5L 18s

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↖ 4L 17s ↑ 5L 17s 6L 17s ↗
← 4L 18s 5L 18s 6L 18s →
↙ 4L 19s ↓ 5L 19s 6L 19s ↘ 
┌╥┬┬┬╥┬┬┬┬╥┬┬┬╥┬┬┬┬╥┬┬┬┬┐
│║│││║││││║│││║││││║│││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssssLsssLssssLssss
ssssLssssLsssLssssLsssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 9\23 to 2\5 (469.6¢ to 480.0¢)
Dark 3\5 to 14\23 (720.0¢ to 730.4¢)
TAMNAMS information
Descends from 5L 3s
Ancestor's step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 5L 13s
Sister 18L 5s
Daughters 23L 5s, 5L 23s
Neutralized 10L 13s
2-Flought 28L 18s, 5L 41s
Equal tunings
Equalized (L:s = 1:1) 9\23 (469.6¢)
Supersoft (L:s = 4:3) 29\74 (470.3¢)
Soft (L:s = 3:2) 20\51 (470.6¢)
Semisoft (L:s = 5:3) 31\79 (470.9¢)
Basic (L:s = 2:1) 11\28 (471.4¢)
Semihard (L:s = 5:2) 24\61 (472.1¢)
Hard (L:s = 3:1) 13\33 (472.7¢)
Superhard (L:s = 4:1) 15\38 (473.7¢)
Collapsed (L:s = 1:0) 2\5 (480.0¢)

5L 18s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 18 small steps, repeating every octave. 5L 18s is a great-grandchild scale of 5L 3s, expanding it by 15 tones. Generators that produce this scale range from 469.6¢ to 480¢, or from 720¢ to 730.4¢.

Modes

Modes of 5L 18s
UDP Cyclic
order		 Step
pattern
22|0 1 LsssLssssLsssLssssLssss
21|1 10 LsssLssssLssssLsssLssss
20|2 19 LssssLsssLssssLsssLssss
19|3 5 LssssLsssLssssLssssLsss
18|4 14 LssssLssssLsssLssssLsss
17|5 23 sLsssLssssLsssLssssLsss
16|6 9 sLsssLssssLssssLsssLsss
15|7 18 sLssssLsssLssssLsssLsss
14|8 4 sLssssLsssLssssLssssLss
13|9 13 sLssssLssssLsssLssssLss
12|10 22 ssLsssLssssLsssLssssLss
11|11 8 ssLsssLssssLssssLsssLss
10|12 17 ssLssssLsssLssssLsssLss
9|13 3 ssLssssLsssLssssLssssLs
8|14 12 ssLssssLssssLsssLssssLs
7|15 21 sssLsssLssssLsssLssssLs
6|16 7 sssLsssLssssLssssLsssLs
5|17 16 sssLssssLsssLssssLsssLs
4|18 2 sssLssssLsssLssssLssssL
3|19 11 sssLssssLssssLsssLssssL
2|20 20 ssssLsssLssssLsssLssssL
1|21 6 ssssLsssLssssLssssLsssL
0|22 15 ssssLssssLsssLssssLsssL

