User:Moremajorthanmajor/16wtn - Revision history

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

2025-09-01T09:31:06Z

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

← Older revision		Revision as of 09:31, 1 September 2025
Line 117:		Line 117:

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

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

Sintel: Sintel moved page 16wtn to User:Moremajorthanmajor/16wtn

2025-03-31T17:17:21Z

Sintel moved page 16wtn to User:Moremajorthanmajor/16wtn

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

Xenwolf: cat+todo

2021-06-02T06:58:12Z

cat+todo

← Older revision		Revision as of 06:58, 2 June 2021
Line 115:		Line 115:
	\|A		\|A
	\|}		\|}

			[[Category:Well tempered nonet]]

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

Moremajorthanmajor at 06:31, 2 June 2021

2021-06-02T06:31:58Z

← Older revision		Revision as of 06:31, 2 June 2021
Line 1:		Line 1:
	'''16WTN''' is optimally the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]].		'''16WTN''' is optimally the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]].

	== ~~Optimal~~ Intervals ==		== Patent Intervals ==
	The best tunings of 16WTN can be interpreted as tunings for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. For the notation of these modes, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι [J]).		The best tunings of 16WTN can be interpreted as tunings for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. For the notation of these modes, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι [J]).
	{\| class="wikitable"		{\| class="wikitable"

Moremajorthanmajor at 06:30, 2 June 2021

2021-06-02T06:30:10Z

← Older revision		Revision as of 06:30, 2 June 2021
Line 8:		Line 8:
	!Target a		!Target a
	!Target b		!Target b
			!Alternating [[EDO\|edo]] and *ed(9/8) a
			!Alternating edo and *ed(9/8) b
	!Annapolis[6L 4s]		!Annapolis[6L 4s]
	\|-		\|-
	!1		\|1
	! colspan="2" \|87.7444		! colspan="2" \|87.7444
			\|92.3077
			\|85.7143
	\|Α#		\|Α#
	\|-		\|-
	!2		\|2
	! colspan="2" \|175.48875		! colspan="2" \|175.48875
			\|184.6154
			\|171.4286
	\|Β		\|Β
	\|-		\|-
	!3		\|3
	! colspan="2" \|263.2331		! colspan="2" \|263.2331
			\|276.9231
			\|257.1429
	\|Γ		\|Γ
	\|-		\|-
	!4		\|4
	! colspan="2" \|350.9775		! colspan="2" \|350.9775
			\|369.2308
			\|342.8571
	\|Γ#		\|Γ#
	\|-		\|-
	!5		\|5
	! colspan="2" \|438.7219		! colspan="2" \|438.7219
			\|461.5385
			\|428.5714
	\|Δ		\|Δ
	\|-		\|-
	!6		\|6
	! colspan="2" \|526.46625		! colspan="2" \|526.46625
			\|553.84615
			\|51<span style="line-height: 1.5;">4.2857</span>
	\|Δ#		\|Δ#
	\|-		\|-
	!7		\|7
	! colspan="2" \|614.2106		! colspan="2" \|614.2106
			\|646.15385
			\|600.000
	\|Ε		\|Ε
	\|-		\|-
	!'''8'''		\|'''8'''
	! colspan="2" \|'''701.955'''		! colspan="2" \|'''701.955'''
			\|738.4615
			\|685.7143
	\|'''Ϛ/Ϝ'''		\|'''Ϛ/Ϝ'''
	\|-		\|-
Line 45:		Line 63:
	\|801.564		\|801.564
	\|784.9625		\|784.9625
			\|830.7692
			\|771.4286
	\|Ϛ#/Ϝ#		\|Ϛ#/Ϝ#
	\|-		\|-
Line 50:		Line 70:
	\|901.173		\|901.173
	\|867.97		\|867.97
			\|923.0769
			\|857.1429
	\|Ζ		\|Ζ
	\|-		\|-
Line 55:		Line 77:
	\|1000.782		\|1000.782
	\|950.9775		\|950.9775
			\|1015.3846
			\|942.8571
	\|Η		\|Η
	\|-		\|-
Line 60:		Line 84:
	\|1101.391		\|1101.391
	\|1033.985		\|1033.985
			\|1107.6923
			\|1028.5714
	\|Η#		\|Η#
	\|-		\|-
Line 65:		Line 91:
	\|1200		\|1200
	\|1116.9925		\|1116.9925
			\|1200
			\|1114.2857
	\|Θ		\|Θ
	\|-		\|-
	\|14		\|14
	\|1299.609		\|1299.609
			\|1200
			\|1267.97
	\|1200		\|1200
	\|Θ#		\|Θ#
Line 75:		Line 105:
	\|1398.218		\|1398.218
	\|1283.0075		\|1283.0075
			\|1333.94
			\|1301.955
	\|I (J)		\|I (J)
	\|-		\|-
Line 80:		Line 112:
	\|1497.827		\|1497.827
	\|1366.015		\|1366.015
			! colspan="2" \|1403.91
	\|A		\|A
	\|}		\|}

