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2L 2s: Difference between revisions

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Wikispaces>JosephRuhf
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m == Intervals == {{MOS intervals}}
 
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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>
 
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-09-13 18:45:48 UTC</tt>.<br>
{{MOS intro}}
: The original revision id was <tt>559134359</tt>.<br>
 
: The revision comment was: <tt></tt><br>
This scale is the parent of all half-octave-repeating MOS scales.
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>
== Names ==
<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">This tetrad has the special property that it is the smallest collection of notes which can create the feeling of "completely representing&lt;span style="line-height: 1.5;"&gt;" a particular regular temperament in a "standard" way. However, it only works in even-numbered edxs, for it contains sqrt(x), and it becomes a very weakly "complete" representation of a regular temperament as L:s grows large.&lt;/span&gt;
[[TAMNAMS]] uses the name '''biwood''', based on the n-wood series.
Golden bi-equal tetrad: 0-phi-phi+1-2*phi+1/(2*phi+2)edx in edo: major 0-370.82-600-970.82 cents, minor 0-229.18-600-829.18 cents
 
Natural logarithm bi-equal tetrad: 0-e-e+1-2e+1/(2e+2)edx in edo: major 0-438.635.82-600-1038.635 cents, minor 0-162.365-600-762.365 cents
== Modes ==
Bi-equal wheel tetrad: 0-pi-pi+1-tau+1/(2*tau+2)edx in edo: major 0-455.128-600-1055.128 cents, &lt;span style="line-height: 1.5;"&gt;minor 0-144.872-600-744.872 cents&lt;/span&gt;</pre></div>
{{MOS mode degrees}}
<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;2L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tetrad has the special property that it is the smallest collection of notes which can create the feeling of &amp;quot;completely representing&lt;span style="line-height: 1.5;"&gt;&amp;quot; a particular regular temperament in a &amp;quot;standard&amp;quot; way. However, it only works in even-numbered edxs, for it contains sqrt(x), and it becomes a very weakly &amp;quot;complete&amp;quot; representation of a regular temperament as L:s grows large.&lt;/span&gt;&lt;br /&gt;
== Intervals ==
Golden bi-equal tetrad: 0-phi-phi+1-2*phi+1/(2*phi+2)edx in edo: major 0-370.82-600-970.82 cents, minor 0-229.18-600-829.18 cents&lt;br /&gt;
{{MOS intervals}}
Natural logarithm bi-equal tetrad: 0-e-e+1-2e+1/(2e+2)edx in edo: major 0-438.635.82-600-1038.635 cents, minor 0-162.365-600-762.365 cents&lt;br /&gt;
 
Bi-equal wheel tetrad: 0-pi-pi+1-tau+1/(2*tau+2)edx in edo: major 0-455.128-600-1055.128 cents, &lt;span style="line-height: 1.5;"&gt;minor 0-144.872-600-744.872 cents&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)
* Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)
 
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 1\4 || || || || || || 300.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 6\22 || 327.273 || 6 || 5 || 1.200 ||
|-
| || || || || 5\18 || || 333.333 || 5 || 4 || 1.250 ||
|-
| || || || || || 9\32 || 337.500 || 9 || 7 || 1.286 ||
|-
| || || || 4\14 || || || 342.857 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\38 || 347.368 || 11 || 8 || 1.375 ||
|-
| || || || || 7\24 || || 350.000 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\34 || 352.941 || 10 || 7 || 1.429 ||
|-
| || || 3\10 || || || || 360.000 || 3 || 2 || 1.500 ||
|-
| || || || || || 11\36 || 366.667 || 11 || 7 || 1.571 || [[Baladic]]
|-
| || || || || 8\26 || || 369.231 || 8 || 5 || 1.600 ||
|-
| || || || || || 13\42 || 371.429 || 13 || 8 || 1.625 || Golden [[Lemba]] (370.8204¢)
|-
| || || || 5\16 || || || 375.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 12\38 || 378.947 || 12 || 7 || 1.714 ||
|-
| || || || || 7\22 || || 381.818 || 7 || 4 || 1.750 ||
|-
| || || || || || 9\28 || 385.714 || 9 || 5 || 1.800 ||
|-
| || 2\6 || || || || || 400.000 || 2 || 1 || 2.000 || Basic 2L 2s  
|-
| || || || || || 9\26 || 415.385 || 9 || 4 || 2.250 || [[Unidec]] is around here
|-
| || || || || 7\20 || || 420.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 12\34 || 423.529 || 12 || 5 || 2.400 ||
|-
| || || || 5\14 || || || 428.571 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\36 || 433.333 || 13 || 5 || 2.600 || Golden [[Hedgehog]]-[[supers]] (434.1641¢)
|-
| || || || || 8\22 || || 436.364 || 8 || 3 || 2.667 ||
|-
| || || || || || 11\30 || 440.000 || 11 || 4 || 2.750 ||
|-
| || || 3\8 || || || || 450.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 10\26 || 461.538 || 10 || 3 || 3.333 || [[Fifive]]
|-
| || || || || 7\18 || || 466.667 || 7 || 2 || 3.500 ||
|-
| || || || || || 11\28 || 471.429 || 11 || 3 || 3.667 ||
|-
| || || || 4\10 || || || 480.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 9\22 || 490.909 || 9 || 2 || 4.500 || [[Diaschismic]] / [[Pajara]]
|-
| || || || || 5\12 || || 500.000 || 5 || 1 || 5.000 || [[Injera]] is around here
|-
| || || || || || 6\14 || 514.286 || 6 || 1 || 6.000 || [[Vishnu]]↓
|-
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
|}
 
{{todo|expand}}
[[Category:Tetrad]]
[[Category:4-tone scales]]
Retrieved from "https://en.xen.wiki/w/2L_2s"