User:Moremajorthanmajor/14wtn - Revision history

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

2025-09-01T09:31:36Z

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

← Older revision		Revision as of 09:31, 1 September 2025
Line 74:		Line 74:

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

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

Sintel: Sintel moved page 14wtn to User:Moremajorthanmajor/14wtn

2025-03-31T17:17:06Z

Sintel moved page 14wtn to User:Moremajorthanmajor/14wtn

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

Xenwolf: cat+todo

2021-06-02T06:57:49Z

cat+todo

← Older revision		Revision as of 06:57, 2 June 2021
Line 72:		Line 72:
	\|1403.91		\|1403.91
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 04:14, 2 June 2021

2021-06-02T04:14:05Z

← Older revision		Revision as of 04:14, 2 June 2021
Line 1:		Line 1:
	The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.		The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

	== ~~Optimal~~ Intervals ==		== Patent Intervals ==
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
Line 7:		Line 7:
	!Target a		!Target a
	!Target b		!Target b
			!Alternating [[EDO\|edo]] and *ed(9/8)
	\|-		\|-
	!1		\|1
	! colspan="2" \|100.2793		! colspan="2" \|100.2793
			\|100
	\|-		\|-
	!2		\|2
	! colspan="2" \|200.5586		! colspan="2" \|200.5586
			\|200
	\|-		\|-
	!3		\|3
	! colspan="2" \|300.8379		! colspan="2" \|300.8379
			\|300
	\|-		\|-
	!4		\|4
	! colspan="2" \|401.1171		! colspan="2" \|401.1171
			\|400
	\|-		\|-
	!5		\|5
	! colspan="2" \|501.3964		! colspan="2" \|501.3964
			\|500
	\|-		\|-
	!6		\|6
	! colspan="2" \|601.6757		! colspan="2" \|601.6757
			\|600
	\|-		\|-
	!7		\|7
	! colspan="2" \|701.955		! colspan="2" \|701.955
			\|700
	\|-		\|-
	\|8		\|8
	\|801.564		\|801.564
	\|784.9625		\|784.9625
			\|800
	\|-		\|-
	\|9		\|9
	\|901.173		\|901.173
	\|867.97		\|867.97
			\|900
	\|-		\|-
	\|10		\|10
	\|1000.782		\|1000.782
	\|950.9775		\|950.9775
			\|1000
	\|-		\|-
	\|11		\|11
	\|1101.391		\|1101.391
	\|1033.985		\|1033.985
			\|1100
	\|-		\|-
	\|12		\|12
	\|1200		\|1200
	\|1116.9925		\|1116.9925
			\|1200
	\|-		\|-
	\|13		\|13
	\|1299.609		\|1299.609
	\|1200		\|1200
			\|1301.955
	\|-		\|-
	\|14		\|14
	\|1398.218		\|1398.218
	\|1283.0075		\|1283.0075
			\|1403.91
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T02:33:27Z

Optimal Intervals

← Older revision		Revision as of 02:33, 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" \|100.2793		! colspan="2" \|100.2793
	\|-		\|-
	!2		!2
	! colspan="4" \|200.5586		! colspan="2" \|200.5586
	\|-		\|-
	!3		!3
	! colspan="4" \|300.8379		! colspan="2" \|300.8379
	\|-		\|-
	!4		!4
	! colspan="4" \|401.1171		! colspan="2" \|401.1171
	\|-		\|-
	!5		!5
	! colspan="4" \|501.3964		! colspan="2" \|501.3964
	\|-		\|-
	!6		!6
	! colspan="4" \|601.6757		! colspan="2" \|601.6757
	\|-		\|-
	!7		!7
	! colspan="4" \|701.955		! colspan="2" \|701.955
	\|-		\|-
	!8		\|8
	~~! colspan="2"~~ \|801.564		\|801.564
	~~! colspan="2"~~ \|784.9625		\|784.9625
	\|-		\|-
	!9		\|9
	~~! colspan="2"~~ \|901.173		\|901.173
	~~! colspan="2"~~ \|867.97		\|867.97
	\|-		\|-
	!10		\|10
	~~! colspan="2"~~ \|1000.782		\|1000.782
	~~! colspan="2"~~ \|950.9775		\|950.9775
	\|-		\|-
	!11		\|11
	~~! colspan="2"~~ \|1101.391		\|1101.391
	~~! colspan="2"~~ \|1033.985		\|1033.985
	\|-		\|-
	!12		\|12
	~~! colspan="2"~~ \|1200		\|1200
	~~! colspan="2"~~ \|1116.9925		\|1116.9925
	\|-		\|-
	\|13		\|13
	\|~~1285~~.~~714~~		\|1299.609
	~~\|1314.2857~~		\|1200
	~~! colspan="2"~~ \|1200
	\|-		\|-
	\|14		\|14
	\|~~1371~~.~~429~~		\|1398.218
	\|~~1428~~.~~5714~~		\|1283.0075
	~~\|1285.714~~
	~~\|1314.2857~~
	\|}		\|}

