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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-~~22 13~~:36:09 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-03 15:18:09 UTC</tt>.

: The original revision id was <tt>~~551907094~~</tt>.

: The original revision id was <tt>564999731</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 ||= ||

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

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||= ||= ||= ||= ||= 7\[[37edo|37]] || || ||= 7 7 7 7 7 2 ||= 227.0 ||= 64.9 ||= ||

|| || || || || || || ||= pi pi pi pi pi 1 ||= 225.6 ||= 71.8 ||= L/s = pi ||

||= ||= ||= 3\[[16edo|16]] ||= ||= || || ||= 3 3 3 3 3 1 ||= 225.0 ||= 75.0 ||= Gorgo is around here

||= ||= ||= 3\[[16edo|16]] ||= ||= || || ||= 3 3 3 3 3 1 ||= 225 ||= 75 ||= Gorgo is around here

L/s = 3 ||

|| || || || || || || ||= e e e e e 1 ||= 223.55 ||= 82.2 ||= L/s = e ||

||= ||= ||= ||= ||= 8\[[43edo|43]] || || ||= 8 8 8 8 8 3 ||= 223.3 ||= 83.7 ||= ||

|| || || || || || || ||= phi+1 phi+1 phi+1 phi+1 phi+1 1 ||= 223 ||= 85.2 || ||

||= ||= ||= ||= 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 ||= Optimum rank range (L/s=2/1) machine ||

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

|| || || || || || || ||= √3 √3 √3 √3 √3 1 ||= 215.2 ||= 124.2 || ||

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

|| || || || || || 13\73 || ||= 13 13 13 13 8 ||= 213.7 ||= 131.5 ||= ||

|| || || || || || || ||= phi phi phi phi 1 ||= ~~1200~~/~~(4+phi)~~ ||= 1200/(1+5phi) ||= Golden machine ||

|| || || || || || || ||= phi phi phi phi phi 1 ||= 213/6 ||= 1200/(1+5phi) ||= Golden machine ||

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

|| || || || || || || ||= pi pi pi pi pi 2 ||= 212.9 ||= 135.5 || ||

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

||= ||= ||= ||= ||= 7\[[40edo|40]] || || ||= 7 7 7 7 7 5 ||= 210 ||= 150 ||= ||

||= ||= ||= ||= 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>

||= 1\[[6edo|6]] ||= ||= ||= ||= || || ||= 1 1 1 1 1 1 ||||= 200 ||= ||</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;">1 1 1 1 1 0

</td>

<td style="text-align: center;">240.0

<td style="text-align: center;">240

</td>

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

<td style="text-align: center;">0

</td>

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<td style="text-align: center;">3 3 3 3 3 1

</td>

<td style="text-align: center;">225.0

<td style="text-align: center;">225

</td>

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

<td style="text-align: center;">75

</td>

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

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">phi+1 phi+1 phi+1 phi+1 phi+1 1

</td>

<td style="text-align: center;">223

</td>

<td style="text-align: center;">85.2

</td>

<td>

</td>

</tr>

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">√3 √3 √3 √3 √3 1

</td>

<td style="text-align: center;">215.2

</td>

<td style="text-align: center;">124.2

</td>

<td>

</td>

</tr>

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<td>

</td>

<td style="text-align: center;">phi phi phi phi 1

<td style="text-align: center;">phi phi phi phi phi 1

</td>

<td style="text-align: center;">~~1200~~/~~(4+phi)~~

<td style="text-align: center;">213/6

</td>

<td style="text-align: center;">1200/(1+5phi)

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">pi pi pi pi pi 2

</td>

<td style="text-align: center;">212.9

</td>

<td style="text-align: center;">135.5

</td>

<td>

</td>

</tr>

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<td style="text-align: center;">7 7 7 7 7 5

</td>

<td style="text-align: center;">210.0

<td style="text-align: center;">210

</td>

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

<td style="text-align: center;">150

</td>

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<td style="text-align: center;">1 1 1 1 1 1

