3L 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>
{{MOS intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-10-29 21:49:29 UTC</tt>.<br>
: The original revision id was <tt>377519686</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 is always proper because its period runs Lsss. It is generated by a diatonic semitone or "trienthird"/2/3-tone of 1/12edo (100 cents) to 1/9edo (133 1/3). It represents, among other chromatic scales, those of the August, Augmented and Augene temperaments.
|| 1/12 ||  ||  ||  ||  || 100 ||
||  ||  ||  ||  || 5/57 || 105.263158 ||
||  ||  ||  || 4/45 ||  || 106 2/3 ||
||  ||  ||  ||  || 7/78 || 107 7/13 ||
||  ||  || 3/33 ||  ||  || 109 1/9 ||
||  ||  ||  ||  || 8/87 || 110.344828 ||
||  ||  ||  || 5/54 ||  || 111 1/9 ||
||  ||  ||  ||  || 7/75 || 112 ||
||  || 2/21 ||  ||  ||  || 114 2/4 ||
||  ||  ||  ||  || 7/72 || 116 2/3 ||
||  ||  ||  || 5/51 ||  || 117.647059 ||
||  ||  ||  ||  || 8/81 || 118 14/27 ||
||  ||  || 3/30 ||  ||  || 120 ||
||  ||  ||  ||  || 7/69 || 121.73913 ||
||  ||  ||  || 4/39 ||  || 123 1/13 ||
||  ||  ||  ||  || 5/48 || 125 ||
|| 1/9 ||  ||  ||  ||  || 133 1/3 ||</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;3L 9s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS is always proper because its period runs Lsss. It is generated by a diatonic semitone or &amp;quot;trienthird&amp;quot;/2/3-tone of 1/12edo (100 cents) to 1/9edo (133 1/3). It represents, among other chromatic scales, those of the August, Augmented and Augene temperaments.&lt;br /&gt;


This MOS represents, among other chromatic scales, that of the [[Augene]] temperament.


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &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;100&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;5/57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105.263158&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;4/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;106 2/3&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/78&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;107 7/13&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;3/33&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 1/9&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;8/87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;110.344828&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;111 1/9&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;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 2/4&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 2/3&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;5/51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.647059&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;8/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;118 14/27&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;3/30&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;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;7/69&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;121.73913&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;4/39&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;5/48&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;1/9&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;133 1/3&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
| 6/5 = [[Misty]]/[[fog]]
| 3/2 = [[Augene]] is around here
| 13/8 = Golden augene (86.6169{{c}})
| 5/2 = [[Inflated]] is around here
| 13/5 = Golden inflated (71.1993{{c}})
| 6/1 = [[Hemiaug]]
}}
 
{{todo|expand}}
 
[[Category:12-tone scales]]

Latest revision as of 06:08, 13 January 2026

↖ 2L 8s ↑ 3L 8s 4L 8s ↗
← 2L 9s 3L 9s 4L 9s →
↙ 2L 10s ↓ 3L 10s 4L 10s ↘
Scale structure
Step pattern LsssLsssLsss
sssLsssLsssL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 3\12 to 1\3 (300.0 ¢ to 400.0 ¢)
Dark 0\3 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to 3L 6s (tcherepnin)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 3L 6s
Sister 9L 3s
Daughters 12L 3s, 3L 12s
Neutralized 6L 6s
2-Flought 15L 9s, 3L 21s
Equal tunings
Equalized (L:s = 1:1) 3\12 (300.0 ¢)
Supersoft (L:s = 4:3) 10\39 (307.7 ¢)
Soft (L:s = 3:2) 7\27 (311.1 ¢)
Semisoft (L:s = 5:3) 11\42 (314.3 ¢)
Basic (L:s = 2:1) 4\15 (320.0 ¢)
Semihard (L:s = 5:2) 9\33 (327.3 ¢)
Hard (L:s = 3:1) 5\18 (333.3 ¢)
Superhard (L:s = 4:1) 6\21 (342.9 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)
View • Talk • Edit

3L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 9 small steps, with a period of 1 large step and 3 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 9s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 300 ¢ to 400 ¢, or from 0 ¢ to 100 ¢.

This MOS represents, among other chromatic scales, that of the Augene temperament.

