User:Moremajorthanmajor/20wtn - Revision history

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

2025-09-01T09:31:47Z

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

← Older revision		Revision as of 09:31, 1 September 2025
Line 89:		Line 89:

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

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

Sintel: Sintel moved page 20wtn to User:Moremajorthanmajor/20wtn

2025-03-31T17:17:58Z

Sintel moved page 20wtn to User:Moremajorthanmajor/20wtn

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

Moremajorthanmajor: /* Patent Intervals */

2021-06-03T03:00:29Z

Patent Intervals

← Older revision		Revision as of 03:00, 3 June 2021
Line 73:		Line 73:
	\|-		\|-
	\|17		\|17
	~~\|1200~~		! colspan="2" \|1200
	\|1200
	\|-		\|-
	\|18		\|18

Moremajorthanmajor: /* Patent Intervals */

2021-06-02T19:18:33Z

Patent Intervals

← Older revision		Revision as of 19:18, 2 June 2021
Line 6:		Line 6:
	!		!
	!Target		!Target
	!Alternating edo and *ed(9/8)		!Alternating [[edo]] and *ed(9/8)
	\|-		\|-
	\|1		\|1

Moremajorthanmajor: /* Patent Intervals */

2021-06-02T16:55:44Z

Patent Intervals

← Older revision		Revision as of 16:55, 2 June 2021
Line 1:		Line 1:
	A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo~~]] and [[18edo~~]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	== Patent Intervals ==		== Patent Intervals ==
Line 5:		Line 5:
	\|+		\|+
	!		!
	!Target a		!Target
	~~!Target b~~		!Alternating edo and *ed(9/8)
	~~!Alternating edo and *ed(9/8) a~~
	!Alternating edo and *ed(9/8) b
	\|-		\|-
	\|1		\|1
	~~! colspan="2"~~ \|70.1955		\|70.1955
	\|70.588		\|70.588
	~~\|66.667~~
	\|-		\|-
	\|2		\|2
	~~! colspan="2"~~ \|140.391		\|140.391
	\|141.1765		\|141.1765
	~~\|133.333~~
	\|-		\|-
	\|3		\|3
	~~! colspan="2"~~ \|210.5865		\|210.5865
	\|211.765		\|211.765
	~~\|200.000~~
	\|-		\|-
	\|4		\|4
	~~! colspan="2"~~ \|280.782		\|280.782
	\|282.353		\|282.353
	~~\|266.667~~
	\|-		\|-
	\|5		\|5
	~~! colspan="2"~~ \|350.9775		\|350.9775
	\|352.941		\|352.941
	~~\|333.333~~
	\|-		\|-
	\|6		\|6
	~~! colspan="2"~~ \|421.173		\|421.173
	\|423.529		\|423.529
	~~\|400.000~~
	\|-		\|-
	\|7		\|7
	~~! colspan="2"~~ \|491.3685		\|491.3685
	\|494.118		\|494.118
	~~\|466.667~~
	\|-		\|-
	\|8		\|8
	~~! colspan="2"~~ \|561.564		\|561.564
	\|564.706		\|564.706
	~~\|533.333~~
	\|-		\|-
	\|9		\|9
	~~! colspan="2"~~ \|631.7595		\|631.7595
	\|635.294		\|635.294
	~~\|600.000~~
	\|-		\|-
	\|10		\|10
	~~! colspan="2"~~ \|701.955		\|701.955
	\|705.882		\|705.882
	~~\|666.667~~
	\|-		\|-
	\|11		\|11
	\|773.104		\|773.104
	~~\|764.211~~
	\|776.471		\|776.471
	~~\|733.333~~
	\|-		\|-
	\|12		\|12
	\|844.254		\|844.254
	~~\|826.466~~
	\|847.059		\|847.059
	~~\|800.000~~
	\|-		\|-
	\|13		\|13
	\|915.403		\|915.403
	~~\|888.722~~
	\|917.647		\|917.647
	~~\|866.667~~
	\|-		\|-
	\|14		\|14
	\|986.552		\|986.552
	~~\|950.9775~~
	\|988.235		\|988.235
	~~\|933.333~~
	\|-		\|-
	\|15		\|15
	\|1057.701		\|1057.701
	~~\|1013.233~~
	\|1058.8235		\|1058.8235
	~~\|1000.000~~
	\|-		\|-
	\|16		\|16
	\|1128.896		\|1128.896
	~~\|1075.489~~
	\|1129.412		\|1129.412
	~~\|1066.667~~
	\|-		\|-
	\|17		\|17
	\|1200		\|1200
	~~\|1137.744~~
	\|1200		\|1200
	~~\|1133.333~~
	\|-		\|-
	\|18		\|18
	\|1271.149		\|1271.149
	~~\|1200~~
	\|1267.97		\|1267.97
	~~\|1200~~
	\|-		\|-
	\|19		\|19
	\|1342.299		\|1342.299
	~~\|1262.256~~
	\|1333.94		\|1333.94
	~~\|1301.955~~
	\|-		\|-
	\|20		\|20
	\|1413.448		\|1413.448
	~~\|1324.511~~		\|1403.91
	~~! colspan="2"~~ \|1403.91
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-02T16:31:18Z

