Chirality: Difference between revisions

Revision as of 20:22, 10 June 2015

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Sarzadoce and made on 2015-06-10 20:22:27 UTC.

The original revision id was 553638826.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 20:20:40 UTC</tt>.<br>
+: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-06-10 20:22:27 UTC</tt>.<br>
-: The original revision id was <tt>553638726</tt>.<br>
+: The original revision id was <tt>553638826</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>
@@ Line 10: / Line 10: @@
 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% || 1/1 ||
+|| 1 || 0.0% || 0/1 ||
-|| 2 || 0.0% || 1/1 ||
+|| 2 || 0.0% || 0/1 ||
-|| 3 || 0.0% || 1/1 ||
+|| 3 || 0.0% || 0/1 ||
-|| 4 || 0.0% || 1/1 ||
+|| 4 || 0.0% || 0/1 ||
-|| 5 || 0.0% || 1/1 ||
+|| 5 || 0.0% || 0/1 ||
-|| 6 || 22.2% || 7/9 ||
+|| 6 || 22.2% || 2/9 ||
-|| 7 || 22.2% || 7/9 ||
+|| 7 || 22.2% || 2/9 ||
-|| 8 || 40.0% || 3/5 ||
+|| 8 || 40.0% || 2/5 ||
 || 9 || 50.0% || 1/2 ||
-|| 10 || 60.6% || 13/33 ||
+|| 10 || 60.6% || 20/33 ||
-|| 11 || 66.7% || 1/3 ||
+|| 11 || 66.7% || 2/3 ||
-|| 12 || 75.8% || 81/335 ||
+|| 12 || 75.8% || 254/335 ||
-|| 13 || 80.0% || 1/5 ||
+|| 13 || 80.0% || 4/5 ||
-|| 14 || 84.9% || 175/1161 ||
+|| 14 || 84.9% || 986/1161 ||
-|| 15 || 88.7% || 123/1091 ||
+|| 15 || 88.7% || 968/1091 ||
-|| 16 || 91.2% || 3/34 ||
+|| 16 || 91.2% || 31/34 ||
-|| 17 || 93.4% || 17/257 ||
+|| 17 || 93.4% || 240/257 ||
-|| 18 || 95.0% || 26/519 ||
+|| 18 || 95.0% || 493/519 ||
-|| 19 || 96.3% || 1/27 ||
+|| 19 || 96.3% || 26/27 ||
-|| 20 || 97.2% || 495/17459 ||</pre></div>
+|| 20 || 97.2% || 16964/17459 ||</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chirality&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A scale is called &lt;strong&gt;chiral&lt;/strong&gt; if reversing the order of the steps results in a different scale. The two scales form a &lt;strong&gt;chiral pair&lt;/strong&gt; 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.&lt;br /&gt;
@@ Line 44: / Line 44: @@
          &lt;td&gt;&lt;strong&gt;EDO&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;Percentage of&lt;/strong&gt; &lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;Percentage of&lt;/strong&gt;&lt;br /&gt;
 &lt;strong&gt;Chiral Scales&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
@@ Line 56: / Line 56: @@
          &lt;td&gt;0.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;0/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 64: / Line 64: @@
          &lt;td&gt;0.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;0/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 72: / Line 72: @@
          &lt;td&gt;0.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;0/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 80: / Line 80: @@
          &lt;td&gt;0.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;0/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 88: / Line 88: @@
          &lt;td&gt;0.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;0/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 96: / Line 96: @@
          &lt;td&gt;22.2%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/9&lt;br /&gt;
+         &lt;td&gt;2/9&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 104: / Line 104: @@
          &lt;td&gt;22.2%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/9&lt;br /&gt;
+         &lt;td&gt;2/9&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 112: / Line 112: @@
          &lt;td&gt;40.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/5&lt;br /&gt;
+         &lt;td&gt;2/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 128: / Line 128: @@
          &lt;td&gt;60.6%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13/33&lt;br /&gt;
+         &lt;td&gt;20/33&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 136: / Line 136: @@
          &lt;td&gt;66.7%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/3&lt;br /&gt;
+         &lt;td&gt;2/3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 144: / Line 144: @@
          &lt;td&gt;75.8%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;81/335&lt;br /&gt;
+         &lt;td&gt;254/335&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 152: / Line 152: @@
          &lt;td&gt;80.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/5&lt;br /&gt;
+         &lt;td&gt;4/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 160: / Line 160: @@
          &lt;td&gt;84.9%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;175/1161&lt;br /&gt;
+         &lt;td&gt;986/1161&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 168: / Line 168: @@
          &lt;td&gt;88.7%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;123/1091&lt;br /&gt;
+         &lt;td&gt;968/1091&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 176: / Line 176: @@
          &lt;td&gt;91.2%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/34&lt;br /&gt;
+         &lt;td&gt;31/34&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 184: / Line 184: @@
          &lt;td&gt;93.4%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17/257&lt;br /&gt;
+         &lt;td&gt;240/257&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 192: / Line 192: @@
          &lt;td&gt;95.0%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26/519&lt;br /&gt;
+         &lt;td&gt;493/519&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 200: / Line 200: @@
          &lt;td&gt;96.3%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/27&lt;br /&gt;
+         &lt;td&gt;26/27&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 208: / Line 208: @@
          &lt;td&gt;97.2%&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;495/17459&lt;br /&gt;
+         &lt;td&gt;16964/17459&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

Chirality: Difference between revisions

Revision as of 20:22, 10 June 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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