Miracle: Difference between revisions

Line 1:

<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>2012-11-~~03 14~~:24:34 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-11-10 16:24:00 UTC</tt>.

: The original revision id was <tt>~~378898486~~</tt>.

: The original revision id was <tt>381128200</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.

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">~~See~~ [[~~Gamelismic~~ clan#Miracle]].

<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;white-space: pre-wrap ! important" class="old-revision-html">Miracle is an exceptionally efficient linear temperament which is a member of both the [[marvel temperaments]] and the [[gamelismic clan]]. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:

|| # of secors || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 ||

|| JI intervals represented || **1/1** || 16/15~15/14 || **8/7** || **11/9** || 21/16 || **7/5** || **3/2** || **8/5** || **12/7** || **11/6** ||

|| # of secors || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17 || 18 || 19 ||

|| JI intervals represented || 63/32~55/28~108/55~49/25~96/49~88/45 || 22/21~21/20 || **9/8** || **6/5** || **9/7** || **11/8** || 22/15 || **11/7** || 42/25 || **9/5** ||

|| # of secors || 20 || 21 || 22 || || || || || || || ||

|| JI intervals represented || 48/25 || || **11/10** || || || || || || || ||

Some temperaments have 11/9 as a "neutral third", meaning it's exactly half of a 3/2 (tempering out 243/242), and other temperaments (in the [[gamelismic clan]]) have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both 16/15 and 15/14.

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44~49/48~50/49~55/54~56/55~64/63 all tempered together.

=Spectrum of Miracle Tunings by Eigenmonzos=

Line 22:

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|| 11/8 || 116.755 ||

|| 9/7 || 116.792 ||

|| 4/3 || 116.993 ||

|| 4/3 || 116.993 ||</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>Miracle</title></head><body>Miracle is an exceptionally efficient linear temperament which is a member of both the <a class="wiki_link" href="/marvel%20temperaments">marvel temperaments</a> and the <a class="wiki_link" href="/gamelismic%20clan">gamelismic clan</a>. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very &quot;low complexity&quot; (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:

</~~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~~>~~Miracle~~</~~title~~></~~head~~><~~body~~>~~See~~ <a class="wiki_link" href="/~~Gamelismic~~%20clan#Miracle">~~Gamelismic clan~~</a>.

<tr>

<td><ol><li>of secors</li></ol></td>

<td>0

</td>

<td>1

</td>

<td>2

</td>

<td>3

</td>

<td>4

</td>

<td>5

</td>

<td>6

</td>

<td>7

</td>

<td>8

</td>

<td>9

</td>

</tr>

<tr>

<td>JI intervals represented

</td>

<td>1/1

</td>

<td>16/15~15/14

</td>

<td>8/7

</td>

<td>11/9

</td>

<td>21/16

</td>

<td>7/5

</td>

<td>3/2

</td>

<td>8/5

</td>

<td>12/7

</td>

<td>11/6

</td>

</tr>

<tr>

<td><ol><li>of secors</li></ol></td>

<td>10

</td>

<td>11

</td>

<td>12

</td>

<td>13

</td>

<td>14

</td>

<td>15

</td>

<td>16

</td>

<td>17

</td>

<td>18

</td>

<td>19

</td>

</tr>

<tr>

<td>JI intervals represented

</td>

<td>63/32~55/28~108/55~49/25~96/49~88/45

</td>

<td>22/21~21/20

</td>

<td>9/8

</td>

<td>6/5

</td>

<td>9/7

</td>

<td>11/8

</td>

<td>22/15

</td>

<td>11/7

</td>

<td>42/25

</td>

<td>9/5

</td>

</tr>

<tr>

<td><ol><li>of secors</li></ol></td>

<td>20

</td>

<td>21

</td>

<td>22

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

</tr>

<tr>

<td>JI intervals represented

</td>

<td>48/25

</td>

<td>

</td>

<td>11/10

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

</tr>

</table>

Some temperaments have 11/9 as a &quot;neutral third&quot;, meaning it's exactly half of a 3/2 (tempering out 243/242), and other temperaments (in the <a class="wiki_link" href="/gamelismic%20clan">gamelismic clan</a>) have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a &quot;secor&quot;, and it represents both 16/15 and 15/14.

