16edt - Revision history

Fredg999 category edits: Removing from Category:Edt using Cat-a-lot

2025-07-31T15:31:26Z

Removing from Category:Edt using Cat-a-lot

← Older revision		Revision as of 15:31, 31 July 2025
Line 147:		Line 147:
	[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]		[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]

	~~[[Category:Edt]]~~
	[[Category:Macrotonal]]		[[Category:Macrotonal]]
	{{todo\|expand}}		{{todo\|expand}}

ArrowHead294 at 19:01, 14 February 2025

2025-02-14T19:01:18Z

← Older revision		Revision as of 19:01, 14 February 2025
Line 1:		Line 1:
			{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

ArrowHead294 at 14:54, 14 January 2025

2025-01-14T14:54:42Z

Show changes

BudjarnLambeth: {{todo|expand}}

2024-12-21T03:40:32Z

← Older revision		Revision as of 03:40, 21 December 2024
Line 130:		Line 130:
	[[Category:Edt]]		[[Category:Edt]]
	[[Category:Macrotonal]]		[[Category:Macrotonal]]
			{{todo\|expand}}

BudjarnLambeth: Add table of harmonics

2024-10-06T06:33:43Z

Add table of harmonics

@@ Line 4: / Line 4: @@
 == Properties ==
 As the double of [[8edt|8EDT]], this division of the tritave is harmonically fraternal to [[10edo|10EDO]]. Its unit step is ~1.128 cents flat of 1\10EDO. Unlike 10EDO, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13|13:21]] and a decent [[13/7|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.
 == Intervals ==

Cmloegcmluin: /* Related temperament */ "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-08T22:00:08Z

Related temperament: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 22:00, 8 May 2023
Line 88:		Line 88:
	Mapping: [{{val\|1 0 5 4}}, {{val\|0 16 -27 -12}}]<br>		Mapping: [{{val\|1 0 5 4}}, {{val\|0 16 -27 -12}}]<br>
	POTE generator: ~15/14 = 118.965<br>		POTE generator: ~15/14 = 118.965<br>
	~~Vals:~~ 10, 101, 111, 121, 232d<br>		{{Optimal ET sequence\|legend=1\| 10, 101, 111, 121, 232d}}<br>
	Badness: 0.157658<br><br>		Badness: 0.157658<br><br>
	'''11-limit'''<br>		'''11-limit'''<br>

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T19:28:06Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 19:28, 7 May 2023
Line 94:		Line 94:
	Mapping: [{{val\|1 0 5 4 -1}}, {{val\|0 16 -27 -12 45}}]<br>		Mapping: [{{val\|1 0 5 4 -1}}, {{val\|0 16 -27 -12 45}}]<br>
	POTE generator: ~15/14 = 118.968<br>		POTE generator: ~15/14 = 118.968<br>
	~~Vals:~~ 10, 101, 111, 121, 232d<br>		{{Optimal ET sequence\|legend=1\| 10, 101, 111, 121, 232d}}<br>
	Badness: 0.066838<br><br>		Badness: 0.066838<br><br>
	'''13-limit'''<br>		'''13-limit'''<br>
Line 100:		Line 100:
	Mapping: [{{val\|1 0 5 4 -1 4}}, {{val\|0 16 -27 -12 45 -3}}]<br>		Mapping: [{{val\|1 0 5 4 -1 4}}, {{val\|0 16 -27 -12 45 -3}}]<br>
	POTE generator: ~15/14 = 118.968<br>		POTE generator: ~15/14 = 118.968<br>
	~~Vals:~~ 10, 101, 111, 121, 232d<br>		{{Optimal ET sequence\|legend=1\| 10, 101, 111, 121, 232d}}<br>
	Badness: 0.031635<br><br>		Badness: 0.031635<br><br>
	'''17-limit'''<br>		'''17-limit'''<br>
Line 106:		Line 106:
	Mapping: [{{val\|1 0 5 4 -1 4 3}}, {{val\|0 16 -27 -12 45 -3 11}}]<br>		Mapping: [{{val\|1 0 5 4 -1 4 3}}, {{val\|0 16 -27 -12 45 -3 11}}]<br>
	POTE generator: ~15/14 = 118.968<br>		POTE generator: ~15/14 = 118.968<br>
	~~Vals:~~ 10, 101, 111, 121, 232dg<br>		{{Optimal ET sequence\|legend=1\| 10, 101, 111, 121, 232dg}}<br>
	Badness: 0.019707<br><br>		Badness: 0.019707<br><br>

