# What are the 15 possible rhyme schemes for a Quatrain?

Wikipedia says that for a Quatrain there are fifteen possible rhyme schemes.

What are these? I cannot find a full list anywhere.

• I think this might just be a combinatorial thing. If you've only got four lines, there are only a limited number of ways to choose the pattern of the rhymes. (That said, I can only count as many as fifteen if I include the ABCD pattern where no lines rhyme, so I've either miscounted or misunderstood something. Not a poetry expert!) May 26, 2021 at 7:10

Let's build the verse line by line.

• The first one is A (by definition).
• The second line either rhymes with the first (A) or not (B). So that's two possibilities.
• If we have AA, the next line is either A or B (two possibilities); if we have AB, the next line can be A, B or C (three possibilities).
• For the final line:
• AAA can lead to AAAA or AAAB
• AAB can lead to AABA, AABB or AABC
• ABA can lead to ABAA, ABAB or ABAC
• ABB can lead to ABBA, ABBB or ABBC
• ABC can lead to ABCA, ABCB, ABCC or ABCD.

In general, the number of possible rhyme schemes for a poem with n lines is given by the so-called Bell number. In fact, Wikipedia explicitly lists this purpose and the list you're looking for:

### Rhyme schemes

The Bell numbers also count the rhyme schemes of an n-line poem or stanza. A rhyme scheme describes which lines rhyme with each other, and so may be interpreted as a partition of the set of lines into rhyming subsets. Rhyme schemes are usually written as a sequence of Roman letters, one per line, with rhyming lines given the same letter as each other, and with the first lines in each rhyming set labeled in alphabetical order. Thus, the 15 possible four-line rhyme schemes are AAAA, AAAB, AABA, AABB, AABC, ABAA, ABAB, ABAC, ABBA, ABBB, ABBC, ABCA, ABCB, ABCC, and ABCD.

• Thanks - that's what I was trying to get at in my comment, but you've explained much better! :) May 26, 2021 at 13:55
• Ah I see, so it's really just every possible combo. Do they all actually work as rhyme schemes? Also it seems to me that ABCD should be left out, since it would have no rhyming. May 26, 2021 at 17:59
• @stackers I agree - all the sources I found said there must be a rhyme scheme, but also that there are fifteen options, which is only possible if you count "not rhyming" as a rhyme scheme. May 26, 2021 at 18:39