4L 11s: Difference between revisions

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This is a pattern generated by a large minor third of 1/4edo (300) to 4/15edo (320 cents). Because Myna temperament arrives at 3/2 by +10 generators, this is the lowest Myna MOS which has multiple 3/2s.
{{Infobox MOS
| Periods = 1
| nLargeSteps = 4
| nSmallSteps = 11
| Equalized = 4
| Collapsed = 1
| Pattern = LsssLsssLsssLss
}}
{{MOS intro}}


{| class="wikitable"
Because [[myna]] temperament arrives at 3/2 by +10 generators, this is the lowest myna MOS which has multiple 3/2s.
|-
 
| | 4/15
== Modes ==
| |
{{MOS modes}}
| |
 
| |
== Intervals ==
| |
{{MOS intervals}}
| |
 
| | 320
== Scales ==
|-
* [[Cata15]]
| |
* [[Myna15]]
| |
 
| |
== Scale tree ==
| |
{{MOS tuning spectrum
| | 17/64
| 4/3 = [[Catalan]]
| |
| 11/7 = [[Metakleismic]]
| | 318.75
| 13/8 = [[Countercata]]
|-
| 5/3 = [[Kleismic|Hanson/cata]]
| |
| 12/7 = [[Catakleismic]]
| |
| 9/4 = [[Parakleismic]]
| |
| 11/3 = [[Oolong]]
| | 13/49
| 4/1 = [[Starlingtet]]
| |
| 9/2 = [[Myna]]
| |
}}
| | 318.367
 
|-
{{todo|expand}}
| |
[[Category:15-tone scales]]
| |
| |
| |
| | 22/83
| |
| | 318.072
|-
| |
| |
| | 9/34
| |
| |
| |
| | 317.647
|-
| |
| |
| |
| |
| |
| |
| | 317.358
|-
| |
| |
| |
| |
| | 23/87
| |
| | 317.241
|-
| |
| |
| |
| |
| |
| |
| | 317.17
|-
| |
| |
| |
| | 14/53
| |
| |
| | 316.981
|-
| |
| |
| |
| |
| |
| |
| | 316.733
|-
| |
| |
| |
| |
| | 19/72
| |
| | 316.667
|-
| |
| | 5/19
| |
| |
| |
| |
| | 315.7895
|-
| |
| |
| |
| |
| | 16/61
| |
| | 314.754
|-
| |
| |
| |
| | 11/42
| |
| |
| | 314.286
|-
| |
| |
| |
| |
| |
| |
| | 313.972
|-
| |
| |
| |
| |
| | 17/65
| |
| | 313.846
|-
| |
| |
| |
| |
| |
| |
| | 313.7155
|-
| |
| |
| | 6/23
| |
| |
| |
| | 313.0435
|-
| |
| |
| |
| |
| |
| |
| | 312.73
|-
| |
| |
| |
| |
| | 13/50
| |
| | 312
|-
| |
| |
| |
| | 7/27
| |
| |
| | 311.111
|-
| |
| |
| |
| |
| |
| | 15/58
| | 310.345
|-
| |
| |
| |
| |
| | 8/31
| |
| | 309.677
|-
| | 1/4
| |
| |
| |
| |
| |
| | 300
|}

Latest revision as of 00:25, 28 December 2025

↖ 3L 10s ↑ 4L 10s 5L 10s ↗
← 3L 11s 4L 11s 5L 11s →
↙ 3L 12s ↓ 4L 12s 5L 12s ↘
Scale structure
Step pattern LssLsssLsssLsss
sssLsssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\15 to 3\4 (880.0 ¢ to 900.0 ¢)
Dark 1\4 to 4\15 (300.0 ¢ to 320.0 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 4L 7s
Sister 11L 4s
Daughters 15L 4s, 4L 15s
Neutralized 8L 7s
2-Flought 19L 11s, 4L 26s
Equal tunings
Equalized (L:s = 1:1) 11\15 (880.0 ¢)
Supersoft (L:s = 4:3) 36\49 (881.6 ¢)
Soft (L:s = 3:2) 25\34 (882.4 ¢)
Semisoft (L:s = 5:3) 39\53 (883.0 ¢)
Basic (L:s = 2:1) 14\19 (884.2 ¢)
Semihard (L:s = 5:2) 31\42 (885.7 ¢)
Hard (L:s = 3:1) 17\23 (887.0 ¢)
Superhard (L:s = 4:1) 20\27 (888.9 ¢)
Collapsed (L:s = 1:0) 3\4 (900.0 ¢)
View • Talk • Edit

4L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 11 small steps, repeating every octave. 4L 11s is a grandchild scale of 4L 3s, expanding it by 8 tones. Generators that produce this scale range from 880 ¢ to 900 ¢, or from 300 ¢ to 320 ¢.

