Gamelismic clan: Difference between revisions

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<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>2010-06-~~03 15~~:45:19 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-12 16:23:53 UTC</tt>.<br>

: The original revision id was <tt>~~146826735~~</tt>.<br>

: The original revision id was <tt>162007187</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>

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[[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.

===Full seven limit children===

==Full seven limit children==

To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.</pre></div>

To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.

===Rodan===

Commas a = 411/400, b = 245/243, c = 385/384

Minimax 3:-1/19a+3/19-4/19c 5:7/19-2/19b-10/19c

7:-6/19a-1/19b-5/19c 11:-2/19a+6/19b-8/19c

Edos: 87, 128

</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"><html><head><title>Gamelismic clan</title></head><body>The [2,3,5]-<a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&gt;. For any member of the clan, and for the gamelismic temperament itself, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more.<br />

<a class="wiki_link" href="/36edo">36edo</a> is a good tuning for gamelismic itself, though if the full 7-limit is desired, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/77edo">77edo</a> or <a class="wiki_link" href="/118edo">118edo</a> might be preferred. <br />

<br />

<h3 id="toc0"><a name="x--Full seven limit children"></a>Full seven limit children</h3>

<h2 id="toc0"><a name="x-Full seven limit children"></a>Full seven limit children</h2>

To the gamelisma itself we need to add the comma which appears next on the modified <a class="wiki_link" href="/Normal%20lists">normal comma list</a>, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.</body></html></pre></div>

To the gamelisma itself we need to add the comma which appears next on the modified <a class="wiki_link" href="/Normal%20lists">normal comma list</a>, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.<br />

<br />

<h3 id="toc1"><a name="x-Full seven limit children-Rodan"></a>Rodan</h3>

Commas a = 411/400, b = 245/243, c = 385/384<br />

<br />

Minimax 3:-1/19a+3/19-4/19c 5:7/19-2/19b-10/19c<br />

7:-6/19a-1/19b-5/19c 11:-2/19a+6/19b-8/19c<br />

<br />

Edos: 87, 128</body></html></pre></div>

@@ 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>2010-06-03 15:45:19 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-12 16:23:53 UTC</tt>.<br>
-: The original revision id was <tt>146826735</tt>.<br>
+: The original revision id was <tt>162007187</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 9: / Line 9: @@
 [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.
-===Full seven limit children===
+==Full seven limit children==
-To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.</pre></div>
+To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
+===Rodan===
+Commas a =  411/400, b = 245/243, c = 385/384
+Minimax 3:-1/19a+3/19-4/19c 5:7/19-2/19b-10/19c
+:-6/19a-1/19b-5/19c 11:-2/19a+6/19b-8/19c
+Edos: 87, 128
+</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;Gamelismic clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The [2,3,5]-&lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&amp;gt;. For any member of the clan, and for the gamelismic temperament itself, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more.&lt;br /&gt;
 &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; is a good tuning for gamelismic itself, though if the full 7-limit is desired, &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt; or &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; might be preferred. &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Full seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Full seven limit children&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Full seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Full seven limit children&lt;/h2&gt;
-To the gamelisma itself we need to add the comma which appears next on the modified &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt;, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.&lt;/body&gt;&lt;/html&gt;</pre></div>
+To the gamelisma itself we need to add the comma which appears next on the modified &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt;, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.&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-Full seven limit children-Rodan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Rodan&lt;/h3&gt;
+Commas a =  411/400, b = 245/243, c = 385/384&lt;br /&gt;
+&lt;br /&gt;
+Minimax 3:-1/19a+3/19-4/19c 5:7/19-2/19b-10/19c&lt;br /&gt;
+:-6/19a-1/19b-5/19c 11:-2/19a+6/19b-8/19c&lt;br /&gt;
+&lt;br /&gt;
+Edos: 87, 128&lt;/body&gt;&lt;/html&gt;</pre></div>