5L 16s
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Scale structure
Step pattern
LsssLsssLsssLsssLssss
ssssLsssLsssLsssLsssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
4\21 to 1\5 (228.6¢ to 240.0¢)
Dark
4\5 to 17\21 (960.0¢ to 971.4¢)
TAMNAMS information
Descends from
5L 1s
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
5L 11s
Sister
16L 5s
Daughters
21L 5s, 5L 21s
Neutralized
10L 11s
2-Flought
26L 16s, 5L 37s
Equal tunings
Equalized (L:s = 1:1)
4\21 (228.6¢)
Supersoft (L:s = 4:3)
13\68 (229.4¢)
Soft (L:s = 3:2)
9\47 (229.8¢)
Semisoft (L:s = 5:3)
14\73 (230.1¢)
Basic (L:s = 2:1)
5\26 (230.8¢)
Semihard (L:s = 5:2)
11\57 (231.6¢)
Hard (L:s = 3:1)
6\31 (232.3¢)
Superhard (L:s = 4:1)
7\36 (233.3¢)
Collapsed (L:s = 1:0)
1\5 (240.0¢)
↖ 4L 15s | ↑ 5L 15s | 6L 15s ↗ |
← 4L 16s | 5L 16s | 6L 16s → |
↙ 4L 17s | ↓ 5L 17s | 6L 17s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││║│││║│││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssLsssLsssLsssLsssL
5L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 16 small steps, repeating every octave. 5L 16s is a great-grandchild scale of 5L 1s, expanding it by 15 tones. Generators that produce this scale range from 228.6¢ to 240¢, or from 960¢ to 971.4¢.
This is the MOS which splits its small steps 3-3-3-3-4 between its large steps. Its "diatonic" whole tone/supermajor second generator measures no less than 4/21edo (228.571 cents), meaning 8/7 is less than the boundary of "practicality" for it (which is at 31edo).
Modes
UDP | Cyclic order |
Step pattern |
---|---|---|
20|0 | 1 | LsssLsssLsssLsssLssss |
19|1 | 5 | LsssLsssLsssLssssLsss |
18|2 | 9 | LsssLsssLssssLsssLsss |
17|3 | 13 | LsssLssssLsssLsssLsss |
16|4 | 17 | LssssLsssLsssLsssLsss |
15|5 | 21 | sLsssLsssLsssLsssLsss |
14|6 | 4 | sLsssLsssLsssLssssLss |
13|7 | 8 | sLsssLsssLssssLsssLss |
12|8 | 12 | sLsssLssssLsssLsssLss |
11|9 | 16 | sLssssLsssLsssLsssLss |
10|10 | 20 | ssLsssLsssLsssLsssLss |
9|11 | 3 | ssLsssLsssLsssLssssLs |
8|12 | 7 | ssLsssLsssLssssLsssLs |
7|13 | 11 | ssLsssLssssLsssLsssLs |
6|14 | 15 | ssLssssLsssLsssLsssLs |
5|15 | 19 | sssLsssLsssLsssLsssLs |
4|16 | 2 | sssLsssLsssLsssLssssL |
3|17 | 6 | sssLsssLsssLssssLsssL |
2|18 | 10 | sssLsssLssssLsssLsssL |
1|19 | 14 | sssLssssLsssLsssLsssL |
0|20 | 18 | ssssLsssLsssLsssLsssL |
Intervals
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 57.1¢ |
Major 1-mosstep | M1ms | L | 57.1¢ to 240.0¢ | |
2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 114.3¢ |
Major 2-mosstep | M2ms | L + s | 114.3¢ to 240.0¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 171.4¢ |
Major 3-mosstep | M3ms | L + 2s | 171.4¢ to 240.0¢ | |
4-mosstep | Diminished 4-mosstep | d4ms | 4s | 0.0¢ to 228.6¢ |
Perfect 4-mosstep | P4ms | L + 3s | 228.6¢ to 240.0¢ | |
5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 240.0¢ to 285.7¢ |
Major 5-mosstep | M5ms | 2L + 3s | 285.7¢ to 480.0¢ | |
6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 240.0¢ to 342.9¢ |
Major 6-mosstep | M6ms | 2L + 4s | 342.9¢ to 480.0¢ | |
7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 240.0¢ to 400.0¢ |
Major 7-mosstep | M7ms | 2L + 5s | 400.0¢ to 480.0¢ | |
8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 240.0¢ to 457.1¢ |
Major 8-mosstep | M8ms | 2L + 6s | 457.1¢ to 480.0¢ | |
9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 480.0¢ to 514.3¢ |