Optimal Intervals

← Older revision		Revision as of 16:31, 2 June 2021
Line 1:		Line 1:
	A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]] and [[18edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]] and [[18edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten 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" \|70.1955		! colspan="2" \|70.1955
			\|70.588
			\|66.667
	\|-		\|-
	!2		\|2
	! colspan="2" \|140.391		! colspan="2" \|140.391
			\|141.1765
			\|133.333
	\|-		\|-
	!3		\|3
	! colspan="2" \|210.5865		! colspan="2" \|210.5865
			\|211.765
			\|200.000
	\|-		\|-
	!4		\|4
	! colspan="2" \|280.782		! colspan="2" \|280.782
			\|282.353
			\|266.667
	\|-		\|-
	!5		\|5
	! colspan="2" \|350.9775		! colspan="2" \|350.9775
			\|352.941
			\|333.333
	\|-		\|-
	!6		\|6
	! colspan="2" \|421.173		! colspan="2" \|421.173
			\|423.529
			\|400.000
	\|-		\|-
	!7		\|7
	! colspan="2" \|491.3685		! colspan="2" \|491.3685
			\|494.118
			\|466.667
	\|-		\|-
	!8		\|8
	! colspan="2" \|561.564		! colspan="2" \|561.564
			\|564.706
			\|533.333
	\|-		\|-
	!9		\|9
	! colspan="2" \|631.7595		! colspan="2" \|631.7595
			\|635.294
			\|600.000
	\|-		\|-
	!10		\|10
	! colspan="2" \|701.955		! colspan="2" \|701.955
			\|705.882
			\|666.667
	\|-		\|-
	\|11		\|11
	\|773.104		\|773.104
	\|764.211		\|764.211
			\|776.471
			\|733.333
	\|-		\|-
	\|12		\|12
	\|844.254		\|844.254
	\|826.466		\|826.466
			\|847.059
			\|800.000
	\|-		\|-
	\|13		\|13
	\|915.403		\|915.403
	\|888.722		\|888.722
			\|917.647
			\|866.667
	\|-		\|-
	\|14		\|14
	\|986.552		\|986.552
	\|950.9775		\|950.9775
			\|988.235
			\|933.333
	\|-		\|-
	\|15		\|15
	\|1057.701		\|1057.701
	\|1013.233		\|1013.233
			\|1058.8235
			\|1000.000
	\|-		\|-
	\|16		\|16
	\|1128.896		\|1128.896
	\|1075.489		\|1075.489
			\|1129.412
			\|1066.667
	\|-		\|-
	\|17		\|17
	\|1200		\|1200
	\|1137.744		\|1137.744
			\|1200
			\|1133.333
	\|-		\|-
	\|18		\|18
	\|1271.149		\|1271.149
			\|1200
			\|1267.97
	\|1200		\|1200
	\|-		\|-
Line 73:		Line 111:
	\|1342.299		\|1342.299
	\|1262.256		\|1262.256
			\|1333.94
			\|1301.955
	\|-		\|-
	\|20		\|20
	\|1413.448		\|1413.448
	\|1324.511		\|1324.511
			! colspan="2" \|1403.91
	\|}		\|}

