12L 2s: 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>2012-10-30 17:07:49 UTC</tt>.<br>
: The original revision id was <tt>377781428</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 MOS, being two periods of 6L 1s, is always proper. It appears as the mega chromatic scale of Injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4.
Its generator is a neutral semitone of 1/14edo (85 5/7 cents) to 1/12edo (100).
|| 1/14 ||  ||  ||  ||  || 85 5/7 ||
||  ||  ||  ||  || 5/68 || 88.235294 ||
||  ||  ||  || 4/54 ||  || 88 8/9 ||
||  ||  ||  ||  || 7/94 || 89.361702 ||
||  ||  || 3/40 ||  ||  || 90 ||
||  ||  ||  ||  || 8/106 || 90.566038 ||
||  ||  ||  || 5/66 ||  || 90 10/11 ||
||  ||  ||  ||  || 7/92 || 91.304348 ||
||  || 2/26 ||  ||  ||  || 92 4/13 ||
||  ||  ||  ||  || 7/90 || 93 1/3 ||
||  ||  ||  || 5/64 ||  || 93.75 ||
||  ||  ||  ||  || 8/102 || 94.117647 ||
||  ||  || 3/38 ||  ||  || 94.736842 ||
||  ||  ||  ||  || 7/88 || 95 5/11 ||
||  ||  ||  || 4/50 ||  || 96 ||
||  ||  ||  ||  || 5/62 || 96.7741935 ||
|| 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 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, being two periods of 6L 1s, is always proper. It appears as the mega chromatic scale of Injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4.&lt;br /&gt;
Its generator is a neutral semitone of 1/14edo (85 5/7 cents) to 1/12edo (100).&lt;br /&gt;


It appears as the mega chromatic scale of [[injera]] temperament, meaning that its harmonic entropy is where +4 generators equals [[5/4]] (simple) or +10 generators equals [[5/3]] (complex).


&lt;table class="wiki_table"&gt;
== Modes ==
    &lt;tr&gt;
{{MOS modes}}
        &lt;td&gt;1/14&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;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;5/68&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.235294&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;4/54&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;7/94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89.361702&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;3/40&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;90&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;8/106&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90.566038&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;7/92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;91.304348&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/26&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 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;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;5/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;93.75&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;8/102&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;3/38&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;94.736842&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;7/88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;95 5/11&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;4/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;96&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;5/62&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;96.7741935&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
| 3/1 = [[Injera]]
}}
 
{{todo|expand}}
 
[[Category:14-tone scales]]

Latest revision as of 16:43, 28 February 2025

↖ 11L 1s ↑ 12L 1s 13L 1s ↗
← 11L 2s 12L 2s 13L 2s →
↙ 11L 3s ↓ 12L 3s 13L 3s ↘
Scale structure
Step pattern LLLLLLsLLLLLLs
sLLLLLLsLLLLLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 1\14 to 1\12 (85.7 ¢ to 100.0 ¢)
Dark 5\12 to 6\14 (500.0 ¢ to 514.3 ¢)
TAMNAMS information
Related to 2L 8s (jaric)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 2L 10s
Sister 2L 12s
Daughters 14L 12s, 12L 14s
Neutralized 10L 4s
2-Flought 26L 2s, 12L 16s
Equal tunings
Equalized (L:s = 1:1) 1\14 (85.7 ¢)
Supersoft (L:s = 4:3) 4\54 (88.9 ¢)
Soft (L:s = 3:2) 3\40 (90.0 ¢)
Semisoft (L:s = 5:3) 5\66 (90.9 ¢)
Basic (L:s = 2:1) 2\26 (92.3 ¢)
Semihard (L:s = 5:2) 5\64 (93.8 ¢)
Hard (L:s = 3:1) 3\38 (94.7 ¢)
Superhard (L:s = 4:1) 4\50 (96.0 ¢)
Collapsed (L:s = 1:0) 1\12 (100.0 ¢)
View • Talk • Edit

12L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 2 small steps, with a period of 6 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. 12L 2s is a grandchild scale of 2L 8s, expanding it by 4 tones. Generators that produce this scale range from 85.7 ¢ to 100 ¢, or from 500 ¢ to 514.3 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

It appears as the mega chromatic scale of injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4 (simple) or +10 generators equals 5/3 (complex).

