# 5L 17s

 ↖ 4L 16s ↑5L 16s 6L 16s ↗ ← 4L 17s 5L 17s 6L 17s → ↙ 4L 18s ↓5L 18s 6L 18s ↘
```┌╥┬┬┬╥┬┬┬╥┬┬┬┬╥┬┬┬╥┬┬┬┬┐
│║│││║│││║││││║│││║│││││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘```
Scale structure
Step pattern LsssLsssLssssLsssLssss
ssssLsssLssssLsssLsssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 13\22 to 3\5 (709.1¢ to 720.0¢)
Dark 2\5 to 9\22 (480.0¢ to 490.9¢)
TAMNAMS information
Descends from 5L 2s (diatonic)
Required step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 5L 12s
Sister 17L 5s
Daughters 22L 5s, 5L 22s
Neutralized 10L 12s
Equal tunings
Equalized (L:s = 1:1) 13\22 (709.1¢)
Supersoft (L:s = 4:3) 42\71 (709.9¢)
Soft (L:s = 3:2) 29\49 (710.2¢)
Semisoft (L:s = 5:3) 45\76 (710.5¢)
Basic (L:s = 2:1) 16\27 (711.1¢)
Semihard (L:s = 5:2) 35\59 (711.9¢)
Hard (L:s = 3:1) 19\32 (712.5¢)
Superhard (L:s = 4:1) 22\37 (713.5¢)
Collapsed (L:s = 1:0) 3\5 (720.0¢)

5L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 17 small steps, repeating every octave. 5L 17s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 709.1¢ to 720¢, or from 480¢ to 490.9¢.

## Modes

Modes of 5L 17s
UDP Rotational order Step pattern
21|0 1 LsssLsssLssssLsssLssss
20|1 14 LsssLssssLsssLsssLssss
19|2 5 LsssLssssLsssLssssLsss
18|3 18 LssssLsssLsssLssssLsss
17|4 9 LssssLsssLssssLsssLsss
16|5 22 sLsssLsssLssssLsssLsss
15|6 13 sLsssLssssLsssLsssLsss
14|7 4 sLsssLssssLsssLssssLss
13|8 17 sLssssLsssLsssLssssLss
12|9 8 sLssssLsssLssssLsssLss
11|10 21 ssLsssLsssLssssLsssLss
10|11 12 ssLsssLssssLsssLsssLss
9|12 3 ssLsssLssssLsssLssssLs
8|13 16 ssLssssLsssLsssLssssLs
7|14 7 ssLssssLsssLssssLsssLs
6|15 20 sssLsssLsssLssssLsssLs
5|16 11 sssLsssLssssLsssLsssLs
4|17 2 sssLsssLssssLsssLssssL
3|18 15 sssLssssLsssLsssLssssL
2|19 6 sssLssssLsssLssssLsssL
1|20 19 ssssLsssLsssLssssLsssL
0|21 10 ssssLsssLssssLsssLsssL

## Scale tree

Scale Tree and Tuning Spectrum of 5L 17s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
13\22 709.091 490.909 1:1 1.000 Equalized 5L 17s
68\115 709.565 490.435 6:5 1.200
55\93 709.677 490.323 5:4 1.250
97\164 709.756 490.244 9:7 1.286
42\71 709.859 490.141 4:3 1.333 Supersoft 5L 17s
113\191 709.948 490.052 11:8 1.375
71\120 710.000 490.000 7:5 1.400
100\169 710.059 489.941 10:7 1.429
29\49 710.204 489.796 3:2 1.500 Soft 5L 17s
103\174 710.345 489.655 11:7 1.571
74\125 710.400 489.600 8:5 1.600
119\201 710.448 489.552 13:8 1.625
45\76 710.526 489.474 5:3 1.667 Semisoft 5L 17s
106\179 710.615 489.385 12:7 1.714
61\103 710.680 489.320 7:4 1.750
77\130 710.769 489.231 9:5 1.800
16\27 711.111 488.889 2:1 2.000 Basic 5L 17s
Scales with tunings softer than this are proper
67\113 711.504 488.496 9:4 2.250
51\86 711.628 488.372 7:3 2.333
86\145 711.724 488.276 12:5 2.400
35\59 711.864 488.136 5:2 2.500 Semihard 5L 17s
89\150 712.000 488.000 13:5 2.600
54\91 712.088 487.912 8:3 2.667
73\123 712.195 487.805 11:4 2.750
19\32 712.500 487.500 3:1 3.000 Hard 5L 17s
60\101 712.871 487.129 10:3 3.333
41\69 713.043 486.957 7:2 3.500
63\106 713.208 486.792 11:3 3.667
22\37 713.514 486.486 4:1 4.000 Superhard 5L 17s
47\79 713.924 486.076 9:2 4.500
25\42 714.286 485.714 5:1 5.000
28\47 714.894 485.106 6:1 6.000
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 17s
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