7L 1s: Difference between revisions

Revision as of 03:33, 28 August 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 guest and made on 2011-08-28 03:33:16 UTC.

The original revision id was 248870269.

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 [[Porcupine family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic pairs|greely]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.

Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
||||||||||||~ [[Generator]] ||~ [[Cent]]s ||~ Scale in [[EDO]] steps ||~ Comments ||
|| 1\7 ||   ||   ||   ||   ||   || 171.43 ||= 1 1 1 1 1 1 1 0 ||   ||
||   ||   ||   || 4\29 ||   ||   || 165.52 ||= 4 4 4 4 4 4 4 1 ||   ||
||   ||   || 3\22 ||   ||   ||   || 163.64 ||= 3 3 3 3 3 3 3 1 ||   ||
||   ||   ||   || 5\37 ||   ||   || 162.16 ||= 5 5 5 5 5 5 5 2 || Porcupine is in this general region ||
||   ||   ||   ||   || 7\52 ||   || 161.54 ||= 7 7 7 7 7 7 7 3 ||   ||
||   || 2\15 ||   ||   ||   ||   || 160 ||= 2 2 2 2 2 2 2 1 ||   ||
||   ||   ||   || 5\38 ||   ||   || 157.89 ||= 5 5 5 5 5 5 5 3 ||   ||
||   ||   ||   ||   ||   || 13\99 || 157.58 ||= 13 13 13 13 13 13 13 8 || Golden porcupine / golden hemikleismic ||
||   ||   ||   ||   || 8\61 ||   || 157.38 ||= 8 8 8 8 8 8 8 5 ||   ||
||   ||   || 3\23 ||   ||   ||   || 156.52 ||= 3 3 3 3 3 3 3 2 ||   ||
||   ||   ||   ||   ||   || 10\77 || 155.84 ||= 10 10 10 10 10 10 10 7 || Greely is around here ||
||   ||   ||   ||   || 7\54 ||   || 155.56 ||= 7 7 7 7 7 7 7 5 ||   ||
||   ||   ||   || 4\31 ||   ||   || 154.84 ||= 4 4 4 4 4 4 4 3 ||   ||
|| 1\8 ||   ||   ||   ||   ||   || 150 ||= 1 1 1 1 1 1 1 1 ||   ||

Original HTML content:

