Quarter-Comma Meantone (Part 4)

I’ve been talking about the marvelous tuning system that dominated western music from about 1550 to 1690: quarter-comma meantone. Above I’ve drawn it in its most mathematically beautiful form. For convenience I’m drawing it in the key of C, but you could use any key.

This scale has lots of ‘just major thirds’, which are pairs of notes with a frequency ratio of 5/4. I’ve drawn them as dark blue arrows.

This scale also has a visible symmetry under reflection across the vertical axis! What ...