User:Moremajorthanmajor/26wtn - Revision history

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

2025-09-01T09:31:50Z

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

← Older revision		Revision as of 09:31, 1 September 2025
Line 154:		Line 154:

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

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

Sintel: Sintel moved page 26wtn to User:Moremajorthanmajor/26wtn

2025-03-31T17:18:37Z

Sintel moved page 26wtn to User:Moremajorthanmajor/26wtn

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

Moremajorthanmajor: /* Patent Intervals */

2021-06-04T00:34:19Z

Patent Intervals

← Older revision		Revision as of 00:34, 4 June 2021
Line 1:		Line 1:
	A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth~~. It is also the largest well temperament a patent tuning related to a nonet smaller than 8\[[7edo]] (1356.5217¢)~~.		A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

	==Patent Intervals==		==Patent Intervals==

Moremajorthanmajor: /* Patent Intervals */

2021-06-03T22:38:33Z

Patent Intervals

← Older revision		Revision as of 22:38, 3 June 2021
Line 1:		Line 1:
	A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. It is also the largest well temperament a patent tuning related to a nonet smaller than 8\[[7edo]] (1356.5217¢).

	==Patent Intervals==		==Patent Intervals==

Moremajorthanmajor: /* Optimal Intervals */

2021-06-03T21:51:14Z

Optimal Intervals

← Older revision		Revision as of 21:51, 3 June 2021
Line 1:		Line 1:
	A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen 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" \|53.9965		! colspan="2" \|53.9965
			\|54.54545
			\|52.1739
	\|-		\|-
	!2		!2
	! colspan="2" \|107.9931		! colspan="2" \|107.9931
			\|109.0909
			\|104.3478
	\|-		\|-
	!3		!3
	! colspan="2" \|161.9896		! colspan="2" \|161.9896
			\|163.6364
			\|156.5217
	\|-		\|-
	!4		!4
	! colspan="2" \|215.9862		! colspan="2" \|215.9862
			\|218.1818
			\|208.6957
	\|-		\|-
	!5		!5
	! colspan="2" \|269.9827		! colspan="2" \|269.9827
			\|272.7273
			\|260.8696
	\|-		\|-
	!6		!6
	! colspan="2" \|323.9792		! colspan="2" \|323.9792
			\|327.2727
			\|313.0435
	\|-		\|-
	!7		!7
	! colspan="2" \|377.9758		! colspan="2" \|377.9758
			\|381.8182
			\|365.2174
	\|-		\|-
	!8		!8
	! colspan="2" \|431.9723		! colspan="2" \|431.9723
			\|436.3636
			\|417.3913
	\|-		\|-
	!9		!9
	! colspan="2" \|485.9688		! colspan="2" \|485.9688
			\|490.9091
			\|469.5652
	\|-		\|-
	!10		!10
	! colspan="2" \|539.9654		! colspan="2" \|539.9654
			\|545.45455
			\|521.7391
	\|-		\|-
	!11		!11
	! colspan="2" \|593.9619		! colspan="2" \|593.9619
			\|600.000
			\|573.913
	\|-		\|-
	!12		!12
	! colspan="2" \|647.9585		! colspan="2" \|647.9585
			\|654.54545
			\|626.087
	\|-		\|-
	!13		!13
	! colspan="2" \|701.9550		! colspan="2" \|701.9550
			\|709.0909
			\|678.2609
	\|-		\|-
	\|14		\|14
	\|757.2933		\|757.2933
	\|751.7595		\|751.7595
			\|763.6364
			\|730.4348
	\|-		\|-
	\|15		\|15
	\|812.6317		\|812.6317
	\|801.564		\|801.564
			\|818.1818
			\|782.6087
	\|-		\|-
	\|16		\|16
	\|867.97		\|867.97
	\|851.3685		\|851.3685
			\|872.7273
			\|834.7826
	\|-		\|-
	\|17		\|17
	\|923.3083		\|923.3083
	\|901.173		\|901.173
			\|927.2727
			\|886.9565
	\|-		\|-
	\|18		\|18
	\|978.6467		\|978.6467
	\|950.9775		\|950.9775
			\|981.8182
			\|939.1304
	\|-		\|-
	\|19		\|19
	\|1033.985		\|1033.985
	\|1000.782		\|1000.782
			\|1036.364
			\|991.3043
	\|-		\|-
	\|20		\|20
	\|1089.3233		\|1089.3233
	\|1050.6865		\|1050.6865
			\|1090.9091
			\|1043.4783
	\|-		\|-
	\|21		\|21
	\|1144.6617		\|1144.6617
	\|1100.391		\|1100.391
			\|1145.45455
			\|1095.6522
	\|-		\|-
	\|22		\|22
	\|1200		\|1200
	\|1150.1955		\|1150.1955
			\|1200.000
			\|1147.8261
	\|-		\|-
	\|23		\|23
	\|1255.3383		\|1255.3383
	\|1200		\|1200
			\|1250.9775
			\|1200.000
	\|-		\|-
	\|24		\|24
	\|1310.6767		\|1310.6767
	\|1249.8045		\|1249.8045
			\|1301.955
			\|1267.97
	\|-		\|-
	\|25		\|25
	\|1366.015		\|1366.015
	\|1299.609		\|1299.609
			\|1352.9325
			\|1333.94
	\|-		\|-
	\|26		\|26
	\|1421.3533		\|1421.3533
	\|1349.4135		\|1349.4135
			! colspan="2" \|1403.91
	\|}		\|}

