1L 11s: Difference between revisions

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{{Infobox MOS
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 11
| Equalized = 11
| Paucitonic = 1
| Pattern = Lsssssssssss
}}
'''1L 11s''' is the MOS pattern Lsssssssssss with small steps ranging from 0\1 (0¢) to 1\12 (one step of [[12edo]] = 100¢).
This MOS, also called the "happy dodecatonic", is not a complete scale for any "interesting" temperament ― the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Perhaps the only use for it is to extend it to 13 tones, i.e. to make it into a different MOS.
This MOS, also called the "happy dodecatonic", is not a complete scale for any "interesting" temperament ― the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Perhaps the only use for it is to extend it to 13 tones, i.e. to make it into a different MOS.


{| class="wikitable"
== Modes ==
! colspan="8" | generator
* 11|0 Lsssssssssss
! | L
* 10|1 sLssssssssss
! | s
* 9|2 ssLsssssssss
! | L/s
* 8|3 sssLssssssss
! | gen (cents)
* 7|4 ssssLsssssss
! | comment
* 6|5 sssssLssssss
* 5|6 ssssssLsssss
* 4|7 sssssssLssss
* 3|8 ssssssssLsss
* 2|9 sssssssssLss
* 1|10 ssssssssssLs
* 0|11 sssssssssssL
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1100 cents (11\12) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 100 cents (1\12)
 
{| class="wikitable center-all"
! colspan="8" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 1\12 || || || || || || || || 100.000 || 1 || 1 || 1.000 ||
|-
| || || || || || || || 7\85 || 98.824 || 8 || 7 || 1.143 || [[Passionate]]/[[pash]]
|-
| || || || || || || 6\73 || || 98.630 || 7 || 6 || 1.167 || Passionate
|-
| || || || || || 5\61 || || || 98.361 || 6 || 5 || 1.200 ||
|-
| || || || || 4\49 || || || || 97.959 || 5 || 4 || 1.250 || [[Passion]]
|-
| || || || || || 7\86 || || || 97.674 || 9 || 7 || 1.286 ||
|-
| || || || 3\37 || || || || || 97.297 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\99 || || || 96.970 || 11 || 8 || 1.375 ||
|-
| || || || || 5\62 || || || || 96.774 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\87 || || || 96.552 || 10 || 7 || 1.429 ||
|-
| || || 2\25 || || || || || || 96.000 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\88 || || || 95.455 || 11 || 7 || 1.571 ||
|-
| || || || || 5\63 || || || || 95.238 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\101 || || || 95.050 || 13 || 8 || 1.625 || Unnamed golden tuning (95.1020¢)
|-
| || || || 3\38 || || || || || 94.737 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\89 || || || 94.382 || 12 || 7 || 1.714 ||
|-
| || || || || 4\51 || || || || 94.118 || 7 || 4 || 1.750 ||
|-
|-
| | 0\1
| || || || || || 5\64 || || || 93.750 || 9 || 5 || 1.800 ||  