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 3L 9s
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 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 200.0 ¢
Major 2-mosstep M2ms L + s 200.0 ¢ to 400.0 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 300.0 ¢
Perfect 3-mosstep P3ms L + 2s 300.0 ¢ to 400.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 400.0 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 400.0 ¢ to 500.0 ¢
Augmented 5-mosstep A5ms 2L + 3s 500.0 ¢ to 800.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 400.0 ¢ to 600.0 ¢
Major 6-mosstep M6ms 2L + 4s 600.0 ¢ to 800.0 ¢
7-mosstep Diminished 7-mosstep d7ms L + 6s 400.0 ¢ to 700.0 ¢
Perfect 7-mosstep P7ms 2L + 5s 700.0 ¢ to 800.0 ¢
8-mosstep Perfect 8-mosstep P8ms 2L + 6s 800.0 ¢
9-mosstep Perfect 9-mosstep P9ms 2L + 7s 800.0 ¢ to 900.0 ¢
Augmented 9-mosstep A9ms 3L + 6s 900.0 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 800.0 ¢ to 1000.0 ¢
Major 10-mosstep M10ms 3L + 7s 1000.0 ¢ to 1200.0 ¢
11-mosstep Diminished 11-mosstep d11ms 2L + 9s 800.0 ¢ to 1100.0 ¢
Perfect 11-mosstep P11ms 3L + 8s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 3L + 9s 1200.0 ¢

Generator chain

Generator chain of 3L 9s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
4 Augmented 0-mosdegree A0md Augmented 4-mosdegree A4md Augmented 8-mosdegree A8md
3 Augmented 1-mosdegree A1md Augmented 5-mosdegree A5md Augmented 9-mosdegree A9md
2 Major 2-mosdegree M2md Major 6-mosdegree M6md Major 10-mosdegree M10md
1 Perfect 3-mosdegree P3md Perfect 7-mosdegree P7md Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 4-mosdegree		 P0md
P4md		 Perfect 4-mosdegree
Perfect 8-mosdegree		 P4md
P8md		 Perfect 8-mosdegree
Perfect 12-mosdegree		 P8md
P12md
−1 Perfect 1-mosdegree P1md Perfect 5-mosdegree P5md Perfect 9-mosdegree P9md
−2 Minor 2-mosdegree m2md Minor 6-mosdegree m6md Minor 10-mosdegree m10md
−3 Diminished 3-mosdegree d3md Diminished 7-mosdegree d7md Diminished 11-mosdegree d11md
−4 Diminished 4-mosdegree d4md Diminished 8-mosdegree d8md Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 3L 9s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
9|0(3) 1 LsssLsssLsss Perf. Aug. Maj. Perf. Perf. Aug. Maj. Perf. Perf. Aug. Maj. Perf. Perf.
6|3(3) 4 sLsssLsssLss Perf. Perf. Maj. Perf. Perf. Perf. Maj. Perf. Perf. Perf. Maj. Perf. Perf.
3|6(3) 3 ssLsssLsssLs Perf. Perf. Min. Perf. Perf. Perf. Min. Perf. Perf. Perf. Min. Perf. Perf.
0|9(3) 2 sssLsssLsssL Perf. Perf. Min. Dim. Perf. Perf. Min. Dim. Perf. Perf. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\12 300.000 100.000 1:1 1.000 Equalized 3L 9s
16\63 304.762 95.238 6:5 1.200 Misty/fog
13\51 305.882 94.118 5:4 1.250
23\90 306.667 93.333 9:7 1.286
10\39 307.692 92.308 4:3 1.333 Supersoft 3L 9s
27\105 308.571 91.429 11:8 1.375
17\66 309.091 90.909 7:5 1.400
24\93 309.677 90.323 10:7 1.429
7\27 311.111 88.889 3:2 1.500 Soft 3L 9s
Augene is around here
25\96 312.500 87.500 11:7 1.571
18\69 313.043 86.957 8:5 1.600
29\111 313.514 86.486 13:8 1.625 Golden augene (86.6169 ¢)
11\42 314.286 85.714 5:3 1.667 Semisoft 3L 9s
26\99 315.152 84.848 12:7 1.714
15\57 315.789 84.211 7:4 1.750
19\72 316.667 83.333 9:5 1.800
4\15 320.000 80.000 2:1 2.000 Basic 3L 9s
Scales with tunings softer than this are proper
17\63 323.810 76.190 9:4 2.250
13\48 325.000 75.000 7:3 2.333
22\81 325.926 74.074 12:5 2.400
9\33 327.273 72.727 5:2 2.500 Semihard 3L 9s
Inflated is around here
23\84 328.571 71.429 13:5 2.600 Golden inflated (71.1993 ¢)
14\51 329.412 70.588 8:3 2.667
19\69 330.435 69.565 11:4 2.750
5\18 333.333 66.667 3:1 3.000 Hard 3L 9s
16\57 336.842 63.158 10:3 3.333
11\39 338.462 61.538 7:2 3.500
17\60 340.000 60.000 11:3 3.667
6\21 342.857 57.143 4:1 4.000 Superhard 3L 9s
13\45 346.667 53.333 9:2 4.500
7\24 350.000 50.000 5:1 5.000
8\27 355.556 44.444 6:1 6.000 Hemiaug
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 9s
Retrieved from "https://en.xen.wiki/index.php?title=3L_9s&oldid=221423"