Intervals

Intervals of 5L 18s
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 240.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 104.3¢
Major 2-mosstep M2ms L + s 104.3¢ to 240.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 156.5¢
Major 3-mosstep M3ms L + 2s 156.5¢ to 240.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 208.7¢
Major 4-mosstep M4ms L + 3s 208.7¢ to 240.0¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0¢ to 260.9¢
Major 5-mosstep M5ms 2L + 3s 260.9¢ to 480.0¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0¢ to 313.0¢
Major 6-mosstep M6ms 2L + 4s 313.0¢ to 480.0¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0¢ to 365.2¢
Major 7-mosstep M7ms 2L + 5s 365.2¢ to 480.0¢
8-mosstep Minor 8-mosstep m8ms L + 7s 240.0¢ to 417.4¢
Major 8-mosstep M8ms 2L + 6s 417.4¢ to 480.0¢
9-mosstep Diminished 9-mosstep d9ms L + 8s 240.0¢ to 469.6¢
Perfect 9-mosstep P9ms 2L + 7s 469.6¢ to 480.0¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 480.0¢ to 521.7¢
Major 10-mosstep M10ms 3L + 7s 521.7¢ to 720.0¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 480.0¢ to 573.9¢
Major 11-mosstep M11ms 3L + 8s 573.9¢ to 720.0¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 480.0¢ to 626.1¢
Major 12-mosstep M12ms 3L + 9s 626.1¢ to 720.0¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 480.0¢ to 678.3¢
Major 13-mosstep M13ms 3L + 10s 678.3¢ to 720.0¢
14-mosstep Perfect 14-mosstep P14ms 3L + 11s 720.0¢ to 730.4¢
Augmented 14-mosstep A14ms 4L + 10s 730.4¢ to 960.0¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 720.0¢ to 782.6¢
Major 15-mosstep M15ms 4L + 11s 782.6¢ to 960.0¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 720.0¢ to 834.8¢
Major 16-mosstep M16ms 4L + 12s 834.8¢ to 960.0¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 720.0¢ to 887.0¢
Major 17-mosstep M17ms 4L + 13s 887.0¢ to 960.0¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 720.0¢ to 939.1¢
Major 18-mosstep M18ms 4L + 14s 939.1¢ to 960.0¢
19-mosstep Minor 19-mosstep m19ms 4L + 15s 960.0¢ to 991.3¢
Major 19-mosstep M19ms 5L + 14s 991.3¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 4L + 16s 960.0¢ to 1043.5¢
Major 20-mosstep M20ms 5L + 15s 1043.5¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 4L + 17s 960.0¢ to 1095.7¢
Major 21-mosstep M21ms 5L + 16s 1095.7¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 4L + 18s 960.0¢ to 1147.8¢
Major 22-mosstep M22ms 5L + 17s 1147.8¢ to 1200.0¢
23-mosstep Perfect 23-mosstep P23ms 5L + 18s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 18s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\23 469.565 730.435 1:1 1.000 Equalized 5L 18s
47\120 470.000 730.000 6:5 1.200
38\97 470.103 729.897 5:4 1.250
67\171 470.175 729.825 9:7 1.286
29\74 470.270 729.730 4:3 1.333 Supersoft 5L 18s
78\199 470.352 729.648 11:8 1.375
49\125 470.400 729.600 7:5 1.400
69\176 470.455 729.545 10:7 1.429
20\51 470.588 729.412 3:2 1.500 Soft 5L 18s
71\181 470.718 729.282 11:7 1.571
51\130 470.769 729.231 8:5 1.600
82\209 470.813 729.187 13:8 1.625
31\79 470.886 729.114 5:3 1.667 Semisoft 5L 18s
73\186 470.968 729.032 12:7 1.714
42\107 471.028 728.972 7:4 1.750
53\135 471.111 728.889 9:5 1.800
11\28 471.429 728.571 2:1 2.000 Basic 5L 18s
Scales with tunings softer than this are proper
46\117 471.795 728.205 9:4 2.250
35\89 471.910 728.090 7:3 2.333
59\150 472.000 728.000 12:5 2.400
24\61 472.131 727.869 5:2 2.500 Semihard 5L 18s
61\155 472.258 727.742 13:5 2.600
37\94 472.340 727.660 8:3 2.667
50\127 472.441 727.559 11:4 2.750
13\33 472.727 727.273 3:1 3.000 Hard 5L 18s
41\104 473.077 726.923 10:3 3.333
28\71 473.239 726.761 7:2 3.500
43\109 473.394 726.606 11:3 3.667
15\38 473.684 726.316 4:1 4.000 Superhard 5L 18s
32\81 474.074 725.926 9:2 4.500
17\43 474.419 725.581 5:1 5.000
19\48 475.000 725.000 6:1 6.000
2\5 480.000 720.000 1:0 → ∞ Collapsed 5L 18s


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