| |
| |
| |
| |
| |
| |
| |
| | 1
| | 0
| |
| | 0.000
| |
|-
|-
|
| || 1\13 || || || || || || || 92.308 || 2 || 1 || 2.000 || Basic 1L 11s <br>(small steps larger than this are proper)
|
|
|
|
|
|
|1\19
|8
|1
|8.000
|63.159
|
|-
|-
| |
| || || || || || || 5\66 || || 90.909 || 11 || 5 || 2.200 ||  
| |
| |
| |
| |
| |
| | 1\18
| |
| | 7
| | 1
| | 7.000
| | 66.667
| |
|-
|-
| |
| || || || || || 4\53 || || || 90.566 || 9 || 4 || 2.250 ||  
| |
| |
| |
| |
| | 1\17
| |
| |
| | 6
| | 1
| | 6.000
| | 70.588
| |
|-
|-
| |
| || || || || || || 7\93 || || 90.323 || 16 || 7 || 2.286 ||  
| |
| |
| |
| |
| |
| | 2\33
| |
| | 11
| | 2
| | 5.500
| | 72.727
| |
|-
|-
| |
| || || || || 3\40 || || || || 90.000 || 7 || 3 || 2.333 ||  
| |
| |
| |
| | 1\16
| |
| |
| |
| | 5
| | 1
| | 5.000
| | 75.000
| |
|-
|-
| |
| || || || || || || 8\107 || || 89.720 || 19 || 8 || 2.375 ||  
| |
| |
| |
| |
| |
| | 3\47
| |
| | 14
| | 3
| | 4.667
| | 76.596
| |
|-
|-
| |
| || || || || || 5\67 || || || 89.552 || 12 || 5 || 2.400 ||  
| |
| |
| |
| |
| | 2\31
| |
| |
| | 9
| | 2
| | 4.500
| | 77.419
| |
|-
|-
| |
| || || || || || || 7\94 || || 89.362 || 17 || 7 || 2.429 ||  
| |
| |
| |
| |
| |
| | 3\46
| |
| | 13
| | 3
| | 4.333
| | 78.261
| |
|-
|-
| |
| || || || 2\27 || || || || || 88.889 || 5 || 2 || 2.500 ||  
| |
| |
| | 1\15
| |
| |
| |
| |
| | 4
| | 1
| | 4.000
| | 80.000
| |
|-
|-
| |
| || || || || || || 7\95 || || 88.421 || 18 || 7 || 2.571 ||  
| |
| |
| |
| |
| |
| | 4\59
| |
| | 15
| | 4
| | 3.750
| | 81.356
| |
|-
|-
| |
| || || || || || 5\68 || || || 88.235 || 13 || 5 || 2.600 || [[Octacot]]
| |
| |
| |
| |
| | 3\44
| |
| |
| | 11
| | 3
| | 3.667
| | 81.818
| |
|-
|-
| |
| || || || || || || 8\109 || || 88.073 || 21 || 8 || 2.625 || Golden octacot (88.1184¢)
| |
| |
| |
| |
| |
| | 5\73
| |
| | 18
| | 5
| | 3.600
| | 82.192
| |
|-
|-
| |
| || || || || 3\41 || || || || 87.805 || 8 || 3 || 2.667 || Octacot
| |
| |
| |
| | 2\29
| |
| |
| |
| | 7
| | 2
| | 3.500
| | 82.759
| |
|-
|-
| |
| || || || || || || 7\96 || || 87.500 || 19 || 7 || 2.714 ||  
| |
| |
| |
| |
| |
| | 5\72
| |
| | 17
| | 5
| | 3.400
| | 83.333
| |
|-
|-
| |
| || || || || || 4\55 || || || 87.273 || 11 || 4 || 2.750 ||  
| |
| |
| |
| |
| | 3\43
| |
| |
| | 10
| | 3
| | 3.333
| | 83.721
| |
|-
|-
| |
| || || || || || || 5\69 || || 86.957 || 14 || 5 || 2.800 ||  
| |
| |
| |
| |
| |
| | 4\57
| |
| | 13
| | 4
| | 3.250
| | 84.211
| |
|-
|-
| |
| || || 1\14 || || || || || || 85.714 || 3 || 1 || 3.000 ||  
| |
| | 1\14
| |
| |
| |
| |
| |
| | 3
| | 1
| | 3.000
| | 85.714
| |
|-
|-
| |
| || || || || || || || 5\71 || 84.507 || 16 || 5 || 3.200 ||  
| |
| |
| |
| |
| |
| | 5\69
| |
| | 14
| | 5
| | 2.800
| | 86.957
| |
