5L 1s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-~~28 00~~:34:55 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 03:52:05 UTC</tt>.

: The original revision id was <tt>~~248861151~~</tt>.

: The original revision id was <tt>249047721</tt>.

: The revision comment was: <tt></tt>

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

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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 || ||

||= 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 ||

|| || || || || || || 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 || ||

|| || || || || || 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 || ||

||= ||= ||= ||= ||= 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 || ||

||= ||= ||= ||= 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 || ||

||= ||= ||= ||= ||= 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 || ||

||= ||= ||= 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 || ||

||= ||= ||= ||= ||= 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 || ||

||= ||= ||= ||= 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 || ||

||= ||= ||= ||= ||= 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 || ||

||= ||= 2\[[11edo|11]] ||= ||= ||= || || ||= 2 2 2 2 2 1 ||= 218.2 ||= 109.1 ||= Boundary of propriety (generators

||= ||= ||= ||= ||= 7\[[39edo|39]] || || ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 || ||

smaller than this are proper) ||

||= ||= ||= ||= 5\[[28edo|28]] ||= || || ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 || ||

||= ||= ||= ||= ||= 7\[[39edo|39]] || || ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||= ||

|| || || || || || 13\73 || || 13 13... 8 ||= 213.70 ||= 131.5 || ||

||= ||= ||= ||= 5\[[28edo|28]] ||= || || ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||= ||

|| || || || || || || 21\118 || 21 21... 13 ||= 213.56 ||= 132.2 || Golden machine ||

|| || || || || || 13\73 || || 13 13... 8 ||= 213.70 ||= 131.5 ||= ||

||= ||= ||= ||= ||= 8\[[45edo|45]] || || ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 || ||

|| || || || || || || 21\118 || 21 21... 13 ||= 213.56 ||= 132.2 ||= Golden machine ||

||= ||= ||= 3\[[17edo|17]] ||= ||= || || ||= 3 3 3 3 3 2 ||= 211.8 ||= 141.2 || ||

||= ||= ||= ||= ||= 8\[[45edo|45]] || || ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 ||= ||

||= ||= ||= ||= ||= 7\[[40edo|40]] || || ||= 7 7 7 7 7 5 ||= 210.0 ||= 150.0 || ||

||= ||= ||= 3\[[17edo|17]] ||= ||= || || ||= 3 3 3 3 3 2 ||= 211.8 ||= 141.2 ||= Optimum rank range (L/s=3/2) machine ||

||= ||= ||= ||= 4\[[23edo|23]] ||= || || ||= 4 4 4 4 4 3 ||= 208.7 ||= 156.5 || ||

||= ||= ||= ||= ||= 7\[[40edo|40]] || || ||= 7 7 7 7 7 5 ||= 210.0 ||= 150.0 ||= ||

||= ||= ||= ||= ||= 5\[[29edo|29]] || || ||= 5 5 5 5 5 4 ||= 206.9 ||= 165.5 || ||

||= ||= ||= ||= 4\[[23edo|23]] ||= || || ||= 4 4 4 4 4 3 ||= 208.7 ||= 156.5 ||= ||

||= 1\[[6edo|6]] ||= ||= ||= ||= || || ||= 1 1 1 1 1 1 ||= 200.0 ||= 200.0 || ||</pre></div>

||= ||= ||= ||= ||= 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"><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.

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<td style="text-align: center;">0.0

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">33.3

</td>

<td>Slendric is around here

<td style="text-align: center;">Slendric is around here

</td>

</tr>

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<td style="text-align: center;">38.7

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">46.2

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">57.1

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">64.9

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">75.0

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">83.7

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">88.9

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">94.7

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">109.1

</td>

<td>

<td style="text-align: center;">Boundary of propriety (generators

smaller than this are proper)

</td>

</tr>

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<td style="text-align: center;">123.1

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">128.6

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">131.5

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">132.2

</td>

<td>Golden machine

<td style="text-align: center;">Golden machine

</td>

</tr>

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<td style="text-align: center;">133.3

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">141.2

</td>

<td>

<td style="text-align: center;">Optimum rank range (L/s=3/2) machine

</td>

</tr>

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<td style="text-align: center;">150.0

