5L 16s

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↖4L 15s ↑5L 15s 6L 15s↗
←4L 16s5L 16s 6L 16s→
↙4L 17s ↓5L 17s 6L 17s↘
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLsssLsssLsssLssss
ssssLsssLsssLsssLsssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\21 to 1\5 (57.1¢ to 240.0¢)
Small 0\5 to 1\21 (0.0¢ to 57.1¢)
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 (machinoid)
Related MOS scales
Parent 5L 11s
Sister 16L 5s
Daughters 21L 5s
5L 21s
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¢)

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

Modes of 5L 16s
UDP Rotational 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

Scale tree

Scale tree and tuning spectrum of 5L 16s
Generator (in steps of 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