That’s an interesting video.
Back when I was young and hale, and screwing up at Michigan State, there was a music prof who gave musical open lectures where he'd play vintage tunes on pianos as they were tuned in various earlier eras, the try them on the modern tuned piano. He wrote a couple of books about it, alas, I can't recall his name.
The equal temperament system -- where the half step intervals are, in cycles, the 12th root of 2 higher or lower than the adjacent notes -- evolved over the past few centuries, more or less during and since the era of JS Bach.
All of this is a bit like finding out for the first time about how the calendars were changed starting in the 17th century but at different times in different polities, with the final adjustments occurring in the 20th century. :^)