|-
|-
| |
| || || || || || || 4\57 || || 84.211 || 13 || 4 || 3.250 ||  
| |
| |
| |
| |
| | 4\55
| |
| |
| | 11
| | 4
| | 2.750
| | 87.273
| |
|-
|-
| |
| || || || || || || || 7\100 || 84.000 || 23 || 7 || 3.286 ||  
| |
| |
| |
| |
| |
| | 7\96
| |
| | 19
| | 7
| | 2.714
| | 87.500
| |
|-
|-
| |
| || || || || || 3\43 || || || 83.721 || 10 || 3 || 3.333 ||  
| |
| |
| |
| | 3\41
| |
| |
| |
| | 8
| | 3
| | 2.667
| | 87.805
| | Octacot is around here
|-
|-
| |
| || || || || || || || 8\115 || 83.478 || 27 || 8 || 3.375 ||  
| |
| |
| |
| |
| | 5\68
| |
| |
| | 13
| | 5
| | 2.600
| | 88.235
| |
|-
|-
| |
| || || || || || || 5\72 || || 83.333 || 17 || 5 || 3.400 ||  
| |
| |
| |
| |
| |
| | 7\95
| |
| | 18
| | 7
| | 2.571
| | 88.421
| |
|-
|-
| |
| || || || || || || || 7\101 || 83.168 || 24 || 7 || 3.429 ||  
| |
| |
| | 2\27
| |
| |
| |
| |
| | 5
| | 2
| | 2.500
| | 88.889
| |
|-
|-
| |
| || || || || 2\29 || || || || 82.759 || 7 || 2 || 3.500 ||  
| |
| |
| |
| |
| |
| | 7\94
| |
| | 17
| | 7
| | 2.429
| | 89.362
| |
|-
|-
| |
| || || || || || || || 7\102 || 82.353 || 25 || 7 || 3.571 ||  
| |
| |
| |
| |
| | 5\67
| |
| |
| | 12
| | 5
| | 2.400
| | 89.552
| |
|-
|-
| |
| || || || || || || 5\73 || || 82.192 || 18 || 5 || 3.600 ||  
| |
| |
| |
| | 3\40
| |
| |
| |
| | 7
| | 3
| | 2.333
| | 90.000
| |
|-
|-
| |
| || || || || || || || 8\117 || 82.051 || 29 || 8 || 3.625 ||  
| |
| |
| |
| |
| |
| | 7\93
| |
| | 16
| | 7
| | 2.286
| | 90.323
| |
|-
|-
| |
| || || || || || 3\44 || || || 81.818 || 11 || 3 || 3.667 ||  
| |
| |
| |
| |
| | 4\53
| |
| |
| | 9
| | 4
| | 2.250
| | 90.566
| |
|-
|-
| |
| || || || || || || || 7\103 || 81.553 || 26 || 7 || 3.714 ||  
| |
| |
| |
| |
| |
| | 5\66
| |
| | 11
| | 5
| | 2.200
| | 90.909
| |
|-
|-
| |
| || || || || || || 4\59 || || 81.356 || 15 || 4 || 3.750 ||  
| | 1\13
| |
| |
| |
| |
| |
| |
| | 2
| | 1
| | 2.000
| | 92.308
| |
|-
|-
| |
| || || || || || || || 5\74 || 81.081 || 19 || 5 || 3.800 ||  
| |
| |
| |
| |
| |
| | 6\77
| |
| | 11
| | 6
| | 1.833
| | 93.506
| |
|-
|-
| |
| || || || 1\15 || || || || || 80.000 || 4 || 1 || 4.000 ||  
| |
| |
| |
| |
| | 5\64
| |
| |
| | 9
| | 5
| | 1.800
| | 93.750
| |
|-
|-
| |
| || || || || || || || 4\61 || 78.689 || 17 || 4 || 4.250 ||  
| |
| |
| |
| | 4\51
| |
| |
| |
| | 7
| | 4
| | 1.750
| | 94.118
| |
|-
|-
| |
| || || || || || || 3\46 || || 78.261 || 13 || 3 || 4.333 ||  
| |
| |
| |
| |
| | 7\89
| |
| |
| | 12
| | 7
| | 1.714
| | 94.382
| |
|-
|-
| |
| || || || || || || || 5\77 || 77.922 || 22 || 5 || 4.400 || [[Valentine]]
| |
| |
| | 3\38
| |
| |
| |
| |
| | 5
| | 3
| | 1.667
| | 94.737
| |
|-
|-
| |
| || || || || || 2\31 || || || 77.419 || 9 || 2 || 4.500 ||  
| |
| |
| |
| | 5\63
