10L 11s: 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>
| Name =  
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-10-28 15:57:30 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>564248587</tt>.<br>
| nLargeSteps = 10
: The revision comment was: <tt></tt><br>
| nSmallSteps = 11
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 2
<h4>Original Wikitext content:</h4>
| Collapsed = 1
<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 the MOS which splits its large steps 1-1-1-1-1-1-1-1-1-2 between its small steps. It is the simplest MOS which is really useful for Miracle temperament, placing the low estimate for the boundary of "practicality" at 41edo (L:s = 3:1). Its diatonic semitone generator is no smaller than 2/21edo (114.286 cents).
| Pattern = sLsLsLsLsLsLsLsLsLsLs
|| 1/10 ||  ||  ||  ||  || 120 ||
}}
||  ||  ||  ||  || 6/61 || 118.033 ||
{{MOS intro|Other Names=miracloid}}
||  ||  ||  || 5/51 ||  || 117.647 ||
||  ||  ||  ||  || 9/92 || 117.391 ||
||  ||  ||  ||  ||  || 117.171 ||
||  ||  || 4/41 ||  ||  || 117.073 ||
||  ||  ||  ||  ||  || 116.857 ||
||  ||  ||  ||  || 11/113 || 116.814 ||
||  ||  ||  ||  ||  || 116.7725 ||
||  ||  ||  || 7/72 ||  || 116.667 ||
||  ||  ||  ||  || 10/103 || 116.505 ||
||  || 3/31 ||  ||  ||  || 116.192 ||
||  ||  ||  ||  || 11/114 || 115.7895 ||
||  ||  ||  || 8/83 ||  || 115.663 ||
||  ||  ||  ||  ||  || 115.585 ||
||  ||  ||  ||  || 13/135 || 115.556 ||
||  ||  || 5/52 ||  ||  || 115.385 ||
||  ||  ||  ||  || 12/125 || 115.2 ||
||  ||  ||  || 7/73 ||  || 115.0865 ||
||  ||  ||  ||  || 9/94 || 114.894 ||
|| 2/21 ||  ||  ||  ||  || 114.286 ||</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;10L 11s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS which splits its large steps 1-1-1-1-1-1-1-1-1-2 between its small steps. It is the simplest MOS which is really useful for Miracle temperament, placing the low estimate for the boundary of &amp;quot;practicality&amp;quot; at 41edo (L:s = 3:1). Its diatonic semitone generator is no smaller than 2/21edo (114.286 cents).&lt;br /&gt;


This is the simplest MOS for which [[miracle]] temperament can be used{{Clarify}}, placing the low estimate for the boundary of "practicality" at 41edo (L:s = 3:1).
[[User:Eliora|Eliora]] has proposed the name ''miracloid'' for this pattern.


&lt;table class="wiki_table"&gt;
== Intervals ==
    &lt;tr&gt;
{{MOS intervals}}
        &lt;td&gt;1/10&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;120&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;6/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;118.033&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;5/51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.647&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;9/92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.391&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;117.171&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;4/41&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;117.073&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;116.857&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;11/113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.814&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;116.7725&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;7/72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.667&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;10/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.505&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/31&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;116.192&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;11/114&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.7895&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;8/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.663&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;115.585&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;13/135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.556&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;5/52&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;115.385&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;12/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.2&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;7/73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.0865&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;9/94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;114.894&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/21&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;114.286&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale tree ==
{{MOS tuning spectrum
| 3/2 = Approximate range for using [[31/29]] as a generator
| 2/1 = Approximate range for using [[46/43]] as a generator
}}

Latest revision as of 16:32, 28 February 2025

↖ 9L 10s ↑ 10L 10s 11L 10s ↗
← 9L 11s 10L 11s 11L 11s →
↙ 9L 12s ↓ 10L 12s 11L 12s ↘ 
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│║│║│║│║│║│║│││
│││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\21 to 1\10 (114.3 ¢ to 120.0 ¢)
Dark 9\10 to 19\21 (1080.0 ¢ to 1085.7 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 10L 1s
Sister 11L 10s
Daughters 21L 10s, 10L 21s
Neutralized 20L 1s
2-Flought 31L 11s, 10L 32s
Equal tunings
Equalized (L:s = 1:1) 2\21 (114.3 ¢)
Supersoft (L:s = 4:3) 7\73 (115.1 ¢)
Soft (L:s = 3:2) 5\52 (115.4 ¢)
Semisoft (L:s = 5:3) 8\83 (115.7 ¢)
Basic (L:s = 2:1) 3\31 (116.1 ¢)
Semihard (L:s = 5:2) 7\72 (116.7 ¢)
Hard (L:s = 3:1) 4\41 (117.1 ¢)
Superhard (L:s = 4:1) 5\51 (117.6 ¢)
Collapsed (L:s = 1:0) 1\10 (120.0 ¢)

10L 11s, also called miracloid, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 11 small steps, repeating every octave. 10L 11s is a grandchild scale of 1L 9s, expanding it by 11 tones. Generators that produce this scale range from 114.3 ¢ to 120 ¢, or from 1080 ¢ to 1085.7 ¢.

