1L 11s: Difference between revisions

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→Modes: changes MOS mode degrees template to MOS modes template due to size constraints
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{{Todo|review|inline=1|text=Adopt scale tree template, review entries}}{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
The simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, or [[passion]] (5;4 = +3 generators), and even there it implies a val with warts for 3 and (for the most part) 5.
The simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, or [[passion]] (5;4 = +3 generators), and even there it implies a val with warts for 3 and (for the most part) 5.
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* Chroma-positive generator: 1100 cents (11\12) to 1200 cents (1\1)
* Chroma-positive generator: 1100 cents (11\12) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 100 cents (1\12)
* Chroma-negative generator: 0 cents (0\1) to 100 cents (1\12)
 
{{Scale tree}}
{| 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
|-
| || || || || || || || 11\134 || 98.507 || 13 || 11 || 1.182 ||
|-
| || || || || || 5\61 || || || 98.361 || 6 || 5 || 1.200 ||
|-
| || || || || || || || 14\171 || 98.246 || 17 || 14 || 1.214 ||
|-
| || || || || || || 9\110 || || 98.182 || 11 || 9 || 1.222 ||
|-
| || || || || || || || 13\159 || 98.113 || 16 || 13 || 1.231 ||
|-
| || || || || 4\49 || || || || 97.959 || 5 || 4 || 1.250 || [[Passion]]
|-
| || || || || || || || 15\184 || 97.826 || 19 || 15 || 1.267 ||
|-
| || || || || || || 11\135 || || 97.778 || 14 || 11 || 1.273 ||
|-
| || || || || || || || 18\221 || 97.738 || 23 || 18 || 1.278 ||
|-
| || || || || || 7\86 || || || 97.674 || 9 || 7 || 1.286 ||
|-
| || || || || || || || 17\209 || 97.608 || 22 || 17 || 1.294 ||
|-
| || || || || || || 10\123 || || 97.561 || 13 || 10 || 1.300 ||
|-
| || || || || || || || 13\160 || 97.500 || 17 || 13 || 1.308 ||
|-
| || || || 3\37 || || || || || 97.297 || 4 || 3 || 1.333 ||
|-
| || || || || || || || 14\173 || 97.110 || 19 || 14 || 1.357 ||
|-
| || || || || || || 11\136 || || 97.059 || 15 || 11 || 1.364 ||
|-
| || || || || || || || 19\235 || 97.021 || 26 || 19 || 1.368 ||
|-
| || || || || || 8\99 || || || 96.970 || 11 || 8 || 1.375 ||
|-
| || || || || || || || 21\260 || 96.923 || 29 || 21 || 1.381 ||
|-
| || || || || || || 13\161 || || 96.894 || 18 || 13 || 1.385 ||
|-
| || || || || || || || 18\223 || 96.861 || 25 || 18 || 1.389 ||
|-
| || || || || 5\62 || || || || 96.774 || 7 || 5 || 1.400 ||
|-
| || || || || || || || 17\211 || 96.682 || 24 || 17 || 1.412 ||
|-
| || || || || || || 12\149 || || 96.644 || 17 || 12 || 1.417 ||
|-
| || || || || || || || 19\236 || 96.610 || 27 || 19 || 1.421 ||
|-
| || || || || || 7\87 || || || 96.552 || 10 || 7 || 1.429 ||
|-
| || || || || || || || 16\199 || 96.482 || 23 || 16 || 1.438 ||
|-
| || || || || || || 9\112 || || 96.429 || 13 || 9 || 1.444 ||
|-
| || || || || || || || 11\137 || 96.35 || 16 || 11 || 1.455 ||
|-
| || || 2\25 || || || || || || 96.000 || 3 || 2 || 1.500 ||
|-
| || || || || || || || 11\138 || 95.652 || 17 || 11 || 1.545 ||
|-
| || || || || || || 9\113 || || 95.575 || 14 || 9 || 1.556 ||
|-
| || || || || || || || 16\201 || 95.522 || 25 || 16 || 1.563 ||
|-
| || || || || || 7\88 || || || 95.455 || 11 || 7 || 1.571 ||
|-
| || || || || || || || 19\239 || 95.397 || 30 || 19 || 1.579 ||
|-
| || || || || || || 12\151 || || 95.364 || 19 || 12 || 1.583 ||
|-
| || || || || || || || 17\214 || 95.327 || 27 || 17 || 1.588 ||
|-
| || || || || 5\63 || || || || 95.238 || 8 || 5 || 1.600 ||
|-
| || || || || || || || 18\227 || 95.154 || 29 || 18 || 1.611 ||
|-
| || || || || || || 13\164 || || 95.122 || 21 || 13 || 1.615 ||
|-
