Chirality: Difference between revisions
Wikispaces>Sarzadoce **Imported revision 553638826 - Original comment: ** |
Wikispaces>Sarzadoce **Imported revision 553639502 - Original comment: ** |
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<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:Sarzadoce|Sarzadoce]] and made on <tt>2015-06-10 20: | : This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-06-10 20:32:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>553639502</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> | ||
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Scales for which this property does not hold are called **achiral**. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation. | Scales for which this property does not hold are called **achiral**. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation. | ||
|| **EDO** || ** | ==Properties:== | ||
**Chiral Scales** || ** | # Chiral scales can only exist in EDO's larger than 5-EDO | ||
**Chiral Scales** || | # Chiral scales are at least max-variety 3 (they cannot be MOS or DE) | ||
|| 1 || 0.0% || 0/1 || | # Chiral scales have at least 3 notes | ||
|| 2 || 0.0% || 0/1 || | # Chiral scales have a [[http://en.wikipedia.org/wiki/Natural_density|density]] of 1 (see table below) | ||
|| 3 || 0.0% || 0/1 || | |||
|| 4 || 0.0% || 0/1 || | || **EDO** || **Number of** | ||
|| 5 || 0.0% || 0/1 || | **Chiral Scales** || **Percentage of** | ||
|| 6 || 22.2% || 2/9 || | **Chiral Scales** || **Corresponding Ratio** || | ||
|| 7 || 22.2% || 2/9 || | || 1 || 0 || 0.0% || 0/1 || | ||
|| 8 || 40.0% || 2/5 || | || 2 || 0 || 0.0% || 0/1 || | ||
|| 9 || 50.0% || 1/2 || | || 3 || 0 || 0.0% || 0/1 || | ||
|| 10 || 60.6% || 20/33 || | || 4 || 0 || 0.0% || 0/1 || | ||
|| 11 || 66.7% || 2/3 || | || 5 || 0 || 0.0% || 0/1 || | ||
|| 12 || 75.8% || 254/335 || | || 6 || 2 || 22.2% || 2/9 || | ||
|| 13 || 80.0% || 4/5 || | || 7 || 4 || 22.2% || 2/9 || | ||
|| 14 || 84.9% || 986/1161 || | || 8 || 12 || 40.0% || 2/5 || | ||
|| 15 || 88.7% || 968/1091 || | || 9 || 28 || 50.0% || 1/2 || | ||
|| 16 || 91.2% || 31/34 || | || 10 || 60 || 60.6% || 20/33 || | ||
|| 17 || 93.4% || 240/257 || | || 11 || 124 || 66.7% || 2/3 || | ||
|| 18 || 95.0% || 493/519 || | || 12 || 254 || 75.8% || 254/335 || | ||
|| 19 || 96.3% || 26/27 || | || 13 || 504 || 80.0% || 4/5 || | ||
|| 20 || 97.2% || 16964/17459 ||</pre></div> | || 14 || 986 || 84.9% || 986/1161 || | ||
|| 15 || 1936 || 88.7% || 968/1091 || | |||
|| 16 || 3720 || 91.2% || 31/34 || | |||
|| 17 || 7200 || 93.4% || 240/257 || | |||
|| 18 || 13804 || 95.0% || 493/519 || | |||
|| 19 || 26572 || 96.3% || 26/27 || | |||
|| 20 || 50892 || 97.2% || 16964/17459 ||</pre></div> | |||
<h4>Original HTML content:</h4> | <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>Chirality</title></head><body>A scale is called <strong>chiral</strong> if reversing the order of the steps results in a different scale. The two scales form a <strong>chiral pair</strong> and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.<br /> | <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>Chirality</title></head><body>A scale is called <strong>chiral</strong> if reversing the order of the steps results in a different scale. The two scales form a <strong>chiral pair</strong> and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.<br /> | ||
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Scales for which this property does not hold are called <strong>achiral</strong>. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.<br /> | Scales for which this property does not hold are called <strong>achiral</strong>. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Properties:"></a><!-- ws:end:WikiTextHeadingRule:0 -->Properties:</h2> | |||
<ol><li>Chiral scales can only exist in EDO's larger than 5-EDO</li><li>Chiral scales are at least max-variety 3 (they cannot be MOS or DE)</li><li>Chiral scales have at least 3 notes</li><li>Chiral scales have a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Natural_density" rel="nofollow">density</a> of 1 (see table below)</li></ol><br /> | |||
