2L 2s: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

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 19:02:48 UTC</tt>~~.~~<br>~~

~~: The original revision id was <tt>559135183</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<span style~~="~~line-height: 1.5;~~">" 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.<~~/~~span>~~

[[TAMNAMS]] uses the name '''biwood''', based on the n-wood series.

~~Golden bi~~-~~equal tetrad: major 0-phi-phi+~~1~~-2*phi+~~1~~, minor 0-~~1-~~phi+~~1-~~phi+2/(2*phi+2)edx~~

~~in edo: major 0-370~~.~~82-600-970~~.~~82 cents, minor 0~~-~~229~~.~~18-600-829~~.~~18 cents~~

== Modes ==

~~Natural logarithm bi~~-~~equal tetrad: major 0-e-e+~~1-~~2e+~~1~~, minor 0~~-1-e+1-e+2~~/(2e+2)edx~~

~~in edo: major 0~~-~~438~~.~~635~~.82-600-~~1038~~.~~635 cents, minor 0-162~~.~~365-600-762~~.~~365 cents~~

Bi-~~equal wheel tetrad: major 0-pi-pi+~~1-~~tau+~~1~~, minor 0~~-1-~~pi+~~1-~~pi+~~2/(2*tau+2~~)edx~~

== Intervals ==

~~in edo: major 0~~-~~455~~.~~128~~-~~600-1055~~.~~128 cents, <span style="line~~-~~height: 1~~.5~~;">minor 0~~-~~144~~.~~872-600-744~~.~~872 cents</span></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"><html><head><title>2L 2s</title></head><body>This tetrad has the special property that it is the smallest collection of notes which can create the feeling of &quot;completely representing<span style="line-height: 1.5~~;">&quot; a particular regular temperament in a &quot;standard&quot; way~~. ~~However, it only works in even~~-~~numbered edxs, for it contains sqrt~~(x)~~, and it becomes a very weakly &quot;complete&quot; representation of a regular temperament as L:s grows large.</span><br />~~

== Scale tree ==

~~Golden bi-equal tetrad: major 0-phi-phi+1~~-2*phi+1, minor 0-~~1-phi+1-phi+~~2~~/(2*phi+2)edx<br />~~

Generator ranges:

~~in edo: major 0~~-~~370~~.~~82-600-970~~.~~82 cents, minor 0~~-~~229~~.~~18-600-829~~.~~18 cents<br />~~

* Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)

~~Natural logarithm bi~~-~~equal tetrad: major 0-e-e+1-2e+1, minor 0-1-e+1-e+~~2~~/(2e+2)edx<br />~~

* Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)

~~in edo: major 0~~-~~438~~.~~635~~.82-~~600-1038~~.~~635 cents, minor 0~~-~~162~~.~~365-600-762~~.~~365 cents<br~~ /~~>~~

Bi-~~equal wheel tetrad: major 0-pi-pi+~~1-~~tau+~~1~~, minor 0~~-1~~-pi+1-pi+~~2~~/(2*tau+2)edx<br />~~

{| class="wikitable center-all"

~~in edo: major 0-455.128-~~600~~-1055~~.~~128 cents, <span style="line-height:~~ 1~~.5;">minor~~ 0-~~144.872-600-744.872 cents</span></body></html></pre></div>~~

! 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 ||

|}

[[Category:Tetrad]]

[[Category:4-tone scales]]

@@ Line 1: / Line 1: @@
-<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 19:02:48 UTC</tt>.<br>
+{{MOS intro}}
-: The original revision id was <tt>559135183</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: major 0-phi-phi+1-2*phi+1, minor 0-1-phi+1-phi+2/(2*phi+2)edx
-in edo: major 0-370.82-600-970.82 cents, minor 0-229.18-600-829.18 cents
+== Modes ==
-Natural logarithm bi-equal tetrad: major 0-e-e+1-2e+1, minor 0-1-e+1-e+2/(2e+2)edx
+{{MOS mode degrees}}
-in edo: major 0-438.635.82-600-1038.635 cents, minor 0-162.365-600-762.365 cents
-Bi-equal wheel tetrad: major 0-pi-pi+1-tau+1, minor 0-1-pi+1-pi+2/(2*tau+2)edx
+== Intervals ==
-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 intervals}}
-<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;
+== Scale tree ==
-Golden bi-equal tetrad: major 0-phi-phi+1-2*phi+1, minor 0-1-phi+1-phi+2/(2*phi+2)edx&lt;br /&gt;
+Generator ranges:
-in edo: major 0-370.82-600-970.82 cents, minor 0-229.18-600-829.18 cents&lt;br /&gt;
+* Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)
-Natural logarithm bi-equal tetrad: major 0-e-e+1-2e+1, minor 0-1-e+1-e+2/(2e+2)edx&lt;br /&gt;
+* Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)
-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: major 0-pi-pi+1-tau+1, minor 0-1-pi+1-pi+2/(2*tau+2)edx&lt;br /&gt;
+{| class="wikitable center-all"
-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>
+! 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]]