| || || || || || || || 21\265 || 95.094 || 34 || 21 || 1.619 || Unnamed golden tuning (95.1020¢)
|-
| || || || || || 8\101 || || || 95.050 || 13 || 8 || 1.625 ||
|-
| || || || || || || || 19\240 || 95.000 || 31 || 19 || 1.632 ||
|-
| || || || || || || 11\139 || || 94.964 || 18 || 11 || 1.636 ||
|-
| || || || || || || || 14\177 || 94.915 || 23 || 14 || 1.643 ||
|-
| || || || 3\38 || || || || || 94.737 || 5 || 3 || 1.667 ||
|-
| || || || || || || || 13\165 || 94.545 || 22 || 13 || 1.692 ||
|-
| || || || || || || 10\127 || || 94.488 || 17 || 10 || 1.700 ||
|-
| || || || || || || || 17\216 || 94.444 || 29 || 17 || 1.706 ||
|-
| || || || || || 7\89 || || || 94.382 || 12 || 7 || 1.714 ||
|-
| || || || || || || || 18\229 || 94.323 || 31 || 18 || 1.722 ||
|-
| || || || || || || 11\140 || || 94.286 || 19 || 11 || 1.727 ||
|-
| || || || || || || || 15\191 || 94.241 || 26 || 15 || 1.733 ||
|-
| || || || || 4\51 || || || || 94.118 || 7 || 4 || 1.750 ||
|-
| || || || || || || || 13\166 || 93.976 || 23 || 13 || 1.769 ||
|-
| || || || || || || 9\115 || || 93.913 || 16 || 9 || 1.778 ||
|-
| || || || || || || || 14\179 || 93.855 || 25 || 14 || 1.786 ||
|-
| || || || || || 5\64 || || || 93.750 || 9 || 5 || 1.800 ||
|-
| || || || || || || || 11\141 || 93.617 || 20 || 11 || 1.818 ||
|-
| || || || || || || 6\77 || || 93.506 || 11 || 6 || 1.833 ||
|-
| || || || || || || || 7\90 || 93.333 || 13 || 7 || 1.857 ||
|-
| || 1\13 || || || || || || || 92.308 || 2 || 1 || 2.000 || Basic 1L 11s <br>(small steps larger than this are proper)
|-
| || || || || || || || 6\79 || 91.139 || 13 || 6 || 2.167 ||
|-
| || || || || || || 5\66 || || 90.909 || 11 || 5 || 2.200 ||
|-
| || || || || || || || 9\119 || 90.756 || 20 || 9 || 2.222 ||
|-
| || || || || || 4\53 || || || 90.566 || 9 || 4 || 2.250 ||
|-
| || || || || || || || 11\146 || 90.411 || 25 || 11 || 2.273 ||
|-
| || || || || || || 7\93 || || 90.323 || 16 || 7 || 2.286 ||
|-
| || || || || || || || 10\133 || 90.226 || 23 || 10 || 2.300 ||
|-
| || || || || 3\40 || || || || 90.000 || 7 || 3 || 2.333 ||
|-
| || || || || || || || 11\147 || 89.796 || 26 || 11 || 2.364 ||
|-
| || || || || || || 8\107 || || 89.720 || 19 || 8 || 2.375 ||
|-
| || || || || || || || 13\174 || 89.655 || 31 || 13 || 2.385 ||
|-
| || || || || || 5\67 || || || 89.552 || 12 || 5 || 2.400 ||
|-
| || || || || || || || 12\161 || 89.441 || 29 || 12 || 2.417 ||
|-
| || || || || || || 7\94 || || 89.362 || 17 || 7 || 2.429 ||
|-
| || || || || || || || 9\121 || 89.256 || 22 || 9 || 2.444 || [[Slithy]]
|-
| || || || 2\27 || || || || || 88.889 || 5 || 2 || 2.500 ||
|-
| || || || || || || || 9\122 || 88.525 || 23 || 9 || 2.556 ||
|-
| || || || || || || 7\95 || || 88.421 || 18 || 7 || 2.571 ||
|-
| || || || || || || || 12\163 || 88.344 || 31 || 12 || 2.583 ||
|-
| || || || || || 5\68 || || || 88.235 || 13 || 5 || 2.600 ||
|-
| || || || || || || || 13\177 || 88.136 || 34 || 13 || 2.615 || Golden [[octacot]] (88.1184¢)
|-
| || || || || || || 8\109 || || 88.073 || 21 || 8 || 2.625 || Octacot
|-
| || || || || || || || 11\150 || 88.000 || 29 || 11 || 2.636 || Octacot
|-
| || || || || 3\41 || || || || 87.805 || 8 || 3 || 2.667 ||
|-
| || || || || || || || 10\137 || 87.591 || 27 || 10 || 2.700 ||
|-
| || || || || || || 7\96 || || 87.500 || 19 || 7 || 2.714 ||
|-
| || || || || || || || 11\151 || 87.417 || 30 || 11 || 2.727 ||
|-
| || || || || || 4\55 || || || 87.273 || 11 || 4 || 2.750 ||
|-
| || || || || || || || 9\124 || 87.097 || 25 || 9 || 2.777 ||
|-
| || || || || || || 5\69 || || 86.957 || 14 || 5 || 2.800 ||
|-
| || || || || || || || 6\83 || 86.747 || 17 || 6 || 2.833 ||
|-
| || || 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 || [[Marvolo]]
|-
| || || || || || || || 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 ||
|}
 
