666edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:33:07Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:33, 13 March 2026
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	\| [[Hemiennealimmal]] (666cf)		\| [[Hemiennealimmal]] (666cf)
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294 at 22:53, 20 February 2025

2025-02-20T22:53:52Z

← Older revision		Revision as of 22:53, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|666~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:47, 15 January 2025

2025-01-15T17:47:14Z

← Older revision		Revision as of 17:47, 15 January 2025
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	\|-		\|-
	\| 9		\| 9
	\| 175\666<br>(27\666)		\| 175\666<br />(27\666)
	\| 315.315<br>(48.648)		\| 315.315<br />(48.648)
	\| 6/5<br>(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]] (666c)		\| [[Ennealimmal]] (666c)
	\|-		\|-
	\| 18		\| 18
	\| 138\666<br>(27\666)		\| 138\666<br />(27\666)
	\| 248.648<br>(48.648)		\| 248.648<br />(48.648)
	\| 15/13<br>(99/98)		\| 15/13<br />(99/98)
	\| [[Hemiennealimmal]] (666cf)		\| [[Hemiennealimmal]] (666cf)
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==
Line 55:		Line 55:
	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) ~~–~~ classical piano		* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) – classical piano
	* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) ~~–~~ as part of the symphonic metal project Mercury Amalgam		* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) – as part of the symphonic metal project Mercury Amalgam

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:40:10Z

Partial undo

← Older revision		Revision as of 12:40, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 40:		Line 47:
	\| 15/13<br>(99/98)		\| 15/13<br>(99/98)
	\| [[Hemiennealimmal]] (666cf)		\| [[Hemiennealimmal]] (666cf)
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

ArrowHead294 at 04:12, 16 November 2024

2024-11-16T04:12:36Z

← Older revision		Revision as of 04:12, 16 November 2024
Line 15:		Line 15:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 46:		Line 40:
	\| 15/13<br>(99/98)		\| 15/13<br>(99/98)
	\| [[Hemiennealimmal]] (666cf)		\| [[Hemiennealimmal]] (666cf)
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==
Line 54:		Line 48:
	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) – classical piano		* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) – classical piano
	* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) – as part of the symphonic metal project Mercury Amalgam		* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) – as part of the symphonic metal project Mercury Amalgam

	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-02-13T18:19:00Z

+categories

← Older revision		Revision as of 18:19, 13 February 2024
Line 56:		Line 56:
	* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) – classical piano		* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) – classical piano
	* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) – as part of the symphonic metal project Mercury Amalgam		* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) – as part of the symphonic metal project Mercury Amalgam

			[[Category:Listen]]

Eliora: /* Theory */

2024-02-12T12:06:24Z

Theory

← Older revision		Revision as of 12:06, 12 February 2024
Line 5:		Line 5:
	666edo is [[enfactoring\|enfactored]] in the 17-limit, with the same mapping as [[333edo]], but the 2.9.15.21.11.17.19 [[subgroup]] is great for 666edo. Alternatively, it can be used with 2.9.15.7.11.19.23. 666edo provides good direct approximations for: [[15/11]], [[16/11]], [[16/15]], [[13/12]], [[13/10]], [[22/15]], [[23/14]]. 666edo also has a strong approximation for [[11/8]] derived from [[37edo]] and for [[7/6]] derived from 9edo, but on the 2.7/6.11 subgroup it is enfactored, with the same tuning again as 333edo, tempering out the [[37-11-comma]] and the [[septimal ennealimma]]. The 666c val, tempers out [[2401/2400]], [[4375/4374]], and [[9801/9800]] in the 11 limit.		666edo is [[enfactoring\|enfactored]] in the 17-limit, with the same mapping as [[333edo]], but the 2.9.15.21.11.17.19 [[subgroup]] is great for 666edo. Alternatively, it can be used with 2.9.15.7.11.19.23. 666edo provides good direct approximations for: [[15/11]], [[16/11]], [[16/15]], [[13/12]], [[13/10]], [[22/15]], [[23/14]]. 666edo also has a strong approximation for [[11/8]] derived from [[37edo]] and for [[7/6]] derived from 9edo, but on the 2.7/6.11 subgroup it is enfactored, with the same tuning again as 333edo, tempering out the [[37-11-comma]] and the [[septimal ennealimma]]. The 666c val, tempers out [[2401/2400]], [[4375/4374]], and [[9801/9800]] in the 11 limit.

