Mothwellsmic chords - Revision history

FloraC: Adjust the rotation of certain chords to expose the perfect fifth

2024-10-10T10:23:19Z

Adjust the rotation of certain chords to expose the perfect fifth

← Older revision		Revision as of 10:23, 10 October 2024
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	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1–7/6–11/8–3/2 with steps 7/6, 7/6, 12/11, 4/3, and its inverse		* 1–7/6–11/8–3/2 with steps 7/6, 7/6, 12/11, 4/3, and its inverse
	* ~~1–7~~/~~6–11~~/~~8–11~~/6 with steps 7/6, 7/6, 4/3~~, 12/11~~;		* 1–12/11–9/7–3/2 with steps 12/11, 7/6, 7/6, 4/3;
	* ~~1–7~~/~~6–11~~/~~8–7~~/4 with steps 7/6, 7/6~~, 9/7~~, 8/7, and its inverse		* 1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7, and its inverse
	* 1–7/~~6–11~~/~~8–11~~/7 with steps 7/6, 7/6, 8/7, 9/7.		* 1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6.

	For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are		For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
	* ~~1–7~~/~~6–11~~/~~8–11~~/~~7–7~~/4 with steps 7/6, 7/6, 8/7~~, 9~~/8, 8/7;		* 1–9/8–9/7–3/2–7/4 with steps 9/8, 8/7, 7/6, 7/6, 8/7;
	* 1–7/6–11/8–3/2–11/6 with steps 7/6, 7/6, 12/11, 11/9, 12/11.		* 1–7/6–11/8–3/2–11/6 with steps 7/6, 7/6, 12/11, 11/9, 12/11.

	The inversely related pair of chords is		The inversely related pair of chords is
	* 1–7/~~6–11~~/~~8–3~~/2–7/4 with steps 7/6, 7/6~~, 12/11~~, 7/6, 8/7, and its inverse		* 1–7/6–9/7–3/2–7/4 with steps 7/6, 12/11, 7/6, 7/6, 8/7, and its inverse
	* 1–7/~~6–11~~/~~8–11~~/~~7–11~~/6 with steps 7/6, 7/6, 8/7, 7/6~~, 12/11~~.		* 1–7/6–9/7–3/2–12/7 with steps 7/6, 12/11, 7/6, 8/7, 7/6.

	[[Equal temperament]]s with mothwellsmic chords include {{EDOs\| 22, 31, 53, 96, and 127 }}.		[[Equal temperament]]s with mothwellsmic chords include {{EDOs\| 22, 31, 53, 96, and 127 }}.

FloraC: Improve readability; recategorize

2024-10-10T09:10:21Z

Improve readability; recategorize

← Older revision		Revision as of 09:10, 10 October 2024
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	The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:		The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:
	* ~~1-7~~/~~6-11~~/8 with steps 7/6-7/6-16/11.		* 1–7/6–11/8 with steps 7/6, 7/6, 16/11.

	For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* ~~1-11~~/~~8-11~~/~~7-7~~/4 with steps 11/8-8/7-9/8-8/7;		* 1–11/8–11/7–7/4 with steps 11/8, 8/7, 9/8, 8/7;
	* ~~1-7~~/~~6-9~~/~~7-3~~/2 with steps 7/6-12/11-7/6-4/3.		* 1–7/6–9/7–3/2 with steps 7/6, 12/11, 7/6, 4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* ~~1-7~~/~~6-11~~/~~8-3~~/2 with steps 7/6-7/6-12/11-4/3, and its inverse		* 1–7/6–11/8–3/2 with steps 7/6, 7/6, 12/11, 4/3, and its inverse
	* ~~1-7~~/~~6-11~~/~~8-11~~/6 with steps 7/6-7/6-4/3-12/11;		* 1–7/6–11/8–11/6 with steps 7/6, 7/6, 4/3, 12/11;
	* ~~1-7~~/~~6-11~~/~~8-7~~/4 with steps 7/6-7/6-9/7-8/7, and its inverse		* 1–7/6–11/8–7/4 with steps 7/6, 7/6, 9/7, 8/7, and its inverse
	* ~~1-7~~/~~6-11~~/~~8-11~~/7 with steps 7/6-7/6-8/7-9/7.		* 1–7/6–11/8–11/7 with steps 7/6, 7/6, 8/7, 9/7.

	For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are		For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
	* ~~1-7~~/~~6-11~~/~~8-11~~/~~7-7~~/4 with steps 7/6-7/6-8/7-9/8-8/7;		* 1–7/6–11/8–11/7–7/4 with steps 7/6, 7/6, 8/7, 9/8, 8/7;
	* ~~1-7~~/~~6-11~~/~~8-3~~/~~2-11~~/6 with steps 7/6-7/6-12/11-11/9-12/11.		* 1–7/6–11/8–3/2–11/6 with steps 7/6, 7/6, 12/11, 11/9, 12/11.

