5L 1s

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Revision as of 12:11, 23 October 2010 by Wikispaces>Andrew_Heathwaite (**Imported revision 172983893 - Original comment: **)
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This revision was by author Andrew_Heathwaite and made on 2010-10-23 12:11:28 UTC.
The original revision id was 172983893.
The revision comment was:

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Original Wikitext content:

5L 1s refers to moment of symmetry scales with 5 large and 1 small step. When L=s we have [[6edo]], the "whole tone scale" of impressionistic fame. At the other end of the spectrum, we approach [[5edo]], with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a "whole tone" which is smaller than all the others -- perhaps not a "whole tone" at all.

||||||||||~ generator ||~ scale ||~ large step (L) ||~ small step (s) ||
||= 1\[[5edo|5]] ||=   ||=   ||=   ||=   ||= 1 1 1 1 1 0 ||= 240.0 ||= 0.0 ||
||=   ||=   ||=   ||=   ||= 5\[[26edo|26]] ||= 5 5 5 5 5 1 ||= 230.8 ||= 46.2 ||
||=   ||=   ||=   ||= 4\[[21edo|21]] ||=   ||= 4 4 4 4 4 1 ||= 228.6 ||= 57.1 ||
||=   ||=   ||=   ||=   ||= 7\[[37edo|37]] ||= 7 7 7 7 7 2 ||= 227.0 ||= 64.9 ||
||=   ||=   ||= 3\[[16edo|16]] ||=   ||=   ||= 3 3 3 3 3 1 ||= 225.0 ||= 75.0 ||
||=   ||=   ||=   ||=   ||= 8\[[43edo|43]] ||= 8 8 8 8 8 3 ||= 223.3 ||= 83.7 ||
||=   ||=   ||=   ||= 5\[[27edo|27]] ||=   ||= 5 5 5 5 5 2 ||= 222.2 ||= 88.9 ||
||=   ||=   ||=   ||=   ||= 7\[[38edo|38]] ||= 7 7 7 7 7 3 ||= 221.1 ||= 94.7 ||
||=   ||= 2\[[11edo|11]] ||=   ||=   ||=   ||= 2 2 2 2 2 1 ||= 218.2 ||= 109.1 ||
||=   ||=   ||=   ||=   ||= 7\[[39edo|39]] ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||
||=   ||=   ||=   ||= 5\[[28edo|28]] ||=   ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||
||=   ||=   ||=   ||=   ||= 8\[[45edo|45]] ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 ||
||=   ||=   ||= 3\[[17edo|17]] ||=   ||=   ||= 3 3 3 3 3 2 ||= 211.8 ||= 141.2 ||
||=   ||=   ||=   ||=   ||= 7\[[40edo|40]] ||= 7 7 7 7 7 5 ||= 210.0 ||= 150.0 ||
||=   ||=   ||=   ||= 4\[[23edo|23]] ||=   ||= 4 4 4 4 4 3 ||= 208.7 ||= 156.5 ||
||=   ||=   ||=   ||=   ||= 5\[[29edo|29]] ||= 5 5 5 5 5 4 ||= 206.9 ||= 165.5 ||
||= 1\[[6edo|6]] ||=   ||=   ||=   ||=   ||= 1 1 1 1 1 1 ||= 200.0 ||= 200.0 ||

Original HTML content:

<html><head><title>5L 1s</title></head><body>5L 1s refers to moment of symmetry scales with 5 large and 1 small step. When L=s we have <a class="wiki_link" href="/6edo">6edo</a>, the &quot;whole tone scale&quot; of impressionistic fame. At the other end of the spectrum, we approach <a class="wiki_link" href="/5edo">5edo</a>, with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a &quot;whole tone&quot; which is smaller than all the others -- perhaps not a &quot;whole tone&quot; at all.<br />
<br />


