7L 1s: Difference between revisions

Revision as of 10:31, 28 August 2011

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This revision was by author genewardsmith and made on 2011-08-28 10:31:04 UTC.

The original revision id was 248894123.

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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#Greeley|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#Greeley">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:guest|guest]] and made on <tt>2011-08-28 03:33:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-28 10:31:04 UTC</tt>.<br>
-: The original revision id was <tt>248870269</tt>.<br>
+: The original revision id was <tt>248894123</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">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.
+<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">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#Greeley|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.
@@ Line 25: / Line 25: @@
 || 1\8 ||   ||   ||   ||   ||   || 150 ||= 1 1 1 1 1 1 1 1 ||   ||</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;7L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are two notable &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; minima with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern. The first is &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/Chromatic%20pairs"&gt;greely&lt;/a&gt;, 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.&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;7L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are two notable &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; minima with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern. The first is &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/Chromatic%20pairs#Greeley"&gt;greely&lt;/a&gt;, 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.&lt;br /&gt;
 &lt;br /&gt;
 Scales of this form are always &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;proper&lt;/a&gt;, because there is only one small step.&lt;br /&gt;

7L 1s: Difference between revisions

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