Neutral tetrad - Revision history

CompactStar at 00:50, 21 June 2023

2023-06-21T00:50:57Z

← Older revision		Revision as of 00:50, 21 June 2023
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	A '''neutral tetrad''' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.		A '''neutral tetrad''', more commonly known as a '''neutral seventh chord''', is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.		A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

FloraC: Recategorize

2023-04-28T07:28:40Z

Recategorize

← Older revision		Revision as of 07:28, 28 April 2023
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	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:~~Chords~~]]		[[Category:Dyadic chords]]
	[[Category:~~Dyadic~~]]		[[Category:Tetrad]]
	[[Category:Neutral]]		[[Category:Neutral]]
	[[Category:Rastmic]]		[[Category:Rastmic]]
	~~[[Category:Tetrad]]~~

FloraC: Improve categories

2021-03-16T08:44:21Z

Improve categories

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	[[Category:11-limit]]		[[Category:11-limit]]
			[[Category:Chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Neutral]]		[[Category:Neutral]]
	[[Category:~~Rastma~~]]		[[Category:Rastmic]]
	[[Category:Tetrad]]		[[Category:Tetrad]]

Xenwolf: -cat

2020-06-13T16:49:40Z

-cat

← Older revision		Revision as of 16:49, 13 June 2020
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	A ''neutral tetrad'' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.		A '''neutral tetrad''' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.		A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

	The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.		The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.

	[[Category:11-limit]]		[[Category:11-limit]]
	~~[[Category:Chords]]~~
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Neutral]]		[[Category:Neutral]]
	[[Category:Rastma]]		[[Category:Rastma]]
	[[Category:Tetrad]]		[[Category:Tetrad]]

ResonantFrequencies: /* top */re-categorisation (AWB), typos fixed: desribed → described

2019-06-30T23:56:39Z

top: re-categorisation (AWB), typos fixed: desribed → described

← Older revision		Revision as of 23:56, 30 June 2019
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	A ''neutral tetrad'' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[~~rastmic_chords~~\|rastmic]] [[~~Dyadic_chord~~#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[~~24edo\|~~24edo]], which does an excellent version of it.		A ''neutral tetrad'' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be ~~desribed~~ as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.		A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

	The neutral tetrad is also available in [[~~nonoctave\|~~nonoctave]] tunings which divide the [[~~3/2\|~~3/2]] in half, including [[~~4edf\|~~4edf]], [[~~6edf\|~~6edf]] (nonoctave miracle), 8edf or [[~~88cET\|~~88cET]], [[~~16edf\|~~16edf]], and 20edf ([[~~Carlos_Gamma\|~~Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.		The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.
	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:~~chord~~]]		[[Category:Chords]]
	[[Category:~~dyadic~~]]		[[Category:Dyadic]]
	[[Category:~~neutral~~]]		[[Category:Neutral]]
	[[Category:~~rastma~~]]		[[Category:Rastma]]
	[[Category:~~tetrad~~]]		[[Category:Tetrad]]

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 ''neutral tetrad'' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic_chords\|rastmic]] [[Dyadic_chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo\|24edo]], which does an excellent version of it.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-01-22 14:50:45 UTC</tt>.<br>~~
	~~: The original revision id was <tt>294269920</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 //neutral tetrad// is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[~~rastmic chords~~\|rastmic]] [[~~Dyadic chord~~#Essentially~~%20tempered%20dyadic%20chords~~\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.		A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

	The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[~~3_2~~\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.~~</pre></div>~~		The neutral tetrad is also available in [[nonoctave\|nonoctave]] tunings which divide the [[3/2\|3/2]] in half, including [[4edf\|4edf]], [[6edf\|6edf]] (nonoctave miracle), 8edf or [[88cET\|88cET]], [[16edf\|16edf]], and 20edf ([[Carlos_Gamma\|Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.
	~~<h4>Original HTML content:</h4>~~		[[Category:11-limit]]
	~~<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>neutral tetrad</title></head><body>A <em>neutral tetrad</em> is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the <a class="wiki_link" href="/rastmic%20chords">rastmic</a> <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11~~/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27~~-limit ~~JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27~~:~~30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered~~ chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it.<br />		[[Category:chord]]
	~~<br />~~		[[Category:dyadic]]
	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.<br />		[[Category:neutral]]
	~~<br />~~		[[Category:rastma]]
	~~The neutral~~ tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>		[[Category:tetrad]]

Wikispaces>keenanpepper: Imported revision 294269920 - Original comment:

