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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The minimum harmonic entropy scale with this [[MOSScales|MOS]] pattern is [[Jubilismic_clan|diminished]][8], basically the familiar [[Octatonic_scale|octatonic scale]] of 12edo.
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 11:10:13 UTC</tt>.<br>
: The original revision id was <tt>565317985</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">The minimum harmonic entropy scale with this [[MOSScales|MOS]] pattern is [[Jubilismic clan|diminished]][8], basically the familiar [[Octatonic scale|octatonic scale]] of 12edo.


There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\4 ||  ||  ||  ||  || 0 ||=  ||
||  ||  ||  ||  || 1\24 || 50 ||  ||
||  ||  ||  || 1\20 ||  || 60 ||= L/s = 4 ||
||  ||  ||  ||  ||  || 300/(1+pi) ||  ||
||  ||  || 1\16 ||  ||  || 75 ||= L/s = 3 ||
||  ||  ||  ||  ||  || 300/(1+e) ||  ||
||  ||  ||  ||  || 3\44 || 81.82 ||  ||
||  ||  ||  || 2\28 ||  || 85.71 ||  ||
||  || 1\12 ||  ||  ||  || 100 ||= Diminished is around here
Optimum rank range (L/s=2/1) for MOS ||
||  ||  ||  ||  ||  || 300/(1+sqrt(3)) ||  ||
||  ||  ||  || 3\32 ||  || 112.5 ||=  ||
||  ||  ||  ||  || 5\52 || 115.38 ||= Golden diminished ||
||  ||  ||  ||  ||  || 300/(1+pi/2) ||  ||
||  ||  || 2\20 ||  ||  || 120 ||=  ||
|| 1\8 ||  ||  ||  ||  || 150 ||=  ||</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;4L 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The minimum harmonic entropy scale with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern is &lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;diminished&lt;/a&gt;[8], basically the familiar &lt;a class="wiki_link" href="/Octatonic%20scale"&gt;octatonic scale&lt;/a&gt; of 12edo.&lt;br /&gt;
&lt;br /&gt;
There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)&lt;br /&gt;


{| class="wikitable"
|-
! colspan="5" | Generator
! | Cents
! | Comments
|-
| | 0\4
| |
| |
| |
| |
| | 0
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 1\24
| | 50
| |
|-
| |
| |
| |
| | 1\20
| |
| | 60
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| |
| | 300/(1+pi)
| |
|-
| |
| |
| | 1\16
| |
| |
| | 75
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| | 300/(1+e)
| |
|-
| |
| |
| |
| |
| | 3\44
| | 81.82
| |
|-
| |
| |
| |
| | 2\28
| |
| | 85.71
| |
|-
| |
| | 1\12
| |
| |
| |
| | 100
| style="text-align:center;" | Diminished is around here


&lt;table class="wiki_table"&gt;
Optimum rank range (L/s=2/1) for MOS
    &lt;tr&gt;
|-
        &lt;th colspan="5"&gt;Generator&lt;br /&gt;
| |
&lt;/th&gt;
| |
        &lt;th&gt;Cents&lt;br /&gt;
| |
&lt;/th&gt;
| |
        &lt;th&gt;Comments&lt;br /&gt;
| |
&lt;/th&gt;
| | 300/(1+sqrt(3))
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;0\4&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 3\32
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 112.5
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;0&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| | 5\52
&lt;/td&gt;
| | 115.38
    &lt;/tr&gt;
| style="text-align:center;" | Golden diminished
    &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;
| | 300/(1+pi/2)
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;1\24&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;50&lt;br /&gt;
| | 2\20
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 120
    &lt;/tr&gt;
| style="text-align:center;" |
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 1\8
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 150
        &lt;td&gt;1\20&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|}
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60&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;&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;300/(1+pi)&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;1\16&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;75&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;300/(1+e)&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;3\44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81.82&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;2\28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;85.71&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;1\12&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;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diminished is around here&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;300/(1+sqrt(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;3\32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112.5&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;5\52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Golden diminished&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;300/(1+pi/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;2\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;120&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;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;150&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>
Retrieved from "https://en.xen.wiki/w/4L_4s"