Minortonic family: Difference between revisions

Revision as of 15:29, 25 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 xenwolf and made on 2011-03-25 15:29:29 UTC.

The original revision id was 214064634.

The revision comment was:

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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|]
[[EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|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.

[[Comma]]s: 4375/4374, 2100875/2097152

[[POTE generator]]: ~10/9 = 182.458

[[Map]]: [<1 16 32 -15|, <0 -17 -35 21|]
[[EDO]]s: [[7edo|7]], [[13edo|13]], [[33edo|33]], [[46edo|46]], [[125edo|125]], [[171edo|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]].

[[Comma]]s: 250047/250000, 645700815/645657712

[[POTE generator]]: ~10/9 = 182.467

[[Map]]: [<3 14 26 28|, <0 -17 -35 -36|]
[[EDO]]S: 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&gt;. The head of the family is minortonic temperament, with generator a minor tone.<br />
<br />
<a class="wiki_link" href="/Comma">Comma</a>: |-16 35 -17&gt;<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 182.466<br />
<br />
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 16 32|, &lt;0 -17 -35|]<br />
<a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/125edo">125</a>, <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/388edo">388</a>, 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 />
<a class="wiki_link" href="/Comma">Comma</a>s: 4375/4374, 2100875/2097152<br />
<br />
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~10/9 = 182.458<br />
<br />
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]<br />
<a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/13edo">13</a>, <a class="wiki_link" href="/33edo">33</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/125edo">125</a>, <a class="wiki_link" href="/171edo">171</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 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 <a class="wiki_link" href="/Chromatic%20pairs#Terrain">terrain</a>.<br />
<br />
<a class="wiki_link" href="/Comma">Comma</a>s: 250047/250000, 645700815/645657712<br />
<br />
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~10/9 = 182.467<br />
<br />
<a class="wiki_link" href="/Map">Map</a>: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]<br />
<a class="wiki_link" href="/EDO">EDO</a>S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038<br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0140</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-12 14:02:51 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:29:29 UTC</tt>.<br>
-: The original revision id was <tt>209871482</tt>.<br>
+: The original revision id was <tt>214064634</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>
@@ Line 8: / Line 8: @@
 <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&gt;. The head of the family is minortonic temperament, with generator a minor tone.
-Comma: |-16 35 -17&gt;
+[[Comma]]: |-16 35 -17&gt;
 [[POTE tuning|POTE generator]]: ~10/9 = 182.466
-Map: [&lt;1 16 32|, &lt;0 -17 -35|]
+[[Map]]: [&lt;1 16 32|, &lt;0 -17 -35|]
-EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091
+[[EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091
 [[toc|flat]]
@@ Line 22: / Line 22: @@
 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 &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.
-Commas: 4375/4374, 2100875/2097152
+[[Comma]]s: 4375/4374, 2100875/2097152
-POTE generator: ~10/9 = 182.458
+[[POTE generator]]: ~10/9 = 182.458
-Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
+[[Map]]: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
-EDOs: 7, 13, 33, 46, 125, 171
+[[EDO]]s: [[7edo|7]], [[13edo|13]], [[33edo|33]], [[46edo|46]], [[125edo|125]], [[171edo|171]]
-Badness: 0.0252
+[[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
+[[Comma]]s: 250047/250000, 645700815/645657712
-POTE generator: ~10/9 = 182.467
+[[POTE generator]]: ~10/9 = 182.467
-Map: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]
+[[Map]]: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]
-EDOS: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038
+[[EDO]]S: 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>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Minortonic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tempers out the minortone comma, |-16 35 -17&amp;gt;. The head of the family is minortonic temperament, with generator a minor tone.&lt;br /&gt;
 &lt;br /&gt;
-Comma: |-16 35 -17&amp;gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: |-16 35 -17&amp;gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.466&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 16 32|, &amp;lt;0 -17 -35|]&lt;br /&gt;
+&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 16 32|, &amp;lt;0 -17 -35|]&lt;br /&gt;
-EDOs: 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091&lt;br /&gt;
+&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s: &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;, &lt;a class="wiki_link" href="/388edo"&gt;388&lt;/a&gt;, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextTocRule:4:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;a href="#Mitonic"&gt;Mitonic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:5 --&gt;&lt;!-- ws:start:WikiTextTocRule:6: --&gt; | &lt;a href="#Domain"&gt;Domain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;
@@ Line 57: / Line 57: @@
 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 &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;. The wedgie is now &amp;lt;&amp;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.&lt;br /&gt;
 &lt;br /&gt;
-Commas: 4375/4374, 2100875/2097152&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 4375/4374, 2100875/2097152&lt;br /&gt;
 &lt;br /&gt;
-POTE generator: ~10/9 = 182.458&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20generator"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.458&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 16 32 -15|, &amp;lt;0 -17 -35 21|]&lt;br /&gt;
+&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 16 32 -15|, &amp;lt;0 -17 -35 21|]&lt;br /&gt;
-EDOs: 7, 13, 33, 46, 125, 171&lt;br /&gt;
+&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/13edo"&gt;13&lt;/a&gt;, &lt;a class="wiki_link" href="/33edo"&gt;33&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0252&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0252&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Domain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Domain&lt;/h1&gt;
 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 &lt;a class="wiki_link" href="/Chromatic%20pairs#Terrain"&gt;terrain&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-Commas: 250047/250000, 645700815/645657712&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 250047/250000, 645700815/645657712&lt;br /&gt;
 &lt;br /&gt;
-POTE generator: ~10/9 = 182.467&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20generator"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.467&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;3 14 26 28|, &amp;lt;0 -17 -35 -36|]&lt;br /&gt;
+&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;3 14 26 28|, &amp;lt;0 -17 -35 -36|]&lt;br /&gt;
-EDOS: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038&lt;br /&gt;
+&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038&lt;br /&gt;
-Badness: 0.0140&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0140&lt;/body&gt;&lt;/html&gt;</pre></div>

Minortonic family: Difference between revisions

Revision as of 15:29, 25 March 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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