Xenwolf: cat+todo

2021-06-02T06:58:49Z

cat+todo

← Older revision		Revision as of 06:58, 2 June 2021
Line 78:		Line 78:
	\|1324.511		\|1324.511
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 00:00, 2 June 2021

2021-06-02T00:00:34Z

← Older revision		Revision as of 00:00, 2 June 2021
Line 1:		Line 1:
	A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]] and [[18edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]] and [[18edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	== Optimal Intervals ==		== Optimal Intervals ==
Line 40:		Line 40:
	\|11		\|11
	\|773.104		\|773.104
	\|764.~~2106~~		\|764.211
	\|-		\|-
	\|12		\|12
Line 48:		Line 48:
	\|13		\|13
	\|915.403		\|915.403
	\|888.~~7219~~		\|888.722
	\|-		\|-
	\|14		\|14
Line 56:		Line 56:
	\|15		\|15
	\|1057.701		\|1057.701
	\|1013.~~2331~~		\|1013.233
	\|-		\|-
	\|16		\|16
	\|1128.896		\|1128.896
	\|1075.~~48875~~		\|1075.489
	\|-		\|-
	\|17		\|17
	\|1200		\|1200
	\|1137.~~7444~~		\|1137.744
	\|-		\|-
	\|18		\|18
	\|1271.~~1493~~		\|1271.149
	\|1200		\|1200
	\|-		\|-
	\|19		\|19
	\|1342.~~2986~~		\|1342.299
	\|1262.~~2556~~		\|1262.256
	\|-		\|-
	\|20		\|20
	\|1413.~~4479~~		\|1413.448
	\|1324.511		\|1324.511
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T02:18:49Z

Optimal Intervals

← Older revision		Revision as of 02:18, 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" \|70.1955		! colspan="2" \|70.1955
	\|-		\|-
	!2		!2
	! colspan="4" \|140.391		! colspan="2" \|140.391
	\|-		\|-
	!3		!3
	! colspan="4" \|210.5865		! colspan="2" \|210.5865
	\|-		\|-
	!4		!4
	! colspan="4" \|280.782		! colspan="2" \|280.782
	\|-		\|-
	!5		!5
	! colspan="4" \|350.9775		! colspan="2" \|350.9775
	\|-		\|-
	!6		!6
	! colspan="4" \|421.173		! colspan="2" \|421.173
	\|-		\|-
	!7		!7
	! colspan="4" \|491.3685		! colspan="2" \|491.3685
	\|-		\|-
	!8		!8
	! colspan="4" \|561.564		! colspan="2" \|561.564
	\|-		\|-
	!9		!9
	! colspan="4" \|631.7595		! colspan="2" \|631.7595
	\|-		\|-
	!10		!10
	! colspan="4" \|701.955		! colspan="2" \|701.955
	\|-		\|-
	!11		\|11
	~~! colspan="2"~~ \|773.104		\|773.104
	~~! colspan="2"~~ \|764.~~511~~		\|764.2106
	\|-		\|-
	!12		\|12
	~~! colspan="2"~~ \|844.~~253~~		\|844.254
	~~! colspan="2"~~ \|826.~~0675~~		\|826.466
	\|-		\|-
	!13		\|13
	~~! colspan="2"~~ \|915.403		\|915.403
	~~! colspan="2"~~ \|888.~~722~~		\|888.7219
	\|-		\|-
	!14		\|14
	~~! colspan="2"~~ \|986.552		\|986.552
	~~! colspan="2"~~ \|950.9775		\|950.9775
	\|-		\|-
	!15		\|15
	~~! colspan="2"~~ \|1057.701		\|1057.701
	~~! colspan="2"~~ \|~~1012~~.~~233~~		\|1013.2331
	\|-		\|-
	!16		\|16
	~~! colspan="2"~~ \|1128.896		\|1128.896
	~~! colspan="2"~~ \|1075.~~489~~		\|1075.48875
	\|-		\|-
	!17		\|17
	~~! colspan="2"~~ \|1200		\|1200
	~~! colspan="2"~~ \|1137.~~744~~		\|1137.7444
	\|-		\|-
	\|18		\|18
	\|~~1260~~		\|1271.1493
	~~\|1280~~		\|1200
	~~! colspan="2"~~ \|1200
	\|-		\|-
	\|19		\|19
	\|~~1320~~		\|1342.2986
	\|~~1360~~		\|1262.2556
	~~\|1260~~
	~~\|1280~~
	\|-		\|-
	\|20		\|20
	\|~~1380~~		\|1413.4479
	\|~~1440~~		\|1324.511
	~~\|1320~~
	~~\|1360~~
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T00:50:46Z

