888edo - Revision history

ArrowHead294 at 23:00, 20 February 2025

2025-02-20T23:00:29Z

← Older revision		Revision as of 23:00, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|888~~}}		{{ED intro}}

	888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out\|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.		888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out\|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:33:50Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:33, 2 November 2023
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	{{EDO intro\|888}}		{{EDO intro\|888}}

	888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps~~, but otherwise~~ it is excellent in approximating harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out\|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.		888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out\|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 888 factors into ~~2<sup>3</sup> × 3 × 37~~, 888edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, and 444 }}. 1776edo, which doubles it, provides a good correction for harmonic 3.		Since 888 factors into {{factorization\|888}}, 888edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, and 444 }}. 1776edo, which doubles it, provides a good correction for harmonic 3.

FloraC: -complaints that don't belong to an edo page, replaced with more neutral stuff; -redundant categories

2023-10-20T09:39:52Z

-complaints that don't belong to an edo page, replaced with more neutral stuff; -redundant categories

← Older revision		Revision as of 09:39, 20 October 2023
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	{{EDO intro\|888}}		{{EDO intro\|888}}

	== ~~Theory~~ ==		888edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps, but otherwise it is excellent in approximating harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation. The equal temperament [[Tempering out\|tempers out]] [[4096/4095]], [[6656/6655]], [[9801/9800]], [[10648/10647]], 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.

			=== Odd harmonics ===
	{{Harmonics in equal\|888}}		{{Harmonics in equal\|888}}
	888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfect fifth. The usage of 3/2 is so deeply entrenched into nearly all musical traditions of the world, that temperaments which lack a perfect fifth do not get considered, even if other harmonics are excellently approximated.

	~~888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.~~

	~~[[Category:Equal divisions of the octave\|###]]~~ <~~!--~~ 3~~-digit number --~~>		=== Subsets and supersets ===
			Since 888 factors into 2<sup>3</sup> × 3 × 37, 888edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, and 444 }}. 1776edo, which doubles it, provides a good correction for harmonic 3.

BudjarnLambeth at 06:47, 9 July 2023

2023-07-09T06:47:00Z

← Older revision		Revision as of 06:47, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|888}}		{{EDO intro\|888}}

BudjarnLambeth at 05:28, 9 July 2023

2023-07-09T05:28:25Z

← Older revision		Revision as of 05:28, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|888}}		{{EDO intro\|888}}

Plumtree: Infobox ET added

2022-10-04T22:04:03Z

Infobox ET added

← Older revision		Revision as of 22:04, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|888}}		{{EDO intro\|888}}

Fredg999 category edits: Categories

2022-07-04T01:07:36Z

Eliora: Created page with "{{EDO intro|888}} == Theory == {{Harmonics in equal|888}} 888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfec..."

2022-03-29T12:56:52Z

Created page with "{{EDO intro|888}} == Theory == {{Harmonics in equal|888}} 888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfec..."

New page

{{EDO intro|888}}

== Theory ==
{{Harmonics in equal|888}}
888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfect fifth. The usage of 3/2 is so deeply entrenched into nearly all musical traditions of the world, that temperaments which lack a perfect fifth do not get considered, even if other harmonics are excellently approximated.

888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.

← Older revision		Revision as of 01:07, 4 July 2022
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	888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.		888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.

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