Minortonic family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 209863796 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 209871110 - Original comment: ** |
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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>2011-03-12 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-12 14:00:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>209871110</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">This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone.</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">This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone. | ||
Comma: |-16 35 -17> | |||
[[POTE tuning|POTE generator]]: ~10/9 = 182.466 | |||
Map: [<1 16 32|, <0 -17 -35|] | |||
EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 | |||
[[toc|flat]] | |||
=Mitonic= | |||
As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17>. Flipping that gives the 5-limit wedgie <<17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings. | |||
However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. The wedgie is now <<17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic. | |||
Commas: 4375/4374, 2100875/2097152 | |||
POTE generator: ~10/9 = 182.458 | |||
Map: [<1 16 32 -15|, <0 -17 -35 21|] | |||
EDOs: 7, 13, 33, 46, 125, 171 | |||
Badness: 0.0252 | |||
=Domain= | |||
Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic+pairs#Terrain|terrain]]. | |||
Commas: 250047/250000, 645700815/645657712 | |||
POTE generator: ~10/9 = 182.467 | |||
Map: [<3 14 26 28|, <0 -17 -35 -36|] | |||
EDOS: | |||
Badness: 0.0140</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>Minortonic family</title></head><body>This tempers out the minortone comma, |-16 35 -17&gt;. The head of the family is minortonic temperament, with generator a minor tone.</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>Minortonic family</title></head><body>This tempers out the minortone comma, |-16 35 -17&gt;. The head of the family is minortonic temperament, with generator a minor tone.<br /> | ||
<br /> | |||
Comma: |-16 35 -17&gt;<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 182.466<br /> | |||
<br /> | |||
Map: [&lt;1 16 32|, &lt;0 -17 -35|]<br /> | |||
EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextTocRule:4:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Mitonic">Mitonic</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#Domain">Domain</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --> | |||
<!-- ws:end:WikiTextTocRule:7 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Mitonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mitonic</h1> | |||
As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&gt;. Flipping that gives the 5-limit wedgie &lt;&lt;17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.<br /> | |||
<br /> | |||
However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in <a class="wiki_link" href="/171edo">171edo</a>. The wedgie is now &lt;&lt;17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.<br /> | |||
<br /> | |||
Commas: 4375/4374, 2100875/2097152<br /> | |||
<br /> | |||
POTE generator: ~10/9 = 182.458<br /> | |||
<br /> | |||
Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]<br /> | |||
EDOs: 7, 13, 33, 46, 125, 171<br /> | |||
Badness: 0.0252<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Domain"></a><!-- ws:end:WikiTextHeadingRule:2 -->Domain</h1> | |||
Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic+pairs#Terrain|terrain]].<br /> | |||
<br /> | |||
Commas: 250047/250000, 645700815/645657712<br /> | |||
<br /> | |||
POTE generator: ~10/9 = 182.467<br /> | |||
<br /> | |||
Map: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]<br /> | |||
EDOS:<br /> | |||
Badness: 0.0140</body></html></pre></div> | |||
Revision as of 14:00, 12 March 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-03-12 14:00:25 UTC.
- The original revision id was 209871110.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone. Comma: |-16 35 -17> [[POTE tuning|POTE generator]]: ~10/9 = 182.466 Map: [<1 16 32|, <0 -17 -35|] EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 [[toc|flat]] =Mitonic= As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17>. Flipping that gives the 5-limit wedgie <<17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings. However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. The wedgie is now <<17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic. Commas: 4375/4374, 2100875/2097152 POTE generator: ~10/9 = 182.458 Map: [<1 16 32 -15|, <0 -17 -35 21|] EDOs: 7, 13, 33, 46, 125, 171 Badness: 0.0252 =Domain= Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic+pairs#Terrain|terrain]]. Commas: 250047/250000, 645700815/645657712 POTE generator: ~10/9 = 182.467 Map: [<3 14 26 28|, <0 -17 -35 -36|] EDOS: Badness: 0.0140
Original HTML content:
<html><head><title>Minortonic family</title></head><body>This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone.<br /> <br /> Comma: |-16 35 -17><br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 182.466<br /> <br /> Map: [<1 16 32|, <0 -17 -35|]<br /> EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091<br /> <br /> <!-- ws:start:WikiTextTocRule:4:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Mitonic">Mitonic</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#Domain">Domain</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --> <!-- ws:end:WikiTextTocRule:7 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Mitonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mitonic</h1> As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17>. Flipping that gives the 5-limit wedgie <<17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.<br /> <br /> However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in <a class="wiki_link" href="/171edo">171edo</a>. The wedgie is now <<17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.<br /> <br /> Commas: 4375/4374, 2100875/2097152<br /> <br /> POTE generator: ~10/9 = 182.458<br /> <br /> Map: [<1 16 32 -15|, <0 -17 -35 21|]<br /> EDOs: 7, 13, 33, 46, 125, 171<br /> Badness: 0.0252<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Domain"></a><!-- ws:end:WikiTextHeadingRule:2 -->Domain</h1> Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic+pairs#Terrain|terrain]].<br /> <br /> Commas: 250047/250000, 645700815/645657712<br /> <br /> POTE generator: ~10/9 = 182.467<br /> <br /> Map: [<3 14 26 28|, <0 -17 -35 -36|]<br /> EDOS:<br /> Badness: 0.0140</body></html>