User:Moremajorthanmajor/22wtn - Revision history

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

2025-09-01T09:31:21Z

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

← Older revision		Revision as of 09:31, 1 September 2025
Line 132:		Line 132:

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

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

Sintel: Sintel moved page 22wtn to User:Moremajorthanmajor/22wtn

2025-03-31T17:18:12Z

Sintel moved page 22wtn to User:Moremajorthanmajor/22wtn

← Older revision	Revision as of 17:18, 31 March 2025
(No difference)

Moremajorthanmajor at 02:57, 3 June 2021

2021-06-03T02:57:29Z

← Older revision		Revision as of 02:57, 3 June 2021
Line 7:		Line 7:
	!Target a		!Target a
	!Target b		!Target b
	!Alternating edo and *ed(9/8) a		!Alternating [[edo]] and *ed(9/8) a
	!Alternating edo and *ed(9/8) b		!Alternating edo and *ed(9/8) b
	\|-		\|-

Moremajorthanmajor at 20:20, 2 June 2021

2021-06-02T20:20:11Z

← Older revision		Revision as of 20:20, 2 June 2021
Line 1:		Line 1:
	A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	==~~Optimal~~ Intervals==		==Patent Intervals==
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
Line 7:		Line 7:
	!Target a		!Target a
	!Target b		!Target b
			!Alternating edo and *ed(9/8) a
			!Alternating edo and *ed(9/8) b
	\|-		\|-
	!1		\|1
	! colspan="2" \|63.8141		! colspan="2" \|63.8141
			\|66.667
			\|63.1579
	\|-		\|-
	!2		\|2
	! colspan="2" \|127.6282		! colspan="2" \|127.6282
			\|133.333
			\|126.3157
	\|-		\|-
	!3		\|3
	! colspan="2" \|191.4423		! colspan="2" \|191.4423
			\|200.000
			\|189.4737
	\|-		\|-
	!4		\|4
	! colspan="2" \|255.2564		! colspan="2" \|255.2564
			\|266.667
			\|252.6316
	\|-		\|-
	!5		\|5
	! colspan="2" \|319.07045		! colspan="2" \|319.07045
			\|333.333
			\|315.7895
	\|-		\|-
	!6		\|6
	! colspan="2" \|382.88455		! colspan="2" \|382.88455
			\|400.000
			\|378.9474
	\|-		\|-
	!7		\|7
	! colspan="2" \|446.6986		! colspan="2" \|446.6986
			\|466.667
			\|442.1053
	\|-		\|-
	!8		\|8
	! colspan="2" \|510.5127		! colspan="2" \|510.5127
			\|533.333
			\|505.2632
	\|-		\|-
	!9		\|9
	! colspan="2" \|574.3268		! colspan="2" \|574.3268
			\|600.000
			\|568.42105
	\|-		\|-
	!10		\|10
	! colspan="2" \|638.1409		! colspan="2" \|638.1409
			\|666.667
			\|631.57895
	\|-		\|-
	!11		\|11
	! colspan="2" \|701.955		! colspan="2" \|701.955
			\|733.333
			\|694.7368
	\|-		\|-
	\|12		\|12
	\|773.1043		\|773.1043
	\|764.2106		\|764.2106
			\|800.000
			\|757.8947
	\|-		\|-
	\|13		\|13
	\|844.2536		\|844.2536
	\|826.466		\|826.466
			\|866.667
			\|821.0526
	\|-		\|-
	\|14		\|14
	\|915.4029		\|915.4029
	\|888.7219		\|888.7219
			\|933.333
			\|884.2105
	\|-		\|-
	\|15		\|15
	\|986.5522		\|986.5522
	\|950.9775		\|950.9775
			\|1000.000
			\|947.3684
	\|-		\|-
	\|16		\|16
	\|1057.7014		\|1057.7014
	\|1013.2331		\|1013.2331
			\|1066.667
			\|1010.5263
	\|-		\|-
	\|17		\|17
	\|1128.8507		\|1128.8507
	\|1075.48875		\|1075.48875
			\|1133.333
			\|1073.6843
	\|-		\|-
	\|18		\|18
	\|1200		\|1200
	\|1137.7444		\|1137.7444
			\|1200.000
			\|1136.8421
	\|-		\|-
	\|19		\|19
	\|1271.1493		\|1271.1493
	\|1200		\|1200
			\|1250.9775
			\|1200.000
	\|-		\|-
	\|20		\|20
	\|1342.2986		\|1342.2986
	\|1262.2556		\|1262.2556
			\|1301.955
			\|1267.97
	\|-		\|-
	\|21		\|21
	\|1413.4479		\|1413.4479
	\|1324.511		\|1324.511
			\|1352.9325
			\|1333.94
	\|-		\|-
	\|22		\|22
	\|1484.5971		\|1484.5971
	\|1386.7669		\|1386.7669
			! colspan="2" \|1403.91
	\|}		\|}

