How to say "every fourth year" in Latin?

Question

My intuition says that "every fourth year" would translate to Latin as "quarto quoque anno". I read the comic Asterix Olympius in Latin, and on page 11 the druid describes the Olympic games like this:

Certamina sacra, praesidio Iovis tecta, quae quinto quoque anno apparantur Olympiae Graeciae inter Hellenes mense quodam, quem illi Hecatombaeon dicunt.

The ancient Olympic games were held once in every four years. I'm aware that the Roman way of counting can produce an offset of one ("quintus dies post nuptias" means the fourth day after the wedding), but I find such an offset somewhat unnatural when one describes frequency.

So, how would the Romans have said "every fourth year"? Have the numbers used in such an expression varied over time? Are there ancient sources with such an expression where we know the length of time intervals?

Searching for 'quoque anno' in a source or another produces several results, but its hard to say which time period was really meant in the examples. This example is interesting, since it suggests that there was disagreement among Romans as to what quarto quoque anno meant:

It was the intention of Caesar that the bisextum should be inserted peracto quadriennii circuitu, as Censorinus says, or quinto quoque incipiente anno, to use the words of Macrobius. The phrase, however, which Caesar used seems to have been quarto quoque anno, which was interpreted by the priests to mean every third year. The consequence was, that in the year 8 B.C. the Emperor Augustus, finding that three more intercalations had been made than was the intention of the law, gave directions that for the next twelve years there should be no bissextile (Plin. Nat. 18.211). (A Dictionary of Greek and Roman Antiquities: Calendarium)

If "quarto quoque anno" is indeed ambiguous, is there a non-ambiguous way to say "every fourth year"?

Answer 1

I've been thinking of this one and suddenly remebered the use of singulis + period of time in pl. abl. (singulis annis, singulis horis). Singulis quadrienniis is even attested a couple of times: 1, 2, 3.

It seems to be valid to mean an average (yet irregular) frequency, as much as a steady one (e.gr., singulis annis may be every 13th of May, or at whatever date but once in every calendar year). However, that doesn't seem to be such big deal.

Answer 2

It just occurred to me that I could express "every fourth year" as semel quoque quadriennio, literally "once in every period of four years". I think that avoids the ambiguity, but it is not very flexible (I don't want to use that construction to say "every 17th second") and might not be as idiomatic as quarto/quinto quoque anno. Additionally, it only says that the thing occurs once in every four year period, not that it happens at the same time in each period. Anyway, I think it's a decent alternative.