Moremajorthanmajor at 23:55, 1 June 2021

2021-06-01T23:55:21Z

← Older revision		Revision as of 23:55, 1 June 2021
Line 1:		Line 1:
	'''16WTN''' is the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]].		'''16WTN''' is optimally the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]].

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

Moremajorthanmajor at 02:33, 1 June 2021

2021-06-01T02:33:40Z

← Older revision		Revision as of 02:33, 1 June 2021
Line 6:		Line 6:
	\|+		\|+
	!		!
	!Target ~~Minimum~~ a		!Target a
	!Target ~~Maximum a~~		!Target b
	~~!Target Minimum b~~
	~~!Target Maximum~~ b
	!Annapolis[6L 4s]		!Annapolis[6L 4s]
	\|-		\|-
	!1		!1
	! colspan="4" \|87.7444		! colspan="2" \|87.7444
	\|Α#		\|Α#
	\|-		\|-
	!2		!2
	! colspan="4" \|175.48875		! colspan="2" \|175.48875
	\|Β		\|Β
	\|-		\|-
	!3		!3
	! colspan="4" \|263.2331		! colspan="2" \|263.2331
	\|Γ		\|Γ
	\|-		\|-
	!4		!4
	! colspan="4" \|350.9775		! colspan="2" \|350.9775
	\|Γ#		\|Γ#
	\|-		\|-
	!5		!5
	! colspan="4" \|438.7219		! colspan="2" \|438.7219
	\|Δ		\|Δ
	\|-		\|-
	!6		!6
	! colspan="4" \|526.46625		! colspan="2" \|526.46625
	\|Δ#		\|Δ#
	\|-		\|-
	!7		!7
	! colspan="4" \|614.2106		! colspan="2" \|614.2106
	\|Ε		\|Ε
	\|-		\|-
	!'''8'''		!'''8'''
	! colspan="4" \|'''701.955'''		! colspan="2" \|'''701.955'''
	\|'''Ϛ/Ϝ'''		\|'''Ϛ/Ϝ'''
	\|-		\|-
	!9		\|9
	~~! colspan="2"~~ \|801.564		\|801.564
	~~! colspan="2"~~ \|784.9625		\|784.9625
	\|Ϛ#/Ϝ#		\|Ϛ#/Ϝ#
	\|-		\|-
	!10		\|10
	~~! colspan="2"~~ \|901.173		\|901.173
	~~! colspan="2"~~ \|867.97		\|867.97
	\|Ζ		\|Ζ
	\|-		\|-
	!11		\|11
	~~! colspan="2"~~ \|1000.782		\|1000.782
	~~! colspan="2"~~ \|950.9775		\|950.9775
	\|Η		\|Η
	\|-		\|-
	!12		\|12
	~~! colspan="2"~~ \|1101.391		\|1101.391
	~~! colspan="2"~~ \|1033.985		\|1033.985
	\|Η#		\|Η#
	\|-		\|-
	!13		\|13
	~~! colspan="2"~~ \|1200		\|1200
	~~! colspan="2"~~ \|1116.9925		\|1116.9925
	\|Θ		\|Θ
	\|-		\|-
	\|14		\|14
	\|~~1275~~		\|1299.609
	~~\|1300~~		\|1200
	~~! colspan="2"~~ \|1200
	\|Θ#		\|Θ#
	\|-		\|-
	\|15		\|15
	\|~~1350~~		\|1398.218
	\|~~1400~~		\|1283.0075
	~~\|1275~~
	~~\|1300~~
	\|I (J)		\|I (J)
	\|-		\|-
	\|16		\|16
	\|~~1425~~		\|1497.827
	\|~~1500~~		\|1366.015
	~~\|1350~~
	~~\|1400~~
	\|A		\|A
	\|}		\|}

