Lucy tuning: Difference between revisions

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[[de:Lucy-Stimmung]]

{{interwiki

| de = Lucy-Stimmung

}}{{Novelty}}

~~LucyTuning~~ is the meantone tuning advocated by [[~~Charles_Lucy|~~Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[~~cent|~~cent]]s. This is close to the [[~~88edo|~~88edo]] fifth of 695.455 ~~cents~~, 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|~~8/7]], of 200+100/π cents, which extends [[~~5-limit|~~5-limit]] meantone ~~LucyTuning~~ 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|~~50edo]] and [[~~19edo|~~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|~~5/4]], but 2.827 cents sharp of [[~~1-3_Syntonic_Comma_Meantone|~~1/3-comma meantone]]'s major third.

<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 [[Gamelismic clan#Mothra|mothra]] and [[Didymus rank three family#Euterpe|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|~~11-limit]] extended ~~LucyTuning~~ would be

A reasonable mapping for [[11-limit]] extended Lucy tuning would be

&~~lt;1200~~ 1800+300/π 2400+1200/π 3400-100/π 4400-800/π|

: <math>\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 3400 - \frac{100}{π} & 4400 - \frac{800}{π}}</math>

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 ~~LucyTuning~~, 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 ~~LucyTuning~~ 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:

&~~lt;1200~~ 1800+300/π 2400+1200/π 2400+3000/π 5400-3900/π|

: <math>\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 2400 + \frac{3000}{π} & 5400 - \frac{3900}{π}}</math>

Since this does not involve splitting the generator into thirds it is closer to Lucy's 5-limit perspective.

Since this does not involve splitting the generator into thirds, it is closer to Lucy's 5-limit perspective.

[http://www.lucytune.com ~~Link to Lucy Tuning~~ website]

== External links ==

* [http://www.lucytune.com Official website]

* [http://www.myspace.com/lucytuning Myspace profile]

* [http://tonalsoft.com/enc/l/lucy-tuning.aspx LucyTuning and 88-ed2 / 88-edo / 88-ET / 88-tone equal-temperament, and 3/10-comma meantone] on [[Tonalsoft Encyclopedia]]

~~=Music=~~

[[Category:Lucy tuning| ]]

~~[http://www.myspace.com/lucytuning http://www.myspace.com/lucytuning]~~ [[Category:~~listen~~]]

[[Category:Listen]]

[[Category:~~lucy~~]]

[[Category:Meanpop]]

[[Category:~~lucytuning~~]]

[[Category:Meantone]]

[[Category:~~meanpop~~]]

[[Category:Mothra]]

[[Category:~~meantone~~]]

[[Category:Transcendental]]

[[Category:~~mothra~~]]

[[Category:Historical]]

[[Category:~~transcendental~~]]

@@ Line 1: / Line 1: @@
-[[de:Lucy-Stimmung]]
+{{interwiki
+| de = Lucy-Stimmung
+}}{{Novelty}}
-LucyTuning is the meantone tuning advocated by [[Charles_Lucy|Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[cent|cent]]s. This is close to the [[88edo|88edo]] fifth of 695.455 cents, 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|8/7]], of 200+100/π cents, which extends [[5-limit|5-limit]] meantone LucyTuning 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|50edo]] and [[19edo|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|5/4]], but 2.827 cents sharp of [[1-3_Syntonic_Comma_Meantone|1/3-comma meantone]]'s major third.
+<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 [[Gamelismic clan#Mothra|mothra]] and [[Didymus rank three family#Euterpe|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|11-limit]] extended LucyTuning would be
+A reasonable mapping for [[11-limit]] extended Lucy tuning would be
-&lt;1200 1800+300/π 2400+1200/π 3400-100/π 4400-800/π|
+: <math>\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 3400 - \frac{100}{π} & 4400 - \frac{800}{π}}</math>
-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 LucyTuning, 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 LucyTuning 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:
-&lt;1200 1800+300/π 2400+1200/π 2400+3000/π 5400-3900/π|
+: <math>\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 2400 + \frac{3000}{π} & 5400 - \frac{3900}{π}}</math>
-Since this does not involve splitting the generator into thirds it is closer to Lucy's 5-limit perspective.
+Since this does not involve splitting the generator into thirds, it is closer to Lucy's 5-limit perspective.
-[http://www.lucytune.com Link to Lucy Tuning website]
+== External links ==
+* [http://www.lucytune.com Official website]
+* [http://www.myspace.com/lucytuning Myspace profile]
+* [http://tonalsoft.com/enc/l/lucy-tuning.aspx LucyTuning and 88-ed2 / 88-edo / 88-ET / 88-tone equal-temperament, and 3/10-comma meantone] on [[Tonalsoft Encyclopedia]]
-=Music=
+[[Category:Lucy tuning| ]] <!-- main article -->
-[http://www.myspace.com/lucytuning http://www.myspace.com/lucytuning]      [[Category:listen]]
+[[Category:Listen]]
-[[Category:lucy]]
+[[Category:Meanpop]]
-[[Category:lucytuning]]
+[[Category:Meantone]]
-[[Category:meanpop]]
+[[Category:Mothra]]
-[[Category:meantone]]
+[[Category:Transcendental]]
-[[Category:mothra]]
+[[Category:Historical]]
-[[Category:transcendental]]