Intermetricality: the persistence, repetition, or recurrence of rhythms, metres, and patterns, especially unconsciously, especially in folk stories, folk poems, and folk songs. Such patterns may have their origin in non-folk forms, such as the Bible, advertising slogans, and so on, as much as in folk forms. The term intermetricality is akin to intertextuality*, but is more specific.
Off the top of my head, here is a possible modern example. Someone posts a picture of a cat wearing glasses on Facebook, and captions it thus: ‘If you’re under 40 this will remind you of Harry Potter… if you’re over 40 it will remind you of John Lennon’. That particular pattern of balancing two phrases is similar to that found in the Book of Proverbs. This does not necessarily prove a direct relationship between the two but readers will likely be struck by the familiarity of both.
By the way, this word and its definition did not come to me out of nowhere. I coined it to explain something after having been asked to read and comment upon an article by the late Dell Hymes, Ethnopoetics and sociolinguistics: three stories by African-American children, in which he wrote of such repetitions. I don’t pretend to be any kind of expert in this or in any of the academic fields I mention here, I just wanted to establish the coining in a recognisable place and at a recognisable time. Others are now perfectly free to use it.
*The word ‘intertextuality’ was coined by Julia Kristeva, although she herself was probably influenced by the work of semioticians Roland Barthes and Mikhail Bakhtin, and linguist Ferdinand de Saussure