12L 19s: Difference between revisions

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Replaced content with "{{Infobox MOS}} {{MOS intro}} It is associated with sharper meantone temperaments. == Modes == {{MOS modes}} == Scale tree == {{Scale tree|depth=6}}"
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{{Infobox MOS}}
{| class="wikitable"
{{MOS intro}}
! colspan="9" | generator
It is associated with sharper [[meantone]] temperaments.
! | L
== Modes ==
! | s
{{MOS modes}}
! | L/s
== Scale tree ==
! | gen (cents)
{{Scale tree|depth=6}}
! | comment
|-
| | 5\12
| |
| |
| |
| |
| |
| |
|
|
| | 1
| | 0
| |
| | 500.000
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|53\127
| | 9
| | 1
| | 9.000
| | 500.787
| |
|-
| |
| |
| |
| |
| |
| |
| |
|48\115
|
| | 8
| | 1
| | 8.000
| | 500.870
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|91\218
| | 15
| | 2
| | 7.500
| | 500.917
| |
|-
| |
| |
| |
| |
| |
| |
| |43\103
|
|
| | 7
| | 1
| | 7.000
| | 500.971
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|124\297
| | 20
| | 3
| | 6.667
| | 501.010
| |
|-
| |
| |
| |
| |
| |
| |
| |
|81\194
|
| | 13
| | 2
| | 6.500
| | 501.031
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|119\285
| | 19
| | 3
| | 6.333
| | 501.053
| |
|-
| |
| |
| |
| |
| |
| | 38\91
| |
|
|
| | 6
| | 1
| | 6.000
| | 501.099
| |
|-
| |
| |
| |
| |
| |
| |
| |
|109\261
|
| | 17
| | 3
| | 5.667
| | 501.149
| |
|-
| |
| |
| |
| |
| |
| |
| |71\170
|
|
| | 11
| | 2
| | 5.500
| | 501.176
| |
|-
| |
| |
| |
| |
| |
| |
| |
|104\249
|
| | 16
| | 3
| | 5.333
| | 501.205
| |
|-
| |
| |
| |
| |
| | 33\79
| |
| |
|
|
| | 5
| | 1
| | 5.000
| | 501.266
| |
|-
| |
| |
| |
| |
| |
| |
| |
|127\304
|
| | 19
| | 4
| | 4.750
| | 501.316
| |
|-
| |
| |
| |
| |
| |
| |
| |94\225
|
|
| | 14
| | 3
| | 4.667
| | 501.333
| |
|-
| |
| |
| |
| |
| |
| | 61\146
| |
|
|
| | 9
| | 2
| | 4.500
| | 501.370
| |
|-
| |
| |
| |
| |
| |
| |
| |89\213
|
|
| | 13
| | 3
| | 4.333
| | 501.408
| |
|-
| |
| |
| |
| |
| |
| |
| |
|117\280
|
| | 17
| | 4
| | 4.250
| | 501.429
| |
|-
| |
| |
| |
| | 28\67
| |
| |
| |
|
|
| | 4
| | 1
| | 4.000
| | 501.493
| |
|-
| |
| |
| |
| |
| |
| |
| |107\256
|
|
| | 15
| | 4
| | 3.750
| | 501.562
| |
|-
| |
| |
| |
| |
| |
| | 79\189
| |
|
|
| | 11
| | 3
| | 3.667
| | 501.587
| |
|-
| |
| |
| |
| |
| | 51\122
| |
| |
|
|
| | 7
| | 2
| | 3.500
| | 501.639
| |
|-
| |
| |
| |
| |
| |
| |
| |125\299
|
|
| | 17
| | 5
| | 3.400
| | 501.672
| |
|-
| |
| |
| |
| |
| |
| | 74\177
| |
|
|
| | 10
| | 3
| | 3.333
| | 501.695
| |
|-
| |
| |
| |
| |
| |
| |
| |97\232
|
|
| | 13
| | 4
| | 3.250
| | 501.724
| |
|-
| |
| |
| |
| |
| |
| |
| |
|120\287
|
| | 16
| | 5
| | 3.200
| | 501.742
| |
|-
| |
| |
| | 23\55
| |
