Hemimean family: Difference between revisions

Revision as of 12:17, 26 October 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 2011-10-26 12:17:10 UTC.

The original revision id was 268804606.

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:

[[toc|flat]]


The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum of a temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.


[[Comma]]: 3136/3125, hemimean

7 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0>, |6/5 0 0 2/5>, |0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3

Lattice basis: 28/25 length 0.5055 3/2 length 1.5849
Angle(28/25, 3/2) = 90 degrees
Map to lattice: [<0 0 2 5|, <0 1 0 0|]

Map: [<1 0 0 -3|, <0 1 0 0|, <0 0 2 5|] 
[[Generator|Generators]]: 2, 3, 56/25
[[edo|Edos]]: [[217edo|217]], [[229edo|229]], [[328edo|328]], [[359edo|359]], [[446edo|446]]
Badness: 0.000160

[[Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7

=Belobog=
[[Comma|Commas]]: 3136/3125, 441/440

11 limit minimax
[|1 0 0 0 0>, |27/22 6/11 -5/22 -3/11 5/22>, 
|24/11 -4/11 -2/11 2/11 2/11>, 
|27/11 -10/11 -5/11 5/11 5/11>, 
|24/11 -4/11 -13/11 2/11 13/11>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7

Lattice basis: 28/25 0.3829 16/15 1.1705
Angle(28/25, 16/15) = 93.2696
Map to lattice: [<0 -2 2 5 4|, <0 -1 0 0 -2|]

Map: [<1 0 0 -3 -9|, <0 1 0 0 2|, [0 0 2 5 8|]
[[Generator|Generators]]: 2, 3, 56/25
[[edo|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]]
Badness: 0.000609

Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7

Scales: [[belobog31]]

==13-limit==
Commas: 441/440, 1001/1000, 3136/3125

Map: [<1 0 0 -3 -9 15|, <0 1 0 0 2 -2|, <0 0 2 5 8 -7|]
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 378, 465
Badness: 0.00111

==Bellowblog==
Commas: 196/195, 352/351, 625/624

Map: [<1 0 0 -3 -9 -4|, <0 1 0 0 2 -1|, <0 0 2 5 8 8|]
EDOs: 31, 56, 87, 118
Badness: 0.00126

=Siebog=
[[Comma|Commas]]: 3136/3125, 540/539

11 limit minimax
[|1 0 0 0 0>, |0 1 0 0 0>, |8/5 3/5 1/5 0 -1/5>, 
|1 3/2 1/2 0 -1/2>, |8/5 3/5 -4/5 0 4/5>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 4/3

Map: [<1 0 0 -3 8|, <0 1 0 0 3|, <0 0 2 5 -8|]
[[Generator|Generators]]: 2, 3, 768/343
[[edo|Edos]]: 19, 31, 80, 111, [[130edo|130]], [[241edo|241]]
Badness: 0.000870

Original HTML content:

