Quarter-Comma Meantone (Part 5)

I’ve been talking about the quarter-comma meantone tuning system, which dominated western music from about 1550 to 1690. So far I’ve been drawing it using a circle of fifths, as above. This is a diagram where as we go clockwise each note is a fifth higher than the previous one.

But why is this system called ‘meantone’? Briefly, it’s because the size of a whole step between notes in this tuning system—called a ‘tone’—is the geometric mean of the two kinds of whole step in Pythagorean tuning...