We have a presentation program at my job that occurs once every three months. It’s refered to as “quarterly,” indicating it happens four times in one year. They’re thinking of changing it to once every four months, meaning it would happen three times per year. What would the word for this three-time occurance be, as opposed to “quarterly?” Is there such a word?
(I pitched “trimester,” but that didn’t fly.)
triannually
Quadrimestrial.
or triennial
That’s good, because a trimester is three months. 
Giles’ “quadrimestrial” sounds good to me, but I can’t say for sure if it’s a real word.
I think “triannual” would mean once every three years. I think “triennial” is right, but I could have that backwards.
I think you’re just going to have to keep it the way it is (quarterly). It’s worth it just so you don’t have to think up a word to describe it.
How about “everyfourmonthsly”?
Ah! I think you’re on to something here. Not to go into the workings of my job (BOH-ring!), but we have owners who earn rewards every two years, and those are referred to as biennial accounts, so that would mean three-times-a-year would have to be triannualy as an adverb, and triannual as the noun.
Thanks, everyone, as always. This was a major brain fart for me.
The cognate of quarterly is ternary
http://m-w.com/cgi-bin/dictionary?book=Dictionary&va=ternary
Funny thing, one college went from a system of 2 “semesters” per school year, plus a summer “quarter”, to 3 four-month “tri-mesters”.
The English majors tried to explain to the board that “semester” did not mean “semi-” or half of anything, but “six months”.
Thus their new tri-mesters would be “three months”
But of course, none of the board were impressed. None had taken English, as they all were appointed for their “'business skills”, i.e., donations.
A trimester is a third of whatever the total period is. A trimester of a pregnancy is three months, since a pregnancy is nine months, but a trimester of a year is four months. Which still doesn’t lead to an adjectival form.
Which is a good reason to not use those terms, if possible. Even if you do work out for yourself which one is which, will your audience work it out correctly, too?
No. I just checked in my print copy of th Oxford English Dictionary, and:
(1) It defines “trimester” as three months
(2) It says it comes, via French from the Latin “tri” three and “mensis” month.
(3) It says the adjectival form is “trimestrial”, which is consistent with my suggestion “quadrimestrial”.