| |
| |
| |
|
|
| | 3
| | 1
| | 3.000
| | 501.818
| |
|-
| |
| |
| |
| |
| |
| |
| |110\263
|
|
| | 14
| | 5
| | 2.800
| | 501.901
| |
|-
| |
| |
| |
| |
| |
| | 87\208
| |
|
|
| | 11
| | 4
| | 2.750
| | 501.923
| |
|-
| |
| |
| |
| |
| | 64\153
| |
| |
|
|
| | 8
| | 3
| | 2.667
| | 501.961
| |
|-
| |
| |
| |
| |
| |
| | 105\251
| |
|
|
| | 13
| | 5
| | 2.600
| | 501.992
| |
|-
| |
| |
| |
| | 41\98
| |
| |
| |
|
|
| | 5
| | 2
| | 2.500
| | 502.041
| |
|-
| |
| |
| |
| |
| |
| | 100\239
| |
|
|
| | 12
| | 5
| | 2.400
| | 502.092
| |
|-
| |
| |
| |
| |
| | 59\141
| |
| |
|
|
| | 7
| | 3
| | 2.333
| | 502.128
| |
|-
| |
| |
| |
| |
| |
| | 77\184
| |
|
|
| | 9
| | 4
| | 2.250
| | 502.174
| |
|-
| |
| |
| |
| |
| |
| |
| |95\227
|
|
| | 11
| | 5
| | 2.200
| | 502.203
| |
|-
| |
| |
| |
| |
| |
| |
| |
|113\270
|
| | 13
| | 6
| | 2.167
| | 502.222
| |
|-
| |
| | 18\43
| |
| |
| |
| |
| |
|
|
| | 2
| | 1
| | 2.000
| | 502.326
| |
|-
| |
| |
| |
| |
| |
| |
| |
|121\289
|
| | 13
| | 7
| | 1.857
| | 502.422
| |
|-
| |
| |
| |
| |
| |
| |
| |103\246
|
|
| | 11
| | 6
| | 1.833
| | 502.439
| |
|-
| |
| |
| |
| |
| |
| | 85\203
| |
|
|
| | 9
| | 5
| | 1.800
| | 502.463
| |
|-
| |
| |
| |
| |
| | 67\160
| |
| |
|
|
| | 7
| | 4
| | 1.750
| | 502.500
| |
|-
| |
| |
| |
| |
| |
| | 116\277
| |
|
|
| | 12
| | 7
| | 1.714
| | 502.527
| |
|-
| |
| |
| |
| | 49\117
| |
| |
| |
|
|
| | 5
| | 3
| | 1.667
| | 502.564
| |
|-
| |
| |
| |
| |
| |
| | 129\308
| |
|
|
| | 13
| | 8
| | 1.625
| | 502.597
| |
|-
| |
| |
| |
| |
| | 80\191
| |
| |
|
|
| | 8
| | 5
| | 1.600
| | 502.618
| |
|-
| |
| |
| |
| |
| |
| | 111\265
| |
|
|
| | 11
| | 7
| | 1.571
| | 502.642
| |
|-
| |
| |
| | 31\74
| |
| |
| |
| |
|
|
| | 3
| | 2
| | 1.500
| | 502.703
| |
|-
| |
| |
| |
| |
| |
| | 106\253
| |
|
|
| | 10
| | 7
| | 1.429
| | 502.767
| |
|-
| |
| |
| |
| |
| | 75\179
| |
| |
|
|
| | 7
| | 5
| | 1.400
| | 502.793
| |
|-
| |
| |
| |
| |
| |
| | 119\284
| |
|
|
| | 11
| | 8
| | 1.375
| | 502.817
| |
|-
| |
| |
| |
| | 44\105
| |
| |
| |
|
|
| | 4
| | 3
| | 1.333
| | 502.857
| |
|-
| |
| |
| |
| |
| |
| | 101\241
| |
|
|
| | 9
| | 7
| | 1.286
| | 502.905
| |
|-
| |
| |
| |
| |
| | 57\136
| |
| |
|
|
| | 5
| | 4
| | 1.250
| | 502.941
| |
|-
| |
| |
| |
| |
| |
| |
| |127\303
|
|
| | 11
| | 9
| | 1.222
| | 502.970
| |
|-
| |
| |
| |
| |
| |
| | 70\167
| |
|
|
| | 6
| | 5
| | 1.200
| | 502.994
| |
|-
| |
| |
| |
| |
| |
| |
| |83\198
|
|
| | 7
| | 6
| | 1.167
| | 503.030
| |
|-
| |
| |
| |
| |
| |
| |
| |
|96\229
|
| | 8
| | 7
| | 1.143
| | 503.057
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|109\260
| | 9
| | 8
| | 1.125
| | 503.077
| |
|-
| | 13\31
| |
| |
| |
| |
| |
| |
|
|
| | 1
| | 1
| | 1.000
| | 503.226
| |
|}
 
