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2L 4s: Difference between revisions

VisualWikitext
Wikispaces>keenanpepper
**Imported revision 222582054 - Original comment: **
 
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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:keenanpepper|keenanpepper]] and made on <tt>2011-04-24 21:19:31 UTC</tt>.<br>
| Periods = 2
: The original revision id was <tt>222582054</tt>.<br>
| nLargeSteps = 2
: The revision comment was: <tt></tt><br>
| nSmallSteps = 4
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 1
<h4>Original Wikitext content:</h4>
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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]], 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. The true MOS is always proper, but the near-MOS is only proper if the generator is larger than 1\8 of an octave (150 cents).
{{MOS intro}}
||||||||||||||||||||||~ 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 for near-MOS ||
||  ||  ||  || 3\22 ||  ||  ||  ||  ||  ||  ||  || 163.64 || Hedgehog is around here ||
||  ||  || 2\14 ||  ||  ||  ||  ||  ||  ||  ||  || 171.43 ||  ||
|| 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"&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. The true MOS is always proper, but the near-MOS is only proper if the generator is larger than 1\8 of an octave (150 cents).&lt;br /&gt;


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).


&lt;table class="wiki_table"&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;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;
        &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;
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&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
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&lt;/td&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;50&lt;br /&gt;
&lt;/td&gt;
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&lt;/td&gt;
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&lt;/td&gt;
        &lt;td&gt;2\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;52.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Shrutar is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
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        &lt;td&gt;1\22&lt;br /&gt;
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&lt;/td&gt;
        &lt;td&gt;54.55&lt;br /&gt;
&lt;/td&gt;
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&lt;/td&gt;
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        &lt;td&gt;60&lt;br /&gt;
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        &lt;td&gt;66.67&lt;br /&gt;
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        &lt;td&gt;1\14&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;2\22&lt;br /&gt;
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&lt;/td&gt;
        &lt;td&gt;109.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Srutal/Pajara is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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        &lt;td&gt;&lt;br /&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;150&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Boundary of propriety for near-MOS&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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        &lt;td&gt;&lt;br /&gt;
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&lt;/td&gt;
        &lt;td&gt;163.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hedgehog is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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        &lt;td&gt;2\14&lt;br /&gt;
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        &lt;td&gt;171.43&lt;br /&gt;
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        &lt;td&gt;200&lt;br /&gt;
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&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
 
== 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]]
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