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Look up the adjective biweekly in this dictionary and you will see it defined as "occurring every two weeks" AND as "occurring twice a week." Similarly, the adjective bimonthly is defined as "occurring every two months" AND as "occurring twice a month."
For this, we are sorry. But we don't mean "sorry" in the sense that we feel penitence; we are not to blame. We mean "sorry" in the sense that we feel a kind of sorrow aroused by circumstances beyond our control or power to repair. //
One such case, sort of, is very similar to the cases at hand: the language offers us biannual for "twice a year" and biennial for "every two years." This is useful and elegant, but, alas, also frequently botched, with biannual so frequently used to mean "every two years" that we've had to enter that meaning in our dictionaries. But here another solution is readily available: skip biannual altogether and use in its place the common semiannual.
Ah, semi-! Just as a semicircle cuts a circle in half, so too does the prefix semi- semantically cut what it is affixed to in half: semiweekly means unambiguously two times per week; semimonthly means two times per month; semiannual means two times per year.