2L 10s: 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>2015-11-10 15:10:50 UTC</tt>.<br>
: The original revision id was <tt>565944071</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 L s s s s s, is always proper. Its generator is 1/12edo (100 cents) or smaller and it appears as the chromatic scale of Injera and Shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root.
|| 0/2 ||  ||  ||  ||  ||  || 0 ||
||  ||  ||  ||  || 1/20 ||  || 60 ||
||  ||  ||  || 1/18 ||  ||  || 66.667 ||
||  ||  ||  ||  || 2/34 ||  || 70.588 ||
||  ||  ||  ||  ||  ||  || 600/(5+pi) ||
||  ||  || 1/16 ||  ||  ||  || 75 ||
||  ||  ||  ||  ||  ||  || 600/(5+e) ||
||  ||  ||  ||  || 3/46 ||  || 78.261 ||
||  ||  ||  ||  ||  ||  || 600/(6+phi) ||
||  ||  ||  || 2/30 ||  ||  || 80 ||
||  ||  ||  ||  || 3/44 ||  || 81.818 ||
||  || 1/14 ||  ||  ||  ||  || 85.714 ||
||  ||  ||  ||  || 4/54 ||  || 88.889 ||
||  ||  ||  ||  ||  ||  || 600/(5+sqrt(3)) ||
||  ||  ||  || 3/40 ||  ||  || 90 ||
||  ||  ||  ||  ||  ||  || 600/(5+phi) ||
||  ||  ||  ||  || 5/66 ||  || 90.909 ||
||  ||  ||  ||  ||  ||  || 600/(5+pi/2) ||
||  ||  ||  ||  ||  || 7/92 || 91.304 ||
||  ||  || 2/26 ||  ||  ||  || 92.308 ||
||  ||  ||  ||  || 5/64 ||  || 93.75 ||
||  ||  ||  || 3/38 ||  ||  || 94.737 ||
||  ||  ||  ||  || 4/50 ||  || 96 ||
|| 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;2L 10s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, being two periods of L s s s s s, is always proper. Its generator is 1/12edo (100 cents) or smaller and it appears as the chromatic scale of Injera and Shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root.&lt;br /&gt;


2L 10s appears as the chromatic scale of [[injera]] and [[shrutar]] temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root. The systematic name for this MOS scale is '''p-chro jaric''', although [[User:Lériendil|Lériendil]] has proposed the bespoke name '''thalassic''', being an antonym to '''telluric''' as used for [[10L 2s]].


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &lt;td&gt;0/2&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;0&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;1/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60&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;1/18&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;66.667&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;2/34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;70.588&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600/(5+pi)&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;1/16&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;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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600/(5+e)&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;3/46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.261&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600/(6+phi)&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;2/30&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;80&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;3/44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81.818&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;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;85.714&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;4/54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.889&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600/(5+sqrt(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;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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600/(5+phi)&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;5/66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90.909&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600/(5+pi/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;&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;91.304&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;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;92.308&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;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;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;94.737&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;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;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;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 13/8 = Unnamed golden tuning (90.6614{{c}})
| 13/5 = Unnamed golden tuning (78.7605{{c}})
| 10/3 = [[Vishnu]]/[[vishnean]]
| 6/1 = [[Shrutar]]&nbsp;↓
}}
 
[[Category:12-tone scales]]

Latest revision as of 11:41, 10 March 2025

↖ 1L 9s ↑ 2L 9s 3L 9s ↗
← 1L 10s 2L 10s 3L 10s →
↙ 1L 11s ↓ 2L 11s 3L 11s ↘
Scale structure
Step pattern LsssssLsssss
sssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 5\12 to 1\2 (500.0 ¢ to 600.0 ¢)
Dark 0\2 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to 2L 8s (jaric)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 2L 8s
Sister 10L 2s
Daughters 12L 2s, 2L 12s
Neutralized 4L 8s
2-Flought 14L 10s, 2L 22s
Equal tunings
Equalized (L:s = 1:1) 5\12 (500.0 ¢)
Supersoft (L:s = 4:3) 16\38 (505.3 ¢)
Soft (L:s = 3:2) 11\26 (507.7 ¢)
Semisoft (L:s = 5:3) 17\40 (510.0 ¢)
Basic (L:s = 2:1) 6\14 (514.3 ¢)
Semihard (L:s = 5:2) 13\30 (520.0 ¢)
Hard (L:s = 3:1) 7\16 (525.0 ¢)
Superhard (L:s = 4:1) 8\18 (533.3 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)
View • Talk • Edit

2L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 10 small steps, with a period of 1 large step and 5 small steps that repeats every 600.0 ¢, or twice every octave. 2L 10s is a child scale of 2L 8s, expanding it by 2 tones. Generators that produce this scale range from 500 ¢ to 600 ¢, or from 0 ¢ to 100 ¢.

