31st-octave 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>2011-12-01 15:14:49 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-01 16:27:08 UTC</tt>.<br>

: The original revision id was <tt>~~281230670~~</tt>.<br>

: The original revision id was <tt>281262354</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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=Prajapati=

The Hindu god Pradjapati is said to have created the universe by speaking aloud the odd numbers from 1 to 31. People with an interest in 31 may want to try this method themselves.

Commas: 81/80, 126/125, 1029/1024

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=Gallium=

The name of gallium temperament comes from Gallium, the 31st element.

Commas: 81/80, 126/125, 99/98, 121/120

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=Birds=

The birds temperament tempers out the //31-5 comma//, |72 0 -31>, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 "As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it."

The birds temperament tempers out the //31-5 comma//, |72 0 -31>, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 "As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it." It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion.

Commas: 3136/3125, 823543/819200

POTE generator:

POTE generator: ~1029/1024 = 5.155

Map: [<31 49 72 87|, <0 1 0 0|]

Wedgie: <<31 0 0 -72 -87 0|

Edos: 31, 124, 155, 186, 217, 248, 465

Badness: 0.1000

==11-limit==

Commas: 441/440, 3136/3125, 41503/41472

POTE generator: ~385/384 = 4.938

Map: [<31 49 72 87 107|, <0 1 0 0 2|]

EDOs: 31, 186e, 217, 248, 961cd

Badness: 0.0399

==13-limit==

Commas: 441/440, 3136/3125, 1001/1000, 13720/13689

POTE generator: ~385/384 = 5.170

Map: [<31 49 72 87 107 115|, <0 1 0 0 2 -2|]

EDOs: 31, 186e, 217, 248, 465

Badness: 0.0357

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<br />

<h1 id="toc0"><a name="Prajapati"></a>Prajapati</h1>

The Hindu god Pradjapati is said to have created the universe by speaking aloud the odd numbers from 1 to 31. People with an interest in 31 may want to try this method themselves.<br />

<br />

Commas: 81/80, 126/125, 1029/1024<br />

<br />

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<br />

<h1 id="toc3"><a name="Gallium"></a>Gallium</h1>

The name of gallium temperament comes from Gallium, the 31st element.<br />

<br />

Commas: 81/80, 126/125, 99/98, 121/120<br />

<br />

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<br />

<h1 id="toc4"><a name="Birds"></a>Birds</h1>

The birds temperament tempers out the <em>31-5 comma</em>, |72 0 -31&gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 &quot;As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it.&quot;<br />

The birds temperament tempers out the <em>31-5 comma</em>, |72 0 -31&gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 &quot;As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it.&quot; It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion.<br />

