>did I oversimplify it?

yes, but you more than made up for that with this post.
actually®, you don't find triannual in many dictionaries becuase it seems to have gone obsolete (and was used pretty rarely in the first place).


Obs. rare.

Occurring every three years; lasting for three years; = triennial.
1640 Par. Acc. St. Barth. by Exchange in Archæologia XLV. 78 Pd. the ringers for joy of the tryannual Parliament, o. 2. 6. 1656 Earl of Monmouth tr. Boccalini's Advts. fr. Parnass. i. lxix. 133 He was deputed a Triannual President of the Isle of Negrapont.

¶b. Occurring thrice a year.
1901 Daily Chron. 8 June 5/2 The ladies+we learn+will hold ‘tri-annual invitation meetings’.+ That, we suppose, means an invitation once in four months.