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:

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-~~19 15~~:01:46 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-10 20:57:10 UTC</tt>.

: The original revision id was <tt>~~181243043~~</tt>.

: The original revision id was <tt>187268977</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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7-limit

[[Comma|Commas]]: {1029/1024, 126/125}

[[Comma|Commas]]: 1029/1024, 126/125

[[Minimax tuning]]:

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|47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>]

[[Eigenmonzo|Eigenmonzos]]: 2, 9/7

[[POTE tuning|POTE generator]]: 77.864

Algebraic generator: [[Algebraic number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.

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Map: [<1 1 2 3|, <0 9 5 -3|]

[[Generator|Generators]]: 2, 21/20

EDOs: 31, 77, 262

11-limit

[[Comma|Commas]]: {121/120, 126/125, 176/175}

[[Comma|Commas]]: 121/120, 126/125, 176/175

[[Minimax tuning]]:

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|2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>]

[[Eigenmonzo|Eigenmonzos]]: 2, 11/7

Minimax generator: (11/7)^(1/10) = 78.249

[[POTE tuning|POTE generator]]: 77.881

Algebraic generator: Gontrand2, the smallest positive root of 4x^7-8x^6+5, at 77.9989 cents.

Map: [<1 1 2 3 3|, <0 9 5 -3 7|]

[[Edo|Edos]]: [[77edo|77]], [[108edo|108]], [[185edo|185]]

[[Edo|Edos]]: [[31edo|31]], [[77edo|77]], [[108edo|108]], [[185edo|185]]

===Casablanca temperament===

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7-limit

<a class="wiki_link" href="/Comma">Commas</a>: {1029/1024, 126/125}

<a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 126/125

<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:

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|47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;]

<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.864

Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">smaller root</a> of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.

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Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]

<a class="wiki_link" href="/Generator">Generators</a>: 2, 21/20

EDOs: 31, 77, 262

11-limit

<a class="wiki_link" href="/Comma">Commas</a>: {121/120, 126/125, 176/175}

<a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175

<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:

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|2 0 0 -1/2 1/2&gt;, |3 0 0 3/10 -3/10&gt;, |3 0 0 -7/10 7/10&gt;]

<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/7

Minimax generator: (11/7)^(1/10) = 78.249

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.881

Algebraic generator: Gontrand2, the smallest positive root of 4x^7-8x^6+5, at 77.9989 cents.

Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]

<h3 id="toc3"><a name="x--Casablanca temperament"></a>Casablanca 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>2010-11-19 15:01:46 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-10 20:57:10 UTC</tt>.<br>
-: The original revision id was <tt>181243043</tt>.<br>
+: The original revision id was <tt>187268977</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 45: / Line 45: @@
 -limit
-[[Comma|Commas]]: {1029/1024, 126/125}
+[[Comma|Commas]]: 1029/1024, 126/125
 [[Minimax tuning]]:
@@ Line 55: / Line 55: @@
 |47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;]
 [[Eigenmonzo|Eigenmonzos]]: 2, 9/7
+[[POTE tuning|POTE generator]]: 77.864
 Algebraic generator: [[Algebraic number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.
@@ Line 60: / Line 62: @@
 Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]
 [[Generator|Generators]]: 2, 21/20
+EDOs: 31, 77, 262
 -limit
-[[Comma|Commas]]: {121/120, 126/125, 176/175}
+[[Comma|Commas]]: 121/120, 126/125, 176/175
 [[Minimax tuning]]:
@@ Line 68: / Line 71: @@
 |2 0 0 -1/2 1/2&gt;, |3 0 0 3/10 -3/10&gt;, |3 0 0 -7/10 7/10&gt;]
 [[Eigenmonzo|Eigenmonzos]]: 2, 11/7
+Minimax generator: (11/7)^(1/10) = 78.249
+[[POTE tuning|POTE generator]]: 77.881
 Algebraic generator: Gontrand2, the smallest positive root of 4x^7-8x^6+5, at 77.9989 cents.
 Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]
-[[Edo|Edos]]: [[77edo|77]], [[108edo|108]], [[185edo|185]]
+[[Edo|Edos]]: [[31edo|31]], [[77edo|77]], [[108edo|108]], [[185edo|185]]
 ===Casablanca temperament===
@@ Line 148: / Line 154: @@
 &lt;br /&gt;
 -limit&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: {1029/1024, 126/125}&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 1029/1024, 126/125&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
@@ Line 158: / Line 164: @@
 |47/21 10/21 0 -5/21&amp;gt;, |20/7 -2/7 0 1/7&amp;gt;]&lt;br /&gt;
 &lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 9/7&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 77.864&lt;br /&gt;
 &lt;br /&gt;
 Algebraic generator: &lt;a class="wiki_link" href="/Algebraic%20number"&gt;smaller root&lt;/a&gt; of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.&lt;br /&gt;
@@ Line 163: / Line 171: @@
 Map: [&amp;lt;1 1 2 3|, &amp;lt;0 9 5 -3|]&lt;br /&gt;
 &lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 21/20&lt;br /&gt;
+EDOs: 31, 77, 262&lt;br /&gt;
 &lt;br /&gt;
 -limit&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: {121/120, 126/125, 176/175}&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 121/120, 126/125, 176/175&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;:&lt;br /&gt;
@@ Line 171: / Line 180: @@
 |2 0 0 -1/2 1/2&amp;gt;, |3 0 0 3/10 -3/10&amp;gt;, |3 0 0 -7/10 7/10&amp;gt;]&lt;br /&gt;
 &lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/7&lt;br /&gt;
+&lt;br /&gt;
+Minimax generator: (11/7)^(1/10) = 78.249&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 77.881&lt;br /&gt;
 &lt;br /&gt;
 Algebraic generator: Gontrand2, the smallest positive root of 4x^7-8x^6+5, at 77.9989 cents.&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 3 3|, &amp;lt;0 9 5 -3 7|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/77edo"&gt;77&lt;/a&gt;, &lt;a class="wiki_link" href="/108edo"&gt;108&lt;/a&gt;, &lt;a class="wiki_link" href="/185edo"&gt;185&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77&lt;/a&gt;, &lt;a class="wiki_link" href="/108edo"&gt;108&lt;/a&gt;, &lt;a class="wiki_link" href="/185edo"&gt;185&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x--Casablanca temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Casablanca temperament&lt;/h3&gt;