Tungsten meantone - Revision history

BudjarnLambeth: Added links

2024-01-28T01:46:43Z

Added links

← Older revision		Revision as of 01:46, 28 January 2024
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	'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub> is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to 3 + sqrt (10) or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.		'''Tungsten meantone''' is the name given by [[Mason Green]] in 2016 to the variant of [[meantone]] in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub> is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to 3 + sqrt (10) or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.
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	[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).		[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).

	Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone]] (whereas golden meantone instead [[support]]s [[Meanpop\|13-limit meanpop]]).		Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to [[12edo]]. Yet it still has very high [[5-limit\|5-]] and [[7-limit]] accuracy, and can also be extended to the [[13-limit]] via [[grosstone]] (whereas golden meantone instead [[support]]s [[Meanpop\|13-limit meanpop]]).

	The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[Wikipedia:Amusia\|amusia]]-challenged. Melodically it could be considered a "shamble" or [[Wikipedia:Tonality flux\|tone flux]] (smaller than a step, yet still a definite motion).		The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[Wikipedia:Amusia\|amusia]]-challenged. Melodically it could be considered a "shamble" or [[Wikipedia:Tonality flux\|tone flux]] (smaller than a step, yet still a definite motion).

Cmloegcmluin: link to new page for Supports

2022-01-25T18:41:30Z

link to new page for Supports

← Older revision		Revision as of 18:41, 25 January 2022
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	[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).		[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).

	Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone]] (whereas golden meantone instead ~~supports~~ [[Meanpop\|13-limit meanpop]]).		Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone]] (whereas golden meantone instead [[support]]s [[Meanpop\|13-limit meanpop]]).

	The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[Wikipedia:Amusia\|amusia]]-challenged. Melodically it could be considered a "shamble" or [[Wikipedia:Tonality flux\|tone flux]] (smaller than a step, yet still a definite motion).		The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[Wikipedia:Amusia\|amusia]]-challenged. Melodically it could be considered a "shamble" or [[Wikipedia:Tonality flux\|tone flux]] (smaller than a step, yet still a definite motion).

FloraC: Correction

2022-01-13T15:52:34Z

Correction

← Older revision		Revision as of 15:52, 13 January 2022
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	'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub>is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to (6 + sqrt (10)~~)/2~~ or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.		'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub> is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to 3 + sqrt (10) or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.

FloraC: General cleanup

2021-02-02T10:48:01Z

General cleanup

← Older revision		Revision as of 10:48, 2 February 2021
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	'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<~~span style="vertical-align:~~ sub;">6 </~~span~~>of an octave, where S<~~span style="vertical-align:~~ sub;">6 </~~span~~>is the sixth [~~https~~:~~//en.wikipedia.org/wiki/Metallic_mean~~ metallic mean], equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.		'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub>is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to (6 + sqrt (10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[~~Golden_Meantone\|~~golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.

	Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, ~~456...~~ These form a [~~https~~:~~//en.wikipedia.org/wiki/Lucas_sequence~~ Lucas sequence], 2 * ''~~<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">~~U<~~span style="font-size: 11.2px;"~~>n</~~span></span~~>''~~<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">~~(6,−1).~~</span>~~		Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456… These form a [[Wikipedia:Lucas sequence\|Lucas sequence]], 2 × ''U<sub>n</sub>'' (6, −1).

	[[~~74edo\|~~74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).		[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).

	Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[~~Golden_Meantone\|~~golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[~~grosstone\|~~grosstone]] (whereas golden meantone instead supports [[Meanpop\|13-limit meanpop]]).		Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone]] (whereas golden meantone instead supports [[Meanpop\|13-limit meanpop]]).

	The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [~~https~~:~~//en.wikipedia.org/wiki/~~Amusia amusia]-challenged. Melodically it could be considered a "shamble" or [~~https~~:~~//en.wikipedia.org/wiki/Tonality_flux~~ tone flux] (smaller than a step, yet still a definite motion).		The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[Wikipedia:Amusia\|amusia]]-challenged. Melodically it could be considered a "shamble" or [[Wikipedia:Tonality flux\|tone flux]] (smaller than a step, yet still a definite motion).

	"Enharmonicism" (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.		"Enharmonicism" (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.

