User:Moremajorthanmajor/6wtn - Revision history

FloraC: Text replacement - "{{todo|clarify|unify precision|inline=1}}" to ""

2025-09-01T09:31:42Z

Text replacement - "{{todo|clarify|unify precision|inline=1}}" to ""

← Older revision		Revision as of 09:31, 1 September 2025
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	[[Category:Well tempered nonet]]		[[Category:Well tempered nonet]]

	~~{{todo\|clarify\|unify precision\|inline=1}}~~

Sintel: Sintel moved page 6wtn to User:Moremajorthanmajor/6wtn

2025-03-31T17:15:50Z

Sintel moved page 6wtn to User:Moremajorthanmajor/6wtn

← Older revision	Revision as of 17:15, 31 March 2025
(No difference)

Xenwolf: cat+todo

2021-06-02T06:56:20Z

cat+todo

← Older revision		Revision as of 06:56, 2 June 2021
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	\|1403.91		\|1403.91
	\|}		\|}

			[[Category:Well tempered nonet]]

			{{todo\|clarify\|unify precision\|inline=1}}

Moremajorthanmajor at 00:40, 2 June 2021

2021-06-02T00:40:18Z

← Older revision		Revision as of 00:40, 2 June 2021
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	'''6WTN''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio, alternating these with three equal steps of another interval between 200 and 266.667 cents in its patent tunings. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].		'''6WTN''', if the attempt is made to use it as an actual scale, would optimally divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio, alternating these with three equal steps of another interval between 200 and 266.667 cents in its patent tunings. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].

	==~~Optimal~~ Intervals==		==Patent Intervals==
	{\| class="wikitable"		{\| class="wikitable"
			!
			!Optimal
			!Alternating [[EDO\|edo]] and *ed(9/8)
	\|-		\|-
	\|1		\|1
	\|233.985		\|233.985
			\|240
	\|-		\|-
	\|2		\|2
	\|467.97		\|467.97
			\|480
	\|-		\|-
	\|3		\|3
	\|701.955		\|701.955
			\|720
	\|-		\|-
	\|4		\|4
	\|950.9775		\|950.9775
			\|960
	\|-		\|-
	\|5		!5
	\|1200		! colspan="2" \|1200
	\|-		\|-
	\|6		\|6
	\|1449.0225		\|1449.0225
			\|1403.91
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T01:17:29Z

Optimal Intervals

← Older revision		Revision as of 01:17, 1 June 2021
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	==Optimal Intervals==		==Optimal Intervals==
	{\| class="wikitable"		{\| class="wikitable"
	!
	~~!Target Minimum~~
	~~!Target Minimum~~
	\|-		\|-
	!1		\|1
	~~! colspan="2"~~ \|233.985		\|233.985
	\|-		\|-
	!2		\|2
	~~! colspan="2"~~ \|467.97		\|467.97
	\|-		\|-
	!3		\|3
	~~! colspan="2"~~ \|701.955		\|701.955
	\|-		\|-
	!4		\|4
	~~! colspan="2"~~ \|950.9775		\|950.9775
	\|-		\|-
	!5		\|5
	~~! colspan="2"~~ \|1200		\|1200
	\|-		\|-
	\|6		\|6
	\|~~1400~~		\|1449.0225
	~~\|1466~~.~~667~~
	\|}		\|}

Moremajorthanmajor at 23:37, 31 May 2021

2021-05-31T23:37:41Z

← Older revision		Revision as of 23:37, 31 May 2021
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	{\| class="wikitable"		{\| class="wikitable"
	!		!
	~~!Minimum~~
	~~!Maximum~~
	!Target Minimum		!Target Minimum
	!Target Minimum		!Target Minimum
	\|-		\|-
	!1		!1
	! colspan="4" \|233.985		! colspan="2" \|233.985
	\|-		\|-
	!2		!2
	! colspan="4" \|467.97		! colspan="2" \|467.97
	\|-		\|-
	!3		!3
	! colspan="4" \|701.955		! colspan="2" \|701.955
	\|-		\|-
	\|4		!4
	~~\|941.955~~
	~~\|959.098~~
	! colspan="2" \|950.9775		! colspan="2" \|950.9775
	\|-		\|-
	\|5		!5
	~~\|1181.955~~
	~~\|1216.241~~
	! colspan="2" \|1200		! colspan="2" \|1200
	\|-		\|-
	\|6		\|6
	~~\|1421.955~~
	~~\|1473.384~~
	\|1400		\|1400
	\|1466.667		\|1466.667
	\|}		\|}