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">156.5

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">165.5

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">200.0

</td>

<td>

</td>

</tr>

@@ 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:guest|guest]] and made on <tt>2011-08-28 00:34:55 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 03:52:05 UTC</tt>.<br>
-: The original revision id was <tt>248861151</tt>.<br>
+: The original revision id was <tt>249047721</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 12: / Line 12: @@
 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 ||   ||
+||= 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 ||
+||   ||   ||   ||   ||   ||   || 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 ||   ||
+||   ||   ||   ||   ||   || 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 ||   ||
+||=   ||=   ||=   ||=   ||= 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 ||   ||
+||=   ||=   ||=   ||= 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 ||   ||
+||=   ||=   ||=   ||=   ||= 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 ||   ||
+||=   ||=   ||= 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 ||   ||
+||=   ||=   ||=   ||=   ||= 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 ||   ||
+||=   ||=   ||=   ||= 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 ||   ||
+||=   ||=   ||=   ||=   ||= 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 ||   ||
+||=   ||= 2\[[11edo|11]] ||=   ||=   ||=   ||   ||   ||= 2 2 2 2 2 1 ||= 218.2 ||= 109.1 ||= Boundary of propriety (generators
-||=   ||=   ||=   ||=   ||= 7\[[39edo|39]] ||   ||   ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||   ||
+smaller than this are proper) ||
-||=   ||=   ||=   ||= 5\[[28edo|28]] ||=   ||   ||   ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||   ||
+||=   ||=   ||=   ||=   ||= 7\[[39edo|39]] ||   ||   ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||=   ||
-||   ||   ||   ||   ||   || 13\73 ||   || 13 13... 8 ||= 213.70 ||= 131.5 ||   ||
+||=   ||=   ||=   ||= 5\[[28edo|28]] ||=   ||   ||   ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||=   ||
-||   ||   ||   ||   ||   ||   || 21\118 || 21 21... 13 ||= 213.56 ||= 132.2 || Golden machine ||
+||   ||   ||   ||   ||   || 13\73 ||   || 13 13... 8 ||= 213.70 ||= 131.5 ||=   ||
-||=   ||=   ||=   ||=   ||= 8\[[45edo|45]] ||   ||   ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 ||   ||
+||   ||   ||   ||   ||   ||   || 21\118 || 21 21... 13 ||= 213.56 ||= 132.2 ||= Golden machine ||
-||=   ||=   ||= 3\[[17edo|17]] ||=   ||=   ||   ||   ||= 3 3 3 3 3 2 ||= 211.8 ||= 141.2 ||   ||
+||=   ||=   ||=   ||=   ||= 8\[[45edo|45]] ||   ||   ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 ||=   ||
-||=   ||=   ||=   ||=   ||= 7\[[40edo|40]] ||   ||   ||= 7 7 7 7 7 5 ||= 210.0 ||= 150.0 ||   ||
+||=   ||=   ||= 3\[[17edo|17]] ||=   ||=   ||   ||   ||= 3 3 3 3 3 2 ||= 211.8 ||= 141.2 ||= Optimum rank range (L/s=3/2) machine ||
-||=   ||=   ||=   ||= 4\[[23edo|23]] ||=   ||   ||   ||= 4 4 4 4 4 3 ||= 208.7 ||= 156.5 ||   ||
+||=   ||=   ||=   ||=   ||= 7\[[40edo|40]] ||   ||   ||= 7 7 7 7 7 5 ||= 210.0 ||= 150.0 ||=   ||
-||=   ||=   ||=   ||=   ||= 5\[[29edo|29]] ||   ||   ||= 5 5 5 5 5 4 ||= 206.9 ||= 165.5 ||   ||
+||=   ||=   ||=   ||= 4\[[23edo|23]] ||=   ||   ||   ||= 4 4 4 4 4 3 ||= 208.7 ||= 156.5 ||=   ||
-||= 1\[[6edo|6]] ||=   ||=   ||=   ||=   ||   ||   ||= 1 1 1 1 1 1 ||= 200.0 ||= 200.0 ||   ||</pre></div>
+||=   ||=   ||=   ||=   ||= 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 &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;
@@ Line 75: / Line 76: @@
          &lt;td style="text-align: center;"&gt;0.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 99: / Line 100: @@
          &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 style="text-align: center;"&gt;Slendric is around here&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
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          &lt;td style="text-align: center;"&gt;38.7&lt;br /&gt;
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          &lt;td style="text-align: center;"&gt;46.2&lt;br /&gt;
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          &lt;td style="text-align: center;"&gt;57.1&lt;br /&gt;
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          &lt;td style="text-align: center;"&gt;75.0&lt;br /&gt;
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          &lt;td style="text-align: center;"&gt;83.7&lt;br /&gt;
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          &lt;td style="text-align: center;"&gt;88.9&lt;br /&gt;
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+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
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          &lt;td style="text-align: center;"&gt;94.7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
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          &lt;td style="text-align: center;"&gt;109.1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
+smaller than this are proper)&lt;br /&gt;
 &lt;/td&gt;
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          &lt;td style="text-align: center;"&gt;123.1&lt;br /&gt;
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      &lt;/tr&gt;
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          &lt;td style="text-align: center;"&gt;128.6&lt;br /&gt;
 &lt;/td&gt;
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      &lt;/tr&gt;
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          &lt;td style="text-align: center;"&gt;131.5&lt;br /&gt;
 &lt;/td&gt;
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          &lt;td style="text-align: center;"&gt;132.2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Golden machine&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Golden machine&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 435: / Line 437: @@
          &lt;td style="text-align: center;"&gt;133.3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 459: / Line 461: @@
          &lt;td style="text-align: center;"&gt;141.2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Optimum rank range (L/s=3/2) machine&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 483: / Line 485: @@
          &lt;td style="text-align: center;"&gt;150.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 507: / Line 509: @@
          &lt;td style="text-align: center;"&gt;156.5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 531: / Line 533: @@
          &lt;td style="text-align: center;"&gt;165.5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 555: / Line 557: @@
          &lt;td style="text-align: center;"&gt;200.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;