Major 9-mosstep | M9ms | 3L + 6s | 514.3¢ to 720.0¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 480.0¢ to 571.4¢ |
Major 10-mosstep | M10ms | 3L + 7s | 571.4¢ to 720.0¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 2L + 9s | 480.0¢ to 628.6¢ |
Major 11-mosstep | M11ms | 3L + 8s | 628.6¢ to 720.0¢ | |
12-mosstep | Minor 12-mosstep | m12ms | 2L + 10s | 480.0¢ to 685.7¢ |
Major 12-mosstep | M12ms | 3L + 9s | 685.7¢ to 720.0¢ | |
13-mosstep | Minor 13-mosstep | m13ms | 3L + 10s | 720.0¢ to 742.9¢ |
Major 13-mosstep | M13ms | 4L + 9s | 742.9¢ to 960.0¢ | |
14-mosstep | Minor 14-mosstep | m14ms | 3L + 11s | 720.0¢ to 800.0¢ |
Major 14-mosstep | M14ms | 4L + 10s | 800.0¢ to 960.0¢ | |
15-mosstep | Minor 15-mosstep | m15ms | 3L + 12s | 720.0¢ to 857.1¢ |
Major 15-mosstep | M15ms | 4L + 11s | 857.1¢ to 960.0¢ | |
16-mosstep | Minor 16-mosstep | m16ms | 3L + 13s | 720.0¢ to 914.3¢ |
Major 16-mosstep | M16ms | 4L + 12s | 914.3¢ to 960.0¢ | |
17-mosstep | Perfect 17-mosstep | P17ms | 4L + 13s | 960.0¢ to 971.4¢ |
Augmented 17-mosstep | A17ms | 5L + 12s | 971.4¢ to 1200.0¢ | |
18-mosstep | Minor 18-mosstep | m18ms | 4L + 14s | 960.0¢ to 1028.6¢ |
Major 18-mosstep | M18ms | 5L + 13s | 1028.6¢ to 1200.0¢ | |
19-mosstep | Minor 19-mosstep | m19ms | 4L + 15s | 960.0¢ to 1085.7¢ |
Major 19-mosstep | M19ms | 5L + 14s | 1085.7¢ to 1200.0¢ | |
20-mosstep | Minor 20-mosstep | m20ms | 4L + 16s | 960.0¢ to 1142.9¢ |
Major 20-mosstep | M20ms | 5L + 15s | 1142.9¢ to 1200.0¢ | |
21-mosstep | Perfect 21-mosstep | P21ms | 5L + 16s | 1200.0¢ |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
4\21 | 228.571 | 971.429 | 1:1 | 1.000 | Equalized 5L 16s | |||||
21\110 | 229.091 | 970.909 | 6:5 | 1.200 | ||||||
17\89 | 229.213 | 970.787 | 5:4 | 1.250 | ||||||
30\157 | 229.299 | 970.701 | 9:7 | 1.286 | ||||||
13\68 | 229.412 | 970.588 | 4:3 | 1.333 | Supersoft 5L 16s | |||||
35\183 | 229.508 | 970.492 | 11:8 | 1.375 | ||||||
22\115 | 229.565 | 970.435 | 7:5 | 1.400 | ||||||
31\162 | 229.630 | 970.370 | 10:7 | 1.429 | ||||||
9\47 | 229.787 | 970.213 | 3:2 | 1.500 | Soft 5L 16s | |||||
32\167 | 229.940 | 970.060 | 11:7 | 1.571 | ||||||
23\120 | 230.000 | 970.000 | 8:5 | 1.600 | ||||||
37\193 | 230.052 | 969.948 | 13:8 | 1.625 | ||||||
14\73 | 230.137 | 969.863 | 5:3 | 1.667 | Semisoft 5L 16s | |||||
33\172 | 230.233 | 969.767 | 12:7 | 1.714 | ||||||
19\99 | 230.303 | 969.697 | 7:4 | 1.750 | ||||||
24\125 | 230.400 | 969.600 | 9:5 | 1.800 | ||||||
5\26 | 230.769 | 969.231 | 2:1 | 2.000 | Basic 5L 16s Scales with tunings softer than this are proper | |||||
21\109 | 231.193 | 968.807 | 9:4 | 2.250 | ||||||
16\83 | 231.325 | 968.675 | 7:3 | 2.333 | ||||||
27\140 | 231.429 | 968.571 | 12:5 | 2.400 | ||||||
11\57 | 231.579 | 968.421 | 5:2 | 2.500 | Semihard 5L 16s | |||||
28\145 | 231.724 | 968.276 | 13:5 | 2.600 | ||||||
17\88 | 231.818 | 968.182 | 8:3 | 2.667 | ||||||
23\119 | 231.933 | 968.067 | 11:4 | 2.750 | ||||||
6\31 | 232.258 | 967.742 | 3:1 | 3.000 | Hard 5L 16s | |||||
19\98 | 232.653 | 967.347 | 10:3 | 3.333 | ||||||
13\67 | 232.836 | 967.164 | 7:2 | 3.500 | ||||||
20\103 | 233.010 | 966.990 | 11:3 | 3.667 | ||||||
7\36 | 233.333 | 966.667 | 4:1 | 4.000 | Superhard 5L 16s | |||||
15\77 | 233.766 | 966.234 | 9:2 | 4.500 | ||||||
8\41 | 234.146 | 965.854 | 5:1 | 5.000 | ||||||
9\46 | 234.783 | 965.217 | 6:1 | 6.000 | ||||||
1\5 | 240.000 | 960.000 | 1:0 | → ∞ | Collapsed 5L 16s |