Plumtree: Infobox ET added

2022-10-05T19:47:21Z

Infobox ET added

← Older revision		Revision as of 19:47, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''16EDT''' is [[EDT\|equal division of the third harmonic]] into 16 parts of 118.872 cents each (corresponding to 10.0949 [[EDO]]).		'''16EDT''' is [[EDT\|equal division of the third harmonic]] into 16 parts of 118.872 cents each (corresponding to 10.0949 [[EDO]]).

Xenllium at 12:14, 11 September 2021

2021-09-11T12:14:57Z

← Older revision		Revision as of 12:14, 11 September 2021
Line 1:		Line 1:
	~~=Properties=~~		'''16EDT''' is [[EDT\|equal division of the third harmonic]] into 16 parts of 118.872 cents each (corresponding to 10.0949 [[EDO]]).
	~~As the double of~~ [[~~8edt~~\|~~8edt]], this~~ division of the ~~tritave is harmonically fraternal to [[10edo\|10edo~~]]. ~~Its unit step is ~1.128~~ cents ~~flat of 1\10edo~~. ~~Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent~~ [[~~21/13\|13:21~~]] ~~and a decent [[13/7\|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament~~.
	~~[[category:macrotonal]]~~

	=Intervals=		== Properties ==
			As the double of [[8edt\|8EDT]], this division of the tritave is harmonically fraternal to [[10edo\|10EDO]]. Its unit step is ~1.128 cents flat of 1\10EDO. Unlike 10EDO, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13\|13:21]] and a decent [[13/7\|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.

			== Intervals ==

	{\| class="wikitable"		{\| class="wikitable"
Line 11:		Line 12:
	\|-		\|-
	![[cent\|Cents]]		![[cent\|Cents]]
	!Hekts		! Hekts
	\|-		\|-
	\| style="text-align:center;" \| 1		\| style="text-align:center;" \| 1
	\| style="text-align:right;" \| 118.87219		\| style="text-align:right;" \| 118.87219
	\|81.25		\| 81.25
	\|-		\|-
	\| style="text-align:center;" \| 2		\| style="text-align:center;" \| 2
	\| style="text-align:right;" \| 237.74438		\| style="text-align:right;" \| 237.74438
	\|162.5		\| 162.5
	\|-		\|-
	\| style="text-align:center;" \| 3		\| style="text-align:center;" \| 3
	\| style="text-align:right;" \| 356.61656		\| style="text-align:right;" \| 356.61656
	\|243.75		\| 243.75
	\|-		\|-
	\| style="text-align:center;" \| 4		\| style="text-align:center;" \| 4
	\| style="text-align:right;" \| 475.48875		\| style="text-align:right;" \| 475.48875
	\|325		\| 325
	\|-		\|-
	\| style="text-align:center;" \| 5		\| style="text-align:center;" \| 5
	\| style="text-align:right;" \| 594.36094		\| style="text-align:right;" \| 594.36094
	\|406.25		\| 406.25
	\|-		\|-
	\| style="text-align:center;" \| 6		\| style="text-align:center;" \| 6
	\| style="text-align:right;" \| 713.23312		\| style="text-align:right;" \| 713.23312
	\|487.5		\| 487.5
	\|-		\|-
	\| style="text-align:center;" \| 7		\| style="text-align:center;" \| 7
	\| style="text-align:right;" \| 832.10531		\| style="text-align:right;" \| 832.10531
	\|568.75		\| 568.75
	\|-		\|-
	\| style="text-align:center;" \| 8		\| style="text-align:center;" \| 8
	\| style="text-align:right;" \| 950.9775		\| style="text-align:right;" \| 950.9775
	\|650		\| 650
	\|-		\|-
	\| style="text-align:center;" \| 9		\| style="text-align:center;" \| 9
	\| style="text-align:right;" \| 1069.84969		\| style="text-align:right;" \| 1069.84969
	\|731.25		\| 731.25
	\|-		\|-
	\| style="text-align:center;" \| 10		\| style="text-align:center;" \| 10
	\| style="text-align:right;" \| 1188.72188		\| style="text-align:right;" \| 1188.72188
	\|812.5		\| 812.5
	\|-		\|-
	\| style="text-align:center;" \| 11		\| style="text-align:center;" \| 11
	\| style="text-align:right;" \| 1307.59406		\| style="text-align:right;" \| 1307.59406
	\|893.75		\| 893.75
	\|-		\|-
	\| style="text-align:center;" \| 12		\| style="text-align:center;" \| 12
	\| style="text-align:right;" \| 1426.46625		\| style="text-align:right;" \| 1426.46625
	\|975		\| 975
	\|-		\|-
	\| style="text-align:center;" \| 13		\| style="text-align:center;" \| 13
	\| style="text-align:right;" \| 1545.33844		\| style="text-align:right;" \| 1545.33844
	\|1056.25		\| 1056.25
	\|-		\|-
	\| style="text-align:center;" \| 14		\| style="text-align:center;" \| 14
	\| style="text-align:right;" \| 1664.21063		\| style="text-align:right;" \| 1664.21063
	\|1137.5		\| 1137.5
	\|-		\|-
	\| style="text-align:center;" \| 15		\| style="text-align:center;" \| 15
	\| style="text-align:right;" \| 1783.08281		\| style="text-align:right;" \| 1783.08281
	\|1218.75		\| 1218.75
	\|-		\|-
	\| style="text-align:center;" \| 16		\| style="text-align:center;" \| 16
	\| style="text-align:right;" \| 1901.955		\| style="text-align:right;" \| 1901.955
	\|1300		\| 1300
	\|}		\|}