Moremajorthanmajor: /* Optimal Intervals */

2021-06-01T00:09:16Z

Optimal Intervals

← Older revision		Revision as of 00:09, 1 June 2021
Line 6:		Line 6:
	\|+		\|+
	!		!
	!Minimum a		!Target Minimum a
	!Maximum a		!Target Maximum a
	!~~[8\13 99.609¢]~~		!Target Minimum b
	!Minimum b		!Target Maximum b
	!Maximum b
	~~![4\7 83.0075¢]~~
	!Annapolis[6L 4s]		!Annapolis[6L 4s]
	\|-		\|-
	!1		!1
	! colspan="6" \|87.7444		! colspan="4" \|87.7444
	\|Α#		\|Α#
	\|-		\|-
	!2		!2
	! colspan="6" \|175.48875		! colspan="4" \|175.48875
	\|Β		\|Β
	\|-		\|-
	!3		!3
	! colspan="6" \|263.2331		! colspan="4" \|263.2331
	\|Γ		\|Γ
	\|-		\|-
	!4		!4
	! colspan="6" \|350.9775		! colspan="4" \|350.9775
	\|Γ#		\|Γ#
	\|-		\|-
	!5		!5
	! colspan="6" \|438.7219		! colspan="4" \|438.7219
	\|Δ		\|Δ
	\|-		\|-
	!6		!6
	! colspan="6" \|526.46625		! colspan="4" \|526.46625
	\|Δ#		\|Δ#
	\|-		\|-
	!7		!7
	! colspan="6" \|614.2106		! colspan="4" \|614.2106
	\|Ε		\|Ε
	\|-		\|-
	!'''8'''		!'''8'''
	! colspan="6" \|'''701.955'''		! colspan="4" \|'''701.955'''
	\|'''Ϛ/Ϝ'''		\|'''Ϛ/Ϝ'''
	\|-		\|-
	\|9		!9
	~~\|797.955~~		! colspan="2" \|801.564
	~~\|804.8121~~		! colspan="2" \|784.9625
	\|801.564
	~~\|781.955~~
	~~\|787.6693~~
	\|784.9625
	\|Ϛ#/Ϝ#		\|Ϛ#/Ϝ#
	\|-		\|-
	\|10		!10
	~~\|893.955~~		! colspan="2" \|901.173
	~~\|907.6692~~		! colspan="2" \|867.97
	\|901.173
	~~\|861.955~~
	~~\|873.3836~~
	\|867.97
	\|Ζ		\|Ζ
	\|-		\|-
	\|11		!11
	~~\|989.955~~		! colspan="2" \|1000.782
	~~\|1010.5264~~		! colspan="2" \|950.9775
	\|1000.782
	~~\|941.955~~
	~~\|959.0979~~
	\|950.9775
	\|Η		\|Η
	\|-		\|-
	\|12		!12
	~~\|1085.955~~		! colspan="2" \|1101.391
	~~\|1113.3836~~		! colspan="2" \|1033.985
	\|1101.391
	~~\|1021.955~~
	~~\|1044.8121~~
	\|1033.985
	\|Η#		\|Η#
	\|-		\|-
	\|13		!13
	~~\|1181.955~~		! colspan="2" \|1200
	~~\|1216.2407~~		! colspan="2" \|1116.9925
	\|1200
	~~\|1101.955~~
	~~\|1130.5264~~
	\|1116.9925
	\|Θ		\|Θ
	\|-		\|-
	\|14		\|14
	\|~~1277.955~~		\|1275
	\|~~1319.0979~~		\|1300
	~~\|1280.1389~~		! colspan="2" \|1200
	~~\|1181.955~~
	~~\|1216.2407~~
	\|1200
	\|Θ#		\|Θ#
	\|-		\|-
	\|15		\|15
	\|~~1373.955~~		\|1350
	\|~~1421.955~~		\|1400
	\|~~1360.2777~~		\|1275
	\|~~1261.955~~		\|1300
	~~\|1301.955~~
	~~\|1293.83465~~
	\|I (J)		\|I (J)
	\|-		\|-
	\|16		\|16
	\|~~1469.955~~		\|1425
	\|~~1524.8121~~		\|1500
	\|~~1440.4165~~		\|1350
	\|~~1341.955~~		\|1400
	~~! colspan="2" \|1387.6693~~
	\|A		\|A
	\|}		\|}

