An irrational sonnet has 14 lines, just as the traditional sonnet, but differs in its stanza-division and rhyme: there are five stanzas--containing 3, 1, 4, 1 and 5 lines, respectively (these being the first five digits of the irrational number pi), and a rhyme scheme of AAB C BAAB C CDCCD. This form was devised by Oulipo member Jacques Bens (1931-2001) in 1963. (Previous postings concerning the Oulipo occurred on March 25 and August 5.)
Here is a translation (by Laurence Petit and Ravi Shankar) of one from Bens' 41 Sonnets Irrationnels (Gallimard, 1965).
The Presbytery Has Lost None of Its Charm
The presbytery has lost none of its charm
Nor how a garden’s radiance can disarm,
Restoring hand to dog, and bridle to stallion:
But this explanation fails this mystery.
A plague on insight that cracks your talons,
The analysis that dispels your sense of alarm,
Wearing a preposterous cop’s cap for a perm,
Pointing out here the just and there the felon.
No explanation can redeem a mystery
I prefer the faded charms of the presbytery
And the sham radiance of a famous garden;
I prefer (it’s in my nature) the shuddery
Of fear obliterated by this tiny thief’s particularity
to blatancy and fame, like some lamp of Aladdin.
This translation of "The Presbytery Has Lost None of Its Charm" appeared in an Oulipo section of the online journal, Drunken Boat (2006). Drunken Boat also offers details of the masculine and feminine requirements of Bens' rhyme scheme; this same information (in French) and another irrational sonnet by Bens may be found at this Oulipo website.