12L 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>
{{MOS intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-24 10:37:30 UTC</tt>.<br>
: The original revision id was <tt>552006300</tt>.<br>
: The revision comment was: <tt></tt><br>
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>
<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 is an Augene MOS which is generated by a neutral semitone (1/15edo to 1/12edo, 80 to 100 cents). Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].
|| 1/15 ||  ||  ||  ||  || 80 ||
||  ||  ||  ||  || 5/72 || 83 1/3 ||
||  ||  ||  || 4/57 ||  || 84.210526 ||
||  ||  ||  ||  || 7/99 || 84 28/33 ||
||  ||  || 3/42 ||  ||  || 85 5/7 ||
||  ||  ||  ||  || 8/111 || 86 18/37 ||
||  ||  ||  || 5/69 ||  || 86.956522 ||
||  ||  ||  ||  || 7/96 || 87.5 ||
||  || 2/27 ||  ||  ||  || 88 8/9 ||
||  ||  ||  ||  || 7/93 || 90.322581 ||
||  ||  ||  || 5/66 ||  || 90 10/11 ||
||  ||  ||  ||  || 8/105 || 91 3/7 ||
||  ||  ||  ||  ||  || 91.577619 ||
||  ||  || 3/39 ||  ||  || 92 4/13 ||
||  ||  ||  ||  ||  || 92.628832 ||
||  ||  ||  ||  || 7/90 || 93 1/3 ||
||  ||  ||  || 4/51 ||  || 94.117647 ||
||  ||  ||  ||  || 5/63 || 95.238095 ||
|| 1/12 ||  ||  ||  ||  || 100 ||</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;12L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is an Augene MOS which is generated by a neutral semitone (1/15edo to 1/12edo, 80 to 100 cents). Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].&lt;br /&gt;


Having three [[period]]s of [[4L 1s]], it may be more specifically referred to as the [[Ternary]] mode of [[Augene]][15].


&lt;table class="wiki_table"&gt;
== Modes ==
    &lt;tr&gt;
{{MOS modes}}
        &lt;td&gt;1/15&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;80&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;5/72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;83 1/3&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;4/57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;84.210526&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;7/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;84 28/33&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;3/42&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;85 5/7&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;8/111&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;86 18/37&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;5/69&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;86.956522&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;7/96&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;87.5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/27&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;88 8/9&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;7/93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90.322581&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;5/66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90 10/11&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;8/105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;91 3/7&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;91.577619&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;3/39&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;92 4/13&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;92.628832&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;7/90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;93 1/3&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;4/51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;94.117647&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;5/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;95.238095&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/12&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;100&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{{MOS intervals}}
 
== Scale tree ==
{{MOS tuning spectrum}}
 
{{todo|expand}}
 
[[Category:15-tone scales]]

Latest revision as of 16:43, 28 February 2025

↖ 11L 2s ↑ 12L 2s 13L 2s ↗
← 11L 3s 12L 3s 13L 3s →
↙ 11L 4s ↓ 12L 4s 13L 4s ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐
│║║║║│║║║║│║║║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLLs
sLLLLsLLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 1\15 to 1\12 (80.0 ¢ to 100.0 ¢)
Dark 3\12 to 4\15 (300.0 ¢ to 320.0 ¢)
TAMNAMS information
Related to 3L 6s (tcherepnin)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 3L 9s
Sister 3L 12s
Daughters 15L 12s, 12L 15s
Neutralized 9L 6s
2-Flought 27L 3s, 12L 18s
Equal tunings
Equalized (L:s = 1:1) 1\15 (80.0 ¢)
Supersoft (L:s = 4:3) 4\57 (84.2 ¢)
Soft (L:s = 3:2) 3\42 (85.7 ¢)
Semisoft (L:s = 5:3) 5\69 (87.0 ¢)
Basic (L:s = 2:1) 2\27 (88.9 ¢)
Semihard (L:s = 5:2) 5\66 (90.9 ¢)
Hard (L:s = 3:1) 3\39 (92.3 ¢)
Superhard (L:s = 4:1) 4\51 (94.1 ¢)
Collapsed (L:s = 1:0) 1\12 (100.0 ¢)

12L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 3 small steps, with a period of 4 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 12L 3s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 80 ¢ to 100 ¢, or from 300 ¢ to 320 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Having three periods of 4L 1s, it may be more specifically referred to as the Ternary mode of Augene[15].

