6L 1s: Difference between revisions

Revision as of 15:39, 4 November 2015

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2015-11-04 15:39:59 UTC.

The original revision id was 565207855.

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:

There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)

The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.
Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 1\7 ||   ||   ||   ||   ||   || 171.43 ||=   ||
||   ||   ||   ||   ||   || 6\41 || 175.61 ||= Enipucrop is between here and 1\7 ||
||   ||   ||   ||   || 5\34 ||   || 176.47 ||= Tetracot is around here ||
||   ||   ||   || 4\27 ||   ||   || 177.78 ||=   ||
||   ||   || 3\20 ||   ||   ||   || 180 ||=   ||
||   ||   ||   ||   ||   ||   || 180.815 ||   ||
||   ||   ||   ||   || 8\53 ||   || 181.13 ||=   ||
||   ||   ||   ||   ||   ||   || 1200/(5+phi) ||= Unnamed golden temperament (discussed in [[http://launch.groups.yahoo.com/group/tuning/message/100254|this thread]]) ||
||   ||   ||   || 5\33 ||   ||   || 181.82 ||=   ||
||   ||   ||   ||   ||   ||   || 182.44 ||   ||
||   ||   ||   ||   || 7\46 ||   || 182.61 ||   ||
||   || 2\13 ||   ||   ||   ||   || 184.62 ||= Optimum rank range glacial (L/s=2/1) ||
||   ||   ||   || 5\32 ||   ||   || 187.5 ||   ||
||   ||   ||   ||   ||   ||   || 188.03 ||   ||
||   ||   ||   ||   || 8\51 ||   || 188.235 ||   ||
||   ||   ||   ||   ||   ||   || 188.45 ||= <span style="display: block; text-align: center;">L/s = e</span> ||
||   ||   || 3\19 ||   ||   ||   || 189.47 ||= L/s = 3 ||
||   ||   ||   ||   ||   ||   || 189.92 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
||   ||   ||   || 4\25 ||   ||   || 192 ||= L/s = 4 ||
||   ||   ||   ||   || 5\31 ||   || 193.55 ||= Luna/hemithird/roulette is around here ||
|| 1\6 ||   ||   ||   ||   ||   || 200 ||=   ||

Original HTML content:

<html><head><title>6L 1s</title></head><body>There are two notable harmonic entropy minima with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern. The first is <a class="wiki_link" href="/Tetracot%20family">tetracot</a>, in which four generators make a 3/2, and the second is known as <a class="wiki_link" href="/roulette7">roulette7</a>, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament <a class="wiki_link" href="/Chromatic%20pairs#Roulette">roulette</a>. (Other temperaments like &quot;luna&quot;, &quot;hemithird&quot;, and &quot;hemiwürschmidt&quot; have very similar 7-note MOSes.)<br />
<br />
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.<br />
Scales of this form 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="6">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>1\7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>171.43<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\41<br />
</td>
        <td>175.61<br />
</td>
        <td style="text-align: center;">Enipucrop is between here and 1\7<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\34<br />
</td>
        <td><br />
</td>
        <td>176.47<br />
</td>
        <td style="text-align: center;">Tetracot is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\27<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>177.78<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>180<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>180.815<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\53<br />
</td>
        <td><br />
</td>
        <td>181.13<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(5+phi)<br />
</td>
        <td style="text-align: center;">Unnamed golden temperament (discussed in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100254" rel="nofollow">this thread</a>)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\33<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>181.82<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>182.44<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\46<br />
</td>
        <td><br />
</td>
        <td>182.61<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2\13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>184.62<br />
</td>
        <td style="text-align: center;">Optimum rank range glacial (L/s=2/1)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\32<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>187.5<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>188.03<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\51<br />
</td>
        <td><br />
</td>
        <td>188.235<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>188.45<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>189.47<br />
</td>
        <td style="text-align: center;">L/s = 3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>189.92<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>192<br />
</td>
        <td style="text-align: center;">L/s = 4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\31<br />
</td>
        <td><br />
</td>
        <td>193.55<br />
</td>
        <td style="text-align: center;">Luna/hemithird/roulette is around here<br />
</td>
    </tr>
    <tr>
        <td>1\6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>200<br />
</td>
        <td style="text-align: center;"><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:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-22 14:32:09 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 15:39:59 UTC</tt>.<br>
-: The original revision id was <tt>551913648</tt>.<br>
+: The original revision id was <tt>565207855</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 16: / Line 16: @@
 ||   ||   ||   || 4\27 ||   ||   || 177.78 ||=   ||
 ||   ||   || 3\20 ||   ||   ||   || 180 ||=   ||
+||   ||   ||   ||   ||   ||   || 180.815 ||   ||
 ||   ||   ||   ||   || 8\53 ||   || 181.13 ||=   ||
 ||   ||   ||   ||   ||   ||   || 1200/(5+phi) ||= Unnamed golden temperament (discussed in [[http://launch.groups.yahoo.com/group/tuning/message/100254|this thread]]) ||
 ||   ||   ||   || 5\33 ||   ||   || 181.82 ||=   ||
+||   ||   ||   ||   ||   ||   || 182.44 ||   ||
 ||   ||   ||   ||   || 7\46 ||   || 182.61 ||   ||
 ||   || 2\13 ||   ||   ||   ||   || 184.62 ||= Optimum rank range glacial (L/s=2/1) ||
+||   ||   ||   || 5\32 ||   ||   || 187.5 ||   ||
+||   ||   ||   ||   ||   ||   || 188.03 ||   ||
+||   ||   ||   ||   || 8\51 ||   || 188.235 ||   ||
 ||   ||   ||   ||   ||   ||   || 188.45 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
 ||   ||   || 3\19 ||   ||   ||   || 189.47 ||= L/s = 3 ||
@@ Line 131: / Line 136: @@
 &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;180.815&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 185: / Line 208: @@
 &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;182.44&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 221: / Line 262: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Optimum rank range glacial (L/s=2/1)&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;5\32&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;187.5&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;188.03&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;8\51&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;188.235&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

6L 1s: Difference between revisions

Revision as of 15:39, 4 November 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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