In MedL. rithmus was used of accentual, as opposed to quantitative, verse, and, as accentual verse was usually rhymed, the word acquired the meaning which it has in all the Rom[anic]. and Teut[onic] langs. [Weekley]Persistence of older form is due to popular association with Old English rim "number," from PIE root *re(i)- "to reason, count." Paired with reason since at least late 15c. Phrase rhyme or reason "good sense" (chiefly used in the negative) is from late 15c. (see reason (n.)). Rhyme scheme is attested from 1931. Rhyme royal (1841) is a stanza of seven 10-syllable lines rhymed a-b-a-b-b-c-c.