# 17L 3s

 ↖ 16L 2s ↑17L 2s 18L 2s ↗ ← 16L 3s 17L 3s 18L 3s → ↙ 16L 4s ↓17L 4s 18L 4s ↘
```┌╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥┬┐
│║║║║║║│║║║║║║│║║║║║││
││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘```
Scale structure
Step pattern LLLLLLsLLLLLLsLLLLLs
sLLLLLsLLLLLLsLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 7\20 to 6\17 (420.0¢ to 423.5¢)
Dark 11\17 to 13\20 (776.5¢ to 780.0¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Ancestor's step ratio range 4:1 to 5:1
Related MOS scales
Parent 3L 14s
Sister 3L 17s
Daughters 20L 17s, 17L 20s
Neutralized 14L 6s
2-Flought 37L 3s, 17L 23s
Equal tunings
Equalized (L:s = 1:1) 7\20 (420.0¢)
Supersoft (L:s = 4:3) 27\77 (420.8¢)
Soft (L:s = 3:2) 20\57 (421.1¢)
Semisoft (L:s = 5:3) 33\94 (421.3¢)
Basic (L:s = 2:1) 13\37 (421.6¢)
Semihard (L:s = 5:2) 32\91 (422.0¢)
Hard (L:s = 3:1) 19\54 (422.2¢)
Superhard (L:s = 4:1) 25\71 (422.5¢)
Collapsed (L:s = 1:0) 6\17 (423.5¢)

17L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 3 small steps, repeating every octave. 17L 3s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 420¢ to 423.5¢, or from 776.5¢ to 780¢.

## Modes

Modes of 17L 3s
UDP Rotational
Order
Step
Pattern
19|0 1 LLLLLLsLLLLLLsLLLLLs
18|1 8 LLLLLLsLLLLLsLLLLLLs
17|2 15 LLLLLsLLLLLLsLLLLLLs
16|3 2 LLLLLsLLLLLLsLLLLLsL
15|4 9 LLLLLsLLLLLsLLLLLLsL
14|5 16 LLLLsLLLLLLsLLLLLLsL
13|6 3 LLLLsLLLLLLsLLLLLsLL
12|7 10 LLLLsLLLLLsLLLLLLsLL
11|8 17 LLLsLLLLLLsLLLLLLsLL
10|9 4 LLLsLLLLLLsLLLLLsLLL
9|10 11 LLLsLLLLLsLLLLLLsLLL
8|11 18 LLsLLLLLLsLLLLLLsLLL
7|12 5 LLsLLLLLLsLLLLLsLLLL
6|13 12 LLsLLLLLsLLLLLLsLLLL
5|14 19 LsLLLLLLsLLLLLLsLLLL
4|15 6 LsLLLLLLsLLLLLsLLLLL
3|16 13 LsLLLLLsLLLLLLsLLLLL
2|17 20 sLLLLLLsLLLLLLsLLLLL
1|18 7 sLLLLLLsLLLLLsLLLLLL
0|19 14 sLLLLLsLLLLLLsLLLLLL

## Scale tree

Scale Tree and Tuning Spectrum of 17L 3s
Bright Dark L:s Hardness
7\20 420.000 780.000 1:1 1.000 Equalized 17L 3s
41\117 420.513 779.487 6:5 1.200
34\97 420.619 779.381 5:4 1.250
61\174 420.690 779.310 9:7 1.286
27\77 420.779 779.221 4:3 1.333 Supersoft 17L 3s
74\211 420.853 779.147 11:8 1.375
47\134 420.896 779.104 7:5 1.400
67\191 420.942 779.058 10:7 1.429
20\57 421.053 778.947 3:2 1.500 Soft 17L 3s
73\208 421.154 778.846 11:7 1.571
53\151 421.192 778.808 8:5 1.600
86\245 421.224 778.776 13:8 1.625
33\94 421.277 778.723 5:3 1.667 Semisoft 17L 3s
79\225 421.333 778.667 12:7 1.714
46\131 421.374 778.626 7:4 1.750
59\168 421.429 778.571 9:5 1.800
13\37 421.622 778.378 2:1 2.000 Basic 17L 3s
Scales with tunings softer than this are proper
58\165 421.818 778.182 9:4 2.250
45\128 421.875 778.125 7:3 2.333
77\219 421.918 778.082 12:5 2.400
32\91 421.978 778.022 5:2 2.500 Semihard 17L 3s
83\236 422.034 777.966 13:5 2.600
51\145 422.069 777.931 8:3 2.667
70\199 422.111 777.889 11:4 2.750
19\54 422.222 777.778 3:1 3.000 Hard 17L 3s
63\179 422.346 777.654 10:3 3.333
44\125 422.400 777.600 7:2 3.500
69\196 422.449 777.551 11:3 3.667
25\71 422.535 777.465 4:1 4.000 Superhard 17L 3s
56\159 422.642 777.358 9:2 4.500
31\88 422.727 777.273 5:1 5.000
37\105 422.857 777.143 6:1 6.000
6\17 423.529 776.471 1:0 → ∞ Collapsed 17L 3s
 This page is a stub. You can help the Xenharmonic Wiki by expanding it.