User:Moremajorthanmajor/24wtn - Revision history

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

2025-09-01T09:31:23Z

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

← Older revision		Revision as of 09:31, 1 September 2025
Line 143:		Line 143:

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

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

Sintel: Sintel moved page 24wtn to User:Moremajorthanmajor/24wtn

2025-03-31T17:18:25Z

Sintel moved page 24wtn to User:Moremajorthanmajor/24wtn

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

Moremajorthanmajor at 21:52, 3 June 2021

2021-06-03T21:52:25Z

← Older revision		Revision as of 21:52, 3 June 2021
Line 1:		Line 1:
	A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	==~~Optimal~~ Intervals==		==Patent Intervals==
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+

Moremajorthanmajor: /* Optimal Intervals */

2021-06-03T21:19:10Z

Optimal Intervals

← Older revision		Revision as of 21:19, 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) b
	\|-		\|-
	!1		!1
	! colspan="2" \|58.49625		! colspan="2" \|58.49625
			\|60
			\|57.1429
	\|-		\|-
	!2		!2
	! colspan="2" \|116.9925		! colspan="2" \|116.9925
			\|120
			\|114.2857
	\|-		\|-
	!3		!3
	! colspan="2" \|175.48875		! colspan="2" \|175.48875
			\|180
			\|171.4286
	\|-		\|-
	!4		!4
	! colspan="2" \|233.985		! colspan="2" \|233.985
			\|240
			\|228.5714
	\|-		\|-
	!5		!5
	! colspan="2" \|292.48125		! colspan="2" \|292.48125
			\|300
			\|285.7143
	\|-		\|-
	!6		!6
	! colspan="2" \|350.9775		! colspan="2" \|350.9775
			\|360
			\|342.8571
	\|-		\|-
	!7		!7
	! colspan="2" \|409.47375		! colspan="2" \|409.47375
			\|420
			\|400.00
	\|-		\|-
	!8		!8
	! colspan="2" \|467.97		! colspan="2" \|467.97
			\|480
			\|457.1429
	\|-		\|-
	!9		!9
	! colspan="2" \|526.46625		! colspan="2" \|526.46625
			\|540
			\|514.2857
	\|-		\|-
	!10		!10
	! colspan="2" \|584.9625		! colspan="2" \|584.9625
			\|600
			\|571.4286
	\|-		\|-
	!11		!11
	! colspan="2" \|643.45875		! colspan="2" \|643.45875
			\|660
			\|628.5714
	\|-		\|-
	!12		!12
	! colspan="2" \|701.955		! colspan="2" \|701.955
			\|720
			\|685.7143
	\|-		\|-
	\|13		\|13
	\|764.2106		\|764.2106
	\|757.2933		\|757.2933
			\|780
			\|742.8571
	\|-		\|-
	\|14		\|14
	\|826.466		\|826.466
	\|812.6317		\|812.6317
			\|840
			\|800.00
	\|-		\|-
	\|15		\|15
	\|888.7219		\|888.7219
	\|867.97		\|867.97
			\|900
			\|857.1429
	\|-		\|-
	\|16		\|16
	\|950.9775		\|950.9775
	\|923.3083		\|923.3083
			\|960
			\|914.285
	\|-		\|-
	\|17		\|17
	\|1013.2331		\|1013.2331
	\|978.6467		\|978.6467
			\|1020
			\|971.4286
	\|-		\|-
	\|18		\|18
	\|1075.48875		\|1075.48875
	\|1033.985		\|1033.985
			\|1080
			\|1028.5714
	\|-		\|-
	\|19		\|19
	\|1137.7444		\|1137.7444
	\|1089.3233		\|1089.3233
			\|1140
			\|1085.7143
	\|-		\|-
	\|20		\|20
	\|1200		\|1200
	\|1144.6617		\|1144.6617
			\|1200.000
			\|1142.8571
	\|-		\|-
	\|21		\|21
	\|1262.2556		\|1262.2556
	\|1200		\|1200
			\|1250.9775
			\|1200.000
	\|-		\|-
	\|22		\|22
	\|1324.511		\|1324.511
	\|1255.3383		\|1255.3383
			\|1301.955
			\|1267.97
	\|-		\|-
	\|23		\|23
	\|1386.7669		\|1386.7669
	\|1310.6767		\|1310.6767
			\|1352.9325
			\|1333.94
	\|-		\|-
	\|24		\|24
	\|1449.0225		\|1449.0225
	\|1366.015		\|1366.015
			! colspan="2" \|1403.91
	\|}		\|}

