I recently found myself asking the question posed in the title – what comes after primary, secondary, tertiary…?
I had a rough idea, based on my drum line days, and the various types of Tenor drums.
However, this article lays it out nice and neat.
1st = primary, 2nd = secondary, 3rd = tertiary, 4th = quaternary, 5th = quinary, 6th = senary, 7th = septenary, 8th = octonary, 9th = nonary, 10th = denary, 12th = duodenary and 20th = vigenary.
Personally, anything after you hit the 5th level, you might consider another pattern, since you’ll lose your audience, unless they all happen to speak Latin.