703edo - Revision history

ArrowHead294 at 15:59, 20 February 2025

2025-02-20T15:59:33Z

← Older revision		Revision as of 15:59, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|703~~}}		{{ED intro}}

	703edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. ~~The equal temperament~~ [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }} in the 5-limit.		703edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. It [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }} in the 5-limit.

	In the 7-limit, the [[patent val]] {{val\| 703 1114 1632 '''1974''' }} and the 703d [[val]] {{val\| 703 1114 1632 '''1973''' }} may be worth considering.		In the 7-limit, the [[patent val]] {{val\| 703 1114 1632 '''1974''' }} and the 703d [[val]] {{val\| 703 1114 1632 '''1973''' }} may be worth considering.

FloraC: Expand on theory; adopt template: Factorization

2023-11-02T12:32:47Z

Expand on theory; adopt template: Factorization

← Older revision		Revision as of 12:32, 2 November 2023
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	{{EDO intro\|703}}		{{EDO intro\|703}}

	~~703 = 19 × 37, and~~ the equal temperament [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }}. In the 7-limit the [[patent val]] tempers out [[16875/16807]] and [[65625/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].		703edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. The equal temperament [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }} in the 5-limit.

			In the 7-limit, the [[patent val]] {{val\| 703 1114 1632 '''1974''' }} and the 703d [[val]] {{val\| 703 1114 1632 '''1973''' }} may be worth considering.

			Using the patent val, it tempers out [[16875/16807]] and [[65625/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].

			The alternative 703d [[val]] tempers out [[4375/4374]] and [[703125/702464]], supporting 7-limit [[enneadecal]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|703}}		{{Harmonics in equal\|703}}

			=== Subsets and supersets ===
			Since 703 factors into {{factorization\|703}}, 703edo contains [[19edo]] and [[37edo]] as subsets.

FloraC: There was a typo in the ratio

2023-10-22T08:16:38Z

There was a typo in the ratio

← Older revision		Revision as of 08:16, 22 October 2023
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	{{EDO intro\|703}}		{{EDO intro\|703}}

	703 = 19 × 37, and the equal temperament [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }}. In the 7-limit the [[patent val]] tempers out [[16875/16807]] and [[~~65635~~/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].		703 = 19 × 37, and the equal temperament [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }}. In the 7-limit the [[patent val]] tempers out [[16875/16807]] and [[65625/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|703}}		{{Harmonics in equal\|703}}

FloraC: Cleanup; -redundant categories

2023-10-22T08:16:05Z

Cleanup; -redundant categories

← Older revision		Revision as of 08:16, 22 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].		{{EDO intro\|703}}

	[[~~Category:Equal divisions of~~ the ~~octave\|###~~]] <!-- 3-~~digit number~~ -->		703 = 19 × 37, and the equal temperament [[tempering out\|tempers out]] the [[enneadeca]], {{monzo\| -14 -19 19 }}. In the 7-limit the [[patent val]] tempers out [[16875/16807]] and [[65635/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].

			=== Odd harmonics ===
			{{Harmonics in equal\|703}}

BudjarnLambeth at 06:44, 9 July 2023

2023-07-09T06:44:22Z

← Older revision		Revision as of 06:44, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].		The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].

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

BudjarnLambeth at 05:33, 9 July 2023

2023-07-09T05:33:15Z

← Older revision		Revision as of 05:33, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].		The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].

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

Plumtree: Infobox ET added

2022-10-04T22:01:42Z

Infobox ET added

← Older revision		Revision as of 22:01, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].		The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].

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

Fredg999 category edits: Categories

2022-07-04T01:05:35Z

Cmloegcmluin: link to new page for Supports

2022-01-25T18:13:00Z

link to new page for Supports

← Older revision		Revision as of 18:13, 25 January 2022
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	The ''703 equal division'' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it ~~supports~~ and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].		The ''703 equal division'' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].

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 ''703 equal division'' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi 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>2011-10-23 18:20:15 UTC</tt>.<br>~~
	~~: The original revision id was <tt>267694630</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 //703 equal division// divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it supports and gives the [[optimal patent val]] in [[~~Mirkwai family~~\|indra temperament]] and [[~~Mirkwai clan~~#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[~~Mirkwai family~~#Indra-Shibi\|shibi 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>703edo</title></head><body>The <em>703 equal division</em> divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19&gt;. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it supports and gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> in <a class="wiki_link" href="/Mirkwai%20family">indra temperament</a> and <a class="wiki_link" href="/Mirkwai%20clan#Eris">eris temperament</a>. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for <a class="wiki_link" href="/Mirkwai%20family#Indra-Shibi">shibi temperament</a>.</body></html></pre></div>

← Older revision		Revision as of 01:05, 4 July 2022
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	The ''703 equal division'' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].		The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, \|-14 -19 19>. In the 7-limit it tempers out 16875/16807 and 65635/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it [[support]]s and gives the [[Optimal_patent_val\|optimal patent val]] in [[Mirkwai_family\|indra temperament]] and [[Mirkwai_clan#Eris\|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi\|shibi temperament]].

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