2L 10s appears as the chromatic scale of injera and shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root. The systematic name for this MOS scale is p-chro jaric, although Lériendil has proposed the bespoke name thalassic, being an antonym to telluric as used for 10L 2s.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 2L 10s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 100.0 ¢
Augmented 1-mosstep A1ms L 100.0 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 200.0 ¢
Major 2-mosstep M2ms L + s 200.0 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 300.0 ¢
Major 3-mosstep M3ms L + 2s 300.0 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 400.0 ¢
Major 4-mosstep M4ms L + 3s 400.0 ¢ to 600.0 ¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0 ¢ to 500.0 ¢
Perfect 5-mosstep P5ms L + 4s 500.0 ¢ to 600.0 ¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 600.0 ¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 600.0 ¢ to 700.0 ¢
Augmented 7-mosstep A7ms 2L + 5s 700.0 ¢ to 1200.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 600.0 ¢ to 800.0 ¢
Major 8-mosstep M8ms 2L + 6s 800.0 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 600.0 ¢ to 900.0 ¢
Major 9-mosstep M9ms 2L + 7s 900.0 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 600.0 ¢ to 1000.0 ¢
Major 10-mosstep M10ms 2L + 8s 1000.0 ¢ to 1200.0 ¢
11-mosstep Diminished 11-mosstep d11ms L + 10s 600.0 ¢ to 1100.0 ¢
Perfect 11-mosstep P11ms 2L + 9s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 2L + 10s 1200.0 ¢

Generator chain

Generator chain of 2L 10s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
6 Augmented 0-mosdegree A0md Augmented 6-mosdegree A6md
5 Augmented 1-mosdegree A1md Augmented 7-mosdegree A7md
4 Major 2-mosdegree M2md Major 8-mosdegree M8md
3 Major 3-mosdegree M3md Major 9-mosdegree M9md
2 Major 4-mosdegree M4md Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 6-mosdegree		 P0md
P6md		 Perfect 6-mosdegree
Perfect 12-mosdegree		 P6md
P12md
−1 Perfect 1-mosdegree P1md Perfect 7-mosdegree P7md
−2 Minor 2-mosdegree m2md Minor 8-mosdegree m8md
−3 Minor 3-mosdegree m3md Minor 9-mosdegree m9md
−4 Minor 4-mosdegree m4md Minor 10-mosdegree m10md
−5 Diminished 5-mosdegree d5md Diminished 11-mosdegree d11md
−6 Diminished 6-mosdegree d6md Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 2L 10s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
10|0(2) 1 LsssssLsssss Perf. Aug. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Perf. Perf.
8|2(2) 6 sLsssssLssss Perf. Perf. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Perf. Perf.
6|4(2) 5 ssLsssssLsss Perf. Perf. Min. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Perf. Perf.
4|6(2) 4 sssLsssssLss Perf. Perf. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Maj. Perf. Perf.
2|8(2) 3 ssssLsssssLs Perf. Perf. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Perf. Perf.
0|10(2) 2 sssssLsssssL Perf. Perf. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\12 500.000 100.000 1:1 1.000 Equalized 2L 10s
26\62 503.226 96.774 6:5 1.200
21\50 504.000 96.000 5:4 1.250
37\88 504.545 95.455 9:7 1.286
16\38 505.263 94.737 4:3 1.333 Supersoft 2L 10s
43\102 505.882 94.118 11:8 1.375
27\64 506.250 93.750 7:5 1.400
38\90 506.667 93.333 10:7 1.429
11\26 507.692 92.308 3:2 1.500 Soft 2L 10s
39\92 508.696 91.304 11:7 1.571
28\66 509.091 90.909 8:5 1.600
45\106 509.434 90.566 13:8 1.625 Unnamed golden tuning (90.6614 ¢)
17\40 510.000 90.000 5:3 1.667 Semisoft 2L 10s
40\94 510.638 89.362 12:7 1.714
23\54 511.111 88.889 7:4 1.750
29\68 511.765 88.235 9:5 1.800
6\14 514.286 85.714 2:1 2.000 Basic 2L 10s
Scales with tunings softer than this are proper
25\58 517.241 82.759 9:4 2.250
19\44 518.182 81.818 7:3 2.333
32\74 518.919 81.081 12:5 2.400
13\30 520.000 80.000 5:2 2.500 Semihard 2L 10s
33\76 521.053 78.947 13:5 2.600 Unnamed golden tuning (78.7605 ¢)
20\46 521.739 78.261 8:3 2.667
27\62 522.581 77.419 11:4 2.750
7\16 525.000 75.000 3:1 3.000 Hard 2L 10s
22\50 528.000 72.000 10:3 3.333 Vishnu/vishnean
15\34 529.412 70.588 7:2 3.500
23\52 530.769 69.231 11:3 3.667
8\18 533.333 66.667 4:1 4.000 Superhard 2L 10s
17\38 536.842 63.158 9:2 4.500
9\20 540.000 60.000 5:1 5.000
10\22 545.455 54.545 6:1 6.000 Shrutar ↓
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 10s
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