5L 16s
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Step pattern
LsssLsssLsssLsssLssss
ssssLsssLsssLsssLsssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
4\21 to 1\5 (228.6 ¢ to 240.0 ¢)
Dark
4\5 to 17\21 (960.0 ¢ to 971.4 ¢)
Descends from
5L 1s (machinoid)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Parent
5L 11s
Sister
16L 5s
Daughters
21L 5s, 5L 21s
Neutralized
10L 11s
2-Flought
26L 16s, 5L 37s
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 ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││║│││║│││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssLsssLsssLsssLsssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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 ¢), meaning 8/7 is less than the boundary of "practicality" for it (which is at 31edo).
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
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 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
25 | Augmented 16-mosdegree | A16md |
24 | Augmented 12-mosdegree | A12md |
23 | Augmented 8-mosdegree | A8md |
22 | Augmented 4-mosdegree | A4md |
21 | Augmented 0-mosdegree | A0md |
20 | Augmented 17-mosdegree | A17md |
19 | Major 13-mosdegree | M13md |
18 | Major 9-mosdegree | M9md |
17 | Major 5-mosdegree | M5md |
16 | Major 1-mosdegree | M1md |
15 | Major 18-mosdegree | M18md |
14 | Major 14-mosdegree | M14md |
13 | Major 10-mosdegree | M10md |
12 | Major 6-mosdegree | M6md |
11 | Major 2-mosdegree | M2md |
10 | Major 19-mosdegree | M19md |
9 | Major 15-mosdegree | M15md |
8 | Major 11-mosdegree | M11md |
7 | Major 7-mosdegree | M7md |
6 | Major 3-mosdegree | M3md |
5 | Major 20-mosdegree | M20md |
4 | Major 16-mosdegree | M16md |
3 | Major 12-mosdegree | M12md |
2 | Major 8-mosdegree | M8md |
1 | Perfect 4-mosdegree | P4md |
0 | Perfect 0-mosdegree Perfect 21-mosdegree |
P0md P21md |
−1 | Perfect 17-mosdegree | P17md |
−2 | Minor 13-mosdegree | m13md |
−3 | Minor 9-mosdegree | m9md |
−4 | Minor 5-mosdegree | m5md |
−5 | Minor 1-mosdegree | m1md |
−6 | Minor 18-mosdegree | m18md |
−7 | Minor 14-mosdegree | m14md |
−8 | Minor 10-mosdegree | m10md |
−9 | Minor 6-mosdegree | m6md |
−10 | Minor 2-mosdegree | m2md |
−11 | Minor 19-mosdegree | m19md |
−12 | Minor 15-mosdegree | m15md |
−13 | Minor 11-mosdegree | m11md |
−14 | Minor 7-mosdegree | m7md |
−15 | Minor 3-mosdegree | m3md |
−16 | Minor 20-mosdegree | m20md |
−17 | Minor 16-mosdegree | m16md |
−18 | Minor 12-mosdegree | m12md |
−19 | Minor 8-mosdegree | m8md |
−20 | Diminished 4-mosdegree | d4md |
−21 | Diminished 21-mosdegree | d21md |
−22 | Diminished 17-mosdegree | d17md |
−23 | Diminished 13-mosdegree | d13md |
−24 | Diminished 9-mosdegree | d9md |
−25 | Diminished 5-mosdegree | d5md |
Modes
UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | |||
20|0 | 1 | LsssLsssLsssLsssLssss | Perf. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Perf. |
19|1 | 5 | LsssLsssLsssLssssLsss | Perf. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
18|2 | 9 | LsssLsssLssssLsssLsss | Perf. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
17|3 | 13 | LsssLssssLsssLsssLsss | Perf. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
16|4 | 17 | LssssLsssLsssLsssLsss | Perf. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
15|5 | 21 | sLsssLsssLsssLsssLsss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Perf. |
14|6 | 4 | sLsssLsssLsssLssssLss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
13|7 | 8 | sLsssLsssLssssLsssLss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
12|8 | 12 | sLsssLssssLsssLsssLss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
11|9 | 16 | sLssssLsssLsssLsssLss | Perf. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
10|10 | 20 | ssLsssLsssLsssLsssLss | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Maj. | Maj. | Perf. |
9|11 | 3 | ssLsssLsssLsssLssssLs | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
8|12 | 7 | ssLsssLsssLssssLsssLs | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
7|13 | 11 | ssLsssLssssLsssLsssLs | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
6|14 | 15 | ssLssssLsssLsssLsssLs | Perf. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
5|15 | 19 | sssLsssLsssLsssLsssLs | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Maj. | Perf. |
4|16 | 2 | sssLsssLsssLsssLssssL | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Perf. | Min. | Min. | Min. | Perf. |
3|17 | 6 | sssLsssLsssLssssLsssL | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Perf. |
2|18 | 10 | sssLsssLssssLsssLsssL | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Perf. |
1|19 | 14 | sssLssssLsssLsssLsssL | Perf. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Perf. |
0|20 | 18 | ssssLsssLsssLsssLsssL | Perf. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Perf. |
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 |