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3L 3s: Difference between revisions

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**Imported revision 220730208 - Original comment: **
 
m Apparently I have to be more specific in the ToDo
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = triwood
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-15 21:12:49 UTC</tt>.<br>
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<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">Associated with the [[augmented family]].
| Pattern = LsLsLs
|| 0\3 ||  ||  ||  ||  ||  || 0 ||  ||
}}
||  ||  ||  ||  || 1\15 ||  || 80 ||  ||
||  ||  ||  ||  ||  || 2\27 || 88.88 || Optimal augmented is around here ||
||  ||  ||  || 1\12 ||  ||  || 100 ||  ||
||  ||  || 1\9 ||  ||  ||  || 133.33 ||  ||
||  || 1\6 ||  ||  ||  ||  || 200 ||  ||
||  ||  || 2\9 ||  ||  ||  || 266.67 ||  ||
|| 1\3 ||  ||  ||  ||  ||  || 400 ||  ||
True MOS is LssLssLss but interesting near-MOSs include LsLssLsss and LsLsssLss.</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;3L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Associated with the &lt;a class="wiki_link" href="/augmented%20family"&gt;augmented family&lt;/a&gt;.&lt;br /&gt;


{{MOS intro}}


&lt;table class="wiki_table"&gt;
In addition to the true MOS (LsLsLs or sLsLsL), there are also near-MOS patterns of LLsLss and LLssLs, which are only proper if the generator is larger than [[9edo|1\9]].
    &lt;tr&gt;
        &lt;td&gt;0\3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
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&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
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&lt;/td&gt;
    &lt;/tr&gt;
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&lt;/td&gt;
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&lt;/td&gt;
        &lt;td&gt;1\15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Optimal augmented is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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        &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;1\12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
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&lt;/td&gt;
        &lt;td&gt;100&lt;br /&gt;
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&lt;/td&gt;
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        &lt;td&gt;1\9&lt;br /&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;133.33&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\6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;200&lt;br /&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\9&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;266.67&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\3&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;400&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


True MOS is LssLssLss but interesting near-MOSs include LsLssLsss and LsLsssLss.&lt;/body&gt;&lt;/html&gt;</pre></div>
Out of all ''[[Rothenberg propriety|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.
 
== Intervals ==
{{MOS intervals}}
 
== Modes==
{{MOS mode degrees}}
 
==Scale tree==
{{todo|inline=1|complete table|Convert manually-generated scale tree table to MOS tuning spectrum without losing information from the existing table}}
{| class="wikitable center-all"
! colspan="6" rowspan="2" |Generator
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" | Comments
|-
! Chroma-positive
! Chroma-negative
|-
|1\6|| || ||  || || ||200.000||200.000 || 1||1||1.000||
|-
| || ||  ||  || ||6\33||218.182|| 181.818||6||5||1.200||
|-
| || ||  ||  ||5\27|| ||222.222|| 177.778||5||4||1.250||
|-
| || ||  ||  || ||9\48||225.000|| 175.000||9||7||1.286||Oodako
|-
|  ||  || ||4\21|| || ||228.571|| 171.429||4||3||1.333||
|-
| || ||  ||  || ||11\57||231.579||168.421 || 11 ||8||1.375||
|-
| || || || ||7\36|| ||233.333|| 166.667||7||5||1.400||
|-
| || ||  ||  || ||10\51||235.294||164.706 || 10 ||7||1.428||
|-
| || ||3\15 ||  || || ||240.000|| 160.000|| 3||2||1.500||
|-
| || ||  ||  || ||11\54||244.444||155.556 || 11 ||7||1.571||
|-
| || || || ||8\39|| ||246.154|| 153.846||8||5||1.600||Triforce
|-
| ||  ||  || || ||13\63||247.619||152.381 || 13 ||8||1.625|| Unnamed golden tuning
|-
| || || ||5\24|| || ||250.000|| 150.000||5||3||1.667||
|-
| || ||  ||  || ||12\57||252.632||147.368 || 12 ||7||1.714||
|-
| || || || ||7\33|| ||254.545|| 145.455||7||4||1.750||
|-
| || ||  ||  || ||9\42||257.143|| 142.857||9||5||1.800||
|-
| ||2\9 ||  || || || ||266.667||133.333 || 2||1||2.000||Basic triwood
|-
| ||  ||  || ||  || 9\39||276.923|| 123.077||9||4||2.250||
|-
| || ||  ||  ||7\30|| ||280.000|| 120.000||7||3||2.333||Deflated (optimal around here)
|-
| || || || || ||12\51||282.353||117.647 || 12 ||5||2.400||
|-
| || ||  || 5\21||  ||  ||285.714|| 114.286||5||2||2.500||
|-
| || ||  ||  || ||13\54||288.889||111.111 || 13 ||5||2.600|| Unnamed golden tuning
|-
| || || || ||8\33|| ||290.909|| 109.091||8||3||2.667||
|-
| || ||  ||  || ||11\45||293.333||106.667 || 11 ||4||2.750|| August
|-
| || ||3\12|| || || ||300.000|| 100.000|| 3||1||3.000||Trug (optimal around here)
|-
| || || || || ||10\39||307.692||92.308||10||3||3.333||Augene
|-
| || || || ||7\27|| ||311.111|| 88.889||7 ||2 || 3.500||
|-
| || ||  ||  || ||11\42||314.286||85.714||11||3||3.667||
|-
| || || ||4\15 || || ||320.000|| 80.000||4||1 || 4.000||Inflated
|-
| ||  ||  || || ||9\33 ||327.273|| 72.727||9 || 2|| 4.500||
|-
| || ||  ||  ||5\18|| ||333.333|| 66.667||5 ||1 || 5.000||
|-
| || ||  ||  || ||6\21||342.857|| 57.143||6 || 1|| 6.000||Hemiug↓, hemiaug↓
|-
|1\3 ||  || || || || ||400.000||0.000||1 || 0||→ inf||
|}
 
[[Category:Triwood| ]]
[[Category:6-tone scales]]
<!-- main article -->
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