It is a one syllable difference, at most. Fif-teen versus Quar-ter-Past. Or Thir-ty versus Half-past. And for-ty-five versus quar-ter-till.
But it is also about precision. If I say “Let’s meet up at 4:45” that implies a lot more specificity than “let’s meet at quarter to five”. The firmer is an exact time people should meet at and the latter is “around that time”.
https://www.youtube.com/watch?v=NeopkvAP-ag goes into the difference between analog and digital time and what that means with thought processes. But a lot of it boils down to thinking in terms of “parts of a whole” versus “specific times”.
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https://www.piped.video/watch?v=NeopkvAP-ag
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it’s not like people generally pronounce it fully anyways, it’ll come out as “qua’tr” or “quartah” depending on dialect