Because myna temperament arrives at 3/2 by +10 generators, this is the lowest myna MOS which has multiple 3/2s.

Modes

Modes of 4L 11s
UDP Cyclic
order		 Step
pattern
14|0 1 LssLsssLsssLsss
13|1 12 LsssLssLsssLsss
12|2 8 LsssLsssLssLsss
11|3 4 LsssLsssLsssLss
10|4 15 sLssLsssLsssLss
9|5 11 sLsssLssLsssLss
8|6 7 sLsssLsssLssLss
7|7 3 sLsssLsssLsssLs
6|8 14 ssLssLsssLsssLs
5|9 10 ssLsssLssLsssLs
4|10 6 ssLsssLsssLssLs
3|11 2 ssLsssLsssLsssL
2|12 13 sssLssLsssLsssL
1|13 9 sssLsssLssLsssL
0|14 5 sssLsssLsssLssL

Intervals

Intervals of 4L 11s
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 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 300.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 160.0 ¢
Major 2-mosstep M2ms L + s 160.0 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 240.0 ¢
Major 3-mosstep M3ms L + 2s 240.0 ¢ to 300.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 300.0 ¢ to 320.0 ¢
Augmented 4-mosstep A4ms 2L + 2s 320.0 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 300.0 ¢ to 400.0 ¢
Major 5-mosstep M5ms 2L + 3s 400.0 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 300.0 ¢ to 480.0 ¢
Major 6-mosstep M6ms 2L + 4s 480.0 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 300.0 ¢ to 560.0 ¢
Major 7-mosstep M7ms 2L + 5s 560.0 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 600.0 ¢ to 640.0 ¢
Major 8-mosstep M8ms 3L + 5s 640.0 ¢ to 900.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 600.0 ¢ to 720.0 ¢
Major 9-mosstep M9ms 3L + 6s 720.0 ¢ to 900.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 600.0 ¢ to 800.0 ¢
Major 10-mosstep M10ms 3L + 7s 800.0 ¢ to 900.0 ¢
11-mosstep Diminished 11-mosstep d11ms 2L + 9s 600.0 ¢ to 880.0 ¢
Perfect 11-mosstep P11ms 3L + 8s 880.0 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 900.0 ¢ to 960.0 ¢
Major 12-mosstep M12ms 4L + 8s 960.0 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 900.0 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 4L + 9s 1040.0 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 900.0 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 4L + 10s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 4L + 11s 1200.0 ¢

Scales

Scale tree

Scale tree and tuning spectrum of 4L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\15 880.000 320.000 1:1 1.000 Equalized 4L 11s
58\79 881.013 318.987 6:5 1.200
47\64 881.250 318.750 5:4 1.250
83\113 881.416 318.584 9:7 1.286
36\49 881.633 318.367 4:3 1.333 Supersoft 4L 11s
Catalan
97\132 881.818 318.182 11:8 1.375
61\83 881.928 318.072 7:5 1.400
86\117 882.051 317.949 10:7 1.429
25\34 882.353 317.647 3:2 1.500 Soft 4L 11s
89\121 882.645 317.355 11:7 1.571 Metakleismic
64\87 882.759 317.241 8:5 1.600
103\140 882.857 317.143 13:8 1.625 Countercata
39\53 883.019 316.981 5:3 1.667 Semisoft 4L 11s
Hanson/cata
92\125 883.200 316.800 12:7 1.714 Catakleismic
53\72 883.333 316.667 7:4 1.750
67\91 883.516 316.484 9:5 1.800
14\19 884.211 315.789 2:1 2.000 Basic 4L 11s
Scales with tunings softer than this are proper
59\80 885.000 315.000 9:4 2.250 Parakleismic
45\61 885.246 314.754 7:3 2.333
76\103 885.437 314.563 12:5 2.400
31\42 885.714 314.286 5:2 2.500 Semihard 4L 11s
79\107 885.981 314.019 13:5 2.600
48\65 886.154 313.846 8:3 2.667
65\88 886.364 313.636 11:4 2.750
17\23 886.957 313.043 3:1 3.000 Hard 4L 11s
54\73 887.671 312.329 10:3 3.333
37\50 888.000 312.000 7:2 3.500
57\77 888.312 311.688 11:3 3.667 Oolong
20\27 888.889 311.111 4:1 4.000 Superhard 4L 11s
Starlingtet
43\58 889.655 310.345 9:2 4.500 Myna
23\31 890.323 309.677 5:1 5.000
26\35 891.429 308.571 6:1 6.000
3\4 900.000 300.000 1:0 → ∞ Collapsed 4L 11s
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