Minortonic family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 209871110 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 209871482 - 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 14: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-12 14:02:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>209871482</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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=Domain= | =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 | 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 | Commas: 250047/250000, 645700815/645657712 | ||
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Map: [<3 14 26 28|, <0 -17 -35 -36|] | Map: [<3 14 26 28|, <0 -17 -35 -36|] | ||
EDOS: | EDOS: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 | ||
Badness: 0.0140</pre></div> | Badness: 0.0140</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Domain"></a><!-- ws:end:WikiTextHeadingRule:2 -->Domain</h1> | <!-- 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 | 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 <a class="wiki_link" href="/Chromatic%20pairs#Terrain">terrain</a>.<br /> | ||
<br /> | <br /> | ||
Commas: 250047/250000, 645700815/645657712<br /> | Commas: 250047/250000, 645700815/645657712<br /> | ||
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Map: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]<br /> | Map: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]<br /> | ||
EDOS:<br /> | EDOS: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038<br /> | ||
Badness: 0.0140</body></html></pre></div> | Badness: 0.0140</body></html></pre></div> | ||
Revision as of 14:02, 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 14:02:51 UTC.
- The original revision id was 209871482.
- 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: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 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 <a class="wiki_link" href="/Chromatic%20pairs#Terrain">terrain</a>.<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: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038<br /> Badness: 0.0140</body></html>