Lucy tuning: Difference between revisions
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'''Lucy tuning''' is the [[meantone]] tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[ | '''Lucy tuning''' is the [[meantone]] tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[cent]]s. This is close to the [[88edo]] fifth of 695.455 [[cent]]s, and shares its general characteristics such as being a good tuning for [[meantone family|mothra]] and [[Didymus rank three family|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 syntonic comma meantone|1/3-comma meantone]]'s major third. | ||
A reasonable mapping for [[11-limit]] extended Lucy tuning would be | A reasonable mapping for [[11-limit]] extended Lucy tuning would be | ||
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: {{val|1200 1800+300/π 2400+1200/π 3400-100/π 4400-800/π}} | : {{val|1200 1800+300/π 2400+1200/π 3400-100/π 4400-800/π}} | ||
This tempers out the mothra [[ | This tempers out the mothra [[comma]]s 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 [[7/4|just 7/4]]. Another way to extend Lucy tuning is meanpop: | ||
: {{val|1200 1800+300/π 2400+1200/π 2400+3000/π 5400-3900/π}} | : {{val|1200 1800+300/π 2400+1200/π 2400+3000/π 5400-3900/π}} | ||
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[[Category:Mothra]] | [[Category:Mothra]] | ||
[[Category:Transcendental]] | [[Category:Transcendental]] | ||
[[Category:Historical]] | |||
Revision as of 01:47, 27 April 2023
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.