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: https://www.youtube.com/watch?v=1Hqm0dYKUx4
(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)
And that's before even getting into completely alternate approaches, or how strongly harmonics affect perception: https://www.youtube.com/watch?v=VAgXpCK_4gA or https://www.youtube.com/watch?v=AZ8qZCGg4Bk
(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)