	666edo is also used by [[Eliora]] to approximate the "[[Factor 9 grid]]", or the just intonation esoteric scale deconstructed and debunked by Adam Neely. Now, it may be worth noting that the tuning system which truly has an excellent approximation of the Factor 9 grid is 666ed15/14. However, this fact was not spotted by Eliora until after first music was composed in 666edo due to the temperament finder layout making it not immediately obvious what is the interval of equivalence, so the Factor 9 grid representation by 666edo still remains notable given that it is a scale for some of the first music composed in this edo.		666edo is also used by [[Eliora]] to approximate the "[[Factor 9 grid]]", or the just intonation esoteric scale deconstructed and debunked by Adam Neely. Now, it may be worth noting that the tuning system which truly has an excellent approximation of the Factor 9 grid is 666ed15/14, approximately equivalent to [[6691edo]]. However, this fact was not spotted by Eliora until after first music was composed in 666edo due to the temperament finder layout making it not immediately obvious what is the interval of equivalence, so the Factor 9 grid representation by 666edo still remains notable given that it is a scale for some of the first music composed in this edo.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 666 factors into {{factorization\|666}}, 666edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 37, 74, 111, 222, 333 }}, of which 111edo is a notable system due to its accuracy relative to its size.		Since 666 factors into {{factorization\|666}}, 666edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 37, 74, 111, 222, 333 }}, of which 111edo is a notable system due to its accuracy relative to its size.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T12:59:16Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:59, 2 November 2023
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	666 has subset edos {{EDOs\| 2, 3, 6, 9, 18, 37, 74, 111, 222, 333 }}, of which 111edo is a notable system due to its ~~large amount of regular temperaments~~.		Since 666 factors into {{factorization\|666}}, 666edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 37, 74, 111, 222, 333 }}, of which 111edo is a notable system due to its accuracy relative to its size.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 20:		Line 20:
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated <br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 54:		Line 54:
	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''], classical piano		* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''] (2022) – classical piano
	* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''], as part of the symphonic metal project Mercury Amalgam		* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''] (2022) – as part of the symphonic metal project Mercury Amalgam

FloraC: Cleanup and re-evaluate the subgroups; clarify the title row of the rank-2 temp table; -redundant categories

2023-10-22T08:42:57Z

Cleanup and re-evaluate the subgroups; clarify the title row of the rank-2 temp table; -redundant categories

← Older revision		Revision as of 08:42, 22 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	666edo is enfactored in the 17-limit, with the same mapping as [[333edo]]~~. Using precision as a criterion~~, 2.11.19~~.41.43~~ subgroup is great for 666edo. ~~If significant errors are allowed~~, ~~666edo~~ can be used with 2.7.11~~.17~~.19.23. 666edo provides good direct approximations for: [[15/11]], [[16/11]], [[16/15]], [[13/12]], [[13/10]], [[22/15]], [[23/14]]. 666edo also has a strong approximation for [[11/8]] derived from [[37edo]] and for [[7/6]] derived from 9edo, but on the 2.7/6.11 subgroup it is enfactored, with the same tuning again as 333edo, tempering out the [[37-11-comma]] and the [[septimal ennealimma]]. The 666c val, tempers out [[2401/2400]], [[4375/4374]], and [[9801/9800]] in the 11 limit.		666edo is [[enfactoring\|enfactored]] in the 17-limit, with the same mapping as [[333edo]], but the 2.9.15.21.11.17.19 [[subgroup]] is great for 666edo. Alternatively, it can be used with 2.9.15.7.11.19.23. 666edo provides good direct approximations for: [[15/11]], [[16/11]], [[16/15]], [[13/12]], [[13/10]], [[22/15]], [[23/14]]. 666edo also has a strong approximation for [[11/8]] derived from [[37edo]] and for [[7/6]] derived from 9edo, but on the 2.7/6.11 subgroup it is enfactored, with the same tuning again as 333edo, tempering out the [[37-11-comma]] and the [[septimal ennealimma]]. The 666c val, tempers out [[2401/2400]], [[4375/4374]], and [[9801/9800]] in the 11 limit.

