An Irrational Sonnet is a fixed form poem, with fourteen lines, in which the structure is based on the number pi (hence the adjective “irrational”). It is divided into five stanzas successively and respectively composed of 3-1-4-1-5 lines, the first five integers of pi.
(The next number in the sequence is 9; which is why the value is normally given as π = 3.1416, an approximation of the actual 3.14159).
The poem is based on four rhymes (A, B, C, D). In French, rhymes A and C are of the same ‘gender’ (+), and rhymes B and D are of the opposite ‘gender’ (-). In order to make the poem, one needs 4A, 3B, 4C (used over five lines) and 2D.
01. A +
02. A +
03. B –
04. C +
05. B –
06. A +
07. A +
08. B –
09. C + (identical to 04)
10. C +
11. D –
12. C +
13. C +
14. D –
The first time Jacques Bens exposed the principles of what would become known as the “irrational sonnet” was at the Oulipo meeting in March, 1963 (an integral transcription may be found in the “Circulaire number 31” [“Bibliothèque Oulipienne” number 145]). It is on this occasion that he coined the term Oulipolée to name this constraint: “This poem takes as its basis the number pi, (…) Thus, using these first five numbers, we have a poem of five stanza, each composed of 3, 1, 4, 1, and 5 lines. (…) The total of the five first numbers is 14, and maintaining but five stanzas, we come upon an already established total number of lines which niftily leads to our passing salute of the sonnet.” He goes on to explain the structure of the rhymes, including the refrain one line plays in two stanzas, and then gives two examples. Having thus invented a new form, two years later, Bens published 41 sonnets irrationnels (Gallimard).