<html><head><title>7L 1s</title></head><body>There are two notable <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> minima with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern. The first is <a class="wiki_link" href="/Porcupine%20family">porcupine</a>, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is <a class="wiki_link" href="/Chromatic%20pairs">greely</a>, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.<br />
<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"><a class="wiki_link" href="/Generator">Generator</a><br />
</th>
        <th><a class="wiki_link" href="/Cent">Cent</a>s<br />
</th>
        <th>Scale in <a class="wiki_link" href="/EDO">EDO</a> steps<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;">1 1 1 1 1 1 1 0<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>165.52<br />
</td>
        <td style="text-align: center;">4 4 4 4 4 4 4 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>163.64<br />
</td>
        <td style="text-align: center;">3 3 3 3 3 3 3 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\37<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>162.16<br />
</td>
        <td style="text-align: center;">5 5 5 5 5 5 5 2<br />
</td>
        <td>Porcupine is in this general region<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\52<br />
</td>
        <td><br />
</td>
        <td>161.54<br />
</td>
        <td style="text-align: center;">7 7 7 7 7 7 7 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2\15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>160<br />
</td>
        <td style="text-align: center;">2 2 2 2 2 2 2 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\38<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>157.89<br />
</td>
        <td style="text-align: center;">5 5 5 5 5 5 5 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\99<br />
</td>
        <td>157.58<br />
</td>
        <td style="text-align: center;">13 13 13 13 13 13 13 8<br />
</td>
        <td>Golden porcupine / golden hemikleismic<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\61<br />
</td>
        <td><br />
</td>
        <td>157.38<br />
</td>
        <td style="text-align: center;">8 8 8 8 8 8 8 5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>156.52<br />
</td>
        <td style="text-align: center;">3 3 3 3 3 3 3 2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10\77<br />
</td>
        <td>155.84<br />
</td>
        <td style="text-align: center;">10 10 10 10 10 10 10 7<br />
</td>
        <td>Greely is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\54<br />
</td>
        <td><br />
</td>
        <td>155.56<br />
</td>
        <td style="text-align: center;">7 7 7 7 7 7 7 5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>154.84<br />
</td>
        <td style="text-align: center;">4 4 4 4 4 4 4 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>150<br />
</td>
        <td style="text-align: center;">1 1 1 1 1 1 1 1<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:hstraub|hstraub]] and made on <tt>2011-06-21 05:35:45 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-28 03:33:16 UTC</tt>.<br>
-: The original revision id was <tt>237910043</tt>.<br>
+: The original revision id was <tt>248870269</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 11: / Line 11: @@
 ||||||||||||~ [[Generator]] ||~ [[Cent]]s ||~ Scale in [[EDO]] steps ||~ Comments ||
 || 1\7 ||   ||   ||   ||   ||   || 171.43 ||= 1 1 1 1 1 1 1 0 ||   ||
-||   ||   ||   || 4\29 ||   ||   ||   ||= 4 4 4 4 4 4 4 1 ||   ||
+||   ||   ||   || 4\29 ||   ||   || 165.52 ||= 4 4 4 4 4 4 4 1 ||   ||
-||   ||   || 3\22 ||   ||   ||   ||   ||= 3 3 3 3 3 3 3 1 ||   ||
+||   ||   || 3\22 ||   ||   ||   || 163.64 ||= 3 3 3 3 3 3 3 1 ||   ||
-||   ||   ||   || 5\37 ||   ||   ||   ||= 5 5 5 5 5 5 5 2 || Porcupine is in this general region ||
+||   ||   ||   || 5\37 ||   ||   || 162.16 ||= 5 5 5 5 5 5 5 2 || Porcupine is in this general region ||
-||   ||   ||   ||   || 7\52 ||   ||   ||= 7 7 7 7 7 7 7 3 ||   ||
+||   ||   ||   ||   || 7\52 ||   || 161.54 ||= 7 7 7 7 7 7 7 3 ||   ||
 ||   || 2\15 ||   ||   ||   ||   || 160 ||= 2 2 2 2 2 2 2 1 ||   ||
-||   ||   || 3\23 ||   ||   ||   ||   ||= 3 3 3 3 3 3 3 2 ||   ||
+||   ||   ||   || 5\38 ||   ||   || 157.89 ||= 5 5 5 5 5 5 5 3 ||   ||
-||   ||   ||   ||   ||   || 10\77 ||   ||= 10 10 10 10 10 10 10 7 || Greely is around here ||
+||   ||   ||   ||   ||   || 13\99 || 157.58 ||= 13 13 13 13 13 13 13 8 || Golden porcupine / golden hemikleismic ||
-||   ||   ||   ||   || 7\54 ||   ||   ||= 7 7 7 7 7 7 7 5 ||   ||
+||   ||   ||   ||   || 8\61 ||   || 157.38 ||= 8 8 8 8 8 8 8 5 ||   ||
-||   ||   ||   || 4\31 ||   ||   ||   ||= 4 4 4 4 4 4 4 3 ||   ||
+||   ||   || 3\23 ||   ||   ||   || 156.52 ||= 3 3 3 3 3 3 3 2 ||   ||
+||   ||   ||   ||   ||   || 10\77 || 155.84 ||= 10 10 10 10 10 10 10 7 || Greely is around here ||
+||   ||   ||   ||   || 7\54 ||   || 155.56 ||= 7 7 7 7 7 7 7 5 ||   ||
+||   ||   ||   || 4\31 ||   ||   || 154.84 ||= 4 4 4 4 4 4 4 3 ||   ||
 || 1\8 ||   ||   ||   ||   ||   || 150 ||= 1 1 1 1 1 1 1 1 ||   ||</pre></div>
 <h4>Original HTML content:</h4>
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          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;165.52&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4 4 4 4 4 4 4 1&lt;br /&gt;
@@ Line 91: / Line 94: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;163.64&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3 3 3 3 3 3 3 1&lt;br /&gt;
@@ Line 111: / Line 114: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;162.16&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5 5 5 5 5 5 5 2&lt;br /&gt;
@@ Line 131: / Line 134: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;161.54&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 7 7 3&lt;br /&gt;
@@ Line 154: / Line 157: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2 2 2 2 2 2 2 1&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;5\38&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;157.89&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5 5 5 5 5 5 5 3&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;13\99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;157.58&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;13 13 13 13 13 13 13 8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Golden porcupine / golden hemikleismic&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\61&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;157.38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8 8 8 8 8 8 8 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;156.52&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3 3 3 3 3 3 3 2&lt;br /&gt;
@@ Line 191: / Line 254: @@
          &lt;td&gt;10\77&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;155.84&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;10 10 10 10 10 10 10 7&lt;br /&gt;
@@ Line 211: / Line 274: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;155.56&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7 7 7 7 7 7 7 5&lt;br /&gt;
@@ Line 231: / Line 294: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;154.84&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4 4 4 4 4 4 4 3&lt;br /&gt;

7L 1s: Difference between revisions

Revision as of 03:33, 28 August 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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