<br />

Commas: 3136/3125, 823543/819200<br />

<br />

POTE generator:</body></html></pre></div>

POTE generator: ~1029/1024 = 5.155<br />

<br />

Map: [&lt;31 49 72 87|, &lt;0 1 0 0|]<br />

Wedgie: &lt;&lt;31 0 0 -72 -87 0|<br />

Edos: 31, 124, 155, 186, 217, 248, 465<br />

Badness: 0.1000<br />

<br />

<h2 id="toc5"><a name="Birds-11-limit"></a>11-limit</h2>

Commas: 441/440, 3136/3125, 41503/41472<br />

<br />

POTE generator: ~385/384 = 4.938<br />

<br />

Map: [&lt;31 49 72 87 107|, &lt;0 1 0 0 2|]<br />

EDOs: 31, 186e, 217, 248, 961cd<br />

Badness: 0.0399<br />

<br />

<h2 id="toc6"><a name="Birds-13-limit"></a>13-limit</h2>

Commas: 441/440, 3136/3125, 1001/1000, 13720/13689<br />

<br />

POTE generator: ~385/384 = 5.170<br />

<br />

Map: [&lt;31 49 72 87 107 115|, &lt;0 1 0 0 2 -2|]<br />

EDOs: 31, 186e, 217, 248, 465<br />

Badness: 0.0357</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>2011-12-01 15:14:49 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-01 16:27:08 UTC</tt>.<br>
-: The original revision id was <tt>281230670</tt>.<br>
+: The original revision id was <tt>281262354</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: @@
 =Prajapati=
+The Hindu  god Pradjapati is said to have created the universe by speaking aloud the odd numbers from 1 to 31. People with an interest in 31 may want to try this method themselves.
 Commas: 81/80, 126/125, 1029/1024
@@ Line 36: / Line 38: @@
 =Gallium=
+The name of gallium temperament comes from Gallium, the 31st element.
 Commas: 81/80, 126/125, 99/98, 121/120
@@ Line 45: / Line 49: @@
 =Birds=
-The birds temperament tempers out the //31-5 comma//, |72 0 -31&gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 "As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it."
+The birds temperament tempers out the //31-5 comma//, |72 0 -31&gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 "As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it." It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion.
 Commas: 3136/3125, 823543/819200
-POTE generator:
+POTE generator: ~1029/1024 = 5.155
+Map: [&lt;31 49 72 87|, &lt;0 1 0 0|]
+Wedgie: &lt;&lt;31 0 0 -72 -87 0|
+Edos: 31, 124, 155, 186, 217, 248, 465
+Badness: 0.1000
+==11-limit==
+Commas: 441/440, 3136/3125, 41503/41472
+POTE generator: ~385/384 = 4.938
+Map: [&lt;31 49 72 87 107|, &lt;0 1 0 0 2|]
+EDOs: 31, 186e, 217, 248, 961cd
+Badness: 0.0399
+==13-limit==
+Commas: 441/440, 3136/3125, 1001/1000, 13720/13689
+POTE generator: ~385/384 = 5.170
+Map: [&lt;31 49 72 87 107 115|, &lt;0 1 0 0 2 -2|]
+EDOs: 31, 186e, 217, 248, 465
+Badness: 0.0357
@@ Line 59: / Line 88: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Prajapati"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Prajapati&lt;/h1&gt;
+The Hindu  god Pradjapati is said to have created the universe by speaking aloud the odd numbers from 1 to 31. People with an interest in 31 may want to try this method themselves.&lt;br /&gt;
+&lt;br /&gt;
 Commas: 81/80, 126/125, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 86: / Line 117: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Gallium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Gallium&lt;/h1&gt;
+The name of gallium temperament comes from Gallium, the 31st element.&lt;br /&gt;
+&lt;br /&gt;
 Commas: 81/80, 126/125, 99/98, 121/120&lt;br /&gt;
 &lt;br /&gt;
@@ Line 95: / Line 128: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Birds"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Birds&lt;/h1&gt;
-The birds temperament tempers out the &lt;em&gt;31-5 comma&lt;/em&gt;, |72 0 -31&amp;gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 &amp;quot;As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it.&amp;quot;&lt;br /&gt;
+The birds temperament tempers out the &lt;em&gt;31-5 comma&lt;/em&gt;, |72 0 -31&amp;gt;, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 &amp;quot;As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it.&amp;quot; It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion.&lt;br /&gt;
 &lt;br /&gt;
 Commas: 3136/3125, 823543/819200&lt;br /&gt;
 &lt;br /&gt;
-POTE generator:&lt;/body&gt;&lt;/html&gt;</pre></div>
+POTE generator: ~1029/1024 = 5.155&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;31 49 72 87|, &amp;lt;0 1 0 0|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;31 0 0 -72 -87 0|&lt;br /&gt;
+Edos: 31, 124, 155, 186, 217, 248, 465&lt;br /&gt;
+Badness: 0.1000&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Birds-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
+Commas: 441/440, 3136/3125, 41503/41472&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~385/384 = 4.938&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;31 49 72 87 107|, &amp;lt;0 1 0 0 2|]&lt;br /&gt;
+EDOs: 31, 186e, 217, 248, 961cd&lt;br /&gt;
+Badness: 0.0399&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Birds-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
+Commas: 441/440, 3136/3125, 1001/1000, 13720/13689&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~385/384 = 5.170&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;31 49 72 87 107 115|, &amp;lt;0 1 0 0 2 -2|]&lt;br /&gt;
+EDOs: 31, 186e, 217, 248, 465&lt;br /&gt;
+Badness: 0.0357&lt;/body&gt;&lt;/html&gt;</pre></div>