2L 4s: Difference between revisions

Wikispaces>guest
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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 = malic
: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 03:47:05 UTC</tt>.<br>
| Periods = 2
: The original revision id was <tt>249047315</tt>.<br>
| nLargeSteps = 2
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| nSmallSteps = 4
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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">The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of harmonic entropy is [[Diaschismic family|srutal/pajara]], in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is **half** of that (about a quartertone), so 3/2 is a period plus two generators; and [[Porcupine family#Hedgehog|hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).
| Pattern = LssLss
}}


In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.
{{MOS intro}}


Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
The only scale with this mos pattern that is a really significant minimum of [[harmonic entropy]] is [[srutal]]/[[pajara]], in which the period plus the generator is 3/2. Other scales include [[shrutar]], in which the generator is ''half'' of that (about a [[quartertone]]), so 3/2 is a period plus two generators; and [[hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it does not appear in this mos).
||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\2 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  || 0 ||=  ||
||  ||  ||  ||  ||  ||  ||  ||  ||  || 1\24 ||  || 50 ||=  ||
||  ||  ||  ||  ||  ||  ||  ||  ||  ||  || 2\46 || 52.17 ||= Shrutar is around here ||
||  ||  ||  ||  ||  ||  ||  ||  || 1\22 ||  ||  || 54.55 ||=  ||
||  ||  ||  ||  ||  ||  ||  || 1\20 ||  ||  ||  || 60 ||=  ||
||  ||  ||  ||  ||  ||  || 1\18 ||  ||  ||  ||  || 66.67 ||=  ||
||  ||  ||  ||  ||  || 1\16 ||  ||  ||  ||  ||  || 75 ||=  ||
||  ||  ||  ||  || 1\14 ||  ||  ||  ||  ||  ||  || 85.71 ||=  ||
||  ||  ||  || 1\12 ||  ||  ||  ||  ||  ||  ||  || 100 ||=  ||
||  ||  ||  ||  || 2\22 ||  ||  ||  ||  ||  ||  || 109.09 ||= Srutal/Pajara is around here ||
||  ||  || 1\10 ||  ||  ||  ||  ||  ||  ||  ||  || 120 ||=  ||
||  || 1\8 ||  ||  ||  ||  ||  ||  ||  ||  ||  || 150 ||= Boundary of propriety (generators
larger than this are proper) ||
||  ||  ||  || 3\22 ||  ||  ||  ||  ||  ||  ||  || 163.64 ||= Hedgehog and echidna are both around here ||
||  ||  ||  ||  ||  || 8\58 ||  ||  ||  ||  ||  || 165.52 ||=  ||
||  ||  ||  ||  ||  ||  || 13\94 ||  ||  ||  ||  || 165.96 ||= Golden hedgehog/echidna ||
||  ||  ||  ||  || 5\36 ||  ||  ||  ||  ||  ||  || 166.67 ||=  ||
||  ||  || 2\14 ||  ||  ||  ||  ||  ||  ||  ||  || 171.43 ||= Optimum rank range (L/s=3/2) ||
|| 1\6 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  || 200 ||=  ||</pre></div>
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;2L 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The only scale with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern that's a really significant minimum of harmonic entropy is &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal/pajara&lt;/a&gt;, in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is &lt;strong&gt;half&lt;/strong&gt; of that (about a quartertone), so 3/2 is a period plus two generators; and &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).&lt;br /&gt;
&lt;br /&gt;
In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.&lt;br /&gt;
&lt;br /&gt;
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.&lt;br /&gt;


In addition to the true mos with pattern LssLss, all these scales also come in a near-mos version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.


&lt;table class="wiki_table"&gt;
Srutal/pajara probably has the lowest harmonic entropy of all 6-note mos scales. The near-mos version has even lower harmonic entropy.
    &lt;tr&gt;
        &lt;th colspan="11"&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;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0\2&lt;br /&gt;
&lt;/td&gt;
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&lt;/td&gt;
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        &lt;td&gt;0&lt;br /&gt;
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        &lt;td&gt;1\24&lt;br /&gt;
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        &lt;td&gt;50&lt;br /&gt;
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        &lt;td&gt;2\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;52.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Shrutar 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;
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        &lt;td&gt;54.55&lt;br /&gt;
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        &lt;td&gt;66.67&lt;br /&gt;
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        &lt;td&gt;75&lt;br /&gt;
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        &lt;td&gt;85.71&lt;br /&gt;
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        &lt;td&gt;100&lt;br /&gt;
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&lt;/td&gt;
        &lt;td&gt;109.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Srutal/Pajara is around here&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;1\10&lt;br /&gt;
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        &lt;td&gt;120&lt;br /&gt;
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        &lt;td&gt;1\8&lt;br /&gt;
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&lt;/td&gt;
        &lt;td&gt;150&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
larger than this are proper)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;3\22&lt;br /&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;163.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Hedgehog and echidna are both around here&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;165.52&lt;br /&gt;
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        &lt;td&gt;13\94&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;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;&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;&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;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;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;&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;Optimum rank range (L/s=3/2)&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;&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>
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 9/7 = [[Unidec]]
| 13/8 = Golden [[hedgehog]]/[[echidna]]
| 5/3 = Hedgehog (optimal around here)
| 9/4 = [[Crepuscular]]
| 8/3 = [[Octokaidecal]]
| 7/2 = [[Pajara]]
| 9/2 = [[Injera]]
| 6/1 = [[Shrutar]]&nbsp;↓
}}
 
[[Category:6-tone scales]]