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.
 
== Modes ==
{{MOS modes}}
 
== Intervals ==
{{MOS intervals}}
 
== Scales ==
* [[Cata15]]
* [[Myna15]]
 
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
|-
| | 4/15
! Chroma-positive
| |
! Chroma-negative
| |
| |
| |
| |
| | 320
|-
|-
|
| 11\15 || || || || || || 880.000 || 320.000 || 1 || 1 || 1.000 ||
|
|
|
|
|21/79
|318.987
|-
|-
| |  
| || || || || || 58\79 || 881.013 || 318.987 || 6 || 5 || 1.200 ||
| |  
| |  
| |  
| | 17/64
| |  
| | 318.75
|-
|-
| |  
| || || || || 47\64 || || 881.250 || 318.750 || 5 || 4 || 1.250 ||
| |  
| |  
| | 13/49
| |  
| |  
| | 318.367
|-
|-
| |  
| || || || || || 83\113 || 881.416 || 318.584 || 9 || 7 || 1.286 ||
| |  
| |  
| |  
| | 22/83
| |  
| | 318.072
|-
|-
| |  
| || || || 36\49 || || || 881.633 || 318.367 || 4 || 3 || 1.333 || Catalan
| |  
| | 9/34
| |  
| |  
| |  
| | 317.647
|-
|-
| |  
| || || || || || 97\132 || 881.818 || 318.182 || 11 || 8 || 1.375 ||
| |  
| |  
| |  
| |  
| |  
| | 317.358
|-
|-
| |  
| || || || || 61\83 || || 881.928 || 318.072 || 7 || 5 || 1.400 ||
| |  
| |  
| |  
| | 23/87
| |  
| | 317.241
|-
|-
| |  
| || || || || || 86\117 || 882.051 || 317.949 || 10 || 7 || 1.428 ||
| |  
| |  
| |  
| |  
| |  
| | 317.17
|-
|-
| |  
| || || 25\34 || || || || 882.353 || 317.647 || 3 || 2 || 1.500 || L/s = 3/2
| |  
| |  
| | 14/53
| |  
| |  
| | 316.981
|-
|-
| |  
| || || || || || 89\121 || 882.645 || 317.355 || 11 || 7 || 1.571 || Metakleismic
| |  
| |  
| |  
| |  
| |  
| | 316.733
|-
|-
| |  
| || || || || 64\87 || || 882.759 || 317.241 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| | 19/72
| |  
| | 316.667
|-
|-
| |  
| || || || || || 103\140 || 882.857 || 317.143 || 13 || 8 || 1.625 || Countercata
| | 5/19
| |  
| |  
| |  
| |  
| | 315.7895
|-
|-
| |  
| || || || 39\53 || || || 883.019 || 316.981 || 5 || 3 || 1.667 || Hanson/cata
| |  
| |  
| |  
| | 16/61
| |  
| | 314.754
|-
|-
| |  
| || || || || || 92\125 || 883.200 || 316.800 || 12 || 7 || 1.714 || Catakleismic
| |  
| |  
| | 11/42
| |  
| |  
| | 314.286
|-
|-
| |  
| || || || || 53\72 || || 883.333 || 316.667 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| |  
| | 313.972
|-
|-
| |  
| || || || || || 67\91 || 883.516 || 316.484 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| | 17/65
| |  
| | 313.846
|-
|-
| |  
| || 14\19 || || || || || 884.211 || 315.789 || 2 || 1 || 2.000 || Basic 4L 11s<br>(Generators smaller than this are proper)
| |  
| |  
| |  
| |  
| |  
| | 313.7155
|-
|-
| |  
| || || || || || 59\80 || 885.000 || 315.000 || 9 || 4 || 2.250 || Parakleismic
| |  
| | 6/23
| |  
| |  
| |  
| | 313.0435
|-
|-
| |  
| || || || || 45\61 || || 885.246 || 314.754 || 7 || 3 || 2.333 ||
| |  
| |  
| |  
| |  
| |  
| | 312.73
|-
|-
| |  
| || || || || || 76\103 || 885.437 || 314.563 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| | 13/50
| |  
| | 312
|-
|-
| |  
| || || || 31\42 || || || 885.714 || 314.286 || 5 || 2 || 2.500 ||
| |  
| |  
| | 7/27
| |  
| |  
| | 311.111
|-
|-
| |  
| || || || || || 79\107 || 885.981 || 314.019 || 13 || 5 || 2.600 ||
| |  
| |  
| |  
| |  
| | 15/58
| | 310.345
|-
|-
| |  
| || || || || 48\65 || || 886.154 || 313.846 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| | 8/31
| |  
| | 309.677
|-
|-
|
| || || || || || 65\88 || 886.364 || 313.636 || 11 || 4 || 2.750 ||
|
|
|
|
|9/35
|308.571
|-
|-
| | 1/4
| || || 17\23 || || || || 886.957 || 313.043 || 3 || 1 || 3.000 || L/s = 3/1
| |  
|-
| |  
| || || || || || 54\73 || 887.671 || 312.329 || 10 || 3 || 3.333 ||
| |  
|-
| |  
| || || || || 37\50 || || 888.000 || 312.000 || 7 || 2 || 3.500 ||
| |  
|-
| | 300
| || || || || || 57\77 || 888.312 || 311.688 || 11 || 3 || 3.667 || Oolong
|-
| || || || 20\27 || || || 888.889 || 311.111 || 4 || 1 || 4.000 || 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 || → inf ||
|}
|}
{{todo|expand}}
[[Category:15-tone scales]]

Latest revision as of 00:05, 16 December 2024

↖ 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 ¢)

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

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
11\15 880.000 320.000 1 1 1.000
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 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 1.428
25\34 882.353 317.647 3 2 1.500 L/s = 3/2
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 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
(Generators smaller 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
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 L/s = 3/1
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 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 → inf
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