The challenge, should you decide to accept it: use one of these two words in a sentence that sheds some light on their meanings.
Intercalarity – The burden of the song; the putting between, as the burden is between the verses.
Intercalary – adj. 1) Of a day, days, or month: Inserted at intervals in the calendar in order to bring an inexact reckoning of the year into harmony with the solar year. 2) Of a line or stanza: Inserted at intervals in a composition; of the nature of a refrain. 3) Of the nature of an insertion between the original or ordinary members of a series or parts of a whole; interpolated, intervening.
Jilanne Hoffmann 
February 29 is an intercalary day to keep our calendar in tune with Earth’s revolutions around the sun. Hmm, I wonder if I used that correctly?? Great, random words!!
I was going through a period of reading the OED just for fun. I still do it occasionally, but not as often as I’d like.
I was just thinking that Benjamin’s selections in the Arcades Project are intercalary in the physical sense, creating a certain intercalarity amongst themselves.
What do you think? You can see how tempting it would be to create an Arcades project from blog posts and comments!!
I love reading the OED too, especially for the etymology of the words.
I see what you mean by selections in The Arcades being intercalary. I wonder if it is the selections themselves or if it would be the reader who is being intercalary in that instance.
You’re right, these comments ARE becoming their own project!