5L 5s: Difference between revisions

Revision as of 04:10, 29 August 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author guest and made on 2011-08-29 04:10:02 UTC.

The original revision id was 249049123.

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Original Wikitext content:

There is only one significant harmonic entropy minimum with this MOS pattern: [[Archytas clan|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo]], and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5.

The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being [[Rothenberg propriety|proper]] (because 1\15 is in the middle of the range of good blackwood generators).
||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\5 ||   ||   ||   ||   || 0 ||=   ||
||   ||   || 1\20 ||   ||   || 60 ||=   ||
||   || 1\15 ||   ||   ||   || 80 ||= Blackwood is around here
Optimum rank range (L/s=2/1) for MOS ||
||   ||   ||   || 3\40 ||   || 90 ||=   ||
||   ||   ||   ||   || 5\65 || 92.31 ||= Golden blackwood ||
||   ||   || 2\25 ||   ||   || 96 ||=   ||
|| 1\10 ||   ||   ||   ||   || 120 ||=   ||

Original HTML content:

<html><head><title>5L 5s</title></head><body>There is only one significant harmonic entropy minimum with this MOS pattern: <a class="wiki_link" href="/Archytas%20clan">blackwood</a>, in which intervals of the prime numbers 3 and 7 are all represented using steps of <a class="wiki_link" href="/5edo">5edo</a>, and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5.<br />
<br />
The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being <a class="wiki_link" href="/Rothenberg%20propriety">proper</a> (because 1\15 is in the middle of the range of good blackwood generators).<br />


<table class="wiki_table">
    <tr>
        <th colspan="5">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>0\5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>0<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>60<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1\15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>80<br />
</td>
        <td style="text-align: center;">Blackwood is around here<br />
Optimum rank range (L/s=2/1) for MOS<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\40<br />
</td>
        <td><br />
</td>
        <td>90<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\65<br />
</td>
        <td>92.31<br />
</td>
        <td style="text-align: center;">Golden blackwood<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>96<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>1\10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>120<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:guest|guest]] and made on <tt>2011-08-28 04:05:36 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 04:10:02 UTC</tt>.<br>
-: The original revision id was <tt>248871627</tt>.<br>
+: The original revision id was <tt>249049123</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 10: / Line 10: @@
 The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being [[Rothenberg propriety|proper]] (because 1\15 is in the middle of the range of good blackwood generators).
 ||||||||||~ Generator ||~ Cents ||~ Comments ||
-|| 0\5 ||   ||   ||   ||   || 0 ||   ||
+|| 0\5 ||   ||   ||   ||   || 0 ||=   ||
-||   ||   || 1\20 ||   ||   || 60 ||   ||
+||   ||   || 1\20 ||   ||   || 60 ||=   ||
-||   || 1\15 ||   ||   ||   || 80 || Blackwood is around here ||
+||   || 1\15 ||   ||   ||   || 80 ||= Blackwood is around here
-||   ||   ||   || 3\40 ||   || 90 ||   ||
+Optimum rank range (L/s=2/1) for MOS ||
-||   ||   ||   ||   || 5\65 || 92.31 || Golden blackwood ||
+||   ||   ||   || 3\40 ||   || 90 ||=   ||
-||   ||   || 2\25 ||   ||   || 96 ||   ||
+||   ||   ||   ||   || 5\65 || 92.31 ||= Golden blackwood ||
-|| 1\10 ||   ||   ||   ||   || 120 ||   ||</pre></div>
+||   ||   || 2\25 ||   ||   || 96 ||=   ||
+|| 1\10 ||   ||   ||   ||   || 120 ||=   ||</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 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There is only one significant harmonic entropy minimum with this MOS pattern: &lt;a class="wiki_link" href="/Archytas%20clan"&gt;blackwood&lt;/a&gt;, in which intervals of the prime numbers 3 and 7 are all represented using steps of &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5.&lt;br /&gt;
@@ Line 45: / Line 46: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 61: / Line 62: @@
          &lt;td&gt;60&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 77: / Line 78: @@
          &lt;td&gt;80&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Blackwood is around here&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Blackwood is around here&lt;br /&gt;
+Optimum rank range (L/s=2/1) for MOS&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 93: / Line 95: @@
          &lt;td&gt;90&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 109: / Line 111: @@
          &lt;td&gt;92.31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Golden blackwood&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Golden blackwood&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 125: / Line 127: @@
          &lt;td&gt;96&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 141: / Line 143: @@
          &lt;td&gt;120&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

5L 5s: Difference between revisions

Revision as of 04:10, 29 August 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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