Can you please specify the dialect of English you're referring to, instead of falling for the obviously ridiculous notion that there's one English.
I have never heard "quarter of 12", and wasn't aware it was a thing. In Ireland - Hiberno-English, Irish-English, whatever you like - I've only ever said and heard "quarter to 12" for 11.45.
So, serious question: who says "quarter of 12"? It sounds makey-uppy and illogical, so I'm supposing it might be a linguistic development in the old U.S. of A. I don't feel like I've ever heard it in movies or shows though, in spite of having been subjected to a certain amount of U.S. cultural produce, so this is somewhat mysterious to me.
And I'm pretty sure the Spanish matches (except in reverse, like Spanish usually is relative to English):
11:15 -> once y cuarto
11:30 -> once y media
11:45 -> doce menos cuarto
edit: and about the subject of the thread, "por sí" or "por sí mismo." "per" afaik is a preposition like "por" that means to pair or match things: so it can mean by, through, around, with, for, and even times("×") i.e. doesn't mean anything in English.
"si" is the 3rd person reflexive pronoun (when placed after the verb), and is probably similar to "se." ("mismo" is a redundant clarification is Spanish, probably because "si" and "sí" are homonyms.)
Se and si (as used here) are the same word in different cases. I would draw comparisons to latin se and sibi respectively. I'd also draw parallels between sui, suus, secum and suyo, su, consigo.
Quarter to and quarter past are not rare in Britain, so
11:15 -> quarter past 11
11:45 -> quarter to 12
are very normal to me. In fact any number above 5 to or past are normal. Even smaller numbers come up, where, of course, 1 to 1 and 2 to 2 are particular favourites.
I hear quarter to and quarter after a lot. I think rarity might be a regional thing (or perhaps generational—despite growing up four miles from my childhood home, my children have a different Chicago accent than I do and when I did student teaching in the school district where I went to high school, those kids also commented about the difference in accent).
The English terms would be:
11:15 -> quarter after 11, quarter past 11 (both pretty rare, tbh)
11:30 -> half past 11 (this is the only form that is moderately common)
11:45 -> quarter of 12, quarter before 12 (also pretty rare)