11L 3s: Difference between revisions

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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>
| Other names = Ketradektriatoh
: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-04-30 03:32:52 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>327194864</tt>.<br>
| nLargeSteps = 11
: The revision comment was: <tt></tt><br>
| nSmallSteps = 3
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 5
<h4>Original Wikitext content:</h4>
| Collapsed = 4
<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">=&lt;span style="color: #800061; font-size: 103%;"&gt;The Ketradektriatoh Scale&lt;/span&gt;=  
| Pattern = LLLLsLLLLsLLLs
}}
{{MOS intro|Other Names=}}


This is a type of scale which denotes the use of a scale placed between [[11edo|11]] and [[14edo|14]] ED2's, employing a ratio generator between 41/32 ~ 9/7 (being [[25edo|25-ED2]] the middle size of the Ketradektriatoh spectrum, in the 2;1 relation), resulting in a variant of tetradecatonic scale comforms by this form: LLLsLLLLsLLLLs.
== Name ==
Vector Graphics proposes '''ketradekic''' as a name for this scale, based on the name "Ketradektriatoh scale" proposed by [[Osmiorisbendi‎]], adapted to fit scale naming conventions.


__**ED2s that contains this scale:**__
== Modes ==
{{MOS modes}}


**2 2 2 1 2 2 2 2 1 2 2 2 2 1: [[25edo|25]]**
== Intervals ==
3 3 3 1 3 3 3 3 1 3 3 3 3 1: [[36edo|36]]
{{MOS intervals}}
**3 3 3 2 3 3 3 3 2 3 3 3 3 2: [[39edo|39]]**


**4 4 4 1 4 4 4 4 1 4 4 4 4 1: [[47edo|47]]**
== Scale tree ==
4 4 4 2 4 4 4 4 2 4 4 4 4 2: [[50edo|50]]
{{MOS tuning spectrum}}
**4 4 4 3 4 4 4 4 3 4 4 4 4 3: [[53edo|53]]**


5 5 5 2 5 5 5 5 2 5 5 5 5 2: [[61edo|61]]
{{todo|expand}}
5 5 5 3 5 5 5 5 3 5 5 5 5 3: [[64edo|64]]


7 7 7 2 7 7 7 7 2 7 7 7 7 2: [[83edo|83]]
[[Category:14-tone scales]]
7 7 7 3 7 7 7 7 3 7 7 7 7 3: [[86edo|86]]
7 7 7 4 7 7 7 7 4 7 7 7 7 4: [[89edo|89]]
7 7 7 5 7 7 7 7 5 7 7 7 7 5: [[92edo|92]]
 
9 9 9 4 9 9 9 9 4 9 9 9 9 4: [[111edo|111]]
9 9 9 5 9 9 9 9 5 9 9 9 9 5: [[114edo|114]]
 
11 11 11 4 11 11 11 11 4 11 11 11 11 4: [[133edo|133]]
11 11 11 5 11 11 11 11 5 11 11 11 11 5: [[136edo|136]]
11 11 11 6 11 11 11 11 6 11 11 11 11 6: [[139edo|139]]
11 11 11 7 11 11 11 11 7 11 11 11 11 7: [[142edo|142]]
 
