5L 1s: Difference between revisions

Revision as of 04:03, 25 April 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author keenanpepper and made on 2011-04-25 04:03:00 UTC.

The original revision id was 222628848.

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:

5L 1s refers to [[MOSScales]] with 5 large steps and 1 small step. When L=s we have [[6edo]], the equal-tempered "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.

The only notable low-harmonic-entropy scale with this MOS pattern is [[Gamelismic clan|slendric]], in which the large step is 8/7 and three of them make a 3/2.

Scales with this pattern are always [[Rothenberg propriety|proper]], because there is only one small step.
||||||||||||||~ generator ||~ scale ||~ large step (L) ||~ small step (s) ||~ comments ||
||= 1\[[5edo|5]] ||=   ||=   ||=   ||=   ||   ||   ||= 1 1 1 1 1 0 ||= 240.0 ||= 0.0 ||   ||
||   ||   ||   ||   ||   ||   || 7\36 || 7 7 7 7 7 1 ||= 233.3 ||= 33.3 || Slendric is around here ||
||   ||   ||   ||   ||   || 6\31 ||   || 6 6 6 6 6 1 ||= 232.3 ||= 38.7 ||   ||
||=   ||=   ||=   ||=   ||= 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 <a class="wiki_link" href="/MOSScales">MOSScales</a> with 5 large steps and 1 small step. When L=s we have <a class="wiki_link" href="/6edo">6edo</a>, the equal-tempered &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 />
The only notable low-harmonic-entropy scale with this MOS pattern is <a class="wiki_link" href="/Gamelismic%20clan">slendric</a>, in which the large step is 8/7 and three of them make a 3/2.<br />
<br />
Scales with this pattern are always <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>, because there is only one small step.<br />