Modes

Modes of 12L 2s
UDP Cyclic
order		 Step
pattern
12|0(2) 1 LLLLLLsLLLLLLs
10|2(2) 2 LLLLLsLLLLLLsL
8|4(2) 3 LLLLsLLLLLLsLL
6|6(2) 4 LLLsLLLLLLsLLL
4|8(2) 5 LLsLLLLLLsLLLL
2|10(2) 6 LsLLLLLLsLLLLL
0|12(2) 7 sLLLLLLsLLLLLL

Intervals

Intervals of 12L 2s
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 85.7 ¢
Perfect 1-mosstep P1ms L 85.7 ¢ to 100.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 100.0 ¢ to 171.4 ¢
Major 2-mosstep M2ms 2L 171.4 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 200.0 ¢ to 257.1 ¢
Major 3-mosstep M3ms 3L 257.1 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 300.0 ¢ to 342.9 ¢
Major 4-mosstep M4ms 4L 342.9 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 400.0 ¢ to 428.6 ¢
Major 5-mosstep M5ms 5L 428.6 ¢ to 500.0 ¢
6-mosstep Perfect 6-mosstep P6ms 5L + s 500.0 ¢ to 514.3 ¢
Augmented 6-mosstep A6ms 6L 514.3 ¢ to 600.0 ¢
7-mosstep Perfect 7-mosstep P7ms 6L + s 600.0 ¢
8-mosstep Diminished 8-mosstep d8ms 6L + 2s 600.0 ¢ to 685.7 ¢
Perfect 8-mosstep P8ms 7L + s 685.7 ¢ to 700.0 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 700.0 ¢ to 771.4 ¢
Major 9-mosstep M9ms 8L + s 771.4 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 800.0 ¢ to 857.1 ¢
Major 10-mosstep M10ms 9L + s 857.1 ¢ to 900.0 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 900.0 ¢ to 942.9 ¢
Major 11-mosstep M11ms 10L + s 942.9 ¢ to 1000.0 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 1000.0 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 11L + s 1028.6 ¢ to 1100.0 ¢
13-mosstep Perfect 13-mosstep P13ms 11L + 2s 1100.0 ¢ to 1114.3 ¢
Augmented 13-mosstep A13ms 12L + s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 12L + 2s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 2s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\14 85.714 514.286 1:1 1.000 Equalized 12L 2s
6\82 87.805 512.195 6:5 1.200
5\68 88.235 511.765 5:4 1.250
9\122 88.525 511.475 9:7 1.286
4\54 88.889 511.111 4:3 1.333 Supersoft 12L 2s
11\148 89.189 510.811 11:8 1.375
7\94 89.362 510.638 7:5 1.400
10\134 89.552 510.448 10:7 1.429
3\40 90.000 510.000 3:2 1.500 Soft 12L 2s
11\146 90.411 509.589 11:7 1.571
8\106 90.566 509.434 8:5 1.600
13\172 90.698 509.302 13:8 1.625
5\66 90.909 509.091 5:3 1.667 Semisoft 12L 2s
12\158 91.139 508.861 12:7 1.714
7\92 91.304 508.696 7:4 1.750
9\118 91.525 508.475 9:5 1.800
2\26 92.308 507.692 2:1 2.000 Basic 12L 2s
9\116 93.103 506.897 9:4 2.250
7\90 93.333 506.667 7:3 2.333
12\154 93.506 506.494 12:5 2.400
5\64 93.750 506.250 5:2 2.500 Semihard 12L 2s
13\166 93.976 506.024 13:5 2.600
8\102 94.118 505.882 8:3 2.667
11\140 94.286 505.714 11:4 2.750
3\38 94.737 505.263 3:1 3.000 Hard 12L 2s
Injera
10\126 95.238 504.762 10:3 3.333
7\88 95.455 504.545 7:2 3.500
11\138 95.652 504.348 11:3 3.667
4\50 96.000 504.000 4:1 4.000 Superhard 12L 2s
9\112 96.429 503.571 9:2 4.500
5\62 96.774 503.226 5:1 5.000
6\74 97.297 502.703 6:1 6.000
1\12 100.000 500.000 1:0 → ∞ Collapsed 12L 2s
Retrieved from "https://en.xen.wiki/index.php?title=12L_2s&oldid=183736"