Chirality
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Original Wikitext content:
A scale is called **chiral** if reversing the order of the steps results in a different scale. The two scales form a **chiral pair** 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. 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. ==Properties:== # Chiral scales can only exist in EDO's larger than 5-EDO # Chiral scales are at least max-variety 3 (they cannot be MOS or DE) # Chiral scales have at least 3 notes # Chiral scales have a [[http://en.wikipedia.org/wiki/Natural_density|density]] of 1 (see table below) || **EDO** || **Number of** **Chiral Scales** || **Percentage of** **Chiral Scales** || **Corresponding Ratio** || || 1 || 0 || 0.0% || 0/1 || || 2 || 0 || 0.0% || 0/1 || || 3 || 0 || 0.0% || 0/1 || || 4 || 0 || 0.0% || 0/1 || || 5 || 0 || 0.0% || 0/1 || || 6 || 2 || 22.2% || 2/9 || || 7 || 4 || 22.2% || 2/9 || || 8 || 12 || 40.0% || 2/5 || || 9 || 28 || 50.0% || 1/2 || || 10 || 60 || 60.6% || 20/33 || || 11 || 124 || 66.7% || 2/3 || || 12 || 254 || 75.8% || 254/335 || || 13 || 504 || 80.0% || 4/5 || || 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 ||
Original HTML content:
<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 />
<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 />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><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 />
<table class="wiki_table">
<tr>
<td><strong>EDO</strong><br />
</td>
<td><strong>Number of</strong><br />
<strong>Chiral Scales</strong><br />
</td>
<td><strong>Percentage of</strong><br />
<strong>Chiral Scales</strong><br />
</td>
<td><strong>Corresponding Ratio</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0<br />
</td>
<td>0.0%<br />
</td>
<td>0/1<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>0<br />
</td>
<td>0.0%<br />
</td>
<td>0/1<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>0<br />
</td>
<td>0.0%<br />
</td>
<td>0/1<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>0<br />
</td>
<td>0.0%<br />
</td>
<td>0/1<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>0<br />
</td>
<td>0.0%<br />
</td>
<td>0/1<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>2<br />
</td>
<td>22.2%<br />
</td>
<td>2/9<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>4<br />
</td>
<td>22.2%<br />
</td>
<td>2/9<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>12<br />
</td>
<td>40.0%<br />
</td>
<td>2/5<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>28<br />
</td>
<td>50.0%<br />
</td>
<td>1/2<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>60<br />
</td>
<td>60.6%<br />
</td>
<td>20/33<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>124<br />
</td>
<td>66.7%<br />
</td>
<td>2/3<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>254<br />
</td>
<td>75.8%<br />
</td>
<td>254/335<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>504<br />
</td>
<td>80.0%<br />
</td>
<td>4/5<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>986<br />
</td>
<td>84.9%<br />
</td>
<td>986/1161<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>1936<br />
</td>
<td>88.7%<br />
</td>
<td>968/1091<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>3720<br />
</td>
<td>91.2%<br />
</td>
<td>31/34<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>7200<br />
</td>
<td>93.4%<br />
</td>
<td>240/257<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>13804<br />
</td>
<td>95.0%<br />
</td>
<td>493/519<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>26572<br />
</td>
<td>96.3%<br />
</td>
<td>26/27<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>50892<br />
</td>
<td>97.2%<br />
</td>
<td>16964/17459<br />
</td>
</tr>
</table>
</body></html>