Something I could whinge about is so-called Pythagoras, because "he" is so misunderstood.
In fact we don't know much about him. It is doubtful if we have anything of what he ever said. The most likely candidate for anything genuine is a small quote about "not taking outside the circle what belongs in the circle" (i.e. don't blab secrets) in Plato's Laches, but I can't remember the details. Not long ago I was watching a telly prog in which Alice Roberts confidently talked of Pythagoras inventing music theory, but you should notice that they never get past discussing the perfect fifth when asserting that.
No, there were "Pythagoreans", self-appointed followers of Pythagoras. Partly they were scientific and partly they were a vegetarian religious sect. They didn't eat anything with souls. They didn't eat beans, because they thought the flatulence was escaping souls.
The JI major third, known by Ptolemy, had a ratio of 5/4, but Pythagoreans only worked with the ratios 3/2 and 2. You can manipulate 3/2 and 2 to get a chromatic octave, but that process was only finalised in the 15th century or thereabouts. You can't manipulate 3/2 and 2 to get 5/4, so the early Pythagoreans got as far as inventing the major third of 81/64. I would say it was so sharp that no-one ever used it for practical purposes, but I'm probably wrong - there was the problem of building church organs, and Christians were fond of Pythagoreans, and I think it's common knowledge that organs could only play in a few keys because of how out of tune they were.
Sorry to moan, but Alice Roberts gets my goat!
If you read Ancient Greek Music by Martin West, you'll find some oddities. The ancient Greek scale was constructed from, perhaps, approximately the notes EFA and a fourth note. Where did that fourth note go, you ask - it can only be G, surely? Well, no, there were three variants, one had G, one had F# and one placed it between E and F! Tell us how that fits Pythagoras, Alice! It's a good example of how music was first invented for the ear, and then the theory came later.