10L 1s: Difference between revisions

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added name "secoric"
 
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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>2015-11-09 15:10:01 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>565776209</tt>.<br>
| nLargeSteps = 10
: The revision comment was: <tt></tt><br>
| nSmallSteps = 1
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 1
<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 MOS, having a generator of a diatonic semitone between 1/11edo (109.09 cents) and 1/10edo (120), functions as the superdiatonic scale of the Miracle temperment and its unnamed close neighbors.
| Pattern = LLLLLLLLLLs
|| 1/11 ||  ||  ||  ||  || 109.091 ||
}}
||  ||  ||  ||  || 5/54 || 111.111 ||
{{MOS intro}}
||  ||  ||  || 4/43 ||  || 111.628 ||
This MOS functions as the superdiatonic scale{{Clarify}} of [[Miracle]] temperament. Its generator range spans the interval range of [[secor]]s, and therefore the name '''secoric''' has been proposed for this MOS pattern independently by [[Praveen Venkataramana]] and [[User:Lériendil|Lériendil]].
||  ||  ||  ||  || 7/75 || 112 ||
||  ||  || 3/32 ||  ||  || 112.5 ||
||  ||  ||  ||  ||  || 112.818 ||
||  ||  ||  ||  || 8/85 || 112.941 ||
||  ||  ||  ||  ||  || 113.15 ||
||  ||  ||  || 5/53 ||  || 113.2075 ||
||  ||  ||  ||  ||  || 113.45 ||
||  ||  ||  ||  || 7/74 || 113.5135 ||
||  || 2/21 ||  ||  ||  || 114.286 ||
||  ||  ||  ||  || 7/73 || 115.0685 ||
||  ||  ||  || 5/52 ||  || 115.308 ||
||  ||  ||  ||  ||  || 115.585 ||
||  ||  ||  ||  || 8/83 || 115.663 ||
||  ||  ||  ||  ||  || 115.742 ||
||  ||  || 3/31 ||  ||  || 116.129 ||
||  ||  ||  ||  ||  || 116.298 ||
||  ||  ||  ||  || 7/72 || 116.667 ||
||  ||  ||  || 4/41 ||  || 117.073 ||
||  ||  ||  ||  || 5/51 || 117.647 ||
|| 1/10 ||  ||  ||  ||  || 120 ||</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 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, having a generator of a diatonic semitone between 1/11edo (109.09 cents) and 1/10edo (120), functions as the superdiatonic scale of the Miracle temperment and its unnamed close neighbors.&lt;br /&gt;


== Modes ==
{{MOS modes}}


&lt;table class="wiki_table"&gt;
== Intervals ==
    &lt;tr&gt;
{{MOS intervals}}
        &lt;td&gt;1/11&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;109.091&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;5/54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.111&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;4/43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.628&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;7/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112&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;3/32&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;112.5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;112.818&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;8/85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112.941&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;113.15&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;5/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;113.2075&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;113.45&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;7/74&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;113.5135&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/21&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;114.286&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;7/73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.0685&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;5/52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.308&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;8/83&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;115.742&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;3/31&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;116.129&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;116.298&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;7/72&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;4/41&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;5/51&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;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;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale tree ==
{{MOS tuning spectrum
| 7/2 = [[Miracle]]
| 2/1 = Simplest tuning for miracle
}}
 
[[Category:11-tone scales]]

Latest revision as of 11:12, 10 March 2025

← 9L 1s 10L 1s 11L 1s →
↙ 9L 2s ↓ 10L 2s 11L 2s ↘ 
┌╥╥╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLLs
sLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\11 to 1\10 (109.1 ¢ to 120.0 ¢)
Dark 9\10 to 10\11 (1080.0 ¢ to 1090.9 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 1L 9s
Sister 1L 10s
Daughters 11L 10s, 10L 11s
Neutralized 9L 2s
2-Flought 21L 1s, 10L 12s
Equal tunings
Equalized (L:s = 1:1) 1\11 (109.1 ¢)
Supersoft (L:s = 4:3) 4\43 (111.6 ¢)
Soft (L:s = 3:2) 3\32 (112.5 ¢)
Semisoft (L:s = 5:3) 5\53 (113.2 ¢)
Basic (L:s = 2:1) 2\21 (114.3 ¢)
Semihard (L:s = 5:2) 5\52 (115.4 ¢)
Hard (L:s = 3:1) 3\31 (116.1 ¢)
Superhard (L:s = 4:1) 4\41 (117.1 ¢)
Collapsed (L:s = 1:0) 1\10 (120.0 ¢)

10L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 1 small step, repeating every octave. 10L 1s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 109.1 ¢ to 120 ¢, or from 1080 ¢ to 1090.9 ¢. Scales of this form are always proper because there is only one small step. This MOS functions as the superdiatonic scale[clarification needed] of Miracle temperament. Its generator range spans the interval range of secors, and therefore the name secoric has been proposed for this MOS pattern independently by Praveen Venkataramana and Lériendil.

