10L 9s: 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>2015-06-11 23:10:33 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>553737984</tt>.<br>
| nLargeSteps = 10
: The revision comment was: <tt></tt><br>
| nSmallSteps = 9
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 17
<h4>Original Wikitext content:</h4>
| Collapsed = 9
<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 divides its large steps 1-1-1-1-1-1-1-1-2 like the 10edo nonatonic scale. Its 'trienthird' generator falls in the narrow range of 1/10edo (120) to 2/19edo (126 6/19 cents).
| Pattern = LLsLsLsLsLsLsLsLsLs
|| 2/19 ||  ||  ||  ||  || 126 6/19 ||
}}
||  ||  ||  ||  || 9/86 || 125 25/43 ||
{{MOS intro}}
||  ||  ||  || 7/67 ||  || 125 25/67 ||
||  ||  ||  ||  || 12/115 || 125 5/23 ||
||  ||  || 5/48 ||  ||  || 125 ||
||  ||  ||  ||  || 13/125 || 124.8 ||
||  ||  ||  || 8/77 ||  || 124 52/77 ||
||  ||  ||  ||  || 11/106 || 124 28/53 ||
||  || 3/29 ||  ||  ||  || 124 4/29 ||
||  ||  ||  ||  || 10/97 || 123 69/97 ||
||  ||  ||  || 7/68 ||  || 123 9/17 ||
||  ||  ||  ||  || 11/107 || 123.364486 ||
||  ||  ||  ||  ||  || 123.316491 ||
||  ||  || 4/39 ||  ||  || 123 1/13 ||
||  ||  ||  ||  ||  || 122.9691265 ||
||  ||  ||  ||  || 9/88 || 122 8/11 ||
||  ||  ||  || 5/49 ||  || 122 22/19 ||
||  ||  ||  ||  || 6/59 || 122 2/59 ||
|| 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 9s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS divides its large steps 1-1-1-1-1-1-1-1-2 like the 10edo nonatonic scale. Its 'trienthird' generator falls in the narrow range of 1/10edo (120) to 2/19edo (126 6/19 cents).&lt;br /&gt;


== Intervals ==
{{MOS intervals}}


&lt;table class="wiki_table"&gt;
==Scale tree==
    &lt;tr&gt;
{{MOS tuning spectrum}}
        &lt;td&gt;2/19&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;126 6/19&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;9/86&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125 25/43&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;7/67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125 25/67&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;12/115&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125 5/23&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;5/48&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;125&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;13/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124.8&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;8/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124 52/77&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;11/106&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124 28/53&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/29&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;124 4/29&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;10/97&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123 69/97&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;7/68&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123 9/17&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;11/107&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123.364486&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;123.316491&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;4/39&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;123 1/13&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;122.9691265&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;9/88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;122 8/11&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;5/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;122 22/19&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;6/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;122 2/59&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>
{{Stub}}

Latest revision as of 16:37, 28 February 2025

↖ 9L 8s ↑ 10L 8s 11L 8s ↗
← 9L 9s 10L 9s 11L 9s →
↙ 9L 10s ↓ 10L 10s 11L 10s ↘ 
┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐
│║║│║│║│║│║│║│║│║│║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\19 to 9\10 (1073.7 ¢ to 1080.0 ¢)
Dark 1\10 to 2\19 (120.0 ¢ to 126.3 ¢)
TAMNAMS information
Related to 9L 1s (sinatonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 9L 1s
Sister 9L 10s
Daughters 19L 10s, 10L 19s
Neutralized 1L 18s
2-Flought 29L 9s, 10L 28s
Equal tunings
Equalized (L:s = 1:1) 17\19 (1073.7 ¢)
Supersoft (L:s = 4:3) 60\67 (1074.6 ¢)
Soft (L:s = 3:2) 43\48 (1075.0 ¢)
Semisoft (L:s = 5:3) 69\77 (1075.3 ¢)
Basic (L:s = 2:1) 26\29 (1075.9 ¢)
Semihard (L:s = 5:2) 61\68 (1076.5 ¢)
Hard (L:s = 3:1) 35\39 (1076.9 ¢)
Superhard (L:s = 4:1) 44\49 (1077.6 ¢)
Collapsed (L:s = 1:0) 9\10 (1080.0 ¢)

10L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 9 small steps, repeating every octave. 10L 9s is a child scale of 9L 1s, expanding it by 9 tones. Generators that produce this scale range from 1073.7 ¢ to 1080 ¢, or from 120 ¢ to 126.3 ¢.