13 13 13 5 13 13 13 13 5 13 13 13 13 5: [[158edo|158]]
13 13 13 6 13 13 13 13 6 13 13 13 13 6: [[161edo|161]]
13 13 13 7 13 13 13 13 7 13 13 13 13 7: [[164edo|164]]
13 13 13 8 13 13 13 13 8 13 13 13 13 8: [[167edo|167]]</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;11L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="The Ketradektriatoh Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #800061; font-size: 103%;"&gt;The Ketradektriatoh Scale&lt;/span&gt;&lt;/h1&gt;
&lt;br /&gt;
This is a type of scale which denotes the use of a scale placed between &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt; and &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt; ED2's, employing a ratio generator between 41/32 ~ 9/7 (being &lt;a class="wiki_link" href="/25edo"&gt;25-ED2&lt;/a&gt; the middle size of the Ketradektriatoh spectrum, in the 2;1 relation), resulting in a variant of tetradecatonic scale comforms by this form: LLLsLLLLsLLLLs.&lt;br /&gt;
&lt;br /&gt;
&lt;u&gt;&lt;strong&gt;ED2s that contains this scale:&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;2 2 2 1 2 2 2 2 1 2 2 2 2 1: &lt;a class="wiki_link" href="/25edo"&gt;25&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
3 3 3 1 3 3 3 3 1 3 3 3 3 1: &lt;a class="wiki_link" href="/36edo"&gt;36&lt;/a&gt;&lt;br /&gt;
&lt;strong&gt;3 3 3 2 3 3 3 3 2 3 3 3 3 2: &lt;a class="wiki_link" href="/39edo"&gt;39&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;4 4 4 1 4 4 4 4 1 4 4 4 4 1: &lt;a class="wiki_link" href="/47edo"&gt;47&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
4 4 4 2 4 4 4 4 2 4 4 4 4 2: &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;&lt;br /&gt;
&lt;strong&gt;4 4 4 3 4 4 4 4 3 4 4 4 4 3: &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
5 5 5 2 5 5 5 5 2 5 5 5 5 2: &lt;a class="wiki_link" href="/61edo"&gt;61&lt;/a&gt;&lt;br /&gt;
5 5 5 3 5 5 5 5 3 5 5 5 5 3: &lt;a class="wiki_link" href="/64edo"&gt;64&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
7 7 7 2 7 7 7 7 2 7 7 7 7 2: &lt;a class="wiki_link" href="/83edo"&gt;83&lt;/a&gt;&lt;br /&gt;
7 7 7 3 7 7 7 7 3 7 7 7 7 3: &lt;a class="wiki_link" href="/86edo"&gt;86&lt;/a&gt;&lt;br /&gt;
7 7 7 4 7 7 7 7 4 7 7 7 7 4: &lt;a class="wiki_link" href="/89edo"&gt;89&lt;/a&gt;&lt;br /&gt;
7 7 7 5 7 7 7 7 5 7 7 7 7 5: &lt;a class="wiki_link" href="/92edo"&gt;92&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
9 9 9 4 9 9 9 9 4 9 9 9 9 4: &lt;a class="wiki_link" href="/111edo"&gt;111&lt;/a&gt;&lt;br /&gt;
9 9 9 5 9 9 9 9 5 9 9 9 9 5: &lt;a class="wiki_link" href="/114edo"&gt;114&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
11 11 11 4 11 11 11 11 4 11 11 11 11 4: &lt;a class="wiki_link" href="/133edo"&gt;133&lt;/a&gt;&lt;br /&gt;
11 11 11 5 11 11 11 11 5 11 11 11 11 5: &lt;a class="wiki_link" href="/136edo"&gt;136&lt;/a&gt;&lt;br /&gt;
11 11 11 6 11 11 11 11 6 11 11 11 11 6: &lt;a class="wiki_link" href="/139edo"&gt;139&lt;/a&gt;&lt;br /&gt;
11 11 11 7 11 11 11 11 7 11 11 11 11 7: &lt;a class="wiki_link" href="/142edo"&gt;142&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
13 13 13 5 13 13 13 13 5 13 13 13 13 5: &lt;a class="wiki_link" href="/158edo"&gt;158&lt;/a&gt;&lt;br /&gt;
13 13 13 6 13 13 13 13 6 13 13 13 13 6: &lt;a class="wiki_link" href="/161edo"&gt;161&lt;/a&gt;&lt;br /&gt;
13 13 13 7 13 13 13 13 7 13 13 13 13 7: &lt;a class="wiki_link" href="/164edo"&gt;164&lt;/a&gt;&lt;br /&gt;
13 13 13 8 13 13 13 13 8 13 13 13 13 8: &lt;a class="wiki_link" href="/167edo"&gt;167&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 06:29, 18 June 2025

↖ 10L 2s ↑ 11L 2s 12L 2s ↗
← 10L 3s 11L 3s 12L 3s →
↙ 10L 4s ↓ 11L 4s 12L 4s ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLs
sLLLsLLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\14 to 4\11 (428.6 ¢ to 436.4 ¢)
Dark 7\11 to 9\14 (763.6 ¢ to 771.4 ¢)
TAMNAMS information
Related to 3L 5s (checkertonic)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 3L 8s
Sister 3L 11s
Daughters 14L 11s, 11L 14s
Neutralized 8L 6s
2-Flought 25L 3s, 11L 17s
Equal tunings
Equalized (L:s = 1:1) 5\14 (428.6 ¢)
Supersoft (L:s = 4:3) 19\53 (430.2 ¢)
Soft (L:s = 3:2) 14\39 (430.8 ¢)
Semisoft (L:s = 5:3) 23\64 (431.2 ¢)
Basic (L:s = 2:1) 9\25 (432.0 ¢)
Semihard (L:s = 5:2) 22\61 (432.8 ¢)
Hard (L:s = 3:1) 13\36 (433.3 ¢)
Superhard (L:s = 4:1) 17\47 (434.0 ¢)
Collapsed (L:s = 1:0) 4\11 (436.4 ¢)

11L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 3 small steps, repeating every octave. 11L 3s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 428.6 ¢ to 436.4 ¢, or from 763.6 ¢ to 771.4 ¢.