Xenwolf: cat+todo

2021-06-02T06:58:59Z

cat+todo

← Older revision		Revision as of 06:58, 2 June 2021
Line 85:		Line 85:
	\|1386.7669		\|1386.7669
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 00:00, 2 June 2021

2021-06-02T00:00:58Z

← Older revision		Revision as of 00:00, 2 June 2021
Line 1:		Line 1:
	A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

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

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T02:11:02Z

Optimal Intervals

← Older revision		Revision as of 02:11, 1 June 2021
Line 5:		Line 5:
	\|+		\|+
	!		!
	!Target ~~Minimum~~ a		!Target a
	!Target ~~Maximum a~~		!Target b
	~~!Target Minimum b~~
	~~!Target Maximum~~ b
	\|-		\|-
	!1		!1
	! colspan="4" \|63.8141		! colspan="2" \|63.8141
	\|-		\|-
	!2		!2
	! colspan="4" \|127.6282		! colspan="2" \|127.6282
	\|-		\|-
	!3		!3
	! colspan="4" \|191.4423		! colspan="2" \|191.4423
	\|-		\|-
	!4		!4
	! colspan="4" \|255.2564		! colspan="2" \|255.2564
	\|-		\|-
	!5		!5
	! colspan="4" \|319.07045		! colspan="2" \|319.07045
	\|-		\|-
	!6		!6
	! colspan="4" \|382.88455		! colspan="2" \|382.88455
	\|-		\|-
	!7		!7
	! colspan="4" \|446.6986		! colspan="2" \|446.6986
	\|-		\|-
	!8		!8
	! colspan="4" \|510.5127		! colspan="2" \|510.5127
	\|-		\|-
	!9		!9
	! colspan="4" \|574.3268		! colspan="2" \|574.3268
	\|-		\|-
	!10		!10
	! colspan="4" \|638.1409		! colspan="2" \|638.1409
	\|-		\|-
	!11		!11
	! colspan="4" \|701.955		! colspan="2" \|701.955
	\|-		\|-
	!12		\|12
	~~! colspan="2"~~ \|773.~~104~~		\|773.1043
	~~! colspan="2"~~ \|764.~~511~~		\|764.2106
	\|-		\|-
	!13		\|13
	~~! colspan="2"~~ \|844.~~253~~		\|844.2536
	~~! colspan="2"~~ \|826.~~0675~~		\|826.466
	\|-		\|-
	!14		\|14
	~~! colspan="2"~~ \|915.~~403~~		\|915.4029
	~~! colspan="2"~~ \|888.~~722~~		\|888.7219
	\|-		\|-
	!15		\|15
	~~! colspan="2"~~ \|986.~~552~~		\|986.5522
	~~! colspan="2"~~ \|950.9775		\|950.9775
	\|-		\|-
	!16		\|16
	~~! colspan="2"~~ \|1057.~~701~~		\|1057.7014
	~~! colspan="2"~~ \|~~1012~~.~~233~~		\|1013.2331
	\|-		\|-
	!17		\|17
	~~! colspan="2"~~ \|1128.~~896~~		\|1128.8507
	~~! colspan="2"~~ \|1075.~~489~~		\|1075.48875
	\|-		\|-
	!18		\|18
	~~! colspan="2"~~ \|1200		\|1200
	~~! colspan="2"~~ \|1137.~~744~~		\|1137.7444
	\|-		\|-
	\|19		\|19
	\|~~1254~~.~~54545~~		\|1271.1493
	~~\|1272.7273~~		\|1200
	~~! colspan="2"~~ \|1200
	\|-		\|-
	\|20		\|20
	\|~~1309~~.~~0909~~		\|1342.2986
	\|~~1345~~.~~45455~~		\|1262.2556
	~~\|1254.54545~~
	~~\|1272.7273~~
	\|-		\|-
	\|21		\|21
	\|~~1363~~.~~6364~~		\|1413.4479
	\|~~1418~~.~~1818~~		\|1324.511
	~~\|1309.0909~~
	~~\|1345.45455~~
	\|-		\|-
	\|22		\|22
	\|~~1418~~.~~1818~~		\|1484.5971
	\|~~1490~~.~~9091~~		\|1386.7669
	~~\|1363.6364~~
	~~\|1418.1818~~
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T01:15:58Z

