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"?