Good Temperament

On the 2018-06-22 Science Friday podcast "How Abstract Math Can Analyze Social Injustice" mathematician-musician Eugenia Cheng discusses the spaces between musical notes and J S Bach's Well-Tempered Clavier and beauty and joy and math:

... And I feel like I can sense Bach's excitement as he goes through the keys in these pieces. But it's amazing. He's never been able to write in this key before. And so I'm going to play a prelude in F sharp. [PLAYS NOTE ON PIANO]

Now, F sharp is exactly halfway between C and C. That means it's actually the square root of 2 away; the frequency ratio is the square root of 2. This interval is the least consonant interval, the most dissonant. It used to be called the devil in music, because it is the one in which the harmonics interfere with each other the most.

And I feel like I'm just sensing Bach's wonder that he can actually write a piece in F sharp for the first time. And so the piece is quite simple. Some of the pieces that are in more standard keys, like C minor or G minor, are really complicated. And I feel like it's because he's used to writing in those keys. Whereas this one, he's never been to before, so he just sits there and goes, "This is amazing."

Just like if you go to a beautiful beach for the first time. You don't do anything, you just stare at it and you go, "This is beautiful". Then he wanders around different keys feeling how beautiful it is to be able to go in these keys he's never been to before. And he doesn't stay in any of them for very long. And then he comes back to F sharp. And I just feel like it's almost childlike wonder. It's not a complicated piece, but it's in F sharp, which is the square root of 2. ...

(lightly edited transcript; cf Ingressive vs Congressive (2017-07-08), Eugenia Cheng on Thinking (2017-12-30), Many Worlds of Math (2019-03-15), ...) - ^z - 2019-03-31