	The inversely related pair of chords is		The inversely related pair of chords is
	* ~~1-7~~/~~6-11~~/~~8-3~~/~~2-7~~/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse		* 1–7/6–11/8–3/2–7/4 with steps 7/6, 7/6, 12/11, 7/6, 8/7, and its inverse
	* ~~1-7~~/~~6-11~~/~~8-11~~/~~7-11~~/6 with steps 7/6-7/6-8/7-7/6-12/11.		* 1–7/6–11/8–11/7–11/6 with steps 7/6, 7/6, 8/7, 7/6, 12/11.

	Equal ~~divisions~~ with mothwellsmic chords include ~~[[22edo]]~~, ~~[[31edo]]~~, ~~[[53edo]]~~, ~~[[96edo]]~~ and ~~[[127edo]]~~.		[[Equal temperament]]s with mothwellsmic chords include {{EDOs\| 22, 31, 53, 96, and 127 }}.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

Xenllium at 12:03, 27 October 2023

2023-10-27T12:03:24Z

Xenllium at 11:25, 27 October 2023

2023-10-27T11:25:07Z

← Older revision		Revision as of 11:25, 27 October 2023
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	'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].		'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].

			There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.

	The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:		The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:
	* 1-7/6-11/8 with steps 7/6-7/6-16/11.		* 1-7/6-11/8 with steps 7/6-7/6-16/11.

	~~It can be extended to~~ tetrads as		For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
			* 1-11/8-11/7-7/4 with steps 11/8-8/7-9/8-8/7
			* 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3

			The inversely related pairs of chords are
	* 1-7/6-11/8-3/2 with steps 7/6-7/6-12/11-4/3, and its inverse		* 1-7/6-11/8-3/2 with steps 7/6-7/6-12/11-4/3, and its inverse
	* 1-7/6-11/8-11/6 with steps 7/6-7/6-4/3-12/11;		* 1-7/6-11/8-11/6 with steps 7/6-7/6-4/3-12/11;
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	* 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7.		* 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7.

	~~They can be extended to~~ pentads as		For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
			* 1-7/6-11/8-11/7-7/4 with steps 7/6-7/6-8/7-9/8-8/7
			* 1-7/6-11/8-3/2-11/6 with steps 7/6-7/6-12/11-11/9-12/11

			The inversely related pair of chords is
	* 1-7/6-11/8-3/2-7/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse		* 1-7/6-11/8-3/2-7/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse
	* 1-7/6-11/8-14/9-11/6 with steps 7/6-7/6-8/7-7/6-12/11.		* 1-7/6-11/8-14/9-11/6 with steps 7/6-7/6-8/7-7/6-12/11.

	Equal divisions with mothwellsmic ~~triads~~ include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].		Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]

FloraC: FloraC moved page Mothwellsmic triad to Mothwellsmic chords: Not only triads

2023-06-01T09:12:36Z

FloraC moved page Mothwellsmic triad to Mothwellsmic chords: Not only triads

← Older revision	Revision as of 09:12, 1 June 2023
(No difference)

FloraC: +tetrads and pentads

2023-06-01T09:12:16Z

+tetrads and pentads

@@ Line 1: / Line 1: @@
-The '''mothwellsmic triad''' is an [[essentially tempered chord]] which is the [[99/98]] tempering of 1-[[7/6]]-[[11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad]]s include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].
+'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].
 [[Category:11-odd-limit]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
 [[Category:Mothwellsmic]]

FloraC: Recategorize

2023-05-23T11:43:02Z

Recategorize

← Older revision		Revision as of 11:43, 23 May 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
			[[Category:Essentially tempered chords]]
			[[Category:Triads]]
	[[Category:Mothwellsmic]]		[[Category:Mothwellsmic]]
	~~[[Category:Triad]]~~
	~~[[Category:Essentially tempered chords]]~~

	{{~~todo~~\|discuss title}}		{{Todo\| discuss title }}

Xenwolf: recat

2021-05-20T08:08:33Z

recat

← Older revision		Revision as of 08:08, 20 May 2021
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	The '''mothwellsmic triad''' is an [[essentially tempered chord]] which is the [[99/98]] tempering of 1-[[7/6]]-[[11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad]]s include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].		The '''mothwellsmic triad''' is an [[essentially tempered chord]] which is the [[99/98]] tempering of 1-[[7/6]]-[[11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad]]s include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].