Modes

Modes of 10L 1s
UDP Cyclic
order		 Step
pattern
10|0 1 LLLLLLLLLLs
9|1 2 LLLLLLLLLsL
8|2 3 LLLLLLLLsLL
7|3 4 LLLLLLLsLLL
6|4 5 LLLLLLsLLLL
5|5 6 LLLLLsLLLLL
4|6 7 LLLLsLLLLLL
3|7 8 LLLsLLLLLLL
2|8 9 LLsLLLLLLLL
1|9 10 LsLLLLLLLLL
0|10 11 sLLLLLLLLLL

Intervals

Intervals of 10L 1s
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 109.1 ¢
Perfect 1-mosstep P1ms L 109.1 ¢ to 120.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 120.0 ¢ to 218.2 ¢
Major 2-mosstep M2ms 2L 218.2 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 240.0 ¢ to 327.3 ¢
Major 3-mosstep M3ms 3L 327.3 ¢ to 360.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 360.0 ¢ to 436.4 ¢
Major 4-mosstep M4ms 4L 436.4 ¢ to 480.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 480.0 ¢ to 545.5 ¢
Major 5-mosstep M5ms 5L 545.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 600.0 ¢ to 654.5 ¢
Major 6-mosstep M6ms 6L 654.5 ¢ to 720.0 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 720.0 ¢ to 763.6 ¢
Major 7-mosstep M7ms 7L 763.6 ¢ to 840.0 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 840.0 ¢ to 872.7 ¢
Major 8-mosstep M8ms 8L 872.7 ¢ to 960.0 ¢
9-mosstep Minor 9-mosstep m9ms 8L + s 960.0 ¢ to 981.8 ¢
Major 9-mosstep M9ms 9L 981.8 ¢ to 1080.0 ¢
10-mosstep Perfect 10-mosstep P10ms 9L + s 1080.0 ¢ to 1090.9 ¢
Augmented 10-mosstep A10ms 10L 1090.9 ¢ to 1200.0 ¢
11-mosstep Perfect 11-mosstep P11ms 10L + s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\11 109.091 1090.909 1:1 1.000 Equalized 10L 1s
6\65 110.769 1089.231 6:5 1.200
5\54 111.111 1088.889 5:4 1.250
9\97 111.340 1088.660 9:7 1.286
4\43 111.628 1088.372 4:3 1.333 Supersoft 10L 1s
11\118 111.864 1088.136 11:8 1.375
7\75 112.000 1088.000 7:5 1.400
10\107 112.150 1087.850 10:7 1.429
3\32 112.500 1087.500 3:2 1.500 Soft 10L 1s
11\117 112.821 1087.179 11:7 1.571
8\85 112.941 1087.059 8:5 1.600
13\138 113.043 1086.957 13:8 1.625
5\53 113.208 1086.792 5:3 1.667 Semisoft 10L 1s
12\127 113.386 1086.614 12:7 1.714
7\74 113.514 1086.486 7:4 1.750
9\95 113.684 1086.316 9:5 1.800
2\21 114.286 1085.714 2:1 2.000 Basic 10L 1s
Simplest tuning for miracle
9\94 114.894 1085.106 9:4 2.250
7\73 115.068 1084.932 7:3 2.333
12\125 115.200 1084.800 12:5 2.400
5\52 115.385 1084.615 5:2 2.500 Semihard 10L 1s
13\135 115.556 1084.444 13:5 2.600
8\83 115.663 1084.337 8:3 2.667
11\114 115.789 1084.211 11:4 2.750
3\31 116.129 1083.871 3:1 3.000 Hard 10L 1s
10\103 116.505 1083.495 10:3 3.333
7\72 116.667 1083.333 7:2 3.500 Miracle
11\113 116.814 1083.186 11:3 3.667
4\41 117.073 1082.927 4:1 4.000 Superhard 10L 1s
9\92 117.391 1082.609 9:2 4.500
5\51 117.647 1082.353 5:1 5.000
6\61 118.033 1081.967 6:1 6.000
1\10 120.000 1080.000 1:0 → ∞ Collapsed 10L 1s
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