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6L 19s

Revision as of 01:01, 16 December 2024 by BudjarnLambeth (talk | contribs) (== Intervals == {{MOS intervals}})

6L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 19 small steps, repeating every octave. 6L 19s is a great-grandchild scale of 6L 1s, expanding it by 18 tones. Generators that produce this scale range from 192 ¢ to 200 ¢, or from 1000 ¢ to 1008 ¢.

↖ 5L 18s ↑ 6L 18s 7L 18s ↗
← 5L 19s 6L 19s 7L 19s →
↙ 5L 20s ↓ 6L 20s 7L 20s ↘
Scale structure
Step pattern LsssLsssLsssLsssLsssLssss
ssssLsssLsssLsssLsssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\25 to 1\6 (192.0 ¢ to 200.0 ¢)
Dark 5\6 to 21\25 (1000.0 ¢ to 1008.0 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 6L 13s
Sister 19L 6s
Daughters 25L 6s, 6L 25s
Neutralized 12L 13s
2-Flought 31L 19s, 6L 44s
Equal tunings
Equalized (L:s = 1:1) 4\25 (192.0 ¢)
Supersoft (L:s = 4:3) 13\81 (192.6 ¢)
Soft (L:s = 3:2) 9\56 (192.9 ¢)
Semisoft (L:s = 5:3) 14\87 (193.1 ¢)
Basic (L:s = 2:1) 5\31 (193.5 ¢)
Semihard (L:s = 5:2) 11\68 (194.1 ¢)
Hard (L:s = 3:1) 6\37 (194.6 ¢)
Superhard (L:s = 4:1) 7\43 (195.3 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
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This is the MOS where the large steps divide the small steps into groups of 3-3-3-3-3-4. It is generated by a "neutral" whole tone of no less than 4/25edo (192 cents), laying estimates of the boundary of "practicality" between 37edo (minimum) and 43edo (maximum).

Modes

Modes of 6L 19s
UDP Cyclic
order		 Step
pattern
24|0 1 LsssLsssLsssLsssLsssLssss
23|1 5 LsssLsssLsssLsssLssssLsss
22|2 9 LsssLsssLsssLssssLsssLsss
21|3 13 LsssLsssLssssLsssLsssLsss
20|4 17 LsssLssssLsssLsssLsssLsss
19|5 21 LssssLsssLsssLsssLsssLsss
18|6 25 sLsssLsssLsssLsssLsssLsss
17|7 4 sLsssLsssLsssLsssLssssLss
16|8 8 sLsssLsssLsssLssssLsssLss
15|9 12 sLsssLsssLssssLsssLsssLss
14|10 16 sLsssLssssLsssLsssLsssLss
13|11 20 sLssssLsssLsssLsssLsssLss
12|12 24 ssLsssLsssLsssLsssLsssLss
11|13 3 ssLsssLsssLsssLsssLssssLs
10|14 7 ssLsssLsssLsssLssssLsssLs
9|15 11 ssLsssLsssLssssLsssLsssLs
8|16 15 ssLsssLssssLsssLsssLsssLs
7|17 19 ssLssssLsssLsssLsssLsssLs
6|18 23 sssLsssLsssLsssLsssLsssLs
5|19 2 sssLsssLsssLsssLsssLssssL
4|20 6 sssLsssLsssLsssLssssLsssL
3|21 10 sssLsssLsssLssssLsssLsssL
2|22 14 sssLsssLssssLsssLsssLsssL
1|23 18 sssLssssLsssLsssLsssLsssL
0|24 22 ssssLsssLsssLsssLsssLsssL

