User:Moremajorthanmajor/8wtn - Revision history

Sintel: Sintel moved page 8wtn to User:Moremajorthanmajor/8wtn

2025-03-31T17:16:08Z

Sintel moved page 8wtn to User:Moremajorthanmajor/8wtn

← Older revision	Revision as of 17:16, 31 March 2025
(No difference)

Moremajorthanmajor: /* Patent Intervals[1] */

2022-10-22T23:04:32Z

Patent Intervals[1]

← Older revision		Revision as of 23:04, 22 October 2022
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	\|-		\|-
	\| 2		\| 2
	\| ~~[[Tel:~~350.9775~~\|350.9775]]~~		\| 350.9775
	\| 342.857		\| 342.857
	\|-		\|-

Moremajorthanmajor: /* Patent Intervals[1] */

2022-10-22T23:03:47Z

Patent Intervals[1]

← Older revision		Revision as of 23:03, 22 October 2022
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	\|		\|
	! Optimal<ref>[[4 EDF]] + 3ED(4/3)</ref>		! Optimal<ref>[[4 EDF]] + 3ED(4/3)</ref>
	! Alternating EDO and *ed(9/8)<ref>[[7 EDO]] + ~~1ED(~~9/8)</ref>		! Alternating EDO and *ed(9/8)<ref>[[7 EDO]] + 9/8</ref>
	\|-		\|-
	\| 1		\| 1
Line 13:		Line 13:
	\|-		\|-
	\| 2		\| 2
	\| 350.9775		\| [[Tel:350.9775\|350.9775]]
	\| 342.857		\| 342.857
	\|-		\|-

Xenwolf: link 4EDF and 7EDO

2021-06-13T10:15:35Z

link 4EDF and 7EDO

← Older revision		Revision as of 10:15, 13 June 2021
Line 5:		Line 5:
	{\| class="wikitable"		{\| class="wikitable"
	\|		\|
	! Optimal<ref>~~4EDF~~ + 3ED(4/3)</ref>		! Optimal<ref>[[4 EDF]] + 3ED(4/3)</ref>
	! Alternating EDO and *ed(9/8)<ref>~~7EDO~~ + 1ED(9/8)</ref>		! Alternating EDO and *ed(9/8)<ref>[[7 EDO]] + 1ED(9/8)</ref>
	\|-		\|-
	\| 1		\| 1

Xenwolf: /* Patent IntervalsWT Approach by J. Ruhf */

2021-06-13T10:11:02Z

Patent IntervalsWT Approach by J. Ruhf

← Older revision		Revision as of 10:11, 13 June 2021
Line 1:		Line 1:
	'''8WTN''' is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent]]s each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.		'''8WTN''' is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent]]s each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.

	== Patent Intervals<ref>WT ~~Approach~~ by J. Ruhf</ref> ==		== Patent Intervals<ref>a WT approach by J. Ruhf</ref> ==

	{\| class="wikitable"		{\| class="wikitable"

Xenwolf: WT decoded

2021-06-13T10:10:30Z

WT decoded

← Older revision		Revision as of 10:10, 13 June 2021
Line 1:		Line 1:
	'''8WTN''' is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent~~\|cents~~]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.		'''8WTN''' is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent]]s each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.