<table class="wiki_table">
    <tr>
        <th colspan="7">generator<br />
</th>
        <th>scale<br />
</th>
        <th>large step (L)<br />
</th>
        <th>small step (s)<br />
</th>
        <th>comments<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><br />
</td>
        <td><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>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\36<br />
</td>
        <td>7 7 7 7 7 1<br />
</td>
        <td style="text-align: center;">233.3<br />
</td>
        <td style="text-align: center;">33.3<br />
</td>
        <td>Slendric is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\31<br />
</td>
        <td><br />
</td>
        <td>6 6 6 6 6 1<br />
</td>
        <td style="text-align: center;">232.3<br />
</td>
        <td style="text-align: center;">38.7<br />
</td>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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><br />
</td>
        <td><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>
        <td><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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-10-23 12:11:28 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 04:03:00 UTC</tt>.<br>
-: The original revision id was <tt>172983893</tt>.<br>
+: The original revision id was <tt>222628848</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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.
+<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;white-space: pre-wrap ! important" class="old-revision-html">5L 1s refers to [[MOSScales]] with 5 large steps and 1 small step. When L=s we have [[6edo]], the equal-tempered "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) ||
+The only notable low-harmonic-entropy scale with this MOS pattern is [[Gamelismic clan|slendric]], in which the large step is 8/7 and three of them make a 3/2.
-||= 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 ||
+Scales with this pattern are always [[Rothenberg propriety|proper]], because there is only one small step.
-||=   ||=   ||=   ||= 4\[[21edo|21]] ||=   ||= 4 4 4 4 4 1 ||= 228.6 ||= 57.1 ||
+||||||||||||||~ generator ||~ scale ||~ large step (L) ||~ small step (s) ||~ comments ||
-||=   ||=   ||=   ||=   ||= 7\[[37edo|37]] ||= 7 7 7 7 7 2 ||= 227.0 ||= 64.9 ||
+||= 1\[[5edo|5]] ||=   ||=   ||=   ||=   ||   ||   ||= 1 1 1 1 1 0 ||= 240.0 ||= 0.0 ||   ||
-||=   ||=   ||= 3\[[16edo|16]] ||=   ||=   ||= 3 3 3 3 3 1 ||= 225.0 ||= 75.0 ||
+||   ||   ||   ||   ||   ||   || 7\36 || 7 7 7 7 7 1 ||= 233.3 ||= 33.3 || Slendric is around here ||
-||=   ||=   ||=   ||=   ||= 8\[[43edo|43]] ||= 8 8 8 8 8 3 ||= 223.3 ||= 83.7 ||
+||   ||   ||   ||   ||   || 6\31 ||   || 6 6 6 6 6 1 ||= 232.3 ||= 38.7 ||   ||
-||=   ||=   ||=   ||= 5\[[27edo|27]] ||=   ||= 5 5 5 5 5 2 ||= 222.2 ||= 88.9 ||
+||=   ||=   ||=   ||=   ||= 5\[[26edo|26]] ||   ||   ||= 5 5 5 5 5 1 ||= 230.8 ||= 46.2 ||   ||
-||=   ||=   ||=   ||=   ||= 7\[[38edo|38]] ||= 7 7 7 7 7 3 ||= 221.1 ||= 94.7 ||
+||=   ||=   ||=   ||= 4\[[21edo|21]] ||=   ||   ||   ||= 4 4 4 4 4 1 ||= 228.6 ||= 57.1 ||   ||
-||=   ||= 2\[[11edo|11]] ||=   ||=   ||=   ||= 2 2 2 2 2 1 ||= 218.2 ||= 109.1 ||
+||=   ||=   ||=   ||=   ||= 7\[[37edo|37]] ||   ||   ||= 7 7 7 7 7 2 ||= 227.0 ||= 64.9 ||   ||
-||=   ||=   ||=   ||=   ||= 7\[[39edo|39]] ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||
+||=   ||=   ||= 3\[[16edo|16]] ||=   ||=   ||   ||   ||= 3 3 3 3 3 1 ||= 225.0 ||= 75.0 ||   ||
-||=   ||=   ||=   ||= 5\[[28edo|28]] ||=   ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||
+||=   ||=   ||=   ||=   ||= 8\[[43edo|43]] ||   ||   ||= 8 8 8 8 8 3 ||= 223.3 ||= 83.7 ||   ||
-||=   ||=   ||=   ||=   ||= 8\[[45edo|45]] ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 ||
+||=   ||=   ||=   ||= 5\[[27edo|27]] ||=   ||   ||   ||= 5 5 5 5 5 2 ||= 222.2 ||= 88.9 ||   ||
-||=   ||=   ||= 3\[[17edo|17]] ||=   ||=   ||= 3 3 3 3 3 2 ||= 211.8 ||= 141.2 ||
+||=   ||=   ||=   ||=   ||= 7\[[38edo|38]] ||   ||   ||= 7 7 7 7 7 3 ||= 221.1 ||= 94.7 ||   ||
-||=   ||=   ||=   ||=   ||= 7\[[40edo|40]] ||= 7 7 7 7 7 5 ||= 210.0 ||= 150.0 ||
+||=   ||= 2\[[11edo|11]] ||=   ||=   ||=   ||   ||   ||= 2 2 2 2 2 1 ||= 218.2 ||= 109.1 ||   ||
-||=   ||=   ||=   ||= 4\[[23edo|23]] ||=   ||= 4 4 4 4 4 3 ||= 208.7 ||= 156.5 ||
+||=   ||=   ||=   ||=   ||= 7\[[39edo|39]] ||   ||   ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||   ||
-||=   ||=   ||=   ||=   ||= 5\[[29edo|29]] ||= 5 5 5 5 5 4 ||= 206.9 ||= 165.5 ||
+||=   ||=   ||=   ||= 5\[[28edo|28]] ||=   ||   ||   ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||   ||
-||= 1\[[6edo|6]] ||=   ||=   ||=   ||=   ||= 1 1 1 1 1 1 ||= 200.0 ||= 200.0 ||</pre></div>
+||=   ||=   ||=   ||=   ||= 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 ||   ||</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;5L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;5L 1s refers to moment of symmetry scales with 5 large and 1 small step. When L=s we have &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;, the &amp;quot;whole tone scale&amp;quot; of impressionistic fame. At the other end of the spectrum, we approach &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a &amp;quot;whole tone&amp;quot; which is smaller than all the others -- perhaps not a &amp;quot;whole tone&amp;quot; at all.&lt;br /&gt;
+<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;5L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;5L 1s refers to &lt;a class="wiki_link" href="/MOSScales"&gt;MOSScales&lt;/a&gt; with 5 large steps and 1 small step. When L=s we have &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;, the equal-tempered &amp;quot;whole tone scale&amp;quot; of impressionistic fame. At the other end of the spectrum, we approach &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a &amp;quot;whole tone&amp;quot; which is smaller than all the others — perhaps not a &amp;quot;whole tone&amp;quot; at all.&lt;br /&gt;