[[Category:12-tone scales]]

Revision as of 20:51, 22 September 2024

↑ 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 ¢)
View • Talk • Edit

1L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 11 small steps, repeating every octave. 1L 11s is a grandchild scale of 1L 9s, expanding it by 2 tones. Generators that produce this scale range from 1100 ¢ to 1200 ¢, or from 0 ¢ to 100 ¢. The simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, or passion (5;4 = +3 generators), and even there it implies a val with warts for 3 and (for the most part) 5.

Modes

Modes of 1L 11s
UDP Cyclic
order		 Step
pattern
11|0 1 Lsssssssssss
10|1 12 sLssssssssss
9|2 11 ssLsssssssss
8|3 10 sssLssssssss
7|4 9 ssssLsssssss
6|5 8 sssssLssssss
5|6 7 ssssssLsssss
4|7 6 sssssssLssss
3|8 5 ssssssssLsss
2|9 4 sssssssssLss
1|10 3 ssssssssssLs
0|11 2 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)
Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 1L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\12 1100.000 100.000 1:1 1.000 Equalized 1L 11s
56\61 1101.639 98.361 6:5 1.200
45\49 1102.041 97.959 5:4 1.250
79\86 1102.326 97.674 9:7 1.286
34\37 1102.703 97.297 4:3 1.333 Supersoft 1L 11s
91\99 1103.030 96.970 11:8 1.375
57\62 1103.226 96.774 7:5 1.400
80\87 1103.448 96.552 10:7 1.429
23\25 1104.000 96.000 3:2 1.500 Soft 1L 11s
81\88 1104.545 95.455 11:7 1.571
58\63 1104.762 95.238 8:5 1.600
93\101 1104.950 95.050 13:8 1.625
35\38 1105.263 94.737 5:3 1.667 Semisoft 1L 11s
82\89 1105.618 94.382 12:7 1.714
47\51 1105.882 94.118 7:4 1.750
59\64 1106.250 93.750 9:5 1.800
12\13 1107.692 92.308 2:1 2.000 Basic 1L 11s
Scales with tunings softer than this are proper
49\53 1109.434 90.566 9:4 2.250
37\40 1110.000 90.000 7:3 2.333
62\67 1110.448 89.552 12:5 2.400
25\27 1111.111 88.889 5:2 2.500 Semihard 1L 11s
63\68 1111.765 88.235 13:5 2.600
38\41 1112.195 87.805 8:3 2.667
51\55 1112.727 87.273 11:4 2.750
13\14 1114.286 85.714 3:1 3.000 Hard 1L 11s
40\43 1116.279 83.721 10:3 3.333
27\29 1117.241 82.759 7:2 3.500
41\44 1118.182 81.818 11:3 3.667
14\15 1120.000 80.000 4:1 4.000 Superhard 1L 11s
29\31 1122.581 77.419 9:2 4.500
15\16 1125.000 75.000 5:1 5.000
16\17 1129.412 70.588 6:1 6.000
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 11s
Retrieved from "https://en.xen.wiki/index.php?title=1L_11s&oldid=156154"