I was taught that the "bi" prefix was a multiplier and "semi" was a divider.
That meant biweekly, bimonthly, biannually were every 2 weeks, months, years and semi-weekly, semi-monthly, semi-annually were every half a week, half a month, and half a year.
Then the real world intruded and I've been confused ever since. About the only time I hear "semi" and "bi" used on a regular basis the way I expect is with pay periods. Biweekly is every two weeks and semi-monthly is twice a month.
Canada, by the way.
PS: I suppose bisexual and semi trailers also fit my expectations.
bi- means two, as in bicycle: two wheels (circles)
semi- means half, as in semicircle: half of a circle
The problem is that the prefixes can be parsed as affecting either duration/interval as in (bi-week)ly, every two weeks, or frequency as in bi-(weekly), two times weekly. The same applies to semi-.
Personally I find the frequency interpretation a bit of a stretch—"two" is not the same as "two times" or "twice"—so I would tend to read e.g. bimonthly as every two months rather than twice each month.
I prefer the opposite system. If someone said to me: we will meet two weekly, it seems closer to “twice weekly” than once every two weeks. Where as semi weekly saying “half weekly” makes it sound like one half of the weeks we meet and the other half we don’t. I have no idea how anyone thinks that meaning semi-weekly means twice weekly. Even the “we meet every half week” makes little sense to me syntax-wise.
You're essentially assuming the conclusion by grouping it like that. There are three parts to "biweekly", "bi-", "week", and "-ly". "Once per biweek", i.e. once per 14 days (or per fortnight), makes at least as much sense as "two" × "weekly".
I have no idea how anyone thinks that meaning semi-weekly means twice weekly.
Meeting semiweekly (semiweek-ly, if you must hyphenate it) means meeting every semiweek, or every half-week (3.5 days). Which is an odd internal to meet at if taken literally but would result in meeting twice each week. "Semiannually" is a more common example, and I've never seen or heard it used to refer to anything but a 6-month (half-year) interval.
"Semi truck" is not half a truck, but a truck designed to carry one half the weight of the cargo it is hauling. A semi trailer is one designed to have half of its load (by weight) carried by the tow vehicle. A standard trailer gets difficult and possibly dangerous to tow if the weight carried by the tow vehicle (hitch weight) strays too far outside the 8%-12% range.
And just to add to the confusion, Dodge popularized something called the "hemi engine"--an engine with a "hemi head", not half an engine. And "hemi head" refers not to "1/2 an engine head" but to the approximately hemispherical (1/2 sphere) shape of the combustion chambers cast/machined into the engine head.
It all comes down to common usage, either interpretation can work. It's like the phrase "I could care less" now means entirely opposite things to some people.
Biannual means twice a year here. Biennial is used for every two years.
Similarly for biweekly, we have fortnightly for every two weeks which means no-one uses biweekly to mean the same thing.