Kleismic family: 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:

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-~~25 11~~:57:34 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-07 19:29:48 UTC</tt>.

: The original revision id was <tt>~~213990166~~</tt>.

: The original revision id was <tt>234996744</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].

The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14/53 is about perfect as a hanson generator, though 9/34 also makes sense and using [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].

[[POTE tuning|POTE generator]]: 317.007

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Map: [<1 0 1|, <0 6 5|]

EDOs: 15, 19, 34, 53, 458

Music:

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3|Hanson Improv]] by [[Petr Parizek]]

[[http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3|In Hanson11]] by [[Chris Vaisvil]]

=Seven limit children=

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The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.

The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14/53 is about perfect as a hanson generator, though 9/34 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007

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Map: [&lt;1 0 1|, &lt;0 6 5|]

EDOs: 15, 19, 34, 53, 458

Music:

<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3" rel="nofollow">Hanson Improv</a> by <a class="wiki_link" href="/Petr%20Parizek">Petr Parizek</a>

<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3" rel="nofollow">In Hanson11</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>

<h1 id="toc0"><a name="Seven limit children"></a>Seven limit children</h1>

@@ 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>2011-03-25 11:57:34 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-07 19:29:48 UTC</tt>.<br>
-: The original revision id was <tt>213990166</tt>.<br>
+: The original revision id was <tt>234996744</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: @@
-The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
+The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14/53 is about perfect as a hanson generator, though 9/34 also makes sense and using [[19edo]] is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
 [[POTE tuning|POTE generator]]: 317.007
@@ Line 15: / Line 15: @@
 Map: [&lt;1 0 1|, &lt;0 6 5|]
 EDOs: 15, 19, 34, 53, 458
+Music:
+[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3|Hanson Improv]] by [[Petr Parizek]]
+[[http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3|In Hanson11]] by [[Chris Vaisvil]]
 =Seven limit children=
@@ Line 213: / Line 217: @@
 &lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&amp;gt;, and flipping that yields &amp;lt;&amp;lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. 14/53 is about perfect as a generator, though 9/34 also makes sense and using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; is possible. Other tunings include &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;.&lt;br /&gt;
+The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&amp;gt;, and flipping that yields &amp;lt;&amp;lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14/53 is about perfect as a hanson generator, though 9/34 also makes sense and using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; is possible. Other tunings include &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.007&lt;br /&gt;
@@ Line 219: / Line 223: @@
 Map: [&amp;lt;1 0 1|, &amp;lt;0 6 5|]&lt;br /&gt;
 EDOs: 15, 19, 34, 53, 458&lt;br /&gt;
+&lt;br /&gt;
+Music:&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3" rel="nofollow"&gt;Hanson Improv&lt;/a&gt; by &lt;a class="wiki_link" href="/Petr%20Parizek"&gt;Petr Parizek&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3" rel="nofollow"&gt;In Hanson11&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h1&gt;