21:23
• @AlexanderGiles Yes, it's just a matter of how you can put English words in line of poetry, based on how many syllables a typical English word has and where the emphasis is placed in the pronunciation of a typical English word. Commented Mar 11, 2014 at 23:27
• "The Greeks primarily used dactylic hexameter, because that was most convenient for the syllabic emphasis of Greek words..." I think you mean "syllable length patterns".
– fdb
Commented Mar 12, 2014 at 11:40

The most immediate hypothesis originates from our elementary abaci, the digits on our hands. The familiarity of the number perhaps is why our minds gravitated toward it in creating our decimal system.

• interesting, seems like a a nice thing to base a metre on
– Alexander Giles
Commented Mar 11, 2014 at 19:17