Name

Vector Graphics proposes ketradekic as a name for this scale, based on the name "Ketradektriatoh scale" proposed by Osmiorisbendi‎, adapted to fit scale naming conventions.

Modes

Modes of 11L 3s
UDP Cyclic
order		 Step
pattern
13|0 1 LLLLsLLLLsLLLs
12|1 6 LLLLsLLLsLLLLs
11|2 11 LLLsLLLLsLLLLs
10|3 2 LLLsLLLLsLLLsL
9|4 7 LLLsLLLsLLLLsL
8|5 12 LLsLLLLsLLLLsL
7|6 3 LLsLLLLsLLLsLL
6|7 8 LLsLLLsLLLLsLL
5|8 13 LsLLLLsLLLLsLL
4|9 4 LsLLLLsLLLsLLL
3|10 9 LsLLLsLLLLsLLL
2|11 14 sLLLLsLLLLsLLL
1|12 5 sLLLLsLLLsLLLL
0|13 10 sLLLsLLLLsLLLL

Intervals

Intervals of 11L 3s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 109.1 ¢
2-mosstep Minor 2-mosstep m2ms L + s 109.1 ¢ to 171.4 ¢
Major 2-mosstep M2ms 2L 171.4 ¢ to 218.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 218.2 ¢ to 257.1 ¢
Major 3-mosstep M3ms 3L 257.1 ¢ to 327.3 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 327.3 ¢ to 342.9 ¢
Major 4-mosstep M4ms 4L 342.9 ¢ to 436.4 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 327.3 ¢ to 428.6 ¢
Perfect 5-mosstep P5ms 4L + s 428.6 ¢ to 436.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 436.4 ¢ to 514.3 ¢
Major 6-mosstep M6ms 5L + s 514.3 ¢ to 545.5 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 545.5 ¢ to 600.0 ¢
Major 7-mosstep M7ms 6L + s 600.0 ¢ to 654.5 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 654.5 ¢ to 685.7 ¢
Major 8-mosstep M8ms 7L + s 685.7 ¢ to 763.6 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 763.6 ¢ to 771.4 ¢
Augmented 9-mosstep A9ms 8L + s 771.4 ¢ to 872.7 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 763.6 ¢ to 857.1 ¢
Major 10-mosstep M10ms 8L + 2s 857.1 ¢ to 872.7 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 872.7 ¢ to 942.9 ¢
Major 11-mosstep M11ms 9L + 2s 942.9 ¢ to 981.8 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 981.8 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 10L + 2s 1028.6 ¢ to 1090.9 ¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 1090.9 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 11L + 2s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 11L + 3s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 11L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\14 428.571 771.429 1:1 1.000 Equalized 11L 3s
29\81 429.630 770.370 6:5 1.200
24\67 429.851 770.149 5:4 1.250
43\120 430.000 770.000 9:7 1.286
19\53 430.189 769.811 4:3 1.333 Supersoft 11L 3s
52\145 430.345 769.655 11:8 1.375
33\92 430.435 769.565 7:5 1.400
47\131 430.534 769.466 10:7 1.429
14\39 430.769 769.231 3:2 1.500 Soft 11L 3s
51\142 430.986 769.014 11:7 1.571
37\103 431.068 768.932 8:5 1.600
60\167 431.138 768.862 13:8 1.625
23\64 431.250 768.750 5:3 1.667 Semisoft 11L 3s
55\153 431.373 768.627 12:7 1.714
32\89 431.461 768.539 7:4 1.750
41\114 431.579 768.421 9:5 1.800
9\25 432.000 768.000 2:1 2.000 Basic 11L 3s
Scales with tunings softer than this are proper
40\111 432.432 767.568 9:4 2.250
31\86 432.558 767.442 7:3 2.333
53\147 432.653 767.347 12:5 2.400
22\61 432.787 767.213 5:2 2.500 Semihard 11L 3s
57\158 432.911 767.089 13:5 2.600
35\97 432.990 767.010 8:3 2.667
48\133 433.083 766.917 11:4 2.750
13\36 433.333 766.667 3:1 3.000 Hard 11L 3s
43\119 433.613 766.387 10:3 3.333
30\83 433.735 766.265 7:2 3.500
47\130 433.846 766.154 11:3 3.667
17\47 434.043 765.957 4:1 4.000 Superhard 11L 3s
38\105 434.286 765.714 9:2 4.500
21\58 434.483 765.517 5:1 5.000
25\69 434.783 765.217 6:1 6.000
4\11 436.364 763.636 1:0 → ∞ Collapsed 11L 3s
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