Minortonic family: Difference between revisions

Line 1:

~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

This tempers out the minortone comma, |-16 35 -17>. The head of the family is minortonic temperament, with generator a minor tone.

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>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>~~

~~<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.

[[Comma]]: |-16 35 -17>

[[Comma|Comma]]: |-16 35 -17>

[[~~POTE tuning~~|POTE generator]]: ~10/9 = 182.466

[[POTE_tuning|POTE generator]]: ~10/9 = 182.466

[[Map]]: [<1 16 32|, <0 -17 -35|]

[[Map|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]~~]

[[EDO|EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091

__FORCETOC__

=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.

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|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

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

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

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

[[Map]]: [<1 16 32 -15|, <0 -17 -35 21|]

[[Map|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

[[EDO|EDO]]s: [[7edo|7]], [[13edo|13]], [[33edo|33]], [[46edo|46]], [[125edo|125]], [[171edo|171]]

[[Badness|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]].

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

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

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

[[Map|Map]]: [<3 14 26 28|, <0 -17 -35 -36|]

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

[[EDO|EDO]]S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038

[[~~Map~~]]: ~~[<3 14 26 28|, <~~0 ~~-17 -35 -36|]~~

[[Badness|Badness]]: 0.0140

[[~~EDO~~]]~~S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038~~

[[Category:family]]

[[~~Badness~~]]~~: 0.0140</pre></div>~~

[[Category:minortonic]]

~~<h4>Original HTML content~~:~~</h4>~~

[[Category:theory]]

<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 />

[[Category:todo:intro]]

~~<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 />~~

~~<br />~~

<a href="#Mitonic">Mitonic</a> | <a href="#Domain">Domain</a>

~~<br />~~

~~<h1 id="toc0"><a name="Mitonic"></a>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="/Badness">Badness</a>: 0.0252<br />~~

~~<br />~~

~~<h1 id="toc1"><a name="Domain"></a>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></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+This tempers out the minortone comma, |-16 35 -17&gt;. The head of the family is minortonic temperament, with generator a minor tone.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>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>
-<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&gt;. The head of the family is minortonic temperament, with generator a minor tone.
-[[Comma]]: |-16 35 -17&gt;
+[[Comma|Comma]]: |-16 35 -17&gt;
-[[POTE tuning|POTE generator]]: ~10/9 = 182.466
+[[POTE_tuning|POTE generator]]: ~10/9 = 182.466
-[[Map]]: [&lt;1 16 32|, &lt;0 -17 -35|]
+[[Map|Map]]: [&lt;1 16 32|, &lt;0 -17 -35|]
-[[EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091
-[[toc|flat]]
+[[EDO|EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091
+__FORCETOC__
 =Mitonic=
 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.
-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.
+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|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.
-[[Comma]]s: 4375/4374, 2100875/2097152
+[[Comma|Comma]]s: 4375/4374, 2100875/2097152
-[[POTE generator]]: ~10/9 = 182.458
+[[POTE_generator|POTE generator]]: ~10/9 = 182.458
-[[Map]]: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
+[[Map|Map]]: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
-[[EDO]]s: [[7edo|7]], [[13edo|13]], [[33edo|33]], [[46edo|46]], [[125edo|125]], [[171edo|171]]
-[[Badness]]: 0.0252
+[[EDO|EDO]]s: [[7edo|7]], [[13edo|13]], [[33edo|33]], [[46edo|46]], [[125edo|125]], [[171edo|171]]
+[[Badness|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]].
+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|Comma]]s: 250047/250000, 645700815/645657712
+[[POTE_generator|POTE generator]]: ~10/9 = 182.467
-[[Comma]]s: 250047/250000, 645700815/645657712
+[[Map|Map]]: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]
-[[POTE generator]]: ~10/9 = 182.467
+[[EDO|EDO]]S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038
-[[Map]]: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]
+[[Badness|Badness]]: 0.0140
-[[EDO]]S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038
+[[Category:family]]
-[[Badness]]: 0.0140</pre></div>
+[[Category:minortonic]]
-<h4>Original HTML content:</h4>
+[[Category:theory]]
-<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;
+[[Category:todo:intro]]
-&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;
-&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;
-&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;
-&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mitonic&lt;/h1&gt;
-As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&amp;gt;. Flipping that gives the 5-limit wedgie &amp;lt;&amp;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.&lt;br /&gt;
-&lt;br /&gt;
-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;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 4375/4374, 2100875/2097152&lt;br /&gt;
-&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;
-&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;
-&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;
-&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;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 250047/250000, 645700815/645657712&lt;br /&gt;
-&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;
-&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;
-&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;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0140&lt;/body&gt;&lt;/html&gt;</pre></div>