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 [[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-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 (in fact, this corresponds to approximating π as 22/7), and shares its general characteristics such as being a good tuning for [[mothra]] and [[euterpe]] 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

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 {{interwiki
 | de = Lucy-Stimmung
-}}
+}}{{Novelty}}
 <math>
 \def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}
 </math>
-'''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-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 (in fact, this corresponds to approximating π as 22/7), and shares its general characteristics such as being a good tuning for [[mothra]] and [[euterpe]] 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