Miracle: Difference between revisions
Wikispaces>keenanpepper **Imported revision 381128200 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 381128324 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-11-10 16:24: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-11-10 16:24:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>381128324</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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: | <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** || | || 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** || | || 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 || || **11/10** || || || || || || || || | || 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. | 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. | ||
| Line 38: | Line 38: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td> | <td>number of secors<br /> | ||
</td> | |||
<td>0<br /> | <td>0<br /> | ||
</td> | </td> | ||
| Line 85: | Line 86: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>number of secors<br /> | ||
</td> | |||
<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
| Line 132: | Line 134: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>number of secors<br /> | ||
</td> | |||
<td>20<br /> | <td>20<br /> | ||
</td> | </td> | ||