Squbemic chords - Revision history

FloraC: Cleanup

2025-03-19T14:10:48Z

Cleanup

← Older revision		Revision as of 14:10, 19 March 2025
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	'''Squbemic chords''' are [[~~Dyadic~~ chord\|essentially tempered chord]] tempered by the squbema, [[729/728]].		'''Squbemic chords''' are [[dyadic chord\|essentially tempered chord]] tempered by the squbema, [[729/728]].

	[[13-odd-limit]] squebmic chords belong to a tempering of the 2.9.7.13 subgroup, including two triads and three tetrads.		[[13-odd-limit]] squebmic chords belong to a tempering of the 2.9.7.13 subgroup, including two triads and three tetrads.

	The two squbemic triads are in inverse relationship:		The two squbemic triads are in inverse relationship:
	* ~~1-9~~/~~8-13~~/9 ~~chord~~ with steps of 9/8-9/7-18/13;		* 1–9/8–13/9 with steps of 9/8, 9/7, 18/13;
	* ~~1-9~~/~~7-13~~/9 ~~chord~~ with steps of 9/7-9/8-18/13.		* 1–9/7–13/9 with steps of 9/7, 9/8, 18/13.

	They can be extended to palindromic tetrads:		They can be extended to palindromic tetrads:
	* ~~1-9~~/~~8-14~~/~~9-7~~/4 with steps of 9/8-18/13-9/8-8/7;		* 1–9/8–14/9–7/4 with steps of 9/8, 18/13, 9/8, 8/7;
	* ~~1-9~~/~~8-13~~/~~9-13~~/8 with steps of 9/8-9/7-9/8-16/13;		* 1–9/8–13/9–13/8 with steps of 9/8, 9/7, 9/8, 16/13;
	* ~~1-9~~/~~7-13~~/~~9-13~~/7 with steps of 9/7-9/8-9/7-14/13.		* 1–9/7–13/9–13/7 with steps of 9/7, 9/8, 9/7, 14/13.

	Equal temperaments with squbemic chords include {{Optimal ET sequence\| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069 and 1724 }}, with 1724edo giving the optimal patent val.		Equal temperaments with squbemic chords include {{Optimal ET sequence\| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069 and 1724 }}, with 1724edo giving the optimal patent val.

	[[Category:13-odd-limit]]		[[Category:13-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
	[[Category:Squbemic]]		[[Category:Squbemic]]

Xenllium: Update the article

2023-11-02T23:36:04Z

Update the article

← Older revision		Revision as of 23:36, 2 November 2023
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	A '''~~squbemic chord~~''' ~~is a 13-limit~~ [[essentially tempered chord]] ~~which is defined via tempering out~~ the squbema, [[729/728]].		'''Squbemic chords''' are [[Dyadic chord\|essentially tempered chord]] tempered by the squbema, [[729/728]].

	~~There are two squbemic tetrads, the temperings of~~		[[13-odd-limit]] squebmic chords belong to a tempering of the 2.9.7.13 subgroup, including two triads and three tetrads.
	* 1-~~9/8~~-~~14/~~9-7~~/4 with steps of 9/8-18/~~13~~-9/8-8/7~~, and
	* 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13.

	~~These contain~~ two squbemic triads~~, the temperings of~~		The two squbemic triads are in inverse relationship:
	* 1-9/8-13/9 with steps 9/8-9/7-18/13,		* 1-9/8-13/9 chord with steps of 9/8-9/7-18/13;
	* 1-9/7-13/9 with steps 9/7-9/8-18/13.		* 1-9/7-13/9 chord with steps of 9/7-9/8-18/13.

	Equal temperaments with squbemic chords include {{~~EDOs~~\| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724 }}, with 1724edo giving the optimal patent val~~. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit~~.		They can be extended to palindromic tetrads:
			* 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7;
			* 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13;
			* 1-9/7-13/9-13/7 with steps of 9/7-9/8-9/7-14/13.

