## The number of rhyme schemes::Rhyme scheme

### ::concepts

Rhyme::schemes Edwards::science Press::hip-hop Chicago::review Stanza::which Rhyme::rhymes**The number of rhyme schemes**

The number of different possible rhyme schemes for an *n*-line poem is given by the Bell numbers,<ref name="mg">{{#invoke:citation/CS1|citation
|CitationClass=citation
}}. Reprinted with an addendum as "The Tinkly Temple Bells", Chapter 2 of *Fractal Music, Hypercards, and more ... Mathematical Recreations from Scientific American*, W. H. Freeman, 1992, pp. 24–38.</ref>
which for *n* = 1, 2, 3, ... are

- 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, … (sequence A000110 in OEIS).

For instance, there are five different rhyme schemes for a three-line poem: AAA, AAB, ABA, ABB, and ABC. Historically, the first exhaustive listing of rhyme schemes appears to be in the Tale of Genji, an 11th-century Japanese novel whose chapters are headed by diagrams representing the 52 rhyme schemes of a five-line poem.<ref name="mg"/> The number of rhyme schemes in which all lines rhyme with at least one other line is given by the numbers

- 0, 1, 1, 4, 11, 41, 162, 715, 3425, 17722, ... (sequence A000296 in OEIS).

For instance the four such rhyme schemes for a four-line poem are AABB, ABAB, ABBA, and AAAA. Both sequences of numbers may be found on either side of an augmented version of the Bell triangle.

**Rhyme scheme sections**

Intro Function in writing Example rhyme schemes Rhyme schemes in hip-hop music The number of rhyme schemes References External links

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