Xenwolf: cat+todo

2021-06-02T06:59:45Z

cat+todo

← Older revision		Revision as of 06:59, 2 June 2021
Line 92:		Line 92:
	\|1366.015		\|1366.015
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 00:01, 2 June 2021

2021-06-02T00:01:31Z

← Older revision		Revision as of 00:01, 2 June 2021
Line 1:		Line 1:
	A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

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

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T03:21:50Z

Optimal Intervals

← Older revision		Revision as of 03:21, 1 June 2021
Line 5:		Line 5:
	\|+		\|+
	!		!
	!~~Minimum~~ a		!Target a
	!~~Maximum a~~		!Target b
	~~!Minimum b~~
	~~!Maximum~~ b
	\|-		\|-
	!1		!1
	! colspan="4" \|58.49625		! colspan="2" \|58.49625
	\|-		\|-
	!2		!2
	! colspan="4" \|116.9925		! colspan="2" \|116.9925
	\|-		\|-
	!3		!3
	! colspan="4" \|175.48875		! colspan="2" \|175.48875
	\|-		\|-
	!4		!4
	! colspan="4" \|233.985		! colspan="2" \|233.985
	\|-		\|-
	!5		!5
	! colspan="4" \|292.48125		! colspan="2" \|292.48125
	\|-		\|-
	!6		!6
	! colspan="4" \|350.9775		! colspan="2" \|350.9775
	\|-		\|-
	!7		!7
	! colspan="4" \|409.47375		! colspan="2" \|409.47375
	\|-		\|-
	!8		!8
	! colspan="4" \|467.97		! colspan="2" \|467.97
	\|-		\|-
	!9		!9
	! colspan="4" \|526.46625		! colspan="2" \|526.46625
	\|-		\|-
	!10		!10
	! colspan="4" \|584.9625		! colspan="2" \|584.9625
	\|-		\|-
	!11		!11
	! colspan="4" \|643.45875		! colspan="2" \|643.45875
	\|-		\|-
	!12		!12
	! colspan="4" \|701.955		! colspan="2" \|701.955
	\|-		\|-
	\|13		\|13
	\|~~761~~.~~955~~		\|764.2106
	\|~~766~~.~~2407~~		\|757.2933
	~~\|755.2883~~
	~~\|759.0979~~
	\|-		\|-
	\|14		\|14
	\|~~821~~.~~955~~		\|826.466
	\|~~830~~.~~5264~~		\|812.6317
	~~\|808.6117~~
	~~\|816.2407~~
	\|-		\|-
	\|15		\|15
	\|~~881~~.~~955~~		\|888.7219
	\|~~894~~.~~8121~~		\|867.97
	~~\|861.955~~
	~~\|873.3836~~
	\|-		\|-
	\|16		\|16
	\|~~941~~.~~955~~		\|950.9775
	\|~~959~~.~~0979~~		\|923.3083
	~~\|915.2883~~
	~~\|930.5264~~
	\|-		\|-
	\|17		\|17
	\|~~1001~~.~~955~~		\|1013.2331
	\|~~1023~~.~~3836~~		\|978.6467
	~~\|968.6117~~
	~~\|987.6693~~
	\|-		\|-
	\|18		\|18
	\|~~1061~~.~~955~~		\|1075.48875
	\|~~1087~~.~~6693~~		\|1033.985
	~~\|1021.955~~
	~~\|1044.8121~~
	\|-		\|-
	\|19		\|19
	\|~~1121~~.~~955~~		\|1137.7444
	\|~~1151~~.~~955~~		\|1089.3233
	~~\|1075.2883~~
	~~\|1101.955~~
	\|-		\|-
	\|20		\|20
	\|~~1181.955~~		\|1200
	~~\|1216.2407~~		\|1144.6617
	~~\|1128.6117~~
	\|~~1159~~.~~0979~~
	\|-		\|-
	\|21		\|21
	\|~~1241~~.~~955~~		\|1262.2556
	\|~~1280.5264~~		\|1200
	~~\|1181.955~~
	~~\|1216.2407~~
	\|-		\|-
	\|22		\|22
	\|~~1301~~.~~955~~		\|1324.511
	\|~~1344~~.~~8121~~		\|1255.3383
	~~\|1235.2883~~
	~~\|1273.3836~~
	\|-		\|-
	\|23		\|23
	\|~~1361~~.~~955~~		\|1386.7669
	\|~~1409~~.~~0907~~		\|1310.6767
	~~\|1288.6117~~
	~~\|1330.5264~~
	\|-		\|-
	\|24		\|24
	\|~~1441~~.~~955~~		\|1449.0225
	\|~~1473~~.~~3836~~		\|1366.015
	~~\|1341.955~~
	~~\|1387.6693~~
	\|}		\|}