			== Patent Intervals<ref>WT Approach by J. Ruhf</ref> ==

	~~== Patent Intervals ==~~
	{\| class="wikitable"		{\| class="wikitable"
	\|		\|
	!Optimal		! Optimal<ref>4EDF + 3ED(4/3)</ref>
	!Alternating [[EDO~~\|edo]]~~ and *ed(9/8)		! Alternating EDO and *ed(9/8)<ref>7EDO + 1ED(9/8)</ref>
	\|-		\|-
	\|1		\| 1
	\|175.48875		\| 175.48875
	\|171.429		\| 171.429
	\|-		\|-
	\|2		\| 2
	\|350.9775		\| 350.9775
	\|342.857		\| 342.857
	\|-		\|-
	\|3		\| 3
	\|526.46625		\| 526.46625
	\|514.286		\| 514.286
	\|-		\|-
	\|4		\| 4
	\|701.955		\| 701.955
	\|685.714		\| 685.714
	\|-		\|-
	\|5		\| 5
	\|867.97		\| 867.97
	\|857.143		\| 857.143
	\|-		\|-
	\|6		\| 6
	\|1032.985		\| 1032.985
	\|1028.571		\| 1028.571
	\|-		\|-
	!7		\| 7
	! colspan="2" \|1200		\| colspan="2" style="text-align:center" \| 1200
	\|-		\|-
	\|8		\| 8
	\|1366.015		\| 1366.015
	\|1403.91		\| 1403.91
	\|}		\|}

			<references/>

	[[Category:Well tempered nonet]]		[[Category:Well tempered nonet]]

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

Xenwolf: cat+todo

2021-06-02T06:56:43Z

cat+todo

← Older revision		Revision as of 06:56, 2 June 2021
Line 38:		Line 38:
	\|1403.91		\|1403.91
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 01:13, 2 June 2021

2021-06-02T01:13:16Z

← Older revision		Revision as of 01:13, 2 June 2021
Line 1:		Line 1:
	8WTN is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent\|cents]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.		'''8WTN''' is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent\|cents]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.

	== ~~Optimal~~ Intervals ==		== Patent Intervals ==
	{\| class="wikitable"		{\| class="wikitable"
			\|
			!Optimal
			!Alternating [[EDO\|edo]] and *ed(9/8)
	\|-		\|-
	\|1		\|1
	\|175.48875		\|175.48875
			\|171.429
	\|-		\|-
	\|2		\|2
	\|350.9775		\|350.9775
			\|342.857
	\|-		\|-
	\|3		\|3
	\|526.46625		\|526.46625
			\|514.286
	\|-		\|-
	\|4		\|4
	\|701.955		\|701.955
			\|685.714
	\|-		\|-
	\|5		\|5
	\|867.97		\|867.97
			\|857.143
	\|-		\|-
	\|6		\|6
	\|1032.985		\|1032.985
			\|1028.571
	\|-		\|-
	\|7		!7
	\|1200		! colspan="2" \|1200
	\|-		\|-
	\|8		\|8
	\|1366.015		\|1366.015
			\|1403.91
	\|}		\|}

Moremajorthanmajor at 23:51, 1 June 2021

2021-06-01T23:51:07Z

← Older revision		Revision as of 23:51, 1 June 2021
Line 1:		Line 1:
	8WTN is the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent\|cents]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.		8WTN is optimally the [[EDF\|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent\|cents]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family\|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.

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

Moremajorthanmajor at 01:19, 1 June 2021

2021-06-01T01:19:00Z

← Older revision		Revision as of 01:19, 1 June 2021
Line 3:		Line 3:
	== Optimal Intervals ==		== Optimal Intervals ==
	{\| class="wikitable"		{\| class="wikitable"
	!
	~~!Target Minimum~~
	~~!Target Maximum~~
	\|-		\|-
	!1		\|1
	~~! colspan="2"~~ \|175.48875		\|175.48875
	\|-		\|-
	!2		\|2
	~~! colspan="2"~~ \|350.9775		\|350.9775
	\|-		\|-
	!3		\|3
	~~! colspan="2"~~ \|526.46625		\|526.46625
	\|-		\|-
	!4		\|4
	~~! colspan="2"~~ \|701.955		\|701.955
	\|-		\|-
	!5		\|5
	~~! colspan="2"~~ \|867.97		\|867.97
	\|-		\|-
	!6		\|6
	~~! colspan="2"~~ \|1032.985		\|1032.985
	\|-		\|-
	!7		\|7
	~~! colspan="2"~~ \|1200		\|1200
	\|-		\|-
	\|8		\|8
	\|~~1350~~		\|1366.015
	~~\|1400~~
	\|}		\|}