Xenwolf: cat+todo

2021-06-02T07:00:23Z

cat+todo

← Older revision		Revision as of 07:00, 2 June 2021
Line 99:		Line 99:
	\|1349.4135		\|1349.4135
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 00:02, 2 June 2021

2021-06-02T00:02:05Z

← Older revision		Revision as of 00:02, 2 June 2021
Line 1:		Line 1:
	A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

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

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T03:25:48Z

Optimal Intervals

Show changes

Moremajorthanmajor at 18:25, 31 May 2021

2021-05-31T18:25:45Z

← Older revision		Revision as of 18:25, 31 May 2021
Line 1:		Line 1:
	A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. ~~It alternates~~ [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.		A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF\|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen 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 '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of 22edo and 23edo, but with a nonet rather than the 2/1 being constant. It alternates ED..."

2021-05-31T03:10:41Z

Created page with "A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of 22edo and 23edo, but with a nonet rather than the 2/1 being constant. It alternates ED..."

New page

A '''26 tone well tempered nonet''' (26WTN) is related to well temperaments of [[22edo]] and [[23edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 13 equal parts (13EDF) with sequences of thirteen equal steps of 46.15385 to 61.5385 cents each. This will create thirteen 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" |53.9965
|-
!2
! colspan="4" |107.9931
|-
!3
! colspan="4" |161.9896
|-
!4
! colspan="4" |215.9862
|-
!5
! colspan="4" |269.9827
|-
!6
! colspan="4" |323.9792
|-
!7
! colspan="4" |377.9758
|-
!8
! colspan="4" |431.9723
|-
!9
! colspan="4" |485.9688
|-
!10
! colspan="4" |539.9654
|-
!11
! colspan="4" |593.9619
|-
!12
! colspan="4" |647.9585
|-
!13
! colspan="4" |701.9550
|-
|14
|755.2883
|759.0979
|749.955
|753.3836
|-
|15
|808.6117
|816.2407
|797.955
|804.8121
|-
|16
|861.955
|873.3836
|845.955
|856.2407
|-
|17
|915.2883
|930.5264
|893.955
|907.6693
|-
|18
|968.6117
|987.6693
|941.955
|959.0979
|-
|19
|1021.955
|1044.8121
|989.955
|1010.5264
|-
|20
|1075.2883
|1101.955
|1037.955
|1061.955
|-
|21
|1128.6117
|1159.0979
|1085.955
|1113.3836
|-
|22
|1181.955
|1216.2407
|1133.995
|1164.8121
|-
|23
|1235.2883
|1273.3836
|1181.955
|1216.2407
|-
|24
|1288.6117
|1330.5264
|1229.995
|1267.6693
|-
|25
|1341.955
|1387.6693
|1277.995
|1319.0979
|-
|26
|1395.2883
|1444.8121
|1325.995
|1370.5264
|}