Miracle can also be thought of as a <a class="wiki_link" href="/cluster%20temperament">cluster temperament</a> with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44~49/48~50/49~55/54~56/55~64/63 all tempered together.

<h1 id="toc0"><a name="Spectrum of Miracle Tunings by Eigenmonzos"></a>Spectrum of Miracle Tunings by Eigenmonzos</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>2012-11-03 14:24:34 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-11-10 16:24:00 UTC</tt>.<br>
-: The original revision id was <tt>378898486</tt>.<br>
+: The original revision id was <tt>381128200</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">See [[Gamelismic clan#Miracle]].
+<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;white-space: pre-wrap ! important" class="old-revision-html">Miracle is an exceptionally efficient linear temperament which is a member of both the [[marvel temperaments]] and the [[gamelismic clan]]. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:
+|| # of secors || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 ||
+|| JI intervals represented || **1/1** || 16/15~15/14 || **8/7** || **11/9** || 21/16 || **7/5** || **3/2** || **8/5** || **12/7** || **11/6** ||
+|| # of secors || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17 || 18 || 19 ||
+|| JI intervals represented || 63/32~55/28~108/55~49/25~96/49~88/45 || 22/21~21/20 || **9/8** || **6/5** || **9/7** || **11/8** || 22/15 || **11/7** || 42/25 || **9/5** ||
+|| # of secors || 20 || 21 || 22 ||   ||   ||   ||   ||   ||   ||   ||
+|| JI intervals represented || 48/25 ||   || **11/10** ||   ||   ||   ||   ||   ||   ||   ||
+Some temperaments have 11/9 as a "neutral third", meaning it's exactly half of a 3/2 (tempering out 243/242), and other temperaments (in the [[gamelismic clan]]) have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both 16/15 and 15/14.
+Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44~49/48~50/49~55/54~56/55~64/63 all tempered together.
 =Spectrum of Miracle Tunings by Eigenmonzos=
@@ Line 22: / Line 31: @@
 || 11/8 || 116.755 ||
 || 9/7 || 116.792 ||
-|| 4/3 || 116.993 ||
+|| 4/3 || 116.993 ||</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;Miracle&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Miracle is an exceptionally efficient linear temperament which is a member of both the &lt;a class="wiki_link" href="/marvel%20temperaments"&gt;marvel temperaments&lt;/a&gt; and the &lt;a class="wiki_link" href="/gamelismic%20clan"&gt;gamelismic clan&lt;/a&gt;. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very &amp;quot;low complexity&amp;quot; (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:&lt;br /&gt;
-</pre></div>
-<h4>Original HTML content:</h4>
+&lt;table class="wiki_table"&gt;
-<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;Miracle&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;Gamelismic clan&lt;/a&gt;.&lt;br /&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;ol&gt;&lt;li&gt;of secors&lt;/li&gt;&lt;/ol&gt;&lt;/td&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;JI intervals represented&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;1/1&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/15~15/14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;8/7&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;11/9&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;7/5&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;3/2&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;8/5&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;12/7&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;11/6&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;ol&gt;&lt;li&gt;of secors&lt;/li&gt;&lt;/ol&gt;&lt;/td&gt;
+        &lt;td&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;JI intervals represented&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;63/32~55/28~108/55~49/25~96/49~88/45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22/21~21/20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;9/8&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;6/5&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;9/7&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;11/8&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;11/7&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;42/25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;9/5&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;ol&gt;&lt;li&gt;of secors&lt;/li&gt;&lt;/ol&gt;&lt;/td&gt;
+        &lt;td&gt;20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;JI intervals represented&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;48/25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;11/10&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+Some temperaments have 11/9 as a &amp;quot;neutral third&amp;quot;, meaning it's exactly half of a 3/2 (tempering out 243/242), and other temperaments (in the &lt;a class="wiki_link" href="/gamelismic%20clan"&gt;gamelismic clan&lt;/a&gt;) have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a &amp;quot;secor&amp;quot;, and it represents both 16/15 and 15/14.&lt;br /&gt;
+&lt;br /&gt;
+Miracle can also be thought of as a &lt;a class="wiki_link" href="/cluster%20temperament"&gt;cluster temperament&lt;/a&gt; with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44~49/48~50/49~55/54~56/55~64/63 all tempered together.&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="Spectrum of Miracle Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Spectrum of Miracle Tunings by Eigenmonzos&lt;/h1&gt;