10L 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>2014-11-06 22:50:02 UTC</tt>.<br>
The only significant harmonic entropy minimum with this MOS pattern is [[Diaschismic_family|srutal/pajara]], which appears as a 12-note scale of srutal/pajara[12]. The name '''telluric''' has been proposed for this scale by [[User:Lériendil|Lériendil]], after the personal use of "tellurian" for the LLLsLLLLLLsL [[MODMOS]] of 10L 2s.
: The original revision id was <tt>529922256</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">The only significant harmonic entropy minimum with this MOS pattern is [[Diaschismic family|srutal/pajara]][12], which is simply [[2L 8s|decatonic]] with two more notes added in.


All scales with this MOS pattern are [[Rothenberg propriety|proper]], because there is only one small step per period.
== Modes ==
{{MOS modes}}


||||||||~ Generator ||~  ||~  ||~ Cents ||~ Comments ||
== Intervals ==
|| 1\12 ||  ||  ||  ||  ||  || 100 ||=  ||
{{MOS intervals}}
||  ||  ||  ||  ||  || 6\70 || 102.86 ||  ||
||  ||  ||  ||  || 5\58 ||  || 103.45 ||  ||
||  ||  ||  || 4\46 ||  ||  || 104.35 ||=  ||
||  ||  || 3\34 ||  ||  ||  || 105.88 ||= Srutal/pajara is around here ||
||  ||  ||  || 5\56 ||  ||  || 107.14 ||=  ||
||  || 2\22 ||  ||  ||  ||  || 109.09 ||= Boundary of propriety for near-MOS
Optimal rank range (L/s=2/1) for MOS ||
||  ||  ||  || 5\54 ||  ||  || 111.11 ||=  ||
||  ||  || 3\32 ||  ||  ||  || 112.5 ||=  ||
||  ||  ||  || 4\42 ||  ||  || 114.29 ||=  ||
||  ||  ||  ||  || 5\52 ||  || 115.385 ||  ||
||  ||  ||  ||  ||  || 6\62 || 116.13 ||  ||
|| 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 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The only significant harmonic entropy minimum with this MOS pattern is &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal/pajara&lt;/a&gt;[12], which is simply &lt;a class="wiki_link" href="/2L%208s"&gt;decatonic&lt;/a&gt; with two more notes added in.&lt;br /&gt;
&lt;br /&gt;
All scales with this MOS pattern are &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;proper&lt;/a&gt;, because there is only one small step per period.&lt;br /&gt;
&lt;br /&gt;


== Scale tree ==
{{MOS tuning spectrum
| 3/2 = ↕&nbsp;[[Srutal]] / [[pajara]]
}}


&lt;table class="wiki_table"&gt;
[[Category:12-tone scales]]
    &lt;tr&gt;
        &lt;th colspan="4"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;6\70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;102.86&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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\58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;103.45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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\46&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;104.35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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\34&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;105.88&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Srutal/pajara is around here&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\56&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;107.14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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\22&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;109.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety for near-MOS&lt;br /&gt;
Optimal rank range (L/s=2/1) for MOS&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\54&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;111.11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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\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;114.29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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\52&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;td&gt;&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;6\62&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;120&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 12:53, 14 May 2025

↖ 9L 1s ↑ 10L 1s 11L 1s ↗
← 9L 2s 10L 2s 11L 2s →
↙ 9L 3s ↓ 10L 3s 11L 3s ↘
Scale structure
Step pattern LLLLLsLLLLLs
sLLLLLsLLLLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 1\12 to 1\10 (100.0 ¢ to 120.0 ¢)
Dark 4\10 to 5\12 (480.0 ¢ to 500.0 ¢)
TAMNAMS information
Related to 2L 8s (jaric)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 2L 8s
Sister 2L 10s
Daughters 12L 10s, 10L 12s
Neutralized 8L 4s
2-Flought 22L 2s, 10L 14s
Equal tunings
Equalized (L:s = 1:1) 1\12 (100.0 ¢)
Supersoft (L:s = 4:3) 4\46 (104.3 ¢)
Soft (L:s = 3:2) 3\34 (105.9 ¢)
Semisoft (L:s = 5:3) 5\56 (107.1 ¢)
Basic (L:s = 2:1) 2\22 (109.1 ¢)
Semihard (L:s = 5:2) 5\54 (111.1 ¢)
Hard (L:s = 3:1) 3\32 (112.5 ¢)
Superhard (L:s = 4:1) 4\42 (114.3 ¢)
Collapsed (L:s = 1:0) 1\10 (120.0 ¢)
View • Talk • Edit

10L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 2 small steps, with a period of 5 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. 10L 2s is a child scale of 2L 8s, expanding it by 2 tones. Generators that produce this scale range from 100 ¢ to 120 ¢, or from 480 ¢ to 500 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. The only significant harmonic entropy minimum with this MOS pattern is srutal/pajara, which appears as a 12-note scale of srutal/pajara[12]. The name telluric has been proposed for this scale by Lériendil, after the personal use of "tellurian" for the LLLsLLLLLLsL MODMOS of 10L 2s.