Moremajorthanmajor at 22:53, 31 May 2021

2021-05-31T22:53:24Z

← Older revision		Revision as of 22:53, 31 May 2021
Line 8:		Line 8:
	!Minimum a		!Minimum a
	!Maximum a		!Maximum a
			![8\13 99.609¢]
	!Minimum b		!Minimum b
	!Maximum b		!Maximum b
			![4\7 83.0075¢]
	!Annapolis[6L 4s]		!Annapolis[6L 4s]
	\|-		\|-
	!1		!1
	! colspan="4" \|87.7444		! colspan="6" \|87.7444
	\|Α#		\|Α#
	\|-		\|-
	!2		!2
	! colspan="4" \|175.48875		! colspan="6" \|175.48875
	\|Β		\|Β
	\|-		\|-
	!3		!3
	! colspan="4" \|263.2331		! colspan="6" \|263.2331
	\|Γ		\|Γ
	\|-		\|-
	!4		!4
	! colspan="4" \|350.9775		! colspan="6" \|350.9775
	\|Γ#		\|Γ#
	\|-		\|-
	!5		!5
	! colspan="4" \|438.7219		! colspan="6" \|438.7219
	\|Δ		\|Δ
	\|-		\|-
	!6		!6
	! colspan="4" \|526.46625		! colspan="6" \|526.46625
	\|Δ#		\|Δ#
	\|-		\|-
	!7		!7
	! colspan="4" \|614.2106		! colspan="6" \|614.2106
	\|Ε		\|Ε
	\|-		\|-
	!'''8'''		!'''8'''
	! colspan="4" \|'''701.955'''		! colspan="6" \|'''701.955'''
	\|'''Ϛ/Ϝ'''		\|'''Ϛ/Ϝ'''
	\|-		\|-
Line 47:		Line 49:
	\|797.955		\|797.955
	\|804.8121		\|804.8121
			\|801.564
	\|781.955		\|781.955
	\|787.~~6692~~		\|787.6693
			\|784.9625
	\|Ϛ#/Ϝ#		\|Ϛ#/Ϝ#
	\|-		\|-
Line 54:		Line 58:
	\|893.955		\|893.955
	\|907.6692		\|907.6692
			\|901.173
	\|861.955		\|861.955
	\|873.3836		\|873.3836
			\|867.97
	\|Ζ		\|Ζ
	\|-		\|-
Line 61:		Line 67:
	\|989.955		\|989.955
	\|1010.5264		\|1010.5264
			\|1000.782
	\|941.955		\|941.955
	\|959.0979		\|959.0979
			\|950.9775
	\|Η		\|Η
	\|-		\|-
Line 68:		Line 76:
	\|1085.955		\|1085.955
	\|1113.3836		\|1113.3836
			\|1101.391
	\|1021.955		\|1021.955
	\|1044.8121		\|1044.8121
			\|1033.985
	\|Η#		\|Η#
	\|-		\|-
Line 75:		Line 85:
	\|1181.955		\|1181.955
	\|1216.2407		\|1216.2407
			\|1200
	\|1101.955		\|1101.955
	\|1130.5264		\|1130.5264
			\|1116.9925
	\|Θ		\|Θ
	\|-		\|-
Line 82:		Line 94:
	\|1277.955		\|1277.955
	\|1319.0979		\|1319.0979
			\|1280.1389
	\|1181.955		\|1181.955
	\|1216.2407		\|1216.2407
			\|1200
	\|Θ#		\|Θ#
	\|-		\|-
Line 89:		Line 103:
	\|1373.955		\|1373.955
	\|1421.955		\|1421.955
			\|1360.2777
	\|1261.955		\|1261.955
	\|1301.955		\|1301.955
			\|1293.83465
	\|I (J)		\|I (J)
	\|-		\|-
Line 96:		Line 112:
	\|1469.955		\|1469.955
	\|1524.8121		\|1524.8121
			\|1440.4165
	\|1341.955		\|1341.955
	\|1387.~~6792~~		! colspan="2" \|1387.6693
	\|A		\|A
	\|}		\|}

Moremajorthanmajor at 17:55, 31 May 2021

2021-05-31T17:55:30Z

← Older revision		Revision as of 17:55, 31 May 2021
Line 1:		Line 1:
	'''16WTN''' is the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents making its best tunings very nearly [[88cET]].		'''16WTN''' is the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]].

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