pythagoras.lym wrote:From Ancient times up through Bach's Well-tempered Klavier, which I believe is not, as most scholars say, the Equal Tempered system we have in use today.
It was well-tempering he used for that, not 12ET (12-tone equal tempered).
I have a hypothesis that Bach knew that one could never have a "perfect" system and that when Bach composed the Well-Tempered Klavier, he was thinking of tuning using the natural ability of a singer to "adjust" the intonation to make the intervals fit ('αρμονία).
I'm curious to know why you think this needs to be hypothesized. Bach was well aware of tuning issues, including the trade-offs between the sweeter-sounding just intervals versus the ability to modulate to remote keys. It's reported he made life difficult for his organ tuner. And while singers and players of fretless instruments get training in these intonation issues to this day, the WTK is a demonstration of a way to try to get sweet intonation and remote modulation together on a normal fixed-pitch instrument, like a harpsichord. There's no way to adjust the intonation of a harpsichord during a performance (though it might, depending on the weather, adjust its own tuning by surprise).