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6L 17s

Revision as of 00:38, 15 December 2024 by BudjarnLambeth (talk | contribs) (-todo:expand, already stub which is more accurate; add intervals)

6L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 17 small steps, repeating every octave. 6L 17s is a great-grandchild scale of 5L 1s, expanding it by 17 tones. Generators that produce this scale range from 991.3 ¢ to 1000 ¢, or from 200 ¢ to 208.7 ¢.

↖ 5L 16s ↑ 6L 16s 7L 16s ↗
← 5L 17s 6L 17s 7L 17s →
↙ 5L 18s ↓ 6L 18s 7L 18s ↘
Scale structure
Step pattern LssLsssLsssLsssLsssLsss
sssLsssLsssLsssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 19\23 to 5\6 (991.3 ¢ to 1000.0 ¢)
Dark 1\6 to 4\23 (200.0 ¢ to 208.7 ¢)
TAMNAMS information
Related to 5L 1s (machinoid)
With tunings 1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent 6L 11s
Sister 17L 6s
Daughters 23L 6s, 6L 23s
Neutralized 12L 11s
2-Flought 29L 17s, 6L 40s
Equal tunings
Equalized (L:s = 1:1) 19\23 (991.3 ¢)
Supersoft (L:s = 4:3) 62\75 (992.0 ¢)
Soft (L:s = 3:2) 43\52 (992.3 ¢)
Semisoft (L:s = 5:3) 67\81 (992.6 ¢)
Basic (L:s = 2:1) 24\29 (993.1 ¢)
Semihard (L:s = 5:2) 53\64 (993.8 ¢)
Hard (L:s = 3:1) 29\35 (994.3 ¢)
Superhard (L:s = 4:1) 34\41 (995.1 ¢)
Collapsed (L:s = 1:0) 5\6 (1000.0 ¢)
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Modes

Modes of 6L 17s
UDP Cyclic
order		 Step
pattern
22|0 1 LssLsssLsssLsssLsssLsss
21|1 20 LsssLssLsssLsssLsssLsss
20|2 16 LsssLsssLssLsssLsssLsss
19|3 12 LsssLsssLsssLssLsssLsss
18|4 8 LsssLsssLsssLsssLssLsss
17|5 4 LsssLsssLsssLsssLsssLss
16|6 23 sLssLsssLsssLsssLsssLss
15|7 19 sLsssLssLsssLsssLsssLss
14|8 15 sLsssLsssLssLsssLsssLss
13|9 11 sLsssLsssLsssLssLsssLss
12|10 7 sLsssLsssLsssLsssLssLss
11|11 3 sLsssLsssLsssLsssLsssLs
10|12 22 ssLssLsssLsssLsssLsssLs
9|13 18 ssLsssLssLsssLsssLsssLs
8|14 14 ssLsssLsssLssLsssLsssLs
7|15 10 ssLsssLsssLsssLssLsssLs
6|16 6 ssLsssLsssLsssLsssLssLs
5|17 2 ssLsssLsssLsssLsssLsssL
4|18 21 sssLssLsssLsssLsssLsssL
3|19 17 sssLsssLssLsssLsssLsssL
2|20 13 sssLsssLsssLssLsssLsssL
1|21 9 sssLsssLsssLsssLssLsssL
0|22 5 sssLsssLsssLsssLsssLssL

Intervals

Intervals of 6L 17s
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 52.2 ¢
Major 1-mosstep M1ms L 52.2 ¢ to 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 104.3 ¢
Major 2-mosstep M2ms L + s 104.3 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 156.5 ¢
Major 3-mosstep M3ms L + 2s 156.5 ¢ to 200.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 200.0 ¢ to 208.7 ¢
Augmented 4-mosstep A4ms 2L + 2s 208.7 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms 2L + 3s 260.9 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms 2L + 4s 313.0 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 200.0 ¢ to 365.2 ¢
Major 7-mosstep M7ms 2L + 5s 365.2 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 400.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms 3L + 5s 417.4 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms 3L + 6s 469.6 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 400.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms 3L + 7s 521.7 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 400.0 ¢ to 573.9 ¢
Major 11-mosstep M11ms 3L + 8s 573.9 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 600.0 ¢ to 626.1 ¢
Major 12-mosstep M12ms 4L + 8s 626.1 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 600.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 4L + 9s 678.3 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 600.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 4L + 10s 730.4 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 600.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 4L + 11s 782.6 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 800.0 ¢ to 834.8 ¢
Major 16-mosstep M16ms 5L + 11s 834.8 ¢ to 1000.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 800.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 5L + 12s 887.0 ¢ to 1000.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 800.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 5L + 13s 939.1 ¢ to 1000.0 ¢
19-mosstep Diminished 19-mosstep d19ms 4L + 15s 800.0 ¢ to 991.3 ¢
Perfect 19-mosstep P19ms 5L + 14s 991.3 ¢ to 1000.0 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 1000.0 ¢ to 1043.5 ¢
Major 20-mosstep M20ms 6L + 14s 1043.5 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms 5L + 16s 1000.0 ¢ to 1095.7 ¢
Major 21-mosstep M21ms 6L + 15s 1095.7 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 5L + 17s 1000.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 6L + 16s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 6L + 17s 1200.0 ¢

Tuning spectrum

  Todo: review

Review entries from past page revision and enter them into the 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 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
19\23 991.304 208.696 1:1 1.000 Equalized 6L 17s
100\121 991.736 208.264 6:5 1.200
81\98 991.837 208.163 5:4 1.250
143\173 991.908 208.092 9:7 1.286
62\75 992.000 208.000 4:3 1.333 Supersoft 6L 17s
167\202 992.079 207.921 11:8 1.375
105\127 992.126 207.874 7:5 1.400
148\179 992.179 207.821 10:7 1.429
43\52 992.308 207.692 3:2 1.500 Soft 6L 17s
153\185 992.432 207.568 11:7 1.571
110\133 992.481 207.519 8:5 1.600
177\214 992.523 207.477 13:8 1.625
67\81 992.593 207.407 5:3 1.667 Semisoft 6L 17s
158\191 992.670 207.330 12:7 1.714
91\110 992.727 207.273 7:4 1.750
115\139 992.806 207.194 9:5 1.800
24\29 993.103 206.897 2:1 2.000 Basic 6L 17s
Scales with tunings softer than this are proper
101\122 993.443 206.557 9:4 2.250
77\93 993.548 206.452 7:3 2.333
130\157 993.631 206.369 12:5 2.400
53\64 993.750 206.250 5:2 2.500 Semihard 6L 17s
135\163 993.865 206.135 13:5 2.600
82\99 993.939 206.061 8:3 2.667
111\134 994.030 205.970 11:4 2.750
29\35 994.286 205.714 3:1 3.000 Hard 6L 17s
92\111 994.595 205.405 10:3 3.333
63\76 994.737 205.263 7:2 3.500
97\117 994.872 205.128 11:3 3.667
34\41 995.122 204.878 4:1 4.000 Superhard 6L 17s
73\88 995.455 204.545 9:2 4.500
39\47 995.745 204.255 5:1 5.000
44\53 996.226 203.774 6:1 6.000
5\6 1000.000 200.000 1:0 → ∞ Collapsed 6L 17s


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