Quarter-Comma Meantone (Part 2)

Last time I introduced ‘quarter-comma meantone’, the tuning system shown above. Today let’s see if we can understand all the numbers in this picture.

You see 13 circles with letters in them standing for tones in a scale, connected by arrows labeled by numbers. The numbers are the frequency ratios between these tones:

• The blue arrows are ‘just major thirds’, with a frequency ratio of 5/4. It’s the quest for a 12-tone scale with a lot of just major thirds that led people to quarter-comma mea...