Lucy tuning
Lucy tuning is the meantone tuning advocated by Charles Lucy, with a fifth of precisely 600 + 300/π = 695.493 cents. This is close to the 88edo fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for mothra and eupterpe temperaments, providing a mothra generator, an approximate 8/7, of 200+100/π cents, which extends 5-limit meantone Lucy tuning to a version with a mothra (1/3 meantone fifth) generator. As a tuning for 5-limit meantone, it has the softer quality characteristic of the flatter fifth meantones between 50edo and 19edo. It has a major third of 1200/π cents, or 1/π of an octave, 381.972 cents, 4.342 cents flat of 5/4, but 2.827 cents sharp of 1/3-comma meantone's major third.
A reasonable mapping for 11-limit extended Lucy tuning would be
- ⟨1200 1800+300/π 2400+1200/π 3400-100/π 4400-800/π]
This tempers out the mothra commas of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending Lucy tuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/π, a mere 0.659 cents flat of a just 7/4. Another way to extend Lucy tuning is meanpop:
- ⟨1200 1800+300/π 2400+1200/π 2400+3000/π 5400-3900/π]
Since this does not involve splitting the generator into thirds, it is closer to Lucy's 5-limit perspective.