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Wikispaces>genewardsmith
**Imported revision 209503350 - Original comment: **
Wikispaces>keenanpepper
**Imported revision 222789044 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 00:11:19 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 15:53:12 UTC</tt>.<br>
: The original revision id was <tt>209503350</tt>.<br>
: The original revision id was <tt>222789044</tt>.<br>
: The revision comment was: <tt></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>
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>
<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">The range between 2\15 and 5\37, including 3\22, is the [[Porcupine family|porcupine]] range of grumpy. Between 4\31 and 2\15, including 3\23, is the [[Chromatic pairs|greeley]] range.
<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.


Form: L L L L L L L s = Major Scale
Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
L s L L L L L L = Minor Scale
||||||||||||~ Generator ||~ Cents ||~ 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 ||  ||
||  ||  || 3\22 ||  ||  ||  ||  ||= 3 3 3 3 3 3 3 1 ||  ||
||  ||  ||  || 5\37 ||  ||  ||  ||= 5 5 5 5 5 5 5 2 || Porcupine is in this general region ||
||  ||  ||  ||  || 7\52 ||  ||  ||= 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 ||  ||
||  ||  ||  ||  ||  || 10\77 ||  ||= 10 10 10 10 10 10 10 7 || Greely is around here ||
||  ||  ||  ||  || 7\54 ||  ||  ||= 7 7 7 7 7 7 7 5 ||  ||
||  ||  ||  || 4\31 ||  ||  ||  ||= 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>
<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 harmonic entropy 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;
&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;


Equal Temperaments:
2 2 2 2 2 2 2 1
2 1 2 2 2 2 2 2: __[[15edo]]__


3 3 3 3 3 3 3 1
&lt;table class="wiki_table"&gt;
3 1 3 3 3 3 3 3: **__[[22edo]]__**
    &lt;tr&gt;
        &lt;th colspan="6"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Scale in EDO steps&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\7&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;171.43&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1 0&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;4\29&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 style="text-align: center;"&gt;4 4 4 4 4 4 4 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;3\22&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 style="text-align: center;"&gt;3 3 3 3 3 3 3 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\37&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 style="text-align: center;"&gt;5 5 5 5 5 5 5 2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Porcupine is in this general region&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;7\52&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 style="text-align: center;"&gt;7 7 7 7 7 7 7 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;2\15&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;160&lt;br /&gt;
&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;3\23&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 style="text-align: center;"&gt;3 3 3 3 3 3 3 2&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;10\77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10 10 10 10 10 10 10 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Greely is around here&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;7\54&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 style="text-align: center;"&gt;7 7 7 7 7 7 7 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;4\31&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 style="text-align: center;"&gt;4 4 4 4 4 4 4 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;1\8&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;150&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


4 4 4 4 4 4 4 1
&lt;/body&gt;&lt;/html&gt;</pre></div>
4 1 4 4 4 4 4 4: __[[29edo]]__
 
4 4 4 4 4 4 4 2
4 2 4 4 4 4 4 4: __[[30edo]]__
 
5 5 5 5 5 5 5 2
5 2 5 5 5 5 5 5: __**[[37edo]]**__
 
6 6 6 6 6 6 6 2
6 2 6 6 6 6 6 6: __[[44edo]]__
 
6 6 6 6 6 6 6 3
6 3 6 6 6 6 6 6: __[[45edo]]__
 
7 7 7 7 7 7 7 3
7 3 7 7 7 7 7 7: __[[52edo]]__</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;The range between 2\15 and 5\37, including 3\22, is the &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt; range of grumpy. Between 4\31 and 2\15, including 3\23, is the &lt;a class="wiki_link" href="/Chromatic%20pairs"&gt;greeley&lt;/a&gt; range.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Form: L L L L L L L s = Major Scale&lt;br /&gt;
L s L L L L L L = Minor Scale&lt;br /&gt;
&lt;br /&gt;
Equal Temperaments:&lt;br /&gt;
2 2 2 2 2 2 2 1&lt;br /&gt;
2 1 2 2 2 2 2 2: &lt;u&gt;&lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
3 3 3 3 3 3 3 1&lt;br /&gt;
3 1 3 3 3 3 3 3: &lt;strong&gt;&lt;u&gt;&lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;/u&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
4 4 4 4 4 4 4 1&lt;br /&gt;
4 1 4 4 4 4 4 4: &lt;u&gt;&lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
4 4 4 4 4 4 4 2&lt;br /&gt;
4 2 4 4 4 4 4 4: &lt;u&gt;&lt;a class="wiki_link" href="/30edo"&gt;30edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
5 5 5 5 5 5 5 2&lt;br /&gt;
5 2 5 5 5 5 5 5: &lt;u&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt;&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
6 6 6 6 6 6 6 2&lt;br /&gt;
6 2 6 6 6 6 6 6: &lt;u&gt;&lt;a class="wiki_link" href="/44edo"&gt;44edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
6 6 6 6 6 6 6 3&lt;br /&gt;
6 3 6 6 6 6 6 6: &lt;u&gt;&lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
7 7 7 7 7 7 7 3&lt;br /&gt;
7 3 7 7 7 7 7 7: &lt;u&gt;&lt;a class="wiki_link" href="/52edo"&gt;52edo&lt;/a&gt;&lt;/u&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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