Quarter-Comma Meantone (Part 6)

So far I’ve focused on the quarter-comma meantone system in its mathematically beautiful, symmetrical form above. Today I’ll say more about the scale as actually played: how we trim it down from a 13-note scale to a more practical 12-note scale, and what are the intervals between notes in the resulting scale.

The scale above has:

• a lot of thirds with frequency ratios that are exactly 5/4,

• a lot of fifths that are only slightly flat compared to the ideal 3/2,

• a big problem that we need to...