	=Music=		== Related temperament ==
			16EDT is also be thought of as a generator of the ''subsedia'' temperament, which is a [[cluster temperament]] with 10 clusters of notes in an octave.

			; [[Mirkwai clan #Subsedia\|Subsedia]] (10 & 111)
			'''7-limit'''<br>
			Comma list: 16875/16807, 65536/64827<br>
			Mapping: [{{val\|1 0 5 4}}, {{val\|0 16 -27 -12}}]<br>
			POTE generator: ~15/14 = 118.965<br>
			Vals: 10, 101, 111, 121, 232d<br>
			Badness: 0.157658<br><br>
			'''11-limit'''<br>
			Comma list: 540/539, 1375/1372, 65536/64827<br>
			Mapping: [{{val\|1 0 5 4 -1}}, {{val\|0 16 -27 -12 45}}]<br>
			POTE generator: ~15/14 = 118.968<br>
			Vals: 10, 101, 111, 121, 232d<br>
			Badness: 0.066838<br><br>
			'''13-limit'''<br>
			Comma list: 352/351, 540/539, 676/675, 1375/1372<br>
			Mapping: [{{val\|1 0 5 4 -1 4}}, {{val\|0 16 -27 -12 45 -3}}]<br>
			POTE generator: ~15/14 = 118.968<br>
			Vals: 10, 101, 111, 121, 232d<br>
			Badness: 0.031635<br><br>
			'''17-limit'''<br>
			Comma list: 256/255, 352/351, 442/441, 540/539, 715/714<br>
			Mapping: [{{val\|1 0 5 4 -1 4 3}}, {{val\|0 16 -27 -12 45 -3 11}}]<br>
			POTE generator: ~15/14 = 118.968<br>
			Vals: 10, 101, 111, 121, 232dg<br>
			Badness: 0.019707<br><br>

			== Music ==
	[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]		[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]

			[[Category:Edt]]
			[[Category:Macrotonal]]

Moremajorthanmajor at 17:41, 13 April 2019

2019-04-13T17:41:03Z

← Older revision		Revision as of 17:41, 13 April 2019
Line 1:		Line 1:
	=Properties=		=Properties=
	As the double of [[8edt\|8edt]], this division of the tritave is harmonically fraternal to [[10edo\|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13\|13:21]] and a decent [[13/7\|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.[[category:macrotonal]]		As the double of [[8edt\|8edt]], this division of the tritave is harmonically fraternal to [[10edo\|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13\|13:21]] and a decent [[13/7\|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.
			[[category:macrotonal]]