[[category:todo:intro]]
[[category:todo:expand]]

Revision as of 00:56, 21 June 2023

↖ 11L 18s ↑ 12L 18s 13L 18s ↗
← 11L 19s 12L 19s 13L 19s →
↙ 11L 20s ↓ 12L 20s 13L 20s ↘
Scale structure
Step pattern LsLssLsLssLsLssLssLsLssLsLssLss
ssLssLsLssLsLssLssLsLssLsLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 18\31 to 7\12 (696.8 ¢ to 700.0 ¢)
Dark 5\12 to 13\31 (500.0 ¢ to 503.2 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 5:3 to 2:1 (minisoft)
Related MOS scales
Parent 12L 7s
Sister 19L 12s
Daughters 31L 12s, 12L 31s
Neutralized 24L 7s
2-Flought 43L 19s, 12L 50s
Equal tunings
Equalized (L:s = 1:1) 18\31 (696.8 ¢)
Supersoft (L:s = 4:3) 61\105 (697.1 ¢)
Soft (L:s = 3:2) 43\74 (697.3 ¢)
Semisoft (L:s = 5:3) 68\117 (697.4 ¢)
Basic (L:s = 2:1) 25\43 (697.7 ¢)
Semihard (L:s = 5:2) 57\98 (698.0 ¢)
Hard (L:s = 3:1) 32\55 (698.2 ¢)
Superhard (L:s = 4:1) 39\67 (698.5 ¢)
Collapsed (L:s = 1:0) 7\12 (700.0 ¢)
View • Talk • Edit

12L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 19 small steps, repeating every octave. 12L 19s is a great-grandchild scale of 5L 2s, expanding it by 24 tones. Generators that produce this scale range from 696.8 ¢ to 700 ¢, or from 500 ¢ to 503.2 ¢. It is associated with sharper meantone temperaments.

Modes

Modes of 12L 19s
UDP Cyclic
order		 Step
pattern
30|0 1 LsLssLsLssLsLssLssLsLssLsLssLss
29|1 19 LsLssLsLssLssLsLssLsLssLsLssLss
28|2 6 LsLssLsLssLssLsLssLsLssLssLsLss
27|3 24 LsLssLssLsLssLsLssLsLssLssLsLss
26|4 11 LsLssLssLsLssLsLssLssLsLssLsLss
25|5 29 LssLsLssLsLssLsLssLssLsLssLsLss
24|6 16 LssLsLssLsLssLssLsLssLsLssLsLss
23|7 3 LssLsLssLsLssLssLsLssLsLssLssLs
22|8 21 LssLsLssLssLsLssLsLssLsLssLssLs
21|9 8 LssLsLssLssLsLssLsLssLssLsLssLs
20|10 26 LssLssLsLssLsLssLsLssLssLsLssLs
19|11 13 LssLssLsLssLsLssLssLsLssLsLssLs
18|12 31 sLsLssLsLssLsLssLssLsLssLsLssLs
17|13 18 sLsLssLsLssLssLsLssLsLssLsLssLs
16|14 5 sLsLssLsLssLssLsLssLsLssLssLsLs
15|15 23 sLsLssLssLsLssLsLssLsLssLssLsLs
14|16 10 sLsLssLssLsLssLsLssLssLsLssLsLs
13|17 28 sLssLsLssLsLssLsLssLssLsLssLsLs
12|18 15 sLssLsLssLsLssLssLsLssLsLssLsLs
11|19 2 sLssLsLssLsLssLssLsLssLsLssLssL
10|20 20 sLssLsLssLssLsLssLsLssLsLssLssL
9|21 7 sLssLsLssLssLsLssLsLssLssLsLssL
8|22 25 sLssLssLsLssLsLssLsLssLssLsLssL
7|23 12 sLssLssLsLssLsLssLssLsLssLsLssL
6|24 30 ssLsLssLsLssLsLssLssLsLssLsLssL
5|25 17 ssLsLssLsLssLssLsLssLsLssLsLssL
4|26 4 ssLsLssLsLssLssLsLssLsLssLssLsL
3|27 22 ssLsLssLssLsLssLsLssLsLssLssLsL
2|28 9 ssLsLssLssLsLssLsLssLssLsLssLsL
1|29 27 ssLssLsLssLsLssLsLssLssLsLssLsL
0|30 14 ssLssLsLssLsLssLssLsLssLsLssLsL