			Equal temperaments with squbemic chords include {{Optimal ET sequence\| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069 and 1724 }}, with 1724edo giving the optimal patent val.

	[[Category:13-odd-limit]]		[[Category:13-odd-limit]]

FloraC: Recategorize

2023-05-23T11:46:49Z

Recategorize

← Older revision		Revision as of 11:46, 23 May 2023
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	[[Category:13-odd-limit]]		[[Category:13-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Squbemic]]		[[Category:Squbemic]]

FloraC: Improve readability and +categories

2022-02-05T23:25:16Z

Improve readability and +categories

← Older revision		Revision as of 23:25, 5 February 2022
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	A ''squbemic chord'' is a 13-limit [[~~Dyadic_chord\|~~essentially tempered ~~dyadic~~ chord]] which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.		A '''squbemic chord''' is a 13-limit [[essentially tempered chord]] which is defined via tempering out the squbema, [[729/728]].

	Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.		There are two squbemic tetrads, the temperings of
			* 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7, and
			* 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13.

			These contain two squbemic triads, the temperings of
			* 1-9/8-13/9 with steps 9/8-9/7-18/13,
			* 1-9/7-13/9 with steps 9/7-9/8-18/13.

			Equal temperaments with squbemic chords include {{EDOs\| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724 }}, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.

			[[Category:13-odd-limit]]
			[[Category:Essentially tempered chords]]
			[[Category:Triad]]
			[[Category:Tetrad]]
			[[Category:Squbemic]]

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>~~		A ''squbemic chord'' is a 13-limit [[Dyadic_chord\|essentially tempered dyadic chord]] which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.
	~~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>2012-02-20 14:00:20 UTC</tt>.<br>~~
	~~: The original revision id was <tt>303400622</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">A //squbemic chord// is a 13-limit [[~~Dyadic chord~~\|essentially tempered dyadic chord]] which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.

	Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.		Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.

	~~</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>squbemic chords</title></head><body>A <em>squbemic chord</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.<br />
	~~<br />~~
	Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 303400622 - Original comment:

2012-02-20T14:00:20Z

**Imported revision 303400622 - Original comment: **

Wikispaces>genewardsmith: Imported revision 303200316 - Original comment:

2012-02-19T18:34:51Z

**Imported revision 303200316 - 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>2012-02-19 18:34:51 UTC</tt>.<br>
: The original revision id was <tt>303200316</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">A //squbemic chord// is a 13-limit [[Dyadic chord|essentially tempered dyadic chord]] which is defined via tempering out the squbema, 196/195. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.

Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.

</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>squbemic chords</title></head><body>A <em>squbemic chord</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> which is defined via tempering out the squbema, 196/195. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.<br />
<br />
Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.</body></html></pre></div>

← Older revision		Revision as of 14:00, 20 February 2012
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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>2012-02-~~19 18~~:34:51 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2012-02-20 14:00:20 UTC</tt>.<br>
	: The original revision id was <tt>~~303200316~~</tt>.<br>		: The original revision id was <tt>303400622</tt>.<br>
	: The revision comment was: <tt></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>		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>		<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">A //squbemic chord// is a 13-limit [[Dyadic chord\|essentially tempered dyadic chord]] which is defined via tempering out the squbema, ~~196~~/~~195~~. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.		<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">A //squbemic chord// is a 13-limit [[Dyadic chord\|essentially tempered dyadic chord]] which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.

	Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.		Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.
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	</pre></div>		</pre></div>
	<h4>Original HTML content:</h4>		<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>squbemic chords</title></head><body>A <em>squbemic chord</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> which is defined via tempering out the squbema, ~~196~~/~~195~~. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.<br />		<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>squbemic chords</title></head><body>A <em>squbemic chord</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.<br />
	<br />		<br />
	Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.</body></html></pre></div>		Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.</body></html></pre></div>