17L 5s

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↖16L 4s ↑17L 4s 18L 4s↗
←16L 5s17L 5s 18L 5s→
↙16L 6s ↓17L 6s 18L 6s↘
┌╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║║│║║║│║║║││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLsLLLLsLLLsLLLs
sLLLsLLLsLLLLsLLLsLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 9\22 to 7\17 (490.9¢ to 494.1¢)
Dark 10\17 to 13\22 (705.9¢ to 709.1¢)
TAMNAMS information
Descends from 5L 2s (diatonic)
Required step ratio range 3:1 to 4:1 (parahard)
Related MOS scales
Parent 5L 12s
Sister 5L 17s
Daughters 22L 17s, 17L 22s
Neutralized 12L 10s
Equal tunings
Equalized (L:s = 1:1) 9\22 (490.9¢)
Supersoft (L:s = 4:3) 34\83 (491.6¢)
Soft (L:s = 3:2) 25\61 (491.8¢)
Semisoft (L:s = 5:3) 41\100 (492.0¢)
Basic (L:s = 2:1) 16\39 (492.3¢)
Semihard (L:s = 5:2) 39\95 (492.6¢)
Hard (L:s = 3:1) 23\56 (492.9¢)
Superhard (L:s = 4:1) 30\73 (493.2¢)
Collapsed (L:s = 1:0) 7\17 (494.1¢)

17L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 5 small steps, repeating every octave. 17L 5s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 490.9¢ to 494.1¢, or from 705.9¢ to 709.1¢.

This scale is the parent of another MOS scale that exhibits the fractal-like acoustic effects for which Archagall temperament is named- however, this scale also has tuning areas that don't support these effects.

Modes

Modes of 17L 5s
UDP Rotational order Step pattern
21|0 1 LLLLsLLLsLLLLsLLLsLLLs
20|1 10 LLLLsLLLsLLLsLLLLsLLLs
19|2 19 LLLsLLLLsLLLsLLLLsLLLs
18|3 6 LLLsLLLLsLLLsLLLsLLLLs
17|4 15 LLLsLLLsLLLLsLLLsLLLLs
16|5 2 LLLsLLLsLLLLsLLLsLLLsL
15|6 11 LLLsLLLsLLLsLLLLsLLLsL
14|7 20 LLsLLLLsLLLsLLLLsLLLsL
13|8 7 LLsLLLLsLLLsLLLsLLLLsL
12|9 16 LLsLLLsLLLLsLLLsLLLLsL
11|10 3 LLsLLLsLLLLsLLLsLLLsLL
10|11 12 LLsLLLsLLLsLLLLsLLLsLL
9|12 21 LsLLLLsLLLsLLLLsLLLsLL
8|13 8 LsLLLLsLLLsLLLsLLLLsLL
7|14 17 LsLLLsLLLLsLLLsLLLLsLL
6|15 4 LsLLLsLLLLsLLLsLLLsLLL
5|16 13 LsLLLsLLLsLLLLsLLLsLLL
4|17 22 sLLLLsLLLsLLLLsLLLsLLL
3|18 9 sLLLLsLLLsLLLsLLLLsLLL
2|19 18 sLLLsLLLLsLLLsLLLLsLLL
1|20 5 sLLLsLLLLsLLLsLLLsLLLL
0|21 14 sLLLsLLLsLLLLsLLLsLLLL

Scale tree

Scale Tree and Tuning Spectrum of 17L 5s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
9\22 490.909 709.091 1:1 1.000 Equalized 17L 5s
52\127 491.339 708.661 6:5 1.200
43\105 491.429 708.571 5:4 1.250
77\188 491.489 708.511 9:7 1.286
34\83 491.566 708.434 4:3 1.333 Supersoft 17L 5s
93\227 491.630 708.370 11:8 1.375
59\144 491.667 708.333 7:5 1.400
84\205 491.707 708.293 10:7 1.429
25\61 491.803 708.197 3:2 1.500 Soft 17L 5s
91\222 491.892 708.108 11:7 1.571
66\161 491.925 708.075 8:5 1.600
107\261 491.954 708.046 13:8 1.625
41\100 492.000 708.000 5:3 1.667