1L 10s: 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-~~23 16~~:34:03 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-09 11:49:39 UTC</tt>.

: The original revision id was <tt>~~551974672~~</tt>.

: The original revision id was <tt>565733327</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.

<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">This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109 ~~1/9~~ cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).

<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">This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).

|| 0/1 || || || || || 0 ||

|| || || || || 1/15 || 80 ||

|| || || || 1/14 || || 85 ~~5/7~~ ||

|| || || || 1/14 || || 85.714 ||

|| || || || || 2/27 || 88 ~~8/9~~ ||

|| || || || || 2/27 || 88.889 ||

|| || || || || || 1200/(10+pi) ||

|| || || 1/13 || || || 92 ~~4/13~~ ||

|| || || 1/13 || || || 92.308 ||

|| || || || || || 1200/(10+e) ||

|| || || || || 3/38 || 94.~~736842~~ ||

|| || || || || 3/38 || 94.737 ||

|| || || || || || 1200/(11+phi) ||

|| || || || 2/25 || || 96 ||

|| || || || || 3/37 || 97 ~~11/37~~ ||

|| || || || || 3/37 || 97.297 ||

|| || 1/12 || || || || 100 ||

|| || || || || 4/47 || 102.~~12766~~ ||

|| || || || || || 1200/(10+sqrt(3)) ||

|| || || || 3/35 || || 102 6/7 ||

|| || || || || 4/47 || 102.128 ||

|| || || || || 5/58 || 103.~~448276~~ ||

|| || || || 3/35 || || 102.857 ||

|| || || 2/23 || || || 104.~~347826~~ ||

|| || || || || || 1200/(10+phi) ||

|| || || || || 5/57 || 105.~~263158~~ ||

|| || || || || 5/58 || 103.448 ||

|| || || || 3/34 || || 105.~~882353~~ ||

|| || || || || || 1200/(10+pi/2) ||

|| || || || || 4/45 || 106 ~~2/3~~ ||

|| || || 2/23 || || || 104.348 ||

|| 1/11 || || || || || 109 ~~1/11~~ ||</pre></div>

|| || || || || 5/57 || 105.263 ||

|| || || || 3/34 || || 105.882 ||

|| || || || || 4/45 || 106.667 ||

|| 1/11 || || || || || 109.091 ||</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>1L 10s</title></head><body>This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109 ~~1/9~~ cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).

<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>1L 10s</title></head><body>This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).

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<td>

</td>

<td>85 ~~5/7~~

<td>85.714

</td>

</tr>

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<td>2/27

</td>

<td>88 ~~8/9~~

<td>88.889

</td>

</tr>

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<td>

</td>

<td>92 ~~4/13~~

<td>92.308

</td>

</tr>

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<td>3/38

</td>

<td>94.~~736842~~

<td>94.737

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(11+phi)

</td>

</tr>

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<td>3/37

</td>

<td>97 ~~11/37~~

<td>97.297

</td>

</tr>

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</td>

<td>100

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(10+sqrt(3))

</td>

</tr>

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<td>4/47

</td>

<td>102.~~12766~~

<td>102.128

</td>

</tr>

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<td>

</td>

<td>102 6/7

<td>102.857

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(10+phi)

</td>

</tr>

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<td>5/58

</td>

<td>103.~~448276~~

<td>103.448

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>1200/(10+pi/2)