	[[Category:74edo]]		[[Category:74edo]]
	[[Category:~~meantone~~]]		[[Category:Meantone]]

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>~~		'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth [https://en.wikipedia.org/wiki/Metallic_mean metallic mean], equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-10-24 00:47:14 UTC</tt>.<br>~~
	~~: The original revision id was <tt>596666880</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">Tungsten meantone is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S~~<~~span style="vertical-align: sub;"~~>~~6 ~~<~~/span~~>~~of an octave, where S~~<~~span style="vertical-align: sub;"~~>~~6 ~~<~~/span~~>~~is the sixth [[https://en.wikipedia.org/wiki/Metallic_mean\|metallic mean]], equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[Golden_Meantone\|golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.

	Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a [[https://en.wikipedia.org/wiki/Lucas_sequence\|Lucas sequence]], 2 * ~~//<~~span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;"~~>~~U~~<~~span style="font-size: 11.2px;"~~>~~n~~<~~/span~~><~~/span~~>//<~~span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;"~~>~~(6,−1).~~<~~/span~~>~~		Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a [https://en.wikipedia.org/wiki/Lucas_sequence Lucas sequence], 2 * ''<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span>''<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span>

	[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).		[[74edo\|74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).

	Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone]] (whereas golden meantone instead supports [[~~meanpop~~\|13-limit meanpop]]).		Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[Golden_Meantone\|golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone\|grosstone]] (whereas golden meantone instead supports [[Meanpop\|13-limit meanpop]]).

	The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[https://en.wikipedia.org/wiki/Amusia\|amusia]]-challenged. Melodically it could be considered a "shamble" or [[https://en.wikipedia.org/wiki/Tonality_flux\|tone flux]] (smaller than a step, yet still a definite motion).		The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [https://en.wikipedia.org/wiki/Amusia amusia]-challenged. Melodically it could be considered a "shamble" or [https://en.wikipedia.org/wiki/Tonality_flux tone flux] (smaller than a step, yet still a definite motion).

	"Enharmonicism" (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.~~</pre></div>~~		"Enharmonicism" (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.
	~~<h4>Original HTML content~~:~~</h4>~~		[[Category:74edo]]
	~~<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>Tungsten~~ meantone</title></head><body><strong>Tungsten meantone</strong> is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metallic_mean" rel="nofollow">metallic mean</a>, equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.<br />		[[Category:meantone]]
	~~<br />~~
	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to <a class="wiki_link" href="/golden%20meantone">golden meantone</a>, since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.<br />
	~~<br />~~
	Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Lucas_sequence" rel="nofollow">Lucas sequence</a>, 2 * <em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span></em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span><br />
	~~<br />~~
	<a class="wiki_link" href="/74edo">74edo</a> has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).<br />
	~~<br />~~
	Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than <a class="wiki_link" href="/golden%20meantone">golden meantone</a>, as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via <a class="wiki_link" href="/grosstone">grosstone</a> (whereas golden meantone instead supports <a class="wiki_link" href="/meanpop">13-limit meanpop</a>).<br />
	~~<br />~~
	The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Amusia" rel="nofollow">amusia</a>-challenged. Melodically it could be considered a &quot;shamble&quot; or <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Tonality_flux" rel="nofollow">tone flux</a> (smaller than a step, yet still a definite motion).<br />
	~~<br />~~
	~~&quot;Enharmonicism&quot; (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.</body></html></pre></div>~~

Wikispaces>MasonGreen1: Imported revision 596666880 - Original comment:

2016-10-24T00:47:14Z

**Imported revision 596666880 - Original comment: **

Wikispaces>MasonGreen1: Imported revision 596666782 - Original comment:

2016-10-24T00:42:36Z

**Imported revision 596666782 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-10-24 00:42:36 UTC</tt>.<br>
: The original revision id was <tt>596666782</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">**Tungsten meantone** is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth [[https://en.wikipedia.org/wiki/Metallic_mean|metallic mean]], equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios appear between interval sizes appear repeatedly and the scale is thus self-similar.

Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a [[https://en.wikipedia.org/wiki/Lucas_sequence|Lucas sequence]], 2 * //<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span>//<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span>

[[74edo]] has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).

Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than [[golden meantone]], as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via [[grosstone]] (whereas golden meantone instead supports [[meanpop|13-limit meanpop]]).

The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most [[https://en.wikipedia.org/wiki/Amusia|amusia]]-challenged. Melodically it could be considered a "shamble" or [[https://en.wikipedia.org/wiki/Tonality_flux|tone flux]] (smaller than a step, yet still a definite motion).

