Lucy tuning: Difference between revisions

Line 2:

| de = Lucy-Stimmung

}}

'''Lucy tuning''' is the [[meantone]] tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[~~cent|~~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.

'''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

Line 8:

: {{val|1200 1800+300/π 2400+1200/π 3400-100/π 4400-800/π}}

This tempers out the mothra [[~~Comma|~~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:

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}}

Line 24:

[[Category:Mothra]]

[[Category:Transcendental]]

[[Category:Historical]]

@@ Line 2: / Line 2: @@
 | de = Lucy-Stimmung
 }}
-'''Lucy tuning''' is the [[meantone]] tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[cent|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.
+'''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
@@ Line 8: / Line 8: @@
 : {{val|1200 1800+300/π 2400+1200/π 3400-100/π 4400-800/π}}
-This tempers out the mothra [[Comma|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:
+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}}
@@ Line 24: / Line 24: @@
 [[Category:Mothra]]
 [[Category:Transcendental]]
+[[Category:Historical]]