Moremajorthanmajor at 23:21, 31 May 2021

2021-05-31T23:21:19Z

← Older revision		Revision as of 23:21, 31 May 2021
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	!Minimum		!Minimum
	!Maximum		!Maximum
	!~~[3\5 249.0225¢]~~		!Target Minimum
			!Target Minimum
	\|-		\|-
	!1		!1
	! colspan="3" \|233.985		! colspan="4" \|233.985
	\|-		\|-
	!2		!2
	! colspan="3" \|467.97		! colspan="4" \|467.97
	\|-		\|-
	!3		!3
	! colspan="3" \|701.955		! colspan="4" \|701.955
	\|-		\|-
	\|4		\|4
	\|941.955		\|941.955
	\|959.098		\|959.098
	\|950.9775		! colspan="2" \|950.9775
	\|-		\|-
	\|5		\|5
	\|1181.955		\|1181.955
	\|1216.241		\|1216.241
	\|1200		! colspan="2" \|1200
	\|-		\|-
	\|6		\|6
	\|1421.955		\|1421.955
	\|1473.384		\|1473.384
	\|~~1421~~.~~955~~		\|1400
			\|1466.667
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-05-31T20:35:19Z

Optimal Intervals

← Older revision		Revision as of 20:35, 31 May 2021
Line 6:		Line 6:
	!Minimum		!Minimum
	!Maximum		!Maximum
			![3\5 249.0225¢]
	\|-		\|-
	!1		!1
	! colspan="2" \|233.985		! colspan="3" \|233.985
	\|-		\|-
	!2		!2
	! colspan="2" \|467.97		! colspan="3" \|467.97
	\|-		\|-
	!3		!3
	! colspan="2" \|701.955		! colspan="3" \|701.955
	\|-		\|-
	\|4		\|4
	\|941.955		\|941.955
	\|959.098		\|959.098
			\|950.9775
	\|-		\|-
	\|5		\|5
	\|1181.955		\|1181.955
	\|1216.241		\|1216.241
			\|1200
	\|-		\|-
	\|6		\|6
	\|1421.955		\|1421.955
	\|1473.384		\|1473.384
			\|1421.955
	\|}		\|}

Moremajorthanmajor at 17:50, 31 May 2021

2021-05-31T17:50:34Z

← Older revision		Revision as of 17:50, 31 May 2021
Line 1:		Line 1:
	'''6WTN''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio, alternating these with three equal steps of another interval between 200 and 266.667 cents. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].		'''6WTN''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio, alternating these with three equal steps of another interval between 200 and 266.667 cents in its patent tunings. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].

	==Optimal Intervals==		==Optimal Intervals==

Moremajorthanmajor: /* Factoids about 6WTN */

2021-05-30T06:26:38Z

Factoids about 6WTN

← Older revision		Revision as of 06:26, 30 May 2021
Line 1:		Line 1:
	'''6WTN''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio, alternating these with three equal steps of another interval between 200 and 266.667 cents. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].		'''6WTN''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio, alternating these with three equal steps of another interval between 200 and 266.667 cents. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].

	~~==Factoids about 6WTN==~~
	~~The best tunings of 6WTN are related to the [[Gamelismic clan\|gamelismic temperaments]], which temper out 1029/1024 in the 7-limit.~~
	==Optimal Intervals==		==Optimal Intervals==
	{\| class="wikitable"		{\| class="wikitable"