Lucy tuning - Revision history

Overthink: one way to derive 88edo

2026-05-24T01:07:17Z

one way to derive 88edo

← Older revision		Revision as of 01:07, 24 May 2026
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	\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}		\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}
	</math>		</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 [[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.		'''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		A reasonable mapping for [[11-limit]] extended Lucy tuning would be

FloraC: Fix linking

2025-08-27T13:02:20Z

Fix linking

← Older revision		Revision as of 13:02, 27 August 2025
Line 6:		Line 6:
	\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}		\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}
	</math>		</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.		'''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 [[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		A reasonable mapping for [[11-limit]] extended Lucy tuning would be

Hkm: novelty

2025-05-29T02:58:43Z

novelty

← Older revision		Revision as of 02:58, 29 May 2025
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	{{interwiki		{{interwiki
	\| de = Lucy-Stimmung		\| de = Lucy-Stimmung
	}}		}}{{Novelty}}

	<math>		<math>
	\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}		\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}

Lériendil: fixed temp links

2025-03-26T13:30:30Z

fixed temp links

← Older revision		Revision as of 13:30, 26 March 2025
Line 5:		Line 5:
	\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}		\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}
	</math>		</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, 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]] extended Lucy tuning would be		A reasonable mapping for [[11-limit]] extended Lucy tuning would be

Fredg999: External link

2024-07-01T01:37:10Z

External link

← Older revision		Revision as of 01:37, 1 July 2024
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	* [http://www.lucytune.com Official website]		* [http://www.lucytune.com Official website]
	* [http://www.myspace.com/lucytuning Myspace profile]		* [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]]

	[[Category:Lucy tuning\| ]] <!-- main article -->		[[Category:Lucy tuning\| ]] <!-- main article -->

ArrowHead294 at 12:55, 20 June 2024

2024-06-20T12:55:14Z

← Older revision		Revision as of 12:55, 20 June 2024
Line 2:		Line 2:
	\| de = Lucy-Stimmung		\| de = Lucy-Stimmung
	}}		}}
			<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, 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.

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

	: {~~{val\|~~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]]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}}		: <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.

Yourmusic Productions: Bypass redirect

2023-11-19T16:55:53Z

Bypass redirect

← Older revision		Revision as of 16:55, 19 November 2023
Line 2:		Line 2:
	\| de = Lucy-Stimmung		\| de = Lucy-Stimmung
	}}		}}
	'''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.		'''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.

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

BudjarnLambeth: Added category "historical"

2023-04-27T01:47:49Z

Added category "historical"

← Older revision		Revision as of 01:47, 27 April 2023
Line 2:		Line 2:
	\| de = Lucy-Stimmung		\| 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		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}}		: {{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}}		: {{val\|1200 1800+300/π 2400+1200/π 2400+3000/π 5400-3900/π}}
Line 24:		Line 24:
	[[Category:Mothra]]		[[Category:Mothra]]
	[[Category:Transcendental]]		[[Category:Transcendental]]
			[[Category:Historical]]

Fredg999: Categories, markup, used interwiki template

2021-08-30T15:14:13Z

Categories, markup, used interwiki template

← Older revision		Revision as of 15:14, 30 August 2021
Line 1:		Line 1:
	[[de:Lucy-Stimmung]]		{{interwiki
			\| 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\|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

	~~<~~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 [[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\|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:

	~~<~~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}}

	~~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]

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

	* [http://www.~~myspace~~.com~~/lucytuning~~ http://www.myspace.com/lucytuning]		== External links ==
			* [http://www.lucytune.com Official website]
			* [http://www.myspace.com/lucytuning Myspace profile]

			[[Category:Lucy tuning\| ]] <!-- main article -->
	[[Category:Listen]]		[[Category:Listen]]
	~~[[Category:Lucy]]~~
	~~[[Category:Lucytuning]]~~
	[[Category:Meanpop]]		[[Category:Meanpop]]
	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Mothra]]		[[Category:Mothra]]
	[[Category:Transcendental]]		[[Category:Transcendental]]

Xenwolf: Xenwolf moved page Lucy Tuning to Lucy tuning: Rule: only first letter capitalized. Reason: less typing when referenced

2020-06-08T11:57:04Z

Xenwolf moved page Lucy Tuning to Lucy tuning: Rule: only first letter capitalized. Reason: less typing when referenced

← Older revision	Revision as of 11:57, 8 June 2020
(No difference)