Wikispaces>Andrew_Heathwaite |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | Miracle is an exceptionally efficient linear temperament which is a member of both the [[Marvel_temperaments|marvel temperaments]] and the [[Gamelismic_clan|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: |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2014-01-24 08:17:54 UTC</tt>.<br>
| |
| : The original revision id was <tt>484995974</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <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">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:
| |
| || number 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** ||
| |
| || number 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** ||
| |
| || number of secors || 20 || 21 || 22 || || || || || || || ||
| |
| || JI intervals represented || 48/25~27/14 || 33/32 || **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.
| | {| class="wikitable" |
| | |- |
| | | | number 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''' |
| | |- |
| | | | number 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''' |
| | |- |
| | | | number of secors |
| | | | 20 |
| | | | 21 |
| | | | 22 |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | |- |
| | | | JI intervals represented |
| | | | 48/25~27/14 |
| | | | 33/32 |
| | | | '''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|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. |
|
| |
|
| =Spectrum of Miracle Tunings by Eigenmonzos=
| | Miracle can also be thought of as a [[Cluster_temperament|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. |
| ||~ Eigenmonzo ||~ Secor || | |
| || 8/7 || 115.587 ||
| |
| || 11/9 || 115.803 ||
| |
| || 5/4 || 116.241 ||
| |
| || 7/5 || 116.502 ||
| |
| || 6/5 || 116.588 (5 and 7 limit minimax) ||
| |
| || 11/10 || 116.591 ||
| |
| || 12/11 || 116.596 ||
| |
| || 14/11 || 116.617 ||
| |
| || 7/6 || 116.641 ||
| |
| || 10/9 || 116.716 (9 and 11 limit minimax, Secor's definition of secor) ||
| |
| || 11/8 || 116.755 ||
| |
| || 9/7 || 116.792 ||
| |
| || 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:<br />
| |
|
| |
|
| | =Spectrum of Miracle Tunings by Eigenmonzos= |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td>number of secors<br />
| | ! | Eigenmonzo |
| </td>
| | ! | Secor |
| <td>0<br />
| | |- |
| </td>
| | | | 8/7 |
| <td>1<br />
| | | | 115.587 |
| </td>
| | |- |
| <td>2<br />
| | | | 11/9 |
| </td>
| | | | 115.803 |
| <td>3<br />
| | |- |
| </td>
| | | | 5/4 |
| <td>4<br />
| | | | 116.241 |
| </td>
| | |- |
| <td>5<br />
| | | | 7/5 |
| </td>
| | | | 116.502 |
| <td>6<br />
| | |- |
| </td>
| | | | 6/5 |
| <td>7<br />
| | | | 116.588 (5 and 7 limit minimax) |
| </td>
| | |- |
| <td>8<br />
| | | | 11/10 |
| </td>
| | | | 116.591 |
| <td>9<br />
| | |- |
| </td>
| | | | 12/11 |
| </tr>
| | | | 116.596 |
| <tr>
| | |- |
| <td>JI intervals represented<br />
| | | | 14/11 |
| </td>
| | | | 116.617 |
| <td><strong>1/1</strong><br />
| | |- |
| </td>
| | | | 7/6 |
| <td>16/15~15/14<br />
| | | | 116.641 |
| </td>
| | |- |
| <td><strong>8/7</strong><br />
| | | | 10/9 |
| </td>
| | | | 116.716 (9 and 11 limit minimax, Secor's definition of secor) |
| <td><strong>11/9</strong><br />
| | |- |
| </td>
| | | | 11/8 |
| <td>21/16<br />
| | | | 116.755 |
| </td>
| | |- |
| <td><strong>7/5</strong><br />
| | | | 9/7 |
| </td>
| | | | 116.792 |
| <td><strong>3/2</strong><br />
| | |- |
| </td>
| | | | 4/3 |
| <td><strong>8/5</strong><br />
| | | | 116.993 |
| </td>
| | |} |
| <td><strong>12/7</strong><br />
| | [[Category:miracle]] |
| </td>
| | [[Category:temperament]] |
| <td><strong>11/6</strong><br />
| | [[Category:todo:clarify]] |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>number of secors<br />
| |
| </td>
| |
| <td>10<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| <td>12<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| <td>14<br />
| |
| </td>
| |
| <td>15<br />
| |
| </td>
| |
| <td>16<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| <td>18<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>JI intervals represented<br />
| |
| </td>
| |
| <td>63/32~55/28~108/55~49/25~96/49~88/45<br />
| |
| </td>
| |
| <td>22/21~21/20<br />
| |
| </td>
| |
| <td><strong>9/8</strong><br />
| |
| </td>
| |
| <td><strong>6/5</strong><br />
| |
| </td>
| |
| <td><strong>9/7</strong><br />
| |
| </td>
| |
| <td><strong>11/8</strong><br />
| |
| </td>
| |
| <td>22/15<br />
| |
| </td>
| |
| <td><strong>11/7</strong><br />
| |
| </td>
| |
| <td>42/25<br />
| |
| </td>
| |
| <td><strong>9/5</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>number of secors<br />
| |
| </td>
| |
| <td>20<br />
| |
| </td>
| |
| <td>21<br />
| |
| </td>
| |
| <td>22<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>JI intervals represented<br />
| |
| </td>
| |
| <td>48/25~27/14<br />
| |
| </td>
| |
| <td>33/32<br />
| |
| </td>
| |
| <td><strong>11/10</strong><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </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.<br />
| |
| <br />
| |
| 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.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Miracle Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Miracle Tunings by Eigenmonzos</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Secor<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>115.587<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>115.803<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>116.241<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>116.502<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>116.588 (5 and 7 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>116.591<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>116.596<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>116.617<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>116.641<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>116.716 (9 and 11 limit minimax, Secor's definition of secor)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>116.755<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>116.792<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>116.993<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |
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:
| number 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
|
| number 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
|
| number of secors
|
20
|
21
|
22
|
|
|
|
|
|
|
|
| JI intervals represented
|
48/25~27/14
|
33/32
|
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
| Eigenmonzo
|
Secor
|
| 8/7
|
115.587
|
| 11/9
|
115.803
|
| 5/4
|
116.241
|
| 7/5
|
116.502
|
| 6/5
|
116.588 (5 and 7 limit minimax)
|
| 11/10
|
116.591
|
| 12/11
|
116.596
|
| 14/11
|
116.617
|
| 7/6
|
116.641
|
| 10/9
|
116.716 (9 and 11 limit minimax, Secor's definition of secor)
|
| 11/8
|
116.755
|
| 9/7
|
116.792
|
| 4/3
|
116.993
|