[CWuestefeld]

ultra-pedantically: that's true with the "well tempered" tuning that is used almost universally. But this is really just an approximation, and one that our ears have grown used to.

Mathematically speaking, B# <> C. On a piano or other instrument that quantizes tones, we have little choice but to go with the approximation. But for violinists and others that can choose from a spectrum of tones, it's possible to hit those tones exactly. Of course, when playing with others, the violin still needs to quantize just to be in tune with the others.

[kibibu]

Even more pedantically, modern stuff uses equal-temperament, not well-temperament.

Well-temperament still has different intervals depending on key. Even temperament just uses x^n/12 for note n and basis frequency x.

[viraptor]

If anyone wants to do down that rabbit hole for 15min, there's Adam Neely's recent video on the topic: https://youtube.com/watch?v=SZftrA-aCa4