Moremajorthanmajor at 00:05, 1 June 2021

2021-06-01T00:05:31Z

← Older revision		Revision as of 00:05, 1 June 2021
Line 5:		Line 5:
	\|+		\|+
	!		!
	!Minimum		!Target Minimum a
	!Maximum		!Target Maximum a
	!~~[7\12 99.609¢]~~		!Target Minimum b
			!Target Maximum b
	\|-		\|-
	!1		!1
	! colspan="3" \|100.2793		! colspan="4" \|100.2793
	\|-		\|-
	!2		!2
	! colspan="3" \|200.5586		! colspan="4" \|200.5586
	\|-		\|-
	!3		!3
	! colspan="3" \|300.8379		! colspan="4" \|300.8379
	\|-		\|-
	!4		!4
	! colspan="3" \|401.1171		! colspan="4" \|401.1171
	\|-		\|-
	!5		!5
	! colspan="3" \|501.3964		! colspan="4" \|501.3964
	\|-		\|-
	!6		!6
	! colspan="3" \|601.6757		! colspan="4" \|601.6757
	\|-		\|-
	!7		!7
	! colspan="3" \|701.955		! colspan="4" \|701.955
	\|-		\|-
	\|8		!8
	\|~~797~~.~~955~~		! colspan="2" \|801.564
	~~\|804.8121~~		! colspan="2" \|784.9625
	\|~~801~~.~~564~~
	\|-		\|-
	\|9		!9
	\|~~893~~.~~955~~		! colspan="2" \|901.173
	~~\|907.6692~~		! colspan="2" \|867.97
	\|~~901~~.~~173~~
	\|-		\|-
	\|10		!10
	\|~~989~~.~~955~~		! colspan="2" \|1000.782
	~~\|1010.5264~~		! colspan="2" \|950.9775
	\|~~1000~~.~~782~~
	\|-		\|-
	\|11		!11
	\|~~1085~~.~~955~~		! colspan="2" \|1101.391
	~~\|1113.3836~~		! colspan="2" \|1033.985
	\|~~1101~~.~~391~~
	\|-		\|-
	\|12		!12
	\|~~1181.955~~		! colspan="2" \|1200
	\|~~1216~~.~~2407~~		! colspan="2" \|1116.9925
	~~\|1200~~
	\|-		\|-
	\|13		\|13
	\|~~1277~~.~~955~~		\|1285.714
	\|~~1319~~.~~0979~~		\|1314.2857
	\|~~1300.9775~~		! colspan="2" \|1200
	\|-		\|-
	\|14		\|14
	\|~~1373~~.~~955~~		\|1371.429
	\|~~1421~~.~~955~~		\|1428.5714
	\|~~1401~~.~~955~~		\|1285.714
			\|1314.2857
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-05-31T22:08:04Z