| |
| |
| |
| | 8
| | 5
| | 1.600
| | 95.238
| |
|-
|-
| |
| || || || || || || || 5\78 || 76.923 || 23 || 5 || 4.600 ||  
| |
| |
| |
| |
| | 7\88
| |
| |
| | 11
| | 7
| | 1.571
| | 95.455
| |
|-
|-
| |
| || || || || || || 3\47 || || 76.596 || 14 || 3 || 4.667 ||  
| |
| | 2\25
| |
| |
| |
| |
| |
| | 3
| | 2
| | 1.500
| | 96.000
| |
|-
|-
| |
| || || || || || || || 4\63 || 76.190 || 19 || 4 || 4.750 ||  
| |
| |
| |
| |
| | 7\87
| |
| |
| | 10
| | 7
| | 1.429
| | 96.552
| |
|-
|-
| |
| || || || || 1\16 || || || || 75.000 || 5 || 1 || 5.000 ||  
| |
| |
| |
| | 5\62
| |
| |
| |
| | 7
| | 5
| | 1.400
| | 96.774
| |
|-
|-
| |
| || || || || || || || 3\49 || 73.469 || 16 || 3 || 5.333 ||  
| |
| |
| |
| |
| | 8\99
| |
| |
| | 11
| | 8
| | 1.375
| | 96.970
| |
|-
|-
| |
| || || || || || || 2\33 || || 72.727 || 11 || 2 || 5.500 ||  
| |
| |
| | 3\37
| |
| |
| |
| |
| | 4
| | 3
| | 1.333
| | 97.297
| |
|-
|-
| |
| || || || || || || || 3\50 || 72.000 || 17 || 3 || 5.667 ||  
| |
| |
| |
| |
| | 7\86
| |
| |
| | 9
| | 7
| | 1.286
| | 97.674
| |
|-
|-
| |
| || || || || || 1\17 || || || 70.588 || 6 || 1 || 6.000 ||  
| |
| |
| |
| | 4\49
| |
| |
| |
| | 5
| | 4
| | 1.250
| | 97.959
| | Passion is around here
|-
|-
| |
| || || || || || || || 2\35 || 68.571 || 13 || 2 || 6.500 ||  
| |
| |
| |
| |
| | 5\61
| |
| |
| | 6
| | 5
| | 1.200
| | 98.361
| |
|-
|-
| |
| || || || || || || 1\18 || || 66.667 || 7 || 1 || 7.000 ||  
| |
| |
| |
| |
| |
| | 6\73
| |
| | 7
| | 6
| | 1.167
| | 98.630
| |
|-
|-
|
| || || || || || || || 1\19 || 63.158 || 8 || 1 || 8.000 || [[Unicorn]]
|
|
|
|
|
|
|7\85
|8
|7
|1.143
|98.8235
|
|-
|-
| | 1\12
| 0\1 || || || || || || || || 0.000 || 1 || 0 || → inf ||  
| |
| |
| |
| |
| |
| |
| |
| | 1
| | 1
| | 1.000
| | 100.000
| |
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:12-tone scales]]

Revision as of 09:32, 22 February 2022

↑ 1L 10s 2L 10s ↗
1L 11s 2L 11s →
↓ 1L 12s 2L 12s ↘ 
┌╥┬┬┬┬┬┬┬┬┬┬┬┐
│║││││││││││││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lsssssssssss
sssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\12 to 1\1 (1100.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 1L 10s
Sister 11L 1s
Daughters 12L 1s, 1L 12s
Neutralized 2L 10s
2-Flought 13L 11s, 1L 23s
Equal tunings
Equalized (L:s = 1:1) 11\12 (1100.0 ¢)
Supersoft (L:s = 4:3) 34\37 (1102.7 ¢)
Soft (L:s = 3:2) 23\25 (1104.0 ¢)
Semisoft (L:s = 5:3) 35\38 (1105.3 ¢)
Basic (L:s = 2:1) 12\13 (1107.7 ¢)
Semihard (L:s = 5:2) 25\27 (1111.1 ¢)
Hard (L:s = 3:1) 13\14 (1114.3 ¢)
Superhard (L:s = 4:1) 14\15 (1120.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 11s is the MOS pattern Lsssssssssss with small steps ranging from 0\1 (0¢) to 1\12 (one step of 12edo = 100¢).

