I've actually been interested in metrical tagging for a long time. This
is strictly thought experiment, mind you, but I've imagined one way to
automate it for English. The chief task would be to generate a complete
English dictionary that's tagged with syllable-stress information for
each word so that you could match poems against it automatically. Most
dictionaries have some stress information already--they give each word
in the phonetic alphabet, and stressed syllables are marked. The word
"marriage" is 'mer-ij and "impediment" is im-'pe-də-mənt in the
Merriam-Webster, for example.
All one-syllable words would all have to be considered unstressed, most
likely, which of course is not at all the case in either speech or
scansion. But you'd at least be able to see where some of the
unequivocal stresses are. So for "Let me not to the marriage of true
minds / Admit impediment," which is usually scanned something like "let
me NOT to the MARRiage of TRUE MINDS / adMIT imPEDiMENT" you'd get
instead "let me not to the MARRiage of true minds / adMIT imPEDiment."
It'd be a start, anyway. Scansion is terribly subjective in any case,
which is why it's so difficult to automate. About the only other way I
can think to do it would be to get someone to recite the poem (and to do
it well!), record it digitally, analyze the stresses in the audio
recording, and then extract and encode that information. Perfectly
possible, but again not highly automatic.
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