Chirality

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Revision as of 20:22, 10 June 2015 by Wikispaces>Sarzadoce (**Imported revision 553638826 - Original comment: **)
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This revision was by author Sarzadoce and made on 2015-06-10 20:22:27 UTC.
The original revision id was 553638826.
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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.

|| **EDO** || **Percentage of**
**Chiral Scales** || **Ratio of**
**Chiral Scales** ||
|| 1 || 0.0% || 0/1 ||
|| 2 || 0.0% || 0/1 ||
|| 3 || 0.0% || 0/1 ||
|| 4 || 0.0% || 0/1 ||
|| 5 || 0.0% || 0/1 ||
|| 6 || 22.2% || 2/9 ||
|| 7 || 22.2% || 2/9 ||
|| 8 || 40.0% || 2/5 ||
|| 9 || 50.0% || 1/2 ||
|| 10 || 60.6% || 20/33 ||
|| 11 || 66.7% || 2/3 ||
|| 12 || 75.8% || 254/335 ||
|| 13 || 80.0% || 4/5 ||
|| 14 || 84.9% || 986/1161 ||
|| 15 || 88.7% || 968/1091 ||
|| 16 || 91.2% || 31/34 ||
|| 17 || 93.4% || 240/257 ||
|| 18 || 95.0% || 493/519 ||
|| 19 || 96.3% || 26/27 ||
|| 20 || 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 />


<table class="wiki_table">
    <tr>
        <td><strong>EDO</strong><br />
</td>
        <td><strong>Percentage of</strong><br />
<strong>Chiral Scales</strong><br />
</td>
        <td><strong>Ratio of</strong><br />
<strong>Chiral Scales</strong><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0.0%<br />
</td>
        <td>0/1<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0.0%<br />
</td>
        <td>0/1<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0.0%<br />
</td>
        <td>0/1<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0.0%<br />
</td>
        <td>0/1<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0.0%<br />
</td>
        <td>0/1<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>22.2%<br />
</td>
        <td>2/9<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>22.2%<br />
</td>
        <td>2/9<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>40.0%<br />
</td>
        <td>2/5<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>50.0%<br />
</td>
        <td>1/2<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>60.6%<br />
</td>
        <td>20/33<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>66.7%<br />
</td>
        <td>2/3<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>75.8%<br />
</td>
        <td>254/335<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>80.0%<br />
</td>
        <td>4/5<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>84.9%<br />
</td>
        <td>986/1161<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>88.7%<br />
</td>
        <td>968/1091<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>91.2%<br />
</td>
        <td>31/34<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>93.4%<br />
</td>
        <td>240/257<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>95.0%<br />
</td>
        <td>493/519<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>96.3%<br />
</td>
        <td>26/27<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>97.2%<br />
</td>
        <td>16964/17459<br />
</td>
    </tr>
</table>

</body></html>
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