Modes

Modes of 10L 2s
UDP Cyclic
order		 Step
pattern
10|0(2) 1 LLLLLsLLLLLs
8|2(2) 2 LLLLsLLLLLsL
6|4(2) 3 LLLsLLLLLsLL
4|6(2) 4 LLsLLLLLsLLL
2|8(2) 5 LsLLLLLsLLLL
0|10(2) 6 sLLLLLsLLLLL

Intervals

Intervals of 10L 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 100.0 ¢
Perfect 1-mosstep P1ms L 100.0 ¢ to 120.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 120.0 ¢ to 200.0 ¢
Major 2-mosstep M2ms 2L 200.0 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 240.0 ¢ to 300.0 ¢
Major 3-mosstep M3ms 3L 300.0 ¢ to 360.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 360.0 ¢ to 400.0 ¢
Major 4-mosstep M4ms 4L 400.0 ¢ to 480.0 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 480.0 ¢ to 500.0 ¢
Augmented 5-mosstep A5ms 5L 500.0 ¢ to 600.0 ¢
6-mosstep Perfect 6-mosstep P6ms 5L + s 600.0 ¢
7-mosstep Diminished 7-mosstep d7ms 5L + 2s 600.0 ¢ to 700.0 ¢
Perfect 7-mosstep P7ms 6L + s 700.0 ¢ to 720.0 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 720.0 ¢ to 800.0 ¢
Major 8-mosstep M8ms 7L + s 800.0 ¢ to 840.0 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 840.0 ¢ to 900.0 ¢
Major 9-mosstep M9ms 8L + s 900.0 ¢ to 960.0 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 960.0 ¢ to 1000.0 ¢
Major 10-mosstep M10ms 9L + s 1000.0 ¢ to 1080.0 ¢
11-mosstep Perfect 11-mosstep P11ms 9L + 2s 1080.0 ¢ to 1100.0 ¢
Augmented 11-mosstep A11ms 10L + s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 10L + 2s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 2s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\12 100.000 500.000 1:1 1.000 Equalized 10L 2s
6\70 102.857 497.143 6:5 1.200
5\58 103.448 496.552 5:4 1.250
9\104 103.846 496.154 9:7 1.286
4\46 104.348 495.652 4:3 1.333 Supersoft 10L 2s
11\126 104.762 495.238 11:8 1.375
7\80 105.000 495.000 7:5 1.400
10\114 105.263 494.737 10:7 1.429
3\34 105.882 494.118 3:2 1.500 Soft 10L 2s
↕ Srutal / pajara
11\124 106.452 493.548 11:7 1.571
8\90 106.667 493.333 8:5 1.600
13\146 106.849 493.151 13:8 1.625
5\56 107.143 492.857 5:3 1.667 Semisoft 10L 2s
12\134 107.463 492.537 12:7 1.714
7\78 107.692 492.308 7:4 1.750
9\100 108.000 492.000 9:5 1.800
2\22 109.091 490.909 2:1 2.000 Basic 10L 2s
9\98 110.204 489.796 9:4 2.250
7\76 110.526 489.474 7:3 2.333
12\130 110.769 489.231 12:5 2.400
5\54 111.111 488.889 5:2 2.500 Semihard 10L 2s
13\140 111.429 488.571 13:5 2.600
8\86 111.628 488.372 8:3 2.667
11\118 111.864 488.136 11:4 2.750
3\32 112.500 487.500 3:1 3.000 Hard 10L 2s
10\106 113.208 486.792 10:3 3.333
7\74 113.514 486.486 7:2 3.500
11\116 113.793 486.207 11:3 3.667
4\42 114.286 485.714 4:1 4.000 Superhard 10L 2s
9\94 114.894 485.106 9:2 4.500
5\52 115.385 484.615 5:1 5.000
6\62 116.129 483.871 6:1 6.000
1\10 120.000 480.000 1:0 → ∞ Collapsed 10L 2s
Retrieved from "https://en.xen.wiki/index.php?title=10L_2s&oldid=196167"