This MOS, also called the "happy dodecatonic", is not a complete scale for any "interesting" temperament ― the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Perhaps the only use for it is to extend it to 13 tones, i.e. to make it into a different MOS.

Modes

  • 11|0 Lsssssssssss
  • 10|1 sLssssssssss
  • 9|2 ssLsssssssss
  • 8|3 sssLssssssss
  • 7|4 ssssLsssssss
  • 6|5 sssssLssssss
  • 5|6 ssssssLsssss
  • 4|7 sssssssLssss
  • 3|8 ssssssssLsss
  • 2|9 sssssssssLss
  • 1|10 ssssssssssLs
  • 0|11 sssssssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1100 cents (11\12) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 100 cents (1\12)
Small step
(chroma-negative generator) 		Cents L s L/s Comments
1\12 100.000 1 1 1.000
7\85 98.824 8 7 1.143 Passionate/pash
6\73 98.630 7 6 1.167 Passionate
5\61 98.361 6 5 1.200
4\49 97.959 5 4 1.250 Passion
7\86 97.674 9 7 1.286
3\37 97.297 4 3 1.333
8\99 96.970 11 8 1.375
5\62 96.774 7 5 1.400
7\87 96.552 10 7 1.429
2\25 96.000 3 2 1.500
7\88 95.455 11 7 1.571
5\63 95.238 8 5 1.600
8\101 95.050 13 8 1.625 Unnamed golden tuning (95.1020¢)
3\38 94.737 5 3 1.667
7\89 94.382 12 7 1.714
4\51 94.118 7 4 1.750
5\64 93.750 9 5 1.800
1\13 92.308 2 1 2.000 Basic 1L 11s
(small steps larger than this are proper)
5\66 90.909 11 5 2.200
4\53 90.566 9 4 2.250
7\93 90.323 16 7 2.286
3\40 90.000 7 3 2.333
8\107 89.720 19 8 2.375
5\67 89.552 12 5 2.400
7\94 89.362 17 7 2.429
2\27 88.889 5 2 2.500
7\95 88.421 18 7 2.571
5\68 88.235 13 5 2.600 Octacot
8\109 88.073 21 8 2.625 Golden octacot (88.1184¢)
3\41 87.805 8 3 2.667 Octacot
7\96 87.500 19 7 2.714
4\55 87.273 11 4 2.750
5\69 86.957 14 5 2.800
1\14 85.714 3 1 3.000
5\71 84.507 16 5 3.200
4\57 84.211 13 4 3.250
7\100 84.000 23 7 3.286
3\43 83.721 10 3 3.333
8\115 83.478 27 8 3.375
5\72 83.333 17 5 3.400
7\101 83.168 24 7 3.429
2\29 82.759 7 2 3.500
7\102 82.353 25 7 3.571
5\73 82.192 18 5 3.600
8\117 82.051 29 8 3.625
3\44 81.818 11 3 3.667
7\103 81.553 26 7 3.714
4\59 81.356 15 4 3.750
5\74 81.081 19 5 3.800
1\15 80.000 4 1 4.000
4\61 78.689 17 4 4.250
3\46 78.261 13 3 4.333
5\77 77.922 22 5 4.400 Valentine
2\31 77.419 9 2 4.500
5\78 76.923 23 5 4.600
3\47 76.596 14 3 4.667
4\63 76.190 19 4 4.750
1\16 75.000 5 1 5.000
3\49 73.469 16 3 5.333
2\33 72.727 11 2 5.500
3\50 72.000 17 3 5.667
1\17 70.588 6 1 6.000
2\35 68.571 13 2 6.500
1\18 66.667 7 1 7.000
1\19 63.158 8 1 8.000 Unicorn
0\1 0.000 1 0 → inf
Retrieved from "https://en.xen.wiki/index.php?title=1L_11s&oldid=86234"