177edo - Revision history

ArrowHead294 at 14:06, 20 February 2025

2025-02-20T14:06:54Z

← Older revision		Revision as of 14:06, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	177edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1\|3]] is about halfway between its steps. It has good approximations to [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], and [[19/1\|19]], making it suitable for a 2.9.5.7.13.19 [[subgroup]] interpretation, which is equivalent to every other step of [[354edo]].		177edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1\|3]] is about halfway between its steps. It has good approximations to [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], and [[19/1\|19]], making it suitable for a 2.9.5.7.13.19 [[subgroup]] interpretation, which is equivalent to every other step of [[354edo]].

FloraC: Expand

2024-04-25T09:45:48Z

Expand

← Older revision		Revision as of 09:45, 25 April 2024
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	{{EDO intro}}		{{EDO intro}}

	~~The~~ patent val tempers out [[245/243]] and [[2401/2400]] ~~in the 7-limit~~, [[support]]ing and providing a good tuning for the [[octacot]] temperament.		177edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1\|3]] is about halfway between its steps. It has good approximations to [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], and [[19/1\|19]], making it suitable for a 2.9.5.7.13.19 [[subgroup]] interpretation, which is equivalent to every other step of [[354edo]].

			Consider the full 7-limit patent val nonetheless, the equal temperament [[tempering out\|tempers out]] [[245/243]] and [[2401/2400]], [[support]]ing and providing a good tuning for the [[octacot]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 177 factors into {{factorization\|177}}, 177edo contains [[3edo]] and [[59edo]] as its subsets. [[354edo]], which doubles it, provides good correction for the approximation of harmonic 3.		Since 177 factors into {{factorization\|177}}, 177edo contains [[3edo]] and [[59edo]] as its subsets. 354edo, which doubles it, provides good correction for the approximation of harmonic 3.

FloraC: Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

2024-04-25T09:42:22Z

Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

← Older revision		Revision as of 09:42, 25 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot\|octacot temperament]].		{{EDO intro}}

	[[~~Category:Equal divisions of~~ the ~~octave~~\|~~###~~]] ~~<!--~~ 3~~-digit number -->~~		The patent val tempers out [[245/243]] and [[2401/2400]] in the 7-limit, [[support]]ing and providing a good tuning for the [[octacot]] temperament.

			=== Odd harmonics ===
			{{Harmonics in equal\|177}}

			=== Subsets and supersets ===
			Since 177 factors into {{factorization\|177}}, 177edo contains [[3edo]] and [[59edo]] as its subsets. [[354edo]], which doubles it, provides good correction for the approximation of harmonic 3.

Plumtree: Infobox ET added

2022-10-04T21:14:16Z

Infobox ET added

← Older revision		Revision as of 21:14, 4 October 2022
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			{{Infobox ET}}
	The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot\|octacot temperament]].		The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot\|octacot temperament]].

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

Fredg999 category edits: Categories

2022-07-02T21:21:21Z

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot\|octacot temperament]].
	~~This is an imported revision from Wikispaces.~~ The ~~revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-07-08 01:03:12 UTC</tt>.<br>~~
	~~: The original revision id was <tt>240473131</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //177 equal division// divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[~~Tetracot family~~#Octacot\|octacot temperament]]. ~~</pre></div>~~
	~~<h4>Original HTML content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>177edo</title></head><body>The <em>177 equal division</em> divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for <a class="wiki_link" href="/Tetracot%20family#Octacot">octacot temperament</a>.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 240473131 - Original comment:

2011-07-08T01:03:12Z

**Imported revision 240473131 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-08 01:03:12 UTC</tt>.<br>
: The original revision id was <tt>240473131</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //177 equal division// divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot family#Octacot|octacot temperament]]. </pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>177edo</title></head><body>The <em>177 equal division</em> divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for <a class="wiki_link" href="/Tetracot%20family#Octacot">octacot temperament</a>.</body></html></pre></div>

← Older revision		Revision as of 21:21, 2 July 2022
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	The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot\|octacot temperament]].		The ''177 equal division'' divides the octave into 177 equal parts of 6.780 cents each. The patent val tempers out 245/243 and 2401/2400 in the 7-limit, supporting and providing a good tuning for [[Tetracot_family#Octacot\|octacot temperament]].

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