Intervals

Intervals of 6L 19s
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 48.0 ¢
Major 1-mosstep M1ms L 48.0 ¢ to 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 96.0 ¢
Major 2-mosstep M2ms L + s 96.0 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 144.0 ¢
Major 3-mosstep M3ms L + 2s 144.0 ¢ to 200.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 192.0 ¢
Perfect 4-mosstep P4ms L + 3s 192.0 ¢ to 200.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0 ¢ to 240.0 ¢
Major 5-mosstep M5ms 2L + 3s 240.0 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0 ¢ to 288.0 ¢
Major 6-mosstep M6ms 2L + 4s 288.0 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 200.0 ¢ to 336.0 ¢
Major 7-mosstep M7ms 2L + 5s 336.0 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 200.0 ¢ to 384.0 ¢
Major 8-mosstep M8ms 2L + 6s 384.0 ¢ to 400.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0 ¢ to 432.0 ¢
Major 9-mosstep M9ms 3L + 6s 432.0 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 400.0 ¢ to 480.0 ¢
Major 10-mosstep M10ms 3L + 7s 480.0 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 400.0 ¢ to 528.0 ¢
Major 11-mosstep M11ms 3L + 8s 528.0 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 400.0 ¢ to 576.0 ¢
Major 12-mosstep M12ms 3L + 9s 576.0 ¢ to 600.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 600.0 ¢ to 624.0 ¢
Major 13-mosstep M13ms 4L + 9s 624.0 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 600.0 ¢ to 672.0 ¢
Major 14-mosstep M14ms 4L + 10s 672.0 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 600.0 ¢ to 720.0 ¢
Major 15-mosstep M15ms 4L + 11s 720.0 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 600.0 ¢ to 768.0 ¢
Major 16-mosstep M16ms 4L + 12s 768.0 ¢ to 800.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 800.0 ¢ to 816.0 ¢
Major 17-mosstep M17ms 5L + 12s 816.0 ¢ to 1000.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 800.0 ¢ to 864.0 ¢
Major 18-mosstep M18ms 5L + 13s 864.0 ¢ to 1000.0 ¢
19-mosstep Minor 19-mosstep m19ms 4L + 15s 800.0 ¢ to 912.0 ¢
Major 19-mosstep M19ms 5L + 14s 912.0 ¢ to 1000.0 ¢
20-mosstep Minor 20-mosstep m20ms 4L + 16s 800.0 ¢ to 960.0 ¢
Major 20-mosstep M20ms 5L + 15s 960.0 ¢ to 1000.0 ¢
21-mosstep Perfect 21-mosstep P21ms 5L + 16s 1000.0 ¢ to 1008.0 ¢
Augmented 21-mosstep A21ms 6L + 15s 1008.0 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 5L + 17s 1000.0 ¢ to 1056.0 ¢
Major 22-mosstep M22ms 6L + 16s 1056.0 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 5L + 18s 1000.0 ¢ to 1104.0 ¢
Major 23-mosstep M23ms 6L + 17s 1104.0 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 5L + 19s 1000.0 ¢ to 1152.0 ¢
Major 24-mosstep M24ms 6L + 18s 1152.0 ¢ to 1200.0 ¢
25-mosstep Perfect 25-mosstep P25ms 6L + 19s 1200.0 ¢

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 6L 19s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\25 192.000 1008.000 1:1 1.000 Equalized 6L 19s
21\131 192.366 1007.634 6:5 1.200
17\106 192.453 1007.547 5:4 1.250
30\187 192.513 1007.487 9:7 1.286
13\81 192.593 1007.407 4:3 1.333 Supersoft 6L 19s
35\218 192.661 1007.339 11:8 1.375
22\137 192.701 1007.299 7:5 1.400
31\193 192.746 1007.254 10:7 1.429
9\56 192.857 1007.143 3:2 1.500 Soft 6L 19s
32\199 192.965 1007.035 11:7 1.571
23\143 193.007 1006.993 8:5 1.600
37\230 193.043 1006.957 13:8 1.625
14\87 193.103 1006.897 5:3 1.667 Semisoft 6L 19s
33\205 193.171 1006.829 12:7 1.714
19\118 193.220 1006.780 7:4 1.750
24\149 193.289 1006.711 9:5 1.800
5\31 193.548 1006.452 2:1 2.000 Basic 6L 19s
Scales with tunings softer than this are proper
21\130 193.846 1006.154 9:4 2.250
16\99 193.939 1006.061 7:3 2.333
27\167 194.012 1005.988 12:5 2.400
11\68 194.118 1005.882 5:2 2.500 Semihard 6L 19s
28\173 194.220 1005.780 13:5 2.600
17\105 194.286 1005.714 8:3 2.667
23\142 194.366 1005.634 11:4 2.750
6\37 194.595 1005.405 3:1 3.000 Hard 6L 19s
19\117 194.872 1005.128 10:3 3.333
13\80 195.000 1005.000 7:2 3.500
20\123 195.122 1004.878 11:3 3.667
7\43 195.349 1004.651 4:1 4.000 Superhard 6L 19s
15\92 195.652 1004.348 9:2 4.500
8\49 195.918 1004.082 5:1 5.000
9\55 196.364 1003.636 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 19s
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