8L 21s

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↖ 7L 20s ↑ 8L 20s 9L 20s ↗
← 7L 21s 8L 21s 9L 21s →
↙ 7L 22s ↓ 8L 22s 9L 22s ↘ 
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Scale structure
Step pattern LssLsssLssLsssLsssLssLsssLsss
sssLsssLssLsssLsssLssLsssLssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 18\29 to 5\8 (744.8¢ to 750.0¢)
Dark 3\8 to 11\29 (450.0¢ to 455.2¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Ancestor's step ratio range 1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent 8L 13s
Sister 21L 8s
Daughters 29L 8s, 8L 29s
Neutralized 16L 13s
2-Flought 37L 21s, 8L 50s
Equal tunings
Equalized (L:s = 1:1) 18\29 (744.8¢)
Supersoft (L:s = 4:3) 59\95 (745.3¢)
Soft (L:s = 3:2) 41\66 (745.5¢)
Semisoft (L:s = 5:3) 64\103 (745.6¢)
Basic (L:s = 2:1) 23\37 (745.9¢)
Semihard (L:s = 5:2) 51\82 (746.3¢)
Hard (L:s = 3:1) 28\45 (746.7¢)
Superhard (L:s = 4:1) 33\53 (747.2¢)
Collapsed (L:s = 1:0) 5\8 (750.0¢)

8L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 21 small steps, repeating every octave. 8L 21s is a great-grandchild scale of 5L 3s, expanding it by 21 tones. Generators that produce this scale range from 744.8¢ to 750¢, or from 450¢ to 455.2¢.