</td>

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

<td colspan="2" style="text-align: center;">200

~~</td>~~

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

</td>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-22 13:36:09 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-03 15:18:09 UTC</tt>.<br>
-: The original revision id was <tt>551907094</tt>.<br>
+: The original revision id was <tt>564999731</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 ||=   ||
 ||   ||   ||   ||   ||   ||   || 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 ||=   ||
@@ Line 19: / Line 19: @@
 ||=   ||=   ||=   ||=   ||= 7\[[37edo|37]] ||   ||   ||= 7 7 7 7 7 2 ||= 227.0 ||= 64.9 ||=   ||
 ||   ||   ||   ||   ||   ||   ||   ||= pi pi pi pi pi 1 ||= 225.6 ||= 71.8 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
-||=   ||=   ||= 3\[[16edo|16]] ||=   ||=   ||   ||   ||= 3 3 3 3 3 1 ||= 225.0 ||= 75.0 ||= Gorgo is around here
+||=   ||=   ||= 3\[[16edo|16]] ||=   ||=   ||   ||   ||= 3 3 3 3 3 1 ||= 225 ||= 75 ||= Gorgo is around here
 L/s = 3 ||
 ||   ||   ||   ||   ||   ||   ||   ||= e e e e e 1 ||= 223.55 ||= 82.2 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
 ||=   ||=   ||=   ||=   ||= 8\[[43edo|43]] ||   ||   ||= 8 8 8 8 8 3 ||= 223.3 ||= 83.7 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;phi+1 phi+1 phi+1 phi+1 phi+1 1&lt;/span&gt; ||= 223 ||= 85.2 ||   ||
 ||=   ||=   ||=   ||= 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 ||= Optimum rank range (L/s=2/1) machine ||
 ||=   ||=   ||=   ||=   ||= 7\[[39edo|39]] ||   ||   ||= 7 7 7 7 7 4 ||= 215.4 ||= 123.1 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="background-color: #ffffff;"&gt;√3 √3 √3 √3 √3 1&lt;/span&gt; ||= 215.2 ||= 124.2 ||   ||
 ||=   ||=   ||=   ||= 5\[[28edo|28]] ||=   ||   ||   ||= 5 5 5 5 5 3 ||= 214.3 ||= 128.6 ||=   ||
 ||   ||   ||   ||   ||   || 13\73 ||   ||= 13 13 13 13 8 ||= 213.7 ||= 131.5 ||=   ||
-||   ||   ||   ||   ||   ||   ||   ||= phi phi phi phi 1 ||= 1200/(4+phi) ||= 1200/(1+5phi) ||= Golden machine ||
+||   ||   ||   ||   ||   ||   ||   ||= phi phi phi phi phi 1 ||= 213/6 ||= 1200/(1+5phi) ||= Golden machine ||
 ||=   ||=   ||=   ||=   ||= 8\[[45edo|45]] ||   ||   ||= 8 8 8 8 8 5 ||= 213.3 ||= 133.3 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;pi pi pi pi pi 2&lt;/span&gt; ||= 212.9 ||= 135.5 ||   ||
 ||=   ||=   ||= 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 ||=   ||
+||=   ||=   ||=   ||=   ||= 7\[[40edo|40]] ||   ||   ||= 7 7 7 7 7 5 ||= 210 ||= 150 ||=   ||
 ||=   ||=   ||=   ||= 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>
+||= 1\[[6edo|6]] ||=   ||=   ||=   ||=   ||   ||   ||= 1 1 1 1 1 1 ||||= 200 ||=   ||</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 74: / Line 77: @@
          &lt;td style="text-align: center;"&gt;1 1 1 1 1 0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;240.0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;240&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;0.0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 242: / Line 245: @@
          &lt;td style="text-align: center;"&gt;3 3 3 3 3 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;225.0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;225&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;75.0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;75&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Gorgo is around here&lt;br /&gt;
@@ Line 296: / Line 299: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;phi+1 phi+1 phi+1 phi+1 phi+1 1&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;223&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;85.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 392: / Line 419: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff;"&gt;√3 √3 √3 √3 √3 1&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;215.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;124.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 457: / Line 508: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;phi phi phi phi 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;phi phi phi phi phi 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1200/(4+phi)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;213/6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1200/(1+5phi)&lt;br /&gt;
@@ Line 488: / Line 539: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;pi pi pi pi pi 2&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;212.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;135.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 531: / Line 606: @@
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;210.0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;210&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;150.0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;150&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 603: / Line 678: @@
          &lt;td style="text-align: center;"&gt;1 1 1 1 1 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;200.0&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: center;"&gt;200&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;200.0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;