Why It's Impossible to Tune a Piano

I can help with a couple of these. 12 notes is a kludge, because powers of 2^(1/12) well approximate simple ratios. These simple ratios (such as 3:2) sound good. I like this video for explanation: ▶ this video Also, the reason that the letters are in the wrong order is that we're playing the wrong scale. The monks who invented the scale usually sang in A-minor (so we use the first letter for that scale). Nowadays, we use the major scale, which has the same spacing between notes, but in a different order. It just so happens that C-major has the same notes as A-minor, so that's why we count from C. A great channel for this is Michael New, he explains everything very clearly: link Music, much like language, has a lot of technical debt.

minutephysics had a nice video about the mathematics that go behind piano tuning too. "Why It's Impossible to Tune a Piano" ▶ this video

A related video on the numbers behind piano music, on why it is mathematically impossible to perfectly tune a piano : ▶ this video

To +1 the "no objective foundation": browse music theory research a bit! There's a ton of caveats and poor-sounding fits and whatnot for literally every approach, and there's endless discussion of it. E.g. have a MinutePhysics take on how the common 12 note western scale falls apart: ▶ this video And that's before even getting into completely alternate approaches, or how strongly harmonics affect perception: link or link (maybe to clarify: there are objective aspects , in that sound is measurable. but there is nothing like a "grand unified theory" that covers all music, nor are roughly any of the popular ones internally consistent - it's far, far too varied for that, and physics often doesn't allow the desired consistency, causing more variety)