<html><head><title>Hemimean family</title></head><body><!-- ws:start:WikiTextTocRule:8:&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:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Belobog">Belobog</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Siebog">Siebog</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
<!-- ws:end:WikiTextTocRule:13 --><br />
<br />
The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with <a class="wiki_link" href="/Spectrum%20of%20a%20temperament">spectrum</a> 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.<br />
<br />
<br />
<a class="wiki_link" href="/Comma">Comma</a>: 3136/3125, hemimean<br />
<br />
7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |0 1 0 0&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 4/3<br />
<br />
Lattice basis: 28/25 length 0.5055 3/2 length 1.5849<br />
Angle(28/25, 3/2) = 90 degrees<br />
Map to lattice: [&lt;0 0 2 5|, &lt;0 1 0 0|]<br />
<br />
Map: [&lt;1 0 0 -3|, &lt;0 1 0 0|, &lt;0 0 2 5|] <br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 56/25<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/217edo">217</a>, <a class="wiki_link" href="/229edo">229</a>, <a class="wiki_link" href="/328edo">328</a>, <a class="wiki_link" href="/359edo">359</a>, <a class="wiki_link" href="/446edo">446</a><br />
Badness: 0.000160<br />
<br />
<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 3136/625 7 68841472/9765625 to 2.3.25/7<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Belobog"></a><!-- ws:end:WikiTextHeadingRule:0 -->Belobog</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 3136/3125, 441/440<br />
<br />
11 limit minimax<br />
[|1 0 0 0 0&gt;, |27/22 6/11 -5/22 -3/11 5/22&gt;, <br />
|24/11 -4/11 -2/11 2/11 2/11&gt;, <br />
|27/11 -10/11 -5/11 5/11 5/11&gt;, <br />
|24/11 -4/11 -13/11 2/11 13/11&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 9/7<br />
<br />
Lattice basis: 28/25 0.3829 16/15 1.1705<br />
Angle(28/25, 16/15) = 93.2696<br />
Map to lattice: [&lt;0 -2 2 5 4|, &lt;0 -1 0 0 -2|]<br />
<br />
Map: [&lt;1 0 0 -3 -9|, &lt;0 1 0 0 2|, [0 0 2 5 8|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 56/25<br />
<a class="wiki_link" href="/edo">Edos</a>: 12, 31, 87, 118, 130, 217, <a class="wiki_link" href="/248edo">248</a>, <a class="wiki_link" href="/378edo">378</a>, <a class="wiki_link" href="/626edo">626</a><br />
Badness: 0.000609<br />
<br />
Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7<br />
<br />
Scales: <a class="wiki_link" href="/belobog31">belobog31</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Belobog-13-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->13-limit</h2>
Commas: 441/440, 1001/1000, 3136/3125<br />
<br />
Map: [&lt;1 0 0 -3 -9 15|, &lt;0 1 0 0 2 -2|, &lt;0 0 2 5 8 -7|]<br />
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 378, 465<br />
Badness: 0.00111<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Belobog-Bellowblog"></a><!-- ws:end:WikiTextHeadingRule:4 -->Bellowblog</h2>
Commas: 196/195, 352/351, 625/624<br />
<br />
Map: [&lt;1 0 0 -3 -9 -4|, &lt;0 1 0 0 2 -1|, &lt;0 0 2 5 8 8|]<br />
EDOs: 31, 56, 87, 118<br />
Badness: 0.00126<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Siebog"></a><!-- ws:end:WikiTextHeadingRule:6 -->Siebog</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 3136/3125, 540/539<br />
<br />
11 limit minimax<br />
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |8/5 3/5 1/5 0 -1/5&gt;, <br />
|1 3/2 1/2 0 -1/2&gt;, |8/5 3/5 -4/5 0 4/5&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 4/3<br />
<br />
Map: [&lt;1 0 0 -3 8|, &lt;0 1 0 0 3|, &lt;0 0 2 5 -8|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 768/343<br />
<a class="wiki_link" href="/edo">Edos</a>: 19, 31, 80, 111, <a class="wiki_link" href="/130edo">130</a>, <a class="wiki_link" href="/241edo">241</a><br />
Badness: 0.000870</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>2011-08-22 02:15:54 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-26 12:17:10 UTC</tt>.<br>
-: The original revision id was <tt>247576555</tt>.<br>
+: The original revision id was <tt>268804606</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">The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum of a temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.
+<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">[[toc|flat]]
+The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum of a temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.
@@ Line 26: / Line 29: @@
 [[Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7
-==Belobog==
+=Belobog=
 [[Comma|Commas]]: 3136/3125, 441/440
@@ Line 49: / Line 52: @@
 Scales: [[belobog31]]
-===13-limit===
+==13-limit==
 Commas: 441/440, 1001/1000, 3136/3125
@@ Line 56: / Line 59: @@
 Badness: 0.00111
-===Bellowblog===
+==Bellowblog==
 Commas: 196/195, 352/351, 625/624
@@ Line 63: / Line 66: @@
 Badness: 0.00126
-==Siebog==
+=Siebog=
 [[Comma|Commas]]: 3136/3125, 540/539
@@ Line 76: / Line 79: @@
 Badness: 0.000870</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;Hemimean family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with &lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;spectrum&lt;/a&gt; 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.&lt;br /&gt;
+<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;Hemimean family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&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:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Belobog"&gt;Belobog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Siebog"&gt;Siebog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
+&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
+&lt;br /&gt;
+The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with &lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;spectrum&lt;/a&gt; 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
@@ Line 96: / Line 102: @@
 &lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 3136/625 7 68841472/9765625 to 2.3.25/7&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Belobog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Belobog&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Belobog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Belobog&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3136/3125, 441/440&lt;br /&gt;
 &lt;br /&gt;
@@ Line 119: / Line 125: @@
 Scales: &lt;a class="wiki_link" href="/belobog31"&gt;belobog31&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Belobog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Belobog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h2&gt;
 Commas: 441/440, 1001/1000, 3136/3125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 126: / Line 132: @@
 Badness: 0.00111&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Belobog-Bellowblog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Bellowblog&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Belobog-Bellowblog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Bellowblog&lt;/h2&gt;
 Commas: 196/195, 352/351, 625/624&lt;br /&gt;
 &lt;br /&gt;
@@ Line 133: / Line 139: @@
 Badness: 0.00126&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Siebog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Siebog&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Siebog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Siebog&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3136/3125, 540/539&lt;br /&gt;
 &lt;br /&gt;

Hemimean family: Difference between revisions

Revision as of 12:17, 26 October 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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