	=Intervals=		=Intervals=
Line 6:		Line 7:
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! \| Degree		! rowspan="2"\| Degree
	! \| Size in [[cent\|Cents]]		! colspan="2"\| Size in
			\|-
			![[cent\|Cents]]
			!Hekts
	\|-		\|-
	\| style="text-align:center;" \| 1		\| style="text-align:center;" \| 1
	\| style="text-align:right;" \| 118.87219		\| style="text-align:right;" \| 118.87219
			\|81.25
	\|-		\|-
	\| style="text-align:center;" \| 2		\| style="text-align:center;" \| 2
	\| style="text-align:right;" \| 237.74438		\| style="text-align:right;" \| 237.74438
			\|162.5
	\|-		\|-
	\| style="text-align:center;" \| 3		\| style="text-align:center;" \| 3
	\| style="text-align:right;" \| 356.61656		\| style="text-align:right;" \| 356.61656
			\|243.75
	\|-		\|-
	\| style="text-align:center;" \| 4		\| style="text-align:center;" \| 4
	\| style="text-align:right;" \| 475.48875		\| style="text-align:right;" \| 475.48875
			\|325
	\|-		\|-
	\| style="text-align:center;" \| 5		\| style="text-align:center;" \| 5
	\| style="text-align:right;" \| 594.36094		\| style="text-align:right;" \| 594.36094
			\|406.25
	\|-		\|-
	\| style="text-align:center;" \| 6		\| style="text-align:center;" \| 6
	\| style="text-align:right;" \| 713.23312		\| style="text-align:right;" \| 713.23312
			\|487.5
	\|-		\|-
	\| style="text-align:center;" \| 7		\| style="text-align:center;" \| 7
	\| style="text-align:right;" \| 832.10531		\| style="text-align:right;" \| 832.10531
			\|568.75
	\|-		\|-
	\| style="text-align:center;" \| 8		\| style="text-align:center;" \| 8
	\| style="text-align:right;" \| 950.~~97750~~		\| style="text-align:right;" \| 950.9775
			\|650
	\|-		\|-
	\| style="text-align:center;" \| 9		\| style="text-align:center;" \| 9
	\| style="text-align:right;" \| 1069.84969		\| style="text-align:right;" \| 1069.84969
			\|731.25
	\|-		\|-
	\| style="text-align:center;" \| 10		\| style="text-align:center;" \| 10
	\| style="text-align:right;" \| 1188.72188		\| style="text-align:right;" \| 1188.72188
			\|812.5
	\|-		\|-
	\| style="text-align:center;" \| 11		\| style="text-align:center;" \| 11
	\| style="text-align:right;" \| 1307.59406		\| style="text-align:right;" \| 1307.59406
			\|893.75
	\|-		\|-
	\| style="text-align:center;" \| 12		\| style="text-align:center;" \| 12
	\| style="text-align:right;" \| 1426.46625		\| style="text-align:right;" \| 1426.46625
			\|975
	\|-		\|-
	\| style="text-align:center;" \| 13		\| style="text-align:center;" \| 13
	\| style="text-align:right;" \| 1545.33844		\| style="text-align:right;" \| 1545.33844
			\|1056.25
	\|-		\|-
	\| style="text-align:center;" \| 14		\| style="text-align:center;" \| 14
	\| style="text-align:right;" \| 1664.21063		\| style="text-align:right;" \| 1664.21063
			\|1137.5
	\|-		\|-
	\| style="text-align:center;" \| 15		\| style="text-align:center;" \| 15
	\| style="text-align:right;" \| 1783.08281		\| style="text-align:right;" \| 1783.08281
			\|1218.75
	\|-		\|-
	\| style="text-align:center;" \| 16		\| style="text-align:center;" \| 16
	\| style="text-align:right;" \| 1901.~~95500~~		\| style="text-align:right;" \| 1901.955
			\|1300
	\|}		\|}

	=Music=		=Music=
	[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]		[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]

← Older revision		Revision as of 17:41, 13 April 2019
Line 1:		Line 1:
	=Properties=		=Properties=
	As the double of [[8edt\|8edt]], this division of the tritave is harmonically fraternal to [[10edo\|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13\|13:21]] and a decent [[13/7\|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.[[category:macrotonal]]		As the double of [[8edt\|8edt]], this division of the tritave is harmonically fraternal to [[10edo\|10edo]]. Its unit step is ~1.128 cents flat of 1\10edo. Unlike 10edo, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13\|13:21]] and a decent [[13/7\|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood temperament.
			[[category:macrotonal]]

