[ce4]

It does make sense though (once you know where it comes from):

Before the ubiquity of watches, time was announced using church clocks and bell strikes. There's a big bell for hours (low pitch) and a smaller one for announcing quarters (higher pitch).

Signalling zero is not possible using "zero bell strikes", so 00:00 is signalled by 4 strikes of the quarters bell and 12 strikes of the hour bell.

Thus, the sequences go like:

11:15 1x quarter bell

11:30 2x quarter bell

11:45 3x quarter bell

12:00 4x quarter bell + 1x hour bell

Basically it makes sense then as all the quarters belong to the same hour.

[usr1106]

I have used those time expressions for over 55 years. Never thought about the explanation.

[1718627440]

Yes. The other explanation is that time is nothing special, it gets just counted like everything else. You wouldn't say it's a quarter to a full cake either.

[rob74]

If we follow your argument, the number 3.25 would be read "point two five to four" istead of "three point two five". Which is to say, the fact that the quarters are mentioned in connection to the next hour, not the previous one, is indeed unusual.