This is the simplest MOS for which miracle temperament can be used[clarification needed], placing the low estimate for the boundary of "practicality" at 41edo (L:s = 3:1). Eliora has proposed the name miracloid for this pattern.

Intervals

Intervals of 10L 11s
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 57.1 ¢
Major 1-mosstep M1ms L 57.1 ¢ to 120.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 114.3 ¢
Perfect 2-mosstep P2ms L + s 114.3 ¢ to 120.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 120.0 ¢ to 171.4 ¢
Major 3-mosstep M3ms 2L + s 171.4 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 120.0 ¢ to 228.6 ¢
Major 4-mosstep M4ms 2L + 2s 228.6 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 240.0 ¢ to 285.7 ¢
Major 5-mosstep M5ms 3L + 2s 285.7 ¢ to 360.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 240.0 ¢ to 342.9 ¢
Major 6-mosstep M6ms 3L + 3s 342.9 ¢ to 360.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 360.0 ¢ to 400.0 ¢
Major 7-mosstep M7ms 4L + 3s 400.0 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 360.0 ¢ to 457.1 ¢
Major 8-mosstep M8ms 4L + 4s 457.1 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 480.0 ¢ to 514.3 ¢
Major 9-mosstep M9ms 5L + 4s 514.3 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 480.0 ¢ to 571.4 ¢
Major 10-mosstep M10ms 5L + 5s 571.4 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 600.0 ¢ to 628.6 ¢
Major 11-mosstep M11ms 6L + 5s 628.6 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 600.0 ¢ to 685.7 ¢
Major 12-mosstep M12ms 6L + 6s 685.7 ¢ to 720.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 720.0 ¢ to 742.9 ¢
Major 13-mosstep M13ms 7L + 6s 742.9 ¢ to 840.0 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 720.0 ¢ to 800.0 ¢
Major 14-mosstep M14ms 7L + 7s 800.0 ¢ to 840.0 ¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 840.0 ¢ to 857.1 ¢
Major 15-mosstep M15ms 8L + 7s 857.1 ¢ to 960.0 ¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 840.0 ¢ to 914.3 ¢
Major 16-mosstep M16ms 8L + 8s 914.3 ¢ to 960.0 ¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 960.0 ¢ to 971.4 ¢
Major 17-mosstep M17ms 9L + 8s 971.4 ¢ to 1080.0 ¢
18-mosstep Minor 18-mosstep m18ms 8L + 10s 960.0 ¢ to 1028.6 ¢
Major 18-mosstep M18ms 9L + 9s 1028.6 ¢ to 1080.0 ¢
19-mosstep Perfect 19-mosstep P19ms 9L + 10s 1080.0 ¢ to 1085.7 ¢
Augmented 19-mosstep A19ms 10L + 9s 1085.7 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms 9L + 11s 1080.0 ¢ to 1142.9 ¢
Major 20-mosstep M20ms 10L + 10s 1142.9 ¢ to 1200.0 ¢
21-mosstep Perfect 21-mosstep P21ms 10L + 11s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\21 114.286 1085.714 1:1 1.000 Equalized 10L 11s
11\115 114.783 1085.217 6:5 1.200
9\94 114.894 1085.106 5:4 1.250
16\167 114.970 1085.030 9:7 1.286
7\73 115.068 1084.932 4:3 1.333 Supersoft 10L 11s
19\198 115.152 1084.848 11:8 1.375
12\125 115.200 1084.800 7:5 1.400
17\177 115.254 1084.746 10:7 1.429
5\52 115.385 1084.615 3:2 1.500 Soft 10L 11s
Approximate range for using 31/29 as a generator
18\187 115.508 1084.492 11:7 1.571
13\135 115.556 1084.444 8:5 1.600
21\218 115.596 1084.404 13:8 1.625
8\83 115.663 1084.337 5:3 1.667 Semisoft 10L 11s
19\197 115.736 1084.264 12:7 1.714
11\114 115.789 1084.211 7:4 1.750
14\145 115.862 1084.138 9:5 1.800
3\31 116.129 1083.871 2:1 2.000 Basic 10L 11s
Scales with tunings softer than this are proper
Approximate range for using 46/43 as a generator
13\134 116.418 1083.582 9:4 2.250
10\103 116.505 1083.495 7:3 2.333
17\175 116.571 1083.429 12:5 2.400
7\72 116.667 1083.333 5:2 2.500 Semihard 10L 11s
18\185 116.757 1083.243 13:5 2.600
11\113 116.814 1083.186 8:3 2.667
15\154 116.883 1083.117 11:4 2.750
4\41 117.073 1082.927 3:1 3.000 Hard 10L 11s
13\133 117.293 1082.707 10:3 3.333
9\92 117.391 1082.609 7:2 3.500
14\143 117.483 1082.517 11:3 3.667
5\51 117.647 1082.353 4:1 4.000 Superhard 10L 11s
11\112 117.857 1082.143 9:2 4.500
6\61 118.033 1081.967 5:1 5.000
7\71 118.310 1081.690 6:1 6.000
1\10 120.000 1080.000 1:0 → ∞ Collapsed 10L 11s
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