	666edo is also used by [[Eliora]] to approximate the "[[Factor 9 grid]]", or the just intonation esoteric scale deconstructed and debunked by Adam Neely. Now, it may be worth noting that the tuning system which truly has an excellent approximation of the Factor 9 grid is 666ed15/14. However, this fact ~~wasn't~~ spotted by Eliora until after first music was composed in 666edo due to the temperament finder layout making it not immediately obvious what is the interval of equivalence, so the Factor 9 grid representation by 666edo still remains notable given that it's a scale for some of the first music composed in this edo.		666edo is also used by [[Eliora]] to approximate the "[[Factor 9 grid]]", or the just intonation esoteric scale deconstructed and debunked by Adam Neely. Now, it may be worth noting that the tuning system which truly has an excellent approximation of the Factor 9 grid is 666ed15/14. However, this fact was not spotted by Eliora until after first music was composed in 666edo due to the temperament finder layout making it not immediately obvious what is the interval of equivalence, so the Factor 9 grid representation by 666edo still remains notable given that it is a scale for some of the first music composed in this edo.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
			666 has subset edos {{EDOs\| 2, 3, 6, 9, 18, 37, 74, 111, 222, 333 }}, of which 111edo is a notable system due to its large amount of regular temperaments.
	666 has subset edos {{EDOs\|1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333}}, of which 111edo is a notable system due to its large amount of regular temperaments.

	== Regular temperament properties ==		== Regular temperament properties ==
	===Rank-2 temperaments===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods <br>per 8ve		\|+Table of rank-2 temperaments by generator
	!Generator		! Periods<br>per 8ve
	!Cents		! Generator*
	!Associated <br>~~ratio~~		! Cents*
	!Temperaments		! Associated <br>Ratio
			! Temperaments
	\|-		\|-
	\|1		\| 1
	\|175\666		\| 175\666
	\|315.31		\| 315.31
	\|6/5		\| 6/5
	\|[[Parakleismic]] (666b)		\| [[Parakleismic]] (666b)
	\|-		\|-
	\|9		\| 9
	\|35\666		\| 35\666
	\|63.063		\| 63.063
	\|336/323		\| 336/323
	\|[[Enneasoteric]]		\| [[Enneasoteric]]
	\|-		\|-
	\|9		\| 9
	\|175\666<br>(27\666)		\| 175\666<br>(27\666)
	\|315.315<br>(48.648)		\| 315.315<br>(48.648)
	\|6/5<br>(36/35)		\| 6/5<br>(36/35)
	\|[[Ennealimmal]] (666c)		\| [[Ennealimmal]] (666c)
	\|-		\|-
	\|18		\| 18
	\|138\666<br>(27\666)		\| 138\666<br>(27\666)
	\|248.648<br>(48.648)		\| 248.648<br>(48.648)
	\|15/13<br>(99/98)		\| 15/13<br>(99/98)
	\|[[Hemiennealimmal]] (666cf)		\| [[Hemiennealimmal]] (666cf)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

	* Factor9Grid[14]: 39 38 36 35 66 62 59 55 52 49 46 44 42 41		* Factor9Grid[14]: 39 38 36 35 66 62 59 55 52 49 46 44 42 41

	== Music ==		== Music ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s Timeline], classical piano		* [https://www.youtube.com/watch?v=Y4gVyK9vNkk&t=7s ''Timeline''], classical piano
	* [https://www.youtube.com/watch?v=KV0-kT5slZc Church of Original Sin], as part of the symphonic metal project Mercury Amalgam		* [https://www.youtube.com/watch?v=KV0-kT5slZc ''Church of Original Sin''], as part of the symphonic metal project Mercury Amalgam

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

BudjarnLambeth at 06:43, 9 July 2023

2023-07-09T06:43:30Z

← Older revision		Revision as of 06:43, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|666}}		{{EDO intro\|666}}