	=Intervals=		=Intervals=
Line 6:		Line 7:
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! \| Degree		! rowspan="2"\| Degree
	! \| Size in [[cent\|Cents]]		! colspan="2"\| Size in
			\|-
			![[cent\|Cents]]
			!Hekts
	\|-		\|-
	\| style="text-align:center;" \| 1		\| style="text-align:center;" \| 1
	\| style="text-align:right;" \| 118.87219		\| style="text-align:right;" \| 118.87219
			\|81.25
	\|-		\|-
	\| style="text-align:center;" \| 2		\| style="text-align:center;" \| 2
	\| style="text-align:right;" \| 237.74438		\| style="text-align:right;" \| 237.74438
			\|162.5
	\|-		\|-
	\| style="text-align:center;" \| 3		\| style="text-align:center;" \| 3
	\| style="text-align:right;" \| 356.61656		\| style="text-align:right;" \| 356.61656
			\|243.75
	\|-		\|-
	\| style="text-align:center;" \| 4		\| style="text-align:center;" \| 4
	\| style="text-align:right;" \| 475.48875		\| style="text-align:right;" \| 475.48875
			\|325
	\|-		\|-
	\| style="text-align:center;" \| 5		\| style="text-align:center;" \| 5
	\| style="text-align:right;" \| 594.36094		\| style="text-align:right;" \| 594.36094
			\|406.25
	\|-		\|-
	\| style="text-align:center;" \| 6		\| style="text-align:center;" \| 6
	\| style="text-align:right;" \| 713.23312		\| style="text-align:right;" \| 713.23312
			\|487.5
	\|-		\|-
	\| style="text-align:center;" \| 7		\| style="text-align:center;" \| 7
	\| style="text-align:right;" \| 832.10531		\| style="text-align:right;" \| 832.10531
			\|568.75
	\|-		\|-
	\| style="text-align:center;" \| 8		\| style="text-align:center;" \| 8
	\| style="text-align:right;" \| 950.~~97750~~		\| style="text-align:right;" \| 950.9775
			\|650
	\|-		\|-
	\| style="text-align:center;" \| 9		\| style="text-align:center;" \| 9
	\| style="text-align:right;" \| 1069.84969		\| style="text-align:right;" \| 1069.84969
			\|731.25
	\|-		\|-
	\| style="text-align:center;" \| 10		\| style="text-align:center;" \| 10
	\| style="text-align:right;" \| 1188.72188		\| style="text-align:right;" \| 1188.72188
			\|812.5
	\|-		\|-
	\| style="text-align:center;" \| 11		\| style="text-align:center;" \| 11
	\| style="text-align:right;" \| 1307.59406		\| style="text-align:right;" \| 1307.59406
			\|893.75
	\|-		\|-
	\| style="text-align:center;" \| 12		\| style="text-align:center;" \| 12
	\| style="text-align:right;" \| 1426.46625		\| style="text-align:right;" \| 1426.46625
			\|975
	\|-		\|-
	\| style="text-align:center;" \| 13		\| style="text-align:center;" \| 13
	\| style="text-align:right;" \| 1545.33844		\| style="text-align:right;" \| 1545.33844
			\|1056.25
	\|-		\|-
	\| style="text-align:center;" \| 14		\| style="text-align:center;" \| 14
	\| style="text-align:right;" \| 1664.21063		\| style="text-align:right;" \| 1664.21063
			\|1137.5
	\|-		\|-
	\| style="text-align:center;" \| 15		\| style="text-align:center;" \| 15
	\| style="text-align:right;" \| 1783.08281		\| style="text-align:right;" \| 1783.08281
			\|1218.75
	\|-		\|-
	\| style="text-align:center;" \| 16		\| style="text-align:center;" \| 16
	\| style="text-align:right;" \| 1901.~~95500~~		\| style="text-align:right;" \| 1901.955
			\|1300
	\|}		\|}

	=Music=		=Music=
	[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]		[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky\|Peter 'Rush' Kosmorsky]]