 &lt;br /&gt;
+The only notable low-harmonic-entropy scale with this MOS pattern is &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;slendric&lt;/a&gt;, in which the large step is 8/7 and three of them make a 3/2.&lt;br /&gt;
+&lt;br /&gt;
+Scales with this pattern are always &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;proper&lt;/a&gt;, because there is only one small step.&lt;br /&gt;
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;generator&lt;br /&gt;
+         &lt;th colspan="7"&gt;generator&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;scale&lt;br /&gt;
@@ Line 40: / Line 48: @@
 &lt;/th&gt;
          &lt;th&gt;small step (s)&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;comments&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 52: / Line 62: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1 1 1 1 1 0&lt;br /&gt;
@@ Line 58: / Line 72: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;0.0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7\36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7 7 7 7 7 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;233.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;33.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Slendric is around here&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6\31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6 6 6 6 6 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;232.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;38.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 70: / Line 134: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5\&lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5 5 5 5 5 1&lt;br /&gt;
@@ Line 76: / Line 144: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;46.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 88: / Line 158: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4 4 4 4 4 1&lt;br /&gt;
@@ Line 94: / Line 168: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;57.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 106: / Line 182: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7\&lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 2&lt;br /&gt;
@@ Line 112: / Line 192: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;64.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 124: / Line 206: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3 3 3 3 3 1&lt;br /&gt;
@@ Line 130: / Line 216: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;75.0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 142: / Line 230: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8\&lt;a class="wiki_link" href="/43edo"&gt;43&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8 8 8 8 8 3&lt;br /&gt;
@@ Line 148: / Line 240: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;83.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 160: / Line 254: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5 5 5 5 5 2&lt;br /&gt;
@@ Line 166: / Line 264: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;88.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 178: / Line 278: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7\&lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 3&lt;br /&gt;
@@ Line 184: / Line 288: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;94.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 196: / Line 302: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2 2 2 2 2 1&lt;br /&gt;
@@ Line 202: / Line 312: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;109.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 214: / Line 326: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7\&lt;a class="wiki_link" href="/39edo"&gt;39&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 4&lt;br /&gt;
@@ Line 220: / Line 336: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;123.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 232: / Line 350: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5 5 5 5 5 3&lt;br /&gt;
@@ Line 238: / Line 360: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;128.6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 250: / Line 374: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8\&lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8 8 8 8 8 5&lt;br /&gt;
@@ Line 256: / Line 384: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;133.3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 268: / Line 398: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3 3 3 3 3 2&lt;br /&gt;
@@ Line 274: / Line 408: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;141.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 286: / Line 422: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7\&lt;a class="wiki_link" href="/40edo"&gt;40&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 5&lt;br /&gt;
@@ Line 292: / Line 432: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;150.0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 304: / Line 446: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4 4 4 4 4 3&lt;br /&gt;
@@ Line 310: / Line 456: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;156.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 322: / Line 470: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5\&lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5 5 5 5 5 4&lt;br /&gt;
@@ Line 328: / Line 480: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;165.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 340: / Line 494: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1 1 1 1 1 1&lt;br /&gt;
@@ Line 346: / Line 504: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;200.0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

5L 1s: Difference between revisions

Revision as of 04:03, 25 April 2011

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