Starling temperaments: 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>2010-11-14 01:31:12 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-14 01:57:57 UTC</tt>.<br>

: The original revision id was <tt>~~179271497~~</tt>.<br>

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===Sensi temperament===

Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.

Commas: 126/125, 245/243

7-limit minimax

[|1 0 0 0>, |1/13 0 0 7/13>, |5/13 0 0 9/13>, |0 0 0 1>]

Eigenmonzos: 2, 7

9-limit minimax

[|1 0 0 0>, |2/5 14/5 -7/5 0>,

|4/5 18/5 -9/5 0>, |3/5 26/5 -13/5 0>]

Eigenmonzos: 2, 9/5

Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.

Map: [<1 6 8 11|, <0 -7 -9 -13|]

Generators: 2, 14/9

===Valentine temperament===

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<h3 id="toc1"><a name="x--Sensi temperament"></a>Sensi temperament</h3>

Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. <a class="wiki_link" href="/46edo">46edo</a> is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.<br />

<br />

Commas: 126/125, 245/243<br />

<br />

7-limit minimax<br />

[|1 0 0 0&gt;, |1/13 0 0 7/13&gt;, |5/13 0 0 9/13&gt;, |0 0 0 1&gt;]<br />

Eigenmonzos: 2, 7<br />

<br />

9-limit minimax<br />

[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;, <br />

|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;]<br />

Eigenmonzos: 2, 9/5<br />

<br />

Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents. <br />

<br />

Map: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]<br />

Generators: 2, 14/9<br />

<br />

<h3 id="toc2"><a name="x--Valentine temperament"></a>Valentine temperament</h3>

@@ 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>2010-11-14 01:31:12 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-14 01:57:57 UTC</tt>.<br>
-: The original revision id was <tt>179271497</tt>.<br>
+: The original revision id was <tt>179272927</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 22: / Line 22: @@
 ===Sensi temperament===
 Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.
+Commas: 126/125, 245/243
+-limit minimax
+[|1 0 0 0&gt;, |1/13 0 0 7/13&gt;, |5/13 0 0 9/13&gt;, |0 0 0 1&gt;]
+Eigenmonzos: 2, 7
+-limit minimax
+[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;,
+|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;]
+Eigenmonzos: 2, 9/5
+Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents.
+Map: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]
+Generators: 2, 14/9
 ===Valentine temperament===
@@ Line 74: / Line 90: @@
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Sensi temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Sensi temperament&lt;/h3&gt;
 Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt; is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.&lt;br /&gt;
+&lt;br /&gt;
+Commas: 126/125, 245/243&lt;br /&gt;
+&lt;br /&gt;
+-limit minimax&lt;br /&gt;
+[|1 0 0 0&amp;gt;, |1/13 0 0 7/13&amp;gt;, |5/13 0 0 9/13&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 7&lt;br /&gt;
+&lt;br /&gt;
+-limit minimax&lt;br /&gt;
+[|1 0 0 0&amp;gt;, |2/5 14/5 -7/5 0&amp;gt;, &lt;br /&gt;
+|4/5 18/5 -9/5 0&amp;gt;, |3/5 26/5 -13/5 0&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 9/5&lt;br /&gt;
+&lt;br /&gt;
+Algebraic generator: Calista, the real root of x^7-2x^2-1, at 340.6467 cents. &lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 6 8 11|, &amp;lt;0 -7 -9 -13|]&lt;br /&gt;
+Generators: 2, 14/9&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--Valentine temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Valentine temperament&lt;/h3&gt;