2012-01-22T14:50:45Z

**Imported revision 294269920 - Original comment: **

Wikispaces>genewardsmith: Imported revision 285605592 - Original comment:

2011-12-13T14:50:43Z

**Imported revision 285605592 - Original comment: **

Wikispaces>genewardsmith: Imported revision 256601840 - Original comment:

2011-09-21T11:51:16Z

**Imported revision 256601840 - Original comment: **

← Older revision		Revision as of 11:51, 21 September 2011
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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:~~Andrew_Heathwaite~~\|~~Andrew_Heathwaite~~]] and made on <tt>2011-09-21 10:45:06 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-21 11:51:16 UTC</tt>.<br>
	: The original revision id was <tt>~~256569256~~</tt>.<br>		: The original revision id was <tt>256601840</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">The //neutral tetrad//, or rastmic tetrad, is an 11-limit [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it. The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</pre></div>		<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 //neutral tetrad//, or rastmic tetrad, is an 11-limit [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

			The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</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>neutral tetrad</title></head><body>The <em>neutral tetrad</em>, or rastmic tetrad, is an 11-limit <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it. The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>		<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>neutral tetrad</title></head><body>The <em>neutral tetrad</em>, or rastmic tetrad, is an 11-limit <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it. <br />
			<br />
			The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>

Wikispaces>Andrew_Heathwaite: Imported revision 256569256 - Original comment:

2011-09-21T10:45:06Z

**Imported revision 256569256 - Original comment: **

← Older revision		Revision as of 10:45, 21 September 2011
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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:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2011-09-21 10:43:13 UTC</tt>.<br>		: This revision was by author [[User:Andrew_Heathwaite\|Andrew_Heathwaite]] and made on <tt>2011-09-21 10:45:06 UTC</tt>.<br>
	: The original revision id was <tt>~~256568216~~</tt>.<br>		: The original revision id was <tt>256569256</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">The //neutral tetrad//, or rastmic tetrad, is an 11-limit [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it. The neutral tetrad is also available in nonoctave tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]].</pre></div>		<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 //neutral tetrad//, or rastmic tetrad, is an 11-limit [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it. The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</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>neutral tetrad</title></head><body>The <em>neutral tetrad</em>, or rastmic tetrad, is an 11-limit <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it. The neutral tetrad is also available in nonoctave tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>.</body></html></pre></div>		<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>neutral tetrad</title></head><body>The <em>neutral tetrad</em>, or rastmic tetrad, is an 11-limit <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it. The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>

← Older revision		Revision as of 14:50, 22 January 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>~~2011~~-12-13 14:50:43 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-01-22 14:50:45 UTC</tt>.<br>
	: The original revision id was <tt>~~285605592~~</tt>.<br>		: The original revision id was <tt>294269920</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 //neutral tetrad// is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral ~~quintad~~, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.		<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 //neutral tetrad// is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.		A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

	The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</pre></div>		The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</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>neutral tetrad</title></head><body>A <em>neutral tetrad</em> is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the <a class="wiki_link" href="/rastmic%20chords">rastmic</a> <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral ~~quintad~~, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it.<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>neutral tetrad</title></head><body>A <em>neutral tetrad</em> is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the <a class="wiki_link" href="/rastmic%20chords">rastmic</a> <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it.<br />
	<br />		<br />
	A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49. <br />		A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.<br />
	<br />		<br />
	The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>		The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>

← Older revision		Revision as of 14:50, 13 December 2011
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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>2011-09-~~21 11~~:51:16 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-12-13 14:50:43 UTC</tt>.<br>
	: The original revision id was <tt>~~256601840~~</tt>.<br>		: The original revision id was <tt>285605592</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">~~The~~ //neutral tetrad//, or rastmic ~~tetrad, is an 11-limit~~ [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.		<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 //neutral tetrad// is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords\|rastmic]] [[Dyadic chord#Essentially%20tempered%20dyadic%20chords\|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

			A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

	The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</pre></div>		The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3_2\|3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</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>neutral tetrad</title></head><body>~~The~~ <em>neutral tetrad</em>, or rastmic ~~tetrad, is an 11-limit~~ <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it. <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>neutral tetrad</title></head><body>A <em>neutral tetrad</em> is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the <a class="wiki_link" href="/rastmic%20chords">rastmic</a> <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral quintad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it.<br />
			<br />
			A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49. <br />
	<br />		<br />
	The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>		The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot &quot;close at the octave,&quot; unless there is a tempered octave available.</body></html></pre></div>