Intervals

Intervals of 10L 9s
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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 120.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 120.0 ¢ to 126.3 ¢
Augmented 2-mosstep A2ms 2L 126.3 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 120.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms 2L + s 189.5 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 240.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms 3L + s 252.6 ¢ to 360.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 240.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms 3L + 2s 315.8 ¢ to 360.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 360.0 ¢ to 378.9 ¢
Major 6-mosstep M6ms 4L + 2s 378.9 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 360.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 4L + 3s 442.1 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 480.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 5L + 3s 505.3 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 480.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 5L + 4s 568.4 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 600.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 6L + 4s 631.6 ¢ to 720.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 600.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 6L + 5s 694.7 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 720.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 7L + 5s 757.9 ¢ to 840.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 720.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 7L + 6s 821.1 ¢ to 840.0 ¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 840.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 8L + 6s 884.2 ¢ to 960.0 ¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 840.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 8L + 7s 947.4 ¢ to 960.0 ¢
16-mosstep Minor 16-mosstep m16ms 8L + 8s 960.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 9L + 7s 1010.5 ¢ to 1080.0 ¢
17-mosstep Diminished 17-mosstep d17ms 8L + 9s 960.0 ¢ to 1073.7 ¢
Perfect 17-mosstep P17ms 9L + 8s 1073.7 ¢ to 1080.0 ¢
18-mosstep Minor 18-mosstep m18ms 9L + 9s 1080.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 10L + 8s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 10L + 9s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\19 1073.684 126.316 1:1 1.000 Equalized 10L 9s
94\105 1074.286 125.714 6:5 1.200
77\86 1074.419 125.581 5:4 1.250
137\153 1074.510 125.490 9:7 1.286
60\67 1074.627 125.373 4:3 1.333 Supersoft 10L 9s
163\182 1074.725 125.275 11:8 1.375
103\115 1074.783 125.217 7:5 1.400
146\163 1074.847 125.153 10:7 1.429
43\48 1075.000 125.000 3:2 1.500 Soft 10L 9s
155\173 1075.145 124.855 11:7 1.571
112\125 1075.200 124.800 8:5 1.600
181\202 1075.248 124.752 13:8 1.625
69\77 1075.325 124.675 5:3 1.667 Semisoft 10L 9s
164\183 1075.410 124.590 12:7 1.714
95\106 1075.472 124.528 7:4 1.750
121\135 1075.556 124.444 9:5 1.800
26\29 1075.862 124.138 2:1 2.000 Basic 10L 9s
Scales with tunings softer than this are proper
113\126 1076.190 123.810 9:4 2.250
87\97 1076.289 123.711 7:3 2.333
148\165 1076.364 123.636 12:5 2.400
61\68 1076.471 123.529 5:2 2.500 Semihard 10L 9s
157\175 1076.571 123.429 13:5 2.600
96\107 1076.636 123.364 8:3 2.667
131\146 1076.712 123.288 11:4 2.750
35\39 1076.923 123.077 3:1 3.000 Hard 10L 9s
114\127 1077.165 122.835 10:3 3.333
79\88 1077.273 122.727 7:2 3.500
123\137 1077.372 122.628 11:3 3.667
44\49 1077.551 122.449 4:1 4.000 Superhard 10L 9s
97\108 1077.778 122.222 9:2 4.500
53\59 1077.966 122.034 5:1 5.000
62\69 1078.261 121.739 6:1 6.000
9\10 1080.000 120.000 1:0 → ∞ Collapsed 10L 9s
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