<table class="wiki_table">
    <tr>
        <th colspan="5">generator<br />
</th>
        <th>scale<br />
</th>
        <th>large step (L)<br />
</th>
        <th>small step (s)<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">1\<a class="wiki_link" href="/5edo">5</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">1 1 1 1 1 0<br />
</td>
        <td style="text-align: center;">240.0<br />
</td>
        <td style="text-align: center;">0.0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5\<a class="wiki_link" href="/26edo">26</a><br />
</td>
        <td style="text-align: center;">5 5 5 5 5 1<br />
</td>
        <td style="text-align: center;">230.8<br />
</td>
        <td style="text-align: center;">46.2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">4\<a class="wiki_link" href="/21edo">21</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">4 4 4 4 4 1<br />
</td>
        <td style="text-align: center;">228.6<br />
</td>
        <td style="text-align: center;">57.1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">7\<a class="wiki_link" href="/37edo">37</a><br />
</td>
        <td style="text-align: center;">7 7 7 7 7 2<br />
</td>
        <td style="text-align: center;">227.0<br />
</td>
        <td style="text-align: center;">64.9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">3\<a class="wiki_link" href="/16edo">16</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">3 3 3 3 3 1<br />
</td>
        <td style="text-align: center;">225.0<br />
</td>
        <td style="text-align: center;">75.0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">8\<a class="wiki_link" href="/43edo">43</a><br />
</td>
        <td style="text-align: center;">8 8 8 8 8 3<br />
</td>
        <td style="text-align: center;">223.3<br />
</td>
        <td style="text-align: center;">83.7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5\<a class="wiki_link" href="/27edo">27</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5 5 5 5 5 2<br />
</td>
        <td style="text-align: center;">222.2<br />
</td>
        <td style="text-align: center;">88.9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">7\<a class="wiki_link" href="/38edo">38</a><br />
</td>
        <td style="text-align: center;">7 7 7 7 7 3<br />
</td>
        <td style="text-align: center;">221.1<br />
</td>
        <td style="text-align: center;">94.7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">2\<a class="wiki_link" href="/11edo">11</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">2 2 2 2 2 1<br />
</td>
        <td style="text-align: center;">218.2<br />
</td>
        <td style="text-align: center;">109.1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">7\<a class="wiki_link" href="/39edo">39</a><br />
</td>
        <td style="text-align: center;">7 7 7 7 7 4<br />
</td>
        <td style="text-align: center;">215.4<br />
</td>
        <td style="text-align: center;">123.1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5\<a class="wiki_link" href="/28edo">28</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5 5 5 5 5 3<br />
</td>
        <td style="text-align: center;">214.3<br />
</td>
        <td style="text-align: center;">128.6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">8\<a class="wiki_link" href="/45edo">45</a><br />
</td>
        <td style="text-align: center;">8 8 8 8 8 5<br />
</td>
        <td style="text-align: center;">213.3<br />
</td>
        <td style="text-align: center;">133.3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">3\<a class="wiki_link" href="/17edo">17</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">3 3 3 3 3 2<br />
</td>
        <td style="text-align: center;">211.8<br />
</td>
        <td style="text-align: center;">141.2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">7\<a class="wiki_link" href="/40edo">40</a><br />
</td>
        <td style="text-align: center;">7 7 7 7 7 5<br />
</td>
        <td style="text-align: center;">210.0<br />
</td>
        <td style="text-align: center;">150.0<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">4\<a class="wiki_link" href="/23edo">23</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">4 4 4 4 4 3<br />
</td>
        <td style="text-align: center;">208.7<br />
</td>
        <td style="text-align: center;">156.5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5\<a class="wiki_link" href="/29edo">29</a><br />
</td>
        <td style="text-align: center;">5 5 5 5 5 4<br />
</td>
        <td style="text-align: center;">206.9<br />
</td>
        <td style="text-align: center;">165.5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1\<a class="wiki_link" href="/6edo">6</a><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">1 1 1 1 1 1<br />
</td>
        <td style="text-align: center;">200.0<br />
</td>
        <td style="text-align: center;">200.0<br />
</td>
    </tr>
</table>

</body></html>
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