777edo - Revision history

Overthink: /* Subsets and supersets */ fixed the last subset

2025-09-18T04:28:56Z

Subsets and supersets: fixed the last subset

← Older revision		Revision as of 04:28, 18 September 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 777 factors into {{factorization\|777}}, 777edo has subset edos {{EDOs\| 3, 7, 21, 37, 111, and ~~333~~ }}.		Since 777 factors into {{factorization\|777}}, 777edo has subset edos {{EDOs\| 3, 7, 21, 37, 111, and 259}}.

ArrowHead294 at 23:13, 20 February 2025

2025-02-20T23:13:52Z

← Older revision		Revision as of 23:13, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|777~~}}		{{ED intro}}

	777edo is in[[consistent]] to [[5-odd-limit]] and [[harmonic]] [[3/1\|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]], [[13/1\|13]], and [[17/1\|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation. A [[comma basis]] for the 2.9.5.7.11.13 subgroup is {4459/4455, [[41503/41472]], 496125/495616, 105644/105625, [[123201/123200]]}. In addition, it [[tempering out\|tempers out]] the [[landscape comma]] in the 2.9.5.7 subgroup.		777edo is in[[consistent]] to [[5-odd-limit]] and [[harmonic]] [[3/1\|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]], [[13/1\|13]], and [[17/1\|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation. A [[comma basis]] for the 2.9.5.7.11.13 subgroup is {4459/4455, [[41503/41472]], 496125/495616, 105644/105625, [[123201/123200]]}. In addition, it [[tempering out\|tempers out]] the [[landscape comma]] in the 2.9.5.7 subgroup.

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T12:07:51Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:07, 2 November 2023
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	{{EDO intro\|777}}		{{EDO intro\|777}}

	777edo is a [[~~dual~~-~~fifth system~~]] ~~with a~~ [[~~consistency~~\|~~consistency limit~~]] ~~of only 3, 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 ~~with the~~ comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200~~, 105644/105625~~}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup.		777edo is in[[consistent]] to [[5-odd-limit]] and [[harmonic]] [[3/1\|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]], [[13/1\|13]], and [[17/1\|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation. A [[comma basis]] for the 2.9.5.7.11.13 subgroup is {4459/4455, [[41503/41472]], 496125/495616, 105644/105625, [[123201/123200]]}. In addition, it [[tempering out\|tempers out]] the [[landscape comma]] in the 2.9.5.7 subgroup.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 777 factors into ~~3 × 7 × 37~~, 777edo has subset edos {{EDOs\| 3, 7, 21, 37, 111, and 333 }}.		Since 777 factors into {{factorization\|777}}, 777edo has subset edos {{EDOs\| 3, 7, 21, 37, 111, and 333 }}.

FloraC: Rework

2023-10-20T11:52:32Z

Rework

← Older revision		Revision as of 11:52, 20 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.		{{EDO intro\|777}}

	~~== Theory ==~~		777edo is a [[dual-fifth system]] with a [[consistency\|consistency limit]] of only 3, 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 with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup.

	777edo is a dual ~~fifths~~ system with a consistency limit of only 3.

	~~If the harmonic 3 is excluded~~, it is an excellent 2.5.7.9.11.13 subgroup ~~tuning,~~ with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup.

			=== Odd harmonics ===
	{{Harmonics in equal\|777}}		{{Harmonics in equal\|777}}

	~~[[Category:Equal divisions of the octave~~\|~~###]] <!--~~ 3~~-digit number -->~~		=== Subsets and supersets ===
			Since 777 factors into 3 × 7 × 37, 777edo has subset edos {{EDOs\| 3, 7, 21, 37, 111, and 333 }}.

BudjarnLambeth at 06:45, 9 July 2023

2023-07-09T06:45:45Z

← Older revision		Revision as of 06:45, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.		The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.

BudjarnLambeth at 05:30, 9 July 2023

2023-07-09T05:30:02Z

← Older revision		Revision as of 05:30, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.		The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.

Aura at 18:17, 22 December 2022

2022-12-22T18:17:40Z

← Older revision		Revision as of 18:17, 22 December 2022
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	{{Harmonics in equal\|777}}		{{Harmonics in equal\|777}}

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

Eliora: added facts

2022-12-22T01:54:38Z

added facts

← Older revision		Revision as of 01:54, 22 December 2022
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	== Theory ==		== Theory ==

	777edo~~, despite its size,~~ is a dual fifths system with a consistency limit of only 3.		777edo is a dual fifths system with a consistency limit of only 3.

			If the harmonic 3 is excluded, it is an excellent 2.5.7.9.11.13 subgroup tuning, with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup.

	{{Harmonics in equal\|777}}		{{Harmonics in equal\|777}}

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

Aura: Created page with "{{Infobox ET}} The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament pe..."

2022-12-08T14:34:42Z

Created page with "{{Infobox ET}} The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament pe..."

New page

{{Infobox ET}}
The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.

== Theory ==

777edo, despite its size, is a dual fifths system with a consistency limit of only 3.

{{Harmonics in equal|777}}

[[Category:Equal divisions of the octave|####]]