6L 2s: Difference between revisions

Wikispaces>JosephRuhf
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
There is only one significant (though small) harmonic entropy minimum with this MOS pattern: [[Porcupine_family#Hedgehog|hedgehog]], in which two generators are 6/5 and three are 4/3, same as porcupine.
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>2015-11-05 12:32:58 UTC</tt>.<br>
: The original revision id was <tt>565332775</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 is only one significant (though small) harmonic entropy minimum with this MOS pattern: [[Porcupine family#Hedgehog|hedgehog]], in which two generators are 6/5 and three are 4/3, same as porcupine.


In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two flavors. The true MOS is always proper, because there is only one small step per period, but the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).
In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two flavors. The true MOS is always proper, because there is only one small step per period, but the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).
||||||~ Generator ||~  ||~  ||~  ||~ Cents ||~ Comments ||
|| 1\8 ||  ||  ||  ||  ||  || 150 ||=  ||
||  ||  || 3\22 ||  ||  ||  || 163.64 ||= Hedgehog is around here ||
||  ||  ||  ||  ||  ||  || 164.99 ||  ||
||  ||  ||  ||  || 8\58 ||  || 165.52 ||=  ||
||  ||  ||  ||  ||  || 13\94 || 165.96 ||= Golden hedgehog/echidna ||
||  ||  ||  || 5\36 ||  ||  || 166.67 ||=  ||
||  ||  ||  ||  ||  ||  || 167.72 ||  ||
||  || 2\14 ||  ||  ||  ||  || 171.43 ||= Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS ||
||  ||  ||  || 5\34 ||  ||  || 176.47 ||  ||
||  ||  ||  ||  ||  || 13\88 || 177.27 ||  ||
||  ||  ||  ||  || 8\54 ||  || 177.78 ||  ||
||  ||  ||  ||  ||  ||  || 178.15 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
||  ||  || 3\20 ||  ||  ||  || 180 ||= L/s = 3 ||
||  ||  ||  ||  ||  ||  || 180.815 || &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
||  ||  ||  || 4/26 ||  ||  || 184.615 ||= L/s = 4 ||
|| 1\6 ||  ||  ||  ||  ||  || 200 ||=  ||</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;6L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There is only one significant (though small) harmonic entropy minimum with this MOS pattern: &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, in which two generators are 6/5 and three are 4/3, same as porcupine.&lt;br /&gt;
&lt;br /&gt;
In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two flavors. The true MOS is always proper, because there is only one small step per period, but the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).&lt;br /&gt;


{| class="wikitable"
|-
! colspan="3" | Generator
! |
! |
! |
! | Cents
! | Comments
|-
| | 1\8
| |
| |
| |
| |
| |
| | 150
| style="text-align:center;" |
|-
| |
| |
| | 3\22
| |
| |
| |
| | 163.64
| style="text-align:center;" | Hedgehog is around here
|-
| |
| |
| |
| |
| |
| |
| | 164.99
| |
|-
| |
| |
| |
| |
| | 8\58
| |
| | 165.52
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 13\94
| | 165.96
| style="text-align:center;" | Golden hedgehog/echidna
|-
| |
| |
| |
| | 5\36
| |
| |
| | 166.67
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 167.72
| |
|-
| |
| | 2\14
| |
| |
| |
| |
| | 171.43
| style="text-align:center;" | Boundary of propriety for near-MOS


&lt;table class="wiki_table"&gt;
Optimum rank range (L/s=2/1) for MOS
    &lt;tr&gt;
|-
        &lt;th colspan="3"&gt;Generator&lt;br /&gt;
| |
&lt;/th&gt;
| |
        &lt;th&gt;&lt;br /&gt;
| |
&lt;/th&gt;
| | 5\34
        &lt;th&gt;&lt;br /&gt;
| |
&lt;/th&gt;
| |
        &lt;th&gt;&lt;br /&gt;
| | 176.47
&lt;/th&gt;
| |
        &lt;th&gt;Cents&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\8&lt;br /&gt;
| | 13\88
&lt;/td&gt;
| | 177.27
        &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;
| | 8\54
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 177.78
&lt;/td&gt;
| |
        &lt;td&gt;150&lt;br /&gt;
|-
&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;
| | 178.15
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
&lt;/td&gt;
|-
        &lt;td&gt;3\22&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 3\20
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 180
&lt;/td&gt;
| style="text-align:center;" | L/s = 3
        &lt;td&gt;163.64&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td style="text-align: center;"&gt;Hedgehog is around here&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 180.815
        &lt;td&gt;&lt;br /&gt;
| | <span style="display: block; text-align: center;">L/s = pi</span>
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 4/26
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 184.615
&lt;/td&gt;
| style="text-align:center;" | L/s = 4
        &lt;td&gt;164.99&lt;br /&gt;
|-
&lt;/td&gt;
| | 1\6
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 200
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|}
        &lt;td&gt;&lt;br /&gt;
[[Category:mos]]
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8\58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.52&lt;br /&gt;
&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;13\94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.96&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Golden hedgehog/echidna&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\36&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;166.67&lt;br /&gt;
&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;167.72&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\14&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;Boundary of propriety for near-MOS&lt;br /&gt;
Optimum rank range (L/s=2/1) for MOS&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\34&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;176.47&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\88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;177.27&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\54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;177.78&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;178.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&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\20&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&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 3&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;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&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;4/26&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;184.615&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\6&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;200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>