Modes

Modes of 12L 3s
UDP Cyclic
order		 Step
pattern
12|0(3) 1 LLLLsLLLLsLLLLs
9|3(3) 2 LLLsLLLLsLLLLsL
6|6(3) 3 LLsLLLLsLLLLsLL
3|9(3) 4 LsLLLLsLLLLsLLL
0|12(3) 5 sLLLLsLLLLsLLLL

Intervals

Intervals of 12L 3s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 80.0 ¢
Perfect 1-mosstep P1ms L 80.0 ¢ to 100.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 100.0 ¢ to 160.0 ¢
Major 2-mosstep M2ms 2L 160.0 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 200.0 ¢ to 240.0 ¢
Major 3-mosstep M3ms 3L 240.0 ¢ to 300.0 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 300.0 ¢ to 320.0 ¢
Augmented 4-mosstep A4ms 4L 320.0 ¢ to 400.0 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 400.0 ¢
6-mosstep Diminished 6-mosstep d6ms 4L + 2s 400.0 ¢ to 480.0 ¢
Perfect 6-mosstep P6ms 5L + s 480.0 ¢ to 500.0 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 500.0 ¢ to 560.0 ¢
Major 7-mosstep M7ms 6L + s 560.0 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 600.0 ¢ to 640.0 ¢
Major 8-mosstep M8ms 7L + s 640.0 ¢ to 700.0 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 700.0 ¢ to 720.0 ¢
Augmented 9-mosstep A9ms 8L + s 720.0 ¢ to 800.0 ¢
10-mosstep Perfect 10-mosstep P10ms 8L + 2s 800.0 ¢
11-mosstep Diminished 11-mosstep d11ms 8L + 3s 800.0 ¢ to 880.0 ¢
Perfect 11-mosstep P11ms 9L + 2s 880.0 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 900.0 ¢ to 960.0 ¢
Major 12-mosstep M12ms 10L + 2s 960.0 ¢ to 1000.0 ¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 1000.0 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 11L + 2s 1040.0 ¢ to 1100.0 ¢
14-mosstep Perfect 14-mosstep P14ms 11L + 3s 1100.0 ¢ to 1120.0 ¢
Augmented 14-mosstep A14ms 12L + 2s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 12L + 3s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 3s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 80.000 320.000 1:1 1.000 Equalized 12L 3s
6\87 82.759 317.241 6:5 1.200
5\72 83.333 316.667 5:4 1.250
9\129 83.721 316.279 9:7 1.286
4\57 84.211 315.789 4:3 1.333 Supersoft 12L 3s
11\156 84.615 315.385 11:8 1.375
7\99 84.848 315.152 7:5 1.400
10\141 85.106 314.894 10:7 1.429
3\42 85.714 314.286 3:2 1.500 Soft 12L 3s
11\153 86.275 313.725 11:7 1.571
8\111 86.486 313.514 8:5 1.600
13\180 86.667 313.333 13:8 1.625
5\69 86.957 313.043 5:3 1.667 Semisoft 12L 3s
12\165 87.273 312.727 12:7 1.714
7\96 87.500 312.500 7:4 1.750
9\123 87.805 312.195 9:5 1.800
2\27 88.889 311.111 2:1 2.000 Basic 12L 3s
9\120 90.000 310.000 9:4 2.250
7\93 90.323 309.677 7:3 2.333
12\159 90.566 309.434 12:5 2.400
5\66 90.909 309.091 5:2 2.500 Semihard 12L 3s
13\171 91.228 308.772 13:5 2.600
8\105 91.429 308.571 8:3 2.667
11\144 91.667 308.333 11:4 2.750
3\39 92.308 307.692 3:1 3.000 Hard 12L 3s
10\129 93.023 306.977 10:3 3.333
7\90 93.333 306.667 7:2 3.500
11\141 93.617 306.383 11:3 3.667
4\51 94.118 305.882 4:1 4.000 Superhard 12L 3s
9\114 94.737 305.263 9:2 4.500
5\63 95.238 304.762 5:1 5.000
6\75 96.000 304.000 6:1 6.000
1\12 100.000 300.000 1:0 → ∞ Collapsed 12L 3s
Retrieved from "https://en.xen.wiki/index.php?title=12L_3s&oldid=183737"