	[[Category:11-limit]]		[[Category:11-odd-limit]]
	[[Category:Mothwellsmic]]		[[Category:Mothwellsmic]]
	[[Category:Triad]]		[[Category:Triad]]

Xenwolf: simplify wiki text, +cat

2021-05-20T07:04:59Z

simplify wiki text, +cat

← Older revision		Revision as of 07:04, 20 May 2021
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	The '''mothwellsmic triad''' is an [[~~Dyadic_chord\|~~essentially tempered chord]] which is the [[~~99/98\|~~99/98]] tempering of 1-[[~~7/6\|~~7/6]]-[[~~11/8\|~~11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad~~\|triads~~]] include [[22edo~~\|22~~]], [[31edo~~\|31~~]], [[53edo~~\|53~~]], [[96edo~~\|96~~]] and [[127edo~~\|127~~]].		The '''mothwellsmic triad''' is an [[essentially tempered chord]] which is the [[99/98]] tempering of 1-[[7/6]]-[[11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad]]s include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].

	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:~~mothwellsmic~~]]		[[Category:Mothwellsmic]]
	[[Category:~~todo:discuss_title~~]]		[[Category:Triad]]
	[[Category:~~triad~~]]		[[Category:Essentially tempered chords]]

			{{todo\|discuss title}}

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 '''mothwellsmic triad''' is an [[Dyadic_chord\|essentially tempered chord]] which is the [[99/98\|99/98]] tempering of 1-[[7/6\|7/6]]-[[11/8\|11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad\|triads]] include [[22edo\|22]], [[31edo\|31]], [[53edo\|53]], [[96edo\|96]] and [[127edo\|127]].
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~		[[Category:11-limit]]
	~~: This revision was by author [[User:xenwolf\|xenwolf]] and made on <tt>2011-10-20 03:34:19 UTC</tt>.<br>~~		[[Category:mothwellsmic]]
	~~: The original revision id was <tt>266706368</tt>.<br>~~		[[Category:todo:discuss_title]]
	~~: The revision comment was: <tt></tt><br>~~		[[Category:triad]]
	~~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 mothwellsmic triad is an [[~~Dyadic chord~~\|essentially tempered chord]] which is the [[~~99_98~~\|99/98]] tempering of 1-[[~~7_6~~\|7/6]]-[[~~11_8~~\|11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad\|triads]] include [[22edo\|22]], [[31edo\|31]], [[53edo\|53]], [[96edo\|96]] and [[127edo\|127]].~~</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>mothwellsmic~~ triad</title></head><body>The <strong>mothwellsmic triad</strong> is an <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> which is the <a class="wiki_link" href="/99_98">99/98</a> tempering of 1-<a class="wiki_link" href="/7_6">7/6</a>-<a class="wiki_link" href="/11_8">11/8</a>, with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic <a class="wiki_link" href="/triad">triads</a> include <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/96edo">96</a> and <a class="wiki_link" href="/127edo">127</a>.</body></html></pre></div>

← Older revision		Revision as of 12:03, 27 October 2023
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	'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].		'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].

	There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.		There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.

	The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:		The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:
	* 1-7/6-11/8 with steps 7/6-7/6-16/11.		* 1-7/6-11/8 with steps 7/6-7/6-16/11.

	For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* 1-11/8-11/7-7/4 with steps 11/8-8/7-9/8-8/7		* 1-11/8-11/7-7/4 with steps 11/8-8/7-9/8-8/7;
	* 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3		* 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-7/6-11/8-3/2 with steps 7/6-7/6-12/11-4/3, and its inverse		* 1-7/6-11/8-3/2 with steps 7/6-7/6-12/11-4/3, and its inverse
	* 1-7/6-11/8-11/6 with steps 7/6-7/6-4/3-12/11;		* 1-7/6-11/8-11/6 with steps 7/6-7/6-4/3-12/11;
	* 1-7/6-11/8-7/4 with steps 7/6-7/6-9/7-8/7, and its inverse		* 1-7/6-11/8-7/4 with steps 7/6-7/6-9/7-8/7, and its inverse
	* 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7.		* 1-7/6-11/8-11/7 with steps 7/6-7/6-8/7-9/7.

	For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are		For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
	* 1-7/6-11/8-11/7-7/4 with steps 7/6-7/6-8/7-9/8-8/7		* 1-7/6-11/8-11/7-7/4 with steps 7/6-7/6-8/7-9/8-8/7;
	* 1-7/6-11/8-3/2-11/6 with steps 7/6-7/6-12/11-11/9-12/11		* 1-7/6-11/8-3/2-11/6 with steps 7/6-7/6-12/11-11/9-12/11.

	The inversely related pair of chords is		The inversely related pair of chords is
	* 1-7/6-11/8-3/2-7/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse		* 1-7/6-11/8-3/2-7/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse
	* 1-7/6-11/8-14/9-11/6 with steps 7/6-7/6-8/7-7/6-12/11.		* 1-7/6-11/8-11/7-11/6 with steps 7/6-7/6-8/7-7/6-12/11.

	Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].		Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].