Optimal Intervals

← Older revision		Revision as of 00:50, 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 40:		Line 40:
	! colspan="4" \|701.955		! colspan="4" \|701.955
	\|-		\|-
	\|11		!11
	\|~~770.526~~		! colspan="2" \|773.104
	~~\|775.424~~		! colspan="2" \|764.511
	~~\|761~~.~~955~~
	\|~~766~~.~~241~~
	\|-		\|-
	\|12		!12
	\|~~839.098~~		! colspan="2" \|844.253
	~~\|848.894~~		! colspan="2" \|826.0675
	~~\|821~~.~~955~~
	\|~~830~~.~~526~~
	\|-		\|-
	\|13		!13
	\|~~907.669~~		! colspan="2" \|915.403
	~~\|921.363~~		! colspan="2" \|888.722
	~~\|881~~.~~955~~
	\|~~894~~.~~812~~
	\|-		\|-
	\|14		!14
	\|~~976.241~~		! colspan="2" \|986.552
	~~\|995.833~~		! colspan="2" \|950.9775
	~~\|941~~.~~955~~
	\|~~959~~.~~098~~
	\|-		\|-
	\|15		!15
	\|~~1044.812~~		! colspan="2" \|1057.701
	~~\|1069.302~~		! colspan="2" \|1012.233
	~~\|1001~~.~~955~~
	\|~~1023~~.~~384~~
	\|-		\|-
	\|16		!16
	\|~~1113.384~~		! colspan="2" \|1128.896
	~~\|1142.771~~		! colspan="2" \|1075.489
	~~\|1061~~.~~955~~
	\|~~1087~~.~~669~~
	\|-		\|-
	\|17		!17
	\|~~1181.955~~		! colspan="2" \|1200
	~~\|1216.241~~		! colspan="2" \|1137.744
	~~\|1121.955~~
	\|~~1151~~.~~955~~
	\|-		\|-
	\|18		\|18
	\|~~1250.526~~		\|1260
	\|~~1289.71~~		\|1280
	\|~~1181.955~~		! colspan="2" \|1200
	~~\|1216.241~~
	\|-		\|-
	\|19		\|19
	\|~~1319.098~~		\|1320
	\|~~1363.2245~~		\|1360
	\|~~1241.955~~		\|1260
	\|1280~~.526~~		\|1280
	\|-		\|-
	\|20		\|20
	\|~~1387.669~~		\|1380
	\|~~1467.912~~		\|1440
	\|~~1301.955~~		\|1320
	\|~~1344.812~~		\|1360
	\|}		\|}