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<tr> | <tr> | ||
<td><strong>EDO</strong><br /> | <td><strong>EDO</strong><br /> | ||
</td> | |||
<td><strong>Number of</strong><br /> | |||
<strong>Chiral Scales</strong><br /> | |||
</td> | </td> | ||
<td><strong>Percentage of</strong><br /> | <td><strong>Percentage of</strong><br /> | ||
<strong>Chiral Scales</strong><br /> | <strong>Chiral Scales</strong><br /> | ||
</td> | </td> | ||
<td><strong>Ratio | <td><strong>Corresponding Ratio</strong><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <td>1<br /> | ||
</td> | |||
<td>0<br /> | |||
</td> | </td> | ||
<td>0.0%<br /> | <td>0.0%<br /> | ||
| Line 61: | Line 73: | ||
<tr> | <tr> | ||
<td>2<br /> | <td>2<br /> | ||
</td> | |||
<td>0<br /> | |||
</td> | </td> | ||
<td>0.0%<br /> | <td>0.0%<br /> | ||
| Line 69: | Line 83: | ||
<tr> | <tr> | ||
<td>3<br /> | <td>3<br /> | ||
</td> | |||
<td>0<br /> | |||
</td> | </td> | ||
<td>0.0%<br /> | <td>0.0%<br /> | ||
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<tr> | <tr> | ||
<td>4<br /> | <td>4<br /> | ||
</td> | |||
<td>0<br /> | |||
</td> | </td> | ||
<td>0.0%<br /> | <td>0.0%<br /> | ||
| Line 85: | Line 103: | ||
<tr> | <tr> | ||
<td>5<br /> | <td>5<br /> | ||
</td> | |||
<td>0<br /> | |||
</td> | </td> | ||
<td>0.0%<br /> | <td>0.0%<br /> | ||
| Line 93: | Line 113: | ||
<tr> | <tr> | ||
<td>6<br /> | <td>6<br /> | ||
</td> | |||
<td>2<br /> | |||
</td> | </td> | ||
<td>22.2%<br /> | <td>22.2%<br /> | ||
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<tr> | <tr> | ||
<td>7<br /> | <td>7<br /> | ||
</td> | |||
<td>4<br /> | |||
</td> | </td> | ||
<td>22.2%<br /> | <td>22.2%<br /> | ||
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<tr> | <tr> | ||
<td>8<br /> | <td>8<br /> | ||
</td> | |||
<td>12<br /> | |||
</td> | </td> | ||
<td>40.0%<br /> | <td>40.0%<br /> | ||
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<tr> | <tr> | ||
<td>9<br /> | <td>9<br /> | ||
</td> | |||
<td>28<br /> | |||
</td> | </td> | ||
<td>50.0%<br /> | <td>50.0%<br /> | ||
| Line 125: | Line 153: | ||
<tr> | <tr> | ||
<td>10<br /> | <td>10<br /> | ||
</td> | |||
<td>60<br /> | |||
</td> | </td> | ||
<td>60.6%<br /> | <td>60.6%<br /> | ||
| Line 133: | Line 163: | ||
<tr> | <tr> | ||
<td>11<br /> | <td>11<br /> | ||
</td> | |||
<td>124<br /> | |||
</td> | </td> | ||
<td>66.7%<br /> | <td>66.7%<br /> | ||
| Line 141: | Line 173: | ||
<tr> | <tr> | ||
<td>12<br /> | <td>12<br /> | ||
</td> | |||
<td>254<br /> | |||
</td> | </td> | ||
<td>75.8%<br /> | <td>75.8%<br /> | ||
| Line 149: | Line 183: | ||
<tr> | <tr> | ||
<td>13<br /> | <td>13<br /> | ||
</td> | |||
<td>504<br /> | |||
</td> | </td> | ||
<td>80.0%<br /> | <td>80.0%<br /> | ||
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<tr> | <tr> | ||
<td>14<br /> | <td>14<br /> | ||
</td> | |||
<td>986<br /> | |||
</td> | </td> | ||
<td>84.9%<br /> | <td>84.9%<br /> | ||
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<tr> | <tr> | ||
<td>15<br /> | <td>15<br /> | ||
</td> | |||
<td>1936<br /> | |||
</td> | </td> | ||
<td>88.7%<br /> | <td>88.7%<br /> | ||
| Line 173: | Line 213: | ||
<tr> | <tr> | ||
<td>16<br /> | <td>16<br /> | ||
</td> | |||
<td>3720<br /> | |||
</td> | </td> | ||
<td>91.2%<br /> | <td>91.2%<br /> | ||
| Line 181: | Line 223: | ||
<tr> | <tr> | ||
<td>17<br /> | <td>17<br /> | ||
</td> | |||
<td>7200<br /> | |||
</td> | </td> | ||
<td>93.4%<br /> | <td>93.4%<br /> | ||
| Line 189: | Line 233: | ||
<tr> | <tr> | ||
<td>18<br /> | <td>18<br /> | ||
</td> | |||
<td>13804<br /> | |||
</td> | </td> | ||
<td>95.0%<br /> | <td>95.0%<br /> | ||
| Line 197: | Line 243: | ||
<tr> | <tr> | ||
<td>19<br /> | <td>19<br /> | ||
</td> | |||
<td>26572<br /> | |||
</td> | </td> | ||
<td>96.3%<br /> | <td>96.3%<br /> | ||
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<tr> | <tr> | ||
<td>20<br /> | <td>20<br /> | ||
</td> | |||
<td>50892<br /> | |||
</td> | </td> | ||
<td>97.2%<br /> | <td>97.2%<br /> | ||