Scale tree

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 12L 19s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
18\31 696.774 503.226 1:1 1.000 Equalized 12L 19s
115\198 696.970 503.030 7:6 1.167
97\167 697.006 502.994 6:5 1.200
176\303 697.030 502.970 11:9 1.222
79\136 697.059 502.941 5:4 1.250
219\377 697.082 502.918 14:11 1.273
140\241 697.095 502.905 9:7 1.286
201\346 697.110 502.890 13:10 1.300
61\105 697.143 502.857 4:3 1.333 Supersoft 12L 19s
226\389 697.172 502.828 15:11 1.364
165\284 697.183 502.817 11:8 1.375
269\463 697.192 502.808 18:13 1.385
104\179 697.207 502.793 7:5 1.400
251\432 697.222 502.778 17:12 1.417
147\253 697.233 502.767 10:7 1.429
190\327 697.248 502.752 13:9 1.444
43\74 697.297 502.703 3:2 1.500 Soft 12L 19s
197\339 697.345 502.655 14:9 1.556
154\265 697.358 502.642 11:7 1.571
265\456 697.368 502.632 19:12 1.583
111\191 697.382 502.618 8:5 1.600
290\499 697.395 502.605 21:13 1.615
179\308 697.403 502.597 13:8 1.625
247\425 697.412 502.588 18:11 1.636
68\117 697.436 502.564 5:3 1.667 Semisoft 12L 19s
229\394 697.462 502.538 17:10 1.700
161\277 697.473 502.527 12:7 1.714
254\437 697.483 502.517 19:11 1.727
93\160 697.500 502.500 7:4 1.750
211\363 697.521 502.479 16:9 1.778
118\203 697.537 502.463 9:5 1.800
143\246 697.561 502.439 11:6 1.833
25\43 697.674 502.326 2:1 2.000 Basic 12L 19s
Scales with tunings softer than this are proper
132\227 697.797 502.203 11:5 2.200
107\184 697.826 502.174 9:4 2.250
189\325 697.846 502.154 16:7 2.286
82\141 697.872 502.128 7:3 2.333
221\380 697.895 502.105 19:8 2.375
139\239 697.908 502.092 12:5 2.400
196\337 697.923 502.077 17:7 2.429
57\98 697.959 502.041 5:2 2.500 Semihard 12L 19s
203\349 697.994 502.006 18:7 2.571
146\251 698.008 501.992 13:5 2.600
235\404 698.020 501.980 21:8 2.625
89\153 698.039 501.961 8:3 2.667
210\361 698.061 501.939 19:7 2.714
121\208 698.077 501.923 11:4 2.750
153\263 698.099 501.901 14:5 2.800
32\55 698.182 501.818 3:1 3.000 Hard 12L 19s
135\232 698.276 501.724 13:4 3.250
103\177 698.305 501.695 10:3 3.333
174\299 698.328 501.672 17:5 3.400
71\122 698.361 501.639 7:2 3.500
181\311 698.392 501.608 18:5 3.600
110\189 698.413 501.587 11:3 3.667
149\256 698.438 501.562 15:4 3.750
39\67 698.507 501.493 4:1 4.000 Superhard 12L 19s
124\213 698.592 501.408 13:3 4.333
85\146 698.630 501.370 9:2 4.500
131\225 698.667 501.333 14:3 4.667
46\79 698.734 501.266 5:1 5.000
99\170 698.824 501.176 11:2 5.500
53\91 698.901 501.099 6:1 6.000
60\103 699.029 500.971 7:1 7.000
7\12 700.000 500.000 1:0 → ∞ Collapsed 12L 19s
Retrieved from "https://en.xen.wiki/index.php?title=12L_19s&oldid=117252"