"Enharmonicism" (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.</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>Tungsten meantone</title></head><body><strong>Tungsten meantone</strong> is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metallic_mean" rel="nofollow">metallic mean</a>, equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.<br />
<br />
Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to <a class="wiki_link" href="/golden%20meantone">golden meantone</a>, since in each case the same ratios appear between interval sizes appear repeatedly and the scale is thus self-similar.<br />
<br />
Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Lucas_sequence" rel="nofollow">Lucas sequence</a>, 2 * <em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span></em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span><br />
<br />
<a class="wiki_link" href="/74edo">74edo</a> has a fifth only ~0.04 cent narrower than that of tungsten meantone, and thus is a close-enough approximation for all practical purposes. Hence the name tungsten (which has atomic number 74).<br />
<br />
Tungsten has a similar density to gold, but is stronger and harder; likewise, tungsten meantone's sound is brighter and less soft than <a class="wiki_link" href="/golden%20meantone">golden meantone</a>, as a consequence of having a sharper generator; it's also more familiar as it is closer to 12edo. Yet it still has very high 5- and 7-limit accuracy, and can also be extended to the 13-limit via <a class="wiki_link" href="/grosstone">grosstone</a> (whereas golden meantone instead supports <a class="wiki_link" href="/meanpop">13-limit meanpop</a>).<br />
<br />
The diesis of tungsten meantone is almost exactly 31.6 cents; this is slightly larger than a septimal comma. It's small enough that it would never be mistaken for a semitone, yet large enough to be perceivable to all but the most <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Amusia" rel="nofollow">amusia</a>-challenged. Melodically it could be considered a &quot;shamble&quot; or <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Tonality_flux" rel="nofollow">tone flux</a> (smaller than a step, yet still a definite motion).<br />
<br />
&quot;Enharmonicism&quot; (raising or lowering a note by one diesis) is analogous to chromaticism and can also be used to build memorable melodies.</body></html></pre></div>

← Older revision		Revision as of 00:47, 24 October 2016
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	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:MasonGreen1\|MasonGreen1]] and made on <tt>2016-10-24 00:42:36 UTC</tt>.<br>		: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-10-24 00:47:14 UTC</tt>.<br>
	: The original revision id was <tt>~~596666782~~</tt>.<br>		: The original revision id was <tt>596666880</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>
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	<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">Tungsten meantone is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth [[https://en.wikipedia.org/wiki/Metallic_mean\|metallic mean]], equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.		<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">Tungsten meantone is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth [[https://en.wikipedia.org/wiki/Metallic_mean\|metallic mean]], equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios ~~appear~~ between interval sizes appear repeatedly and the scale is thus self-similar.		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.

	Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a [[https://en.wikipedia.org/wiki/Lucas_sequence\|Lucas sequence]], 2 * //<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span>//<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span>		Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a [[https://en.wikipedia.org/wiki/Lucas_sequence\|Lucas sequence]], 2 * //<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span>//<span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span>
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	<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>Tungsten meantone</title></head><body><strong>Tungsten meantone</strong> is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metallic_mean" rel="nofollow">metallic mean</a>, equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.<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>Tungsten meantone</title></head><body><strong>Tungsten meantone</strong> is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<span style="vertical-align: sub;">6 </span>of an octave, where S<span style="vertical-align: sub;">6 </span>is the sixth <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Metallic_mean" rel="nofollow">metallic mean</a>, equal to (6 + sqrt(10))/2 or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.<br />
	<br />		<br />
	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to <a class="wiki_link" href="/golden%20meantone">golden meantone</a>, since in each case the same ratios ~~appear~~ between interval sizes appear repeatedly and the scale is thus self-similar.<br />		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to <a class="wiki_link" href="/golden%20meantone">golden meantone</a>, since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.<br />
	<br />		<br />
	Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Lucas_sequence" rel="nofollow">Lucas sequence</a>, 2 * <em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span></em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span><br />		Successively better approximations of tungsten meantone are given by the following edos: 2, 12, 74, 456... These form a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Lucas_sequence" rel="nofollow">Lucas sequence</a>, 2 * <em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">U<span style="font-size: 11.2px;">n</span></span></em><span style="background-color: #ffffff; color: #252525; font-family: sans-serif; font-size: 14px;">(6,−1).</span><br />