Optimal Intervals

← Older revision		Revision as of 22:08, 31 May 2021
Line 7:		Line 7:
	!Minimum		!Minimum
	!Maximum		!Maximum
			![7\12 99.609¢]
	\|-		\|-
	!1		!1
	! colspan="2" \|100.2793		! colspan="3" \|100.2793
	\|-		\|-
	!2		!2
	! colspan="2" \|200.5586		! colspan="3" \|200.5586
	\|-		\|-
	!3		!3
	! colspan="2" \|300.8379		! colspan="3" \|300.8379
	\|-		\|-
	!4		!4
	! colspan="2" \|401.1171		! colspan="3" \|401.1171
	\|-		\|-
	!5		!5
	! colspan="2" \|501.3964		! colspan="3" \|501.3964
	\|-		\|-
	!6		!6
	! colspan="2" \|601.6757		! colspan="3" \|601.6757
	\|-		\|-
	!7		!7
	! colspan="2" \|701.955		! colspan="3" \|701.955
	\|-		\|-
	\|8		\|8
	\|797.955		\|797.955
	\|804.8121		\|804.8121
			\|801.564
	\|-		\|-
	\|9		\|9
	\|893.955		\|893.955
	\|907.6692		\|907.6692
			\|901.173
	\|-		\|-
	\|10		\|10
	\|989.955		\|989.955
	\|1010.5264		\|1010.5264
			\|1000.782
	\|-		\|-
	\|11		\|11
	\|1085.955		\|1085.955
	\|1113.3836		\|1113.3836
			\|1101.391
	\|-		\|-
	\|12		\|12
	\|1181.955		\|1181.955
	\|1216.2407		\|1216.2407
			\|1200
	\|-		\|-
	\|13		\|13
	\|1277.955		\|1277.955
	\|1319.0979		\|1319.0979
			\|1300.9775
	\|-		\|-
	\|14		\|14
	\|1373.955		\|1373.955
	\|1421.955		\|1421.955
			\|1401.955
	\|}		\|}

Moremajorthanmajor at 05:48, 30 May 2021

2021-05-30T05:48:58Z

Show changes

Moremajorthanmajor: Created page with "The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The pa..."

2021-05-29T03:23:19Z

Created page with "The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The pa..."

New page

The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

== Intervals ==
{| class="wikitable"
|+
!
!''“fifth” 2 = 600¢''
!“nonet” = 1351.429¢
!“nonet” = 1460¢
!''“fifth” 2 = 800¢''
|-
!1
! colspan="4" |100.2793
|-
!2
! colspan="4" |200.5586
|-
!3
! colspan="4" |300.8379
|-
!4
! colspan="4" |401.1171
|-
!5
! colspan="4" |501.3964
|-
!6
! colspan="4" |601.6757
|-
!7
! colspan="4" |701.955
|-
|8
|''787.6692''
|794.7369
|810.2471
|''816.2407''
|-
|9
|''873.3835''
|887.5189
|918.5393
|''930.5264''
|-
|10
|''959.0979''
|980.3008
|1026.8314
|''1044.8121''
|-
|11
|''1044.8121''
|1073.0828
|1135.1236
|''1159.0979''
|-
|12
|''1130.5264''
|1165.8647
|1243.4157
|''1273.3835''
|-
|13
|''1216.2407''
|1258.6466
|1351.7079
|''1387.6693''
|-
|14
|''1301.955''
|1351.429
|1460
|''1501.955''
|}

== Common Tuning ==
{| class="wikitable"
|+
|1
|100.2793
|-
|2
|200.5586
|-
|3
|300.8379
|-
|4
|401.1171
|-
|5
|501.3964
|-
|6
|601.6757
|-
|7
|701.955
|-
|8
|801.955
|-
|9
|901.955
|-
|10
|1001.955
|-
|11
|1101.955
|-
|12
|1201.955
|-
|13
|1301.955
|-
|14
|1401.955
|-
!
!Fifths
|-
|1
|701.6757
|-
|2
|701.3964
|-
|3
|701.1171
|-
|4
|700.8379
|-
|5
|700.5586
|-
|6
|700.2793
|-
|7
|700
|-
|8
|700.2793
|-
|9
|700.5586
|-
|10
|700.8379
|-
|11
|701.1171
|-
|12
|701.3964
|-
|13
|701.6757
|-
|14
|701.955
|}