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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>

Revision as of 00:00, 17 July 2018

The minimum harmonic entropy scale with this MOS pattern is diminished[8], basically the familiar 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.)

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
Retrieved from "https://en.xen.wiki/index.php?title=4L_4s&oldid=831"