Intervals

Intervals of 8L 21s
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 41.4¢
Major 1-mosstep M1ms L 41.4¢ to 150.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 82.8¢
Major 2-mosstep M2ms L + s 82.8¢ to 150.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 124.1¢
Major 3-mosstep M3ms L + 2s 124.1¢ to 150.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0¢ to 165.5¢
Major 4-mosstep M4ms 2L + 2s 165.5¢ to 300.0¢
5-mosstep Minor 5-mosstep m5ms L + 4s 150.0¢ to 206.9¢
Major 5-mosstep M5ms 2L + 3s 206.9¢ to 300.0¢
6-mosstep Minor 6-mosstep m6ms L + 5s 150.0¢ to 248.3¢
Major 6-mosstep M6ms 2L + 4s 248.3¢ to 300.0¢
7-mosstep Minor 7-mosstep m7ms L + 6s 150.0¢ to 289.7¢
Major 7-mosstep M7ms 2L + 5s 289.7¢ to 300.0¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 300.0¢ to 331.0¢
Major 8-mosstep M8ms 3L + 5s 331.0¢ to 450.0¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 300.0¢ to 372.4¢
Major 9-mosstep M9ms 3L + 6s 372.4¢ to 450.0¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 300.0¢ to 413.8¢
Major 10-mosstep M10ms 3L + 7s 413.8¢ to 450.0¢
11-mosstep Perfect 11-mosstep P11ms 3L + 8s 450.0¢ to 455.2¢
Augmented 11-mosstep A11ms 4L + 7s 455.2¢ to 600.0¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 450.0¢ to 496.6¢
Major 12-mosstep M12ms 4L + 8s 496.6¢ to 600.0¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 450.0¢ to 537.9¢
Major 13-mosstep M13ms 4L + 9s 537.9¢ to 600.0¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 450.0¢ to 579.3¢
Major 14-mosstep M14ms 4L + 10s 579.3¢ to 600.0¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 600.0¢ to 620.7¢
Major 15-mosstep M15ms 5L + 10s 620.7¢ to 750.0¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 600.0¢ to 662.1¢
Major 16-mosstep M16ms 5L + 11s 662.1¢ to 750.0¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 600.0¢ to 703.4¢
Major 17-mosstep M17ms 5L + 12s 703.4¢ to 750.0¢
18-mosstep Diminished 18-mosstep d18ms 4L + 14s 600.0¢ to 744.8¢
Perfect 18-mosstep P18ms 5L + 13s 744.8¢ to 750.0¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 750.0¢ to 786.2¢
Major 19-mosstep M19ms 6L + 13s 786.2¢ to 900.0¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 750.0¢ to 827.6¢
Major 20-mosstep M20ms 6L + 14s 827.6¢ to 900.0¢
21-mosstep Minor 21-mosstep m21ms 5L + 16s 750.0¢ to 869.0¢
Major 21-mosstep M21ms 6L + 15s 869.0¢ to 900.0¢
22-mosstep Minor 22-mosstep m22ms 6L + 16s 900.0¢ to 910.3¢
Major 22-mosstep M22ms 7L + 15s 910.3¢ to 1050.0¢
23-mosstep Minor 23-mosstep m23ms 6L + 17s 900.0¢ to 951.7¢
Major 23-mosstep M23ms 7L + 16s 951.7¢ to 1050.0¢
24-mosstep Minor 24-mosstep m24ms 6L + 18s 900.0¢ to 993.1¢
Major 24-mosstep M24ms 7L + 17s 993.1¢ to 1050.0¢
25-mosstep Minor 25-mosstep m25ms 6L + 19s 900.0¢ to 1034.5¢
Major 25-mosstep M25ms 7L + 18s 1034.5¢ to 1050.0¢
26-mosstep Minor 26-mosstep m26ms 7L + 19s 1050.0¢ to 1075.9¢
Major 26-mosstep M26ms 8L + 18s 1075.9¢ to 1200.0¢
27-mosstep Minor 27-mosstep m27ms 7L + 20s 1050.0¢ to 1117.2¢
Major 27-mosstep M27ms 8L + 19s 1117.2¢ to 1200.0¢
28-mosstep Minor 28-mosstep m28ms 7L + 21s 1050.0¢ to 1158.6¢
Major 28-mosstep M28ms 8L + 20s 1158.6¢ to 1200.0¢
29-mosstep Perfect 29-mosstep P29ms 8L + 21s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 8L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
18\29 744.828 455.172 1:1 1.000 Equalized 8L 21s
95\153 745.098 454.902 6:5 1.200
77\124 745.161 454.839 5:4 1.250
136\219 745.205 454.795 9:7 1.286
59\95 745.263 454.737 4:3 1.333 Supersoft 8L 21s
159\256 745.312 454.688 11:8 1.375
100\161 745.342 454.658 7:5 1.400
141\227 745.374 454.626 10:7 1.429
41\66 745.455 454.545 3:2 1.500 Soft 8L 21s
146\235 745.532 454.468 11:7 1.571
105\169 745.562 454.438 8:5 1.600
169\272 745.588 454.412 13:8 1.625
64\103 745.631 454.369 5:3 1.667 Semisoft 8L 21s
151\243 745.679 454.321 12:7 1.714
87\140 745.714 454.286 7:4 1.750
110\177 745.763 454.237 9:5 1.800
23\37 745.946 454.054 2:1 2.000 Basic 8L 21s
Scales with tunings softer than this are proper
97\156 746.154 453.846 9:4 2.250
74\119 746.218 453.782 7:3 2.333
125\201 746.269 453.731 12:5 2.400
51\82 746.341 453.659 5:2 2.500 Semihard 8L 21s
130\209 746.411 453.589 13:5 2.600
79\127 746.457 453.543 8:3 2.667
107\172 746.512 453.488 11:4 2.750
28\45 746.667 453.333 3:1 3.000 Hard 8L 21s
89\143 746.853 453.147 10:3 3.333
61\98 746.939 453.061 7:2 3.500
94\151 747.020 452.980 11:3 3.667
33\53 747.170 452.830 4:1 4.000 Superhard 8L 21s
71\114 747.368 452.632 9:2 4.500
38\61 747.541 452.459 5:1 5.000
43\69 747.826 452.174 6:1 6.000
5\8 750.000 450.000 1:0 → ∞ Collapsed 8L 21s


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