5L 16s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 4L 15s ↑ 5L 15s 6L 15s ↗
← 4L 16s 5L 16s 6L 16s →
↙ 4L 17s ↓ 5L 17s 6L 17s ↘ 
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐
│║│││║│││║│││║│││║│││││
│││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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 (machinoid)
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¢)

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 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 of 5L 16s
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

Scale Tree and Tuning Spectrum of 5L 16s
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
Retrieved from "https://en.xen.wiki/index.php?title=5L_16s&oldid=170816"