</td>

</tr>

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<td>

</td>

<td>104.~~347826~~

<td>104.348

</td>

</tr>

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<td>5/57

</td>

<td>105.~~263158~~

<td>105.263

</td>

</tr>

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<td>

</td>

<td>105.~~882353~~

<td>105.882

</td>

</tr>

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<td>4/45

</td>

<td>106 ~~2/3~~

<td>106.667

</td>

</tr>

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<td>

</td>

<td>109 ~~1/11~~

<td>109.091

</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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 16:34:03 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-09 11:49:39 UTC</tt>.<br>
-: The original revision id was <tt>551974672</tt>.<br>
+: The original revision id was <tt>565733327</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">This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109 1/9 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).
+<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">This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).
 || 0/1 ||   ||   ||   ||   || 0 ||
 ||   ||   ||   ||   || 1/15 || 80 ||
-||   ||   ||   || 1/14 ||   || 85 5/7 ||
+||   ||   ||   || 1/14 ||   || 85.714 ||
-||   ||   ||   ||   || 2/27 || 88 8/9 ||
+||   ||   ||   ||   || 2/27 || 88.889 ||
 ||   ||   ||   ||   ||   || 1200/(10+pi) ||
-||   ||   || 1/13 ||   ||   || 92 4/13 ||
+||   ||   || 1/13 ||   ||   || 92.308 ||
 ||   ||   ||   ||   ||   || 1200/(10+e) ||
-||   ||   ||   ||   || 3/38 || 94.736842 ||
+||   ||   ||   ||   || 3/38 || 94.737 ||
+||   ||   ||   ||   ||   || 1200/(11+phi) ||
 ||   ||   ||   || 2/25 ||   || 96 ||
-||   ||   ||   ||   || 3/37 || 97 11/37 ||
+||   ||   ||   ||   || 3/37 || 97.297 ||
 ||   || 1/12 ||   ||   ||   || 100 ||
-||   ||   ||   ||   || 4/47 || 102.12766 ||
+||   ||   ||   ||   ||   || 1200/(10+sqrt(3)) ||
-||   ||   ||   || 3/35 ||   || 102 6/7 ||
+||   ||   ||   ||   || 4/47 || 102.128 ||
-||   ||   ||   ||   || 5/58 || 103.448276 ||
+||   ||   ||   || 3/35 ||   || 102.857 ||
-||   ||   || 2/23 ||   ||   || 104.347826 ||
+||   ||   ||   ||   ||   || 1200/(10+phi) ||
-||   ||   ||   ||   || 5/57 || 105.263158 ||
+||   ||   ||   ||   || 5/58 || 103.448 ||
-||   ||   ||   || 3/34 ||   || 105.882353 ||
+||   ||   ||   ||   ||   || 1200/(10+pi/2) ||
-||   ||   ||   ||   || 4/45 || 106 2/3 ||
+||   ||   || 2/23 ||   ||   || 104.348 ||
-|| 1/11 ||   ||   ||   ||   || 109 1/11 ||</pre></div>
+||   ||   ||   ||   || 5/57 || 105.263 ||
+||   ||   ||   || 3/34 ||   || 105.882 ||
+||   ||   ||   ||   || 4/45 || 106.667 ||
+|| 1/11 ||   ||   ||   ||   || 109.091 ||</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;1L 10s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109 1/9 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).&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;1L 10s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).&lt;br /&gt;
@@ Line 70: / Line 74: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;85 5/7&lt;br /&gt;
+         &lt;td&gt;85.714&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 84: / Line 88: @@
          &lt;td&gt;2/27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;88 8/9&lt;br /&gt;
+         &lt;td&gt;88.889&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 112: / Line 116: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92 4/13&lt;br /&gt;
+         &lt;td&gt;92.308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 140: / Line 144: @@
          &lt;td&gt;3/38&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;94.736842&lt;br /&gt;
+         &lt;td&gt;94.737&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;1200/(11+phi)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 168: / Line 186: @@
          &lt;td&gt;3/37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;97 11/37&lt;br /&gt;
+         &lt;td&gt;97.297&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 183: / Line 201: @@
 &lt;/td&gt;
          &lt;td&gt;100&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;1200/(10+sqrt(3))&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 196: / Line 228: @@
          &lt;td&gt;4/47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;102.12766&lt;br /&gt;
+         &lt;td&gt;102.128&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 210: / Line 242: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;102 6/7&lt;br /&gt;
+         &lt;td&gt;102.857&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;1200/(10+phi)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 224: / Line 270: @@
          &lt;td&gt;5/58&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;103.448276&lt;br /&gt;
+         &lt;td&gt;103.448&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;1200/(10+pi/2)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 238: / Line 298: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;104.347826&lt;br /&gt;
+         &lt;td&gt;104.348&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 252: / Line 312: @@
          &lt;td&gt;5/57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;105.263158&lt;br /&gt;
+         &lt;td&gt;105.263&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 266: / Line 326: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;105.882353&lt;br /&gt;
+         &lt;td&gt;105.882&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 280: / Line 340: @@
          &lt;td&gt;4/45&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;106 2/3&lt;br /&gt;
+         &lt;td&gt;106.667&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 294: / Line 354: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;109 1/11&lt;br /&gt;
+         &lt;td&gt;109.091&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;