Optimal Intervals

← Older revision		Revision as of 01:15, 1 June 2021
Line 5:		Line 5:
	\|+		\|+
	!		!
	!Minimum a		!Target Minimum a
	!Maximum a		!Target Maximum a
	!Minimum b		!Target Minimum b
	!Maximum b		!Target Maximum b
	\|-		\|-
	!1		!1
Line 43:		Line 43:
	! colspan="4" \|701.955		! colspan="4" \|701.955
	\|-		\|-
	\|12		!12
	\|~~770.5264~~		! colspan="2" \|773.104
	~~\|775.4244~~		! colspan="2" \|764.511
	~~\|761~~.~~955~~
	\|~~766~~.~~2407~~
	\|-		\|-
	\|13		!13
	\|~~839.0979~~		! colspan="2" \|844.253
	~~\|848.8938~~		! colspan="2" \|826.0675
	~~\|821~~.~~955~~
	\|~~830~~.~~5264~~
	\|-		\|-
	\|14		!14
	\|~~907.6692~~		! colspan="2" \|915.403
	~~\|921.3632~~		! colspan="2" \|888.722
	~~\|881~~.~~955~~
	\|~~894~~.~~8121~~
	\|-		\|-
	\|15		!15
	\|~~976.2407~~		! colspan="2" \|986.552
	~~\|995.83255~~		! colspan="2" \|950.9775
	~~\|941~~.~~955~~
	\|~~959~~.~~0979~~
	\|-		\|-
	\|16		!16
	\|~~1044.8121~~		! colspan="2" \|1057.701
	~~\|1069.3019~~		! colspan="2" \|1012.233
	~~\|1001~~.~~955~~
	\|~~1023~~.~~3836~~
	\|-		\|-
	\|17		!17
	\|~~1113.3836~~		! colspan="2" \|1128.896
	~~\|1142.7713~~		! colspan="2" \|1075.489
	~~\|1061~~.~~955~~
	\|~~1087~~.~~6693~~
	\|-		\|-
	\|18		!18
	\|~~1181.955~~		! colspan="2" \|1200
	~~\|1216.2407~~		! colspan="2" \|1137.744
	~~\|1121.955~~
	\|~~1151~~.~~955~~
	\|-		\|-
	\|19		\|19
	\|~~1250~~.~~5264~~		\|1254.54545
	\|~~1289~~.~~7101~~		\|1272.7273
	\|~~1181.955~~		! colspan="2" \|1200
	~~\|1216.2407~~
	\|-		\|-
	\|20		\|20
	\|~~1319~~.~~0979~~		\|1309.0909
	\|~~1363~~.~~1795~~		\|1345.45455
	\|~~1241~~.~~955~~		\|1254.54545
	\|~~1280~~.~~5264~~		\|1272.7273
	\|-		\|-
	\|21		\|21
	\|~~1387~~.~~6692~~		\|1363.6364
	\|~~1436~~.~~6489~~		\|1418.1818
	\|~~1301~~.~~955~~		\|1309.0909
	\|~~1344~~.~~8121~~		\|1345.45455
	\|-		\|-
	\|22		\|22
	\|~~1456~~.~~2407~~		\|1418.1818
	\|~~1510~~.~~1183~~		\|1490.9091
	\|~~1361~~.~~955~~		\|1363.6364
	\|~~1409~~.~~0907~~		\|1418.1818
	\|}		\|}

Moremajorthanmajor at 18:23, 31 May 2021

2021-05-31T18:23:26Z

← Older revision		Revision as of 18:23, 31 May 2021
Line 1:		Line 1:
	A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. ~~It alternates~~ [[EDF\|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

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

Moremajorthanmajor at 02:15, 31 May 2021

2021-05-31T02:15:11Z

← Older revision		Revision as of 02:15, 31 May 2021
Line 77:		Line 77:
	\|1142.7713		\|1142.7713
	\|1061.955		\|1061.955
	\|1087.~~6692~~		\|1087.6693
	\|-		\|-
	\|18		\|18