
Tegan S. answered 03/26/19
Experienced Woodwinds, Piano and Accordion Teacher
I always heard that it came out of Musica Ficta. When playing in a mode focused around F, musicians knew to just play every B as a Bb to avoid the tritone. But it wasn't written, just KNOWN. And most modes didn't really use a B natural anyway, so when expanding the range and function of modes into scales, we already used the letter B for Bb, so it became an H.
Although I'm an American. I'd love to hear from a German musician why this happened, as it's taught there.