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A rhyme scheme is the pattern of rhymes at the end of each line of a poem or song. It is usually referred to by using letters to indicate which lines rhyme; lines designated with the same letter all rhyme with each other.
An example of the ABAB rhyming scheme, from "To Anthea, who may Command him Anything", by Robert Herrick:
Bid me to weep, and I will weep
While I have eyes to see
And having none, yet I will keep
A heart to weep for thee
Function in writing
A basic distinction is between rhyme schemes that apply to a single stanza, and those that continue their pattern throughout an entire poem (see chain rhyme). There are also more elaborate related forms, like the sestina - which requires repetition of exact words in a complex pattern. Rhyming is not a mandatory feature of poetry; a four-line stanza with non-rhyming lines could be described as using the scheme ABCD.
Notation and examples
Notation used below:
ABAB - Four-line stanza, first and third lines rhyme at the end, second and fourth lines rhyme at the end.
AB AB - Two two-line stanzas, with the first lines rhyming at the end and the second lines rhyming at the end.
AB,AB - Single two-line stanza, with the two lines having both a single internal rhyme and a conventional rhyme at the end.
aBaB - Two different possible meanings for a four-line stanza:
First and third lines rhyme at the end, second and fourth lines are repeated verbatim.
A1abA2 A1abA2 - Two stanzas, where the first lines of both stanzas are exactly the same, and the last lines of both stanzas are the same. The second lines of the two stanzas are different, but rhyme at the end with the first and last lines. (In other words, all the "A" and "a" lines rhyme with each other, but not with the "b" lines.)
A tristich or tercet is any three-line stanza or poem; common rhyme schemes for these are AAA (triplet) and ABA (enclosed tercet). The only other possibilities for three-line poems are AAB, ABB, and ABC. Multiple tercets can be combined into longer poems, as in the terza rima form.
Triplet: AAA, often repeating such as: AAA BBB CCC DDD...
Terza rima: ABA BCB CDC ..., ending on YZY Z; YZY ZZ; or YZY ZYZ
Villanelle: A1bA2 abA1 abA2 abA1 abA2 abA1A2, where A1 and A2 are lines repeated exactly which rhyme with the "a" lines
Couplets are the most common type of rhyme scheme in old school rap and are still regularly used, though complex rhyme schemes have progressively become more frequent. Rather than relying on end rhymes, rap's rhyme schemes can have rhymes placed anywhere in the bars of music to create a structure. There can also be numerous rhythmic elements which all work together in the same scheme - this is called internal rhyme in traditional poetry, though as rap's rhymes schemes can be anywhere in the bar, they could all be internal, so the term is not always used. Rap verses can also employ 'extra rhymes', which do not structure the verse like the main rhyme schemes, but which add to the overall sound of the verse.
The number of different possible rhyme schemes for an n-line poem is given by the Bell numbers,
which for n = 1, 2, 3, ... are
1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, .. (sequence in the OEIS).
Examples: We find one rhyme scheme for a one-line poem (A), two different rhyme schemes for a two-line poem (AA, AB), and five for a three-line poem: AAA, AAB, ABA, ABB, and ABC.
These counts, however, include rhyme schemes in which rhyme is not employed at all (ABCD). There are many fewer rhyme schemes when all lines must rhyme with at least one other line; a count of these is given by the numbers,
0, 1, 1, 4, 11, 41, 162, 715, 3425, 17722, ... (sequence in the OEIS).
For example, for a three-line poem, there is only one rhyming scheme in which every line rhymes with at least one other (AAA), while for a four-line poem, there are four such schemes (AABB, ABAB, ABBA, and AAAA).
^Bradley, Adam, 2009, Book of Rhymes: The Poetics of Hip-Hop, Basic Civitas Books, p. 73.
^Edwards, Paul, 2009, How to Rap: The Art & Science of the Hip-Hop MC, Chicago Review Press, p. 107.
^ abEdwards, Paul, 2009, How to Rap: The Art & Science of the Hip-Hop MC, Chicago Review Press, p. 104.
^Bradley, Adam, 2009, Book of Rhymes: The Poetics of Hip-Hop, Basic Civitas Books, p. 74.
^Edwards, Paul, 2009, How to Rap: The Art & Science of the Hip-Hop MC, Chicago Review Press, p. 103.
^Gardner, Martin (1978), "The Bells: versatile numbers that can count partitions of a set, primes and even rhymes", Scientific American, 238: 24-30, doi:10.1038/scientificamerican0578-24. 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.