Sort of. It's certainly playing with the form of the Italian Sonnet. Like the Italian sonnet, "Why Brownlee Left" is broken up into an octave and a sestet. This is Muldoon indicating to us that this should at least recall the sonnet form. However, unlike the sonnet, "Why Brownlee Left" does not follow a rhyme scheme (an Italian sonnet is usually rhymed abbaabba cdecde, and the English sonnet usually ababcdcdefefgg) nor is it written in iambic pentameter (the lines are varying lengths rather than 10 syllables each). Muldoon is not a sloppy writer though; he's making this poem more about Brownlee, but also about the sonnet--this is metafiction in that respect. Just like Brownlee, who left when he had every reason to be content, poets are leaving behind the form of the sonnet (in exchange for the free verse we more typically see today) when they had every reason to be content with the sonnet form. That's one reading of it anyway.
So, is this a sonnet? Sort of us. It's either commentary on the tradition of the sonnet, or it is an imperfect sonnet, or more likely it's both.
A sonnet is a type of poem that is composed of 14 rhyming lines. When writing a sonnet, it is generally aligned to the left instead of centered. William Shakespeare was a famous writer of sonnets.
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