Moremajorthanmajor at 18:24, 31 May 2021

2021-05-31T18:24:22Z

← Older revision		Revision as of 18:24, 31 May 2021
Line 1:		Line 1:
	A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings ~~alternates~~ [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

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

Moremajorthanmajor at 18:24, 31 May 2021

2021-05-31T18:24:11Z

← Older revision		Revision as of 18:24, 31 May 2021
Line 1:		Line 1:
	A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternates [[EDF\|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

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

Moremajorthanmajor: Created page with "A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of 20edo and 21edo, but with a nonet rather than the 2/1 being constant. It alternates ED..."

2021-05-31T02:51:20Z

Created page with "A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of 20edo and 21edo, but with a nonet rather than the 2/1 being constant. It alternates ED..."

New page

A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

==Optimal Intervals==
{| class="wikitable"
|+
!
!Minimum a
!Maximum a
!Minimum b
!Maximum b
|-
!1
! colspan="4" |58.49625
|-
!2
! colspan="4" |116.9925
|-
!3
! colspan="4" |175.48875
|-
!4
! colspan="4" |233.985
|-
!5
! colspan="4" |292.48125
|-
!6
! colspan="4" |350.9775
|-
!7
! colspan="4" |409.47375
|-
!8
! colspan="4" |467.97
|-
!9
! colspan="4" |526.46625
|-
!10
! colspan="4" |584.9625
|-
!11
! colspan="4" |643.45875
|-
!12
! colspan="4" |701.955
|-
|13
|761.955
|766.2407
|755.2883
|759.0979
|-
|14
|821.955
|830.5264
|808.6117
|816.2407
|-
|15
|881.955
|894.8121
|861.955
|873.3836
|-
|16
|941.955
|959.0979
|915.2883
|930.5264
|-
|17
|1001.955
|1023.3836
|968.6117
|987.6693
|-
|18
|1061.955
|1087.6693
|1021.955
|1044.8121
|-
|19
|1121.955
|1151.955
|1075.2883
|1101.955
|-
|20
|1181.955
|1216.2407
|1128.6117
|1159.0979
|-
|21
|1241.955
|1280.5264
|1181.955
|1216.2407
|-
|22
|1301.955
|1344.8121
|1235.2883
|1273.3836
|-
|23
|1361.955
|1409.0907
|1288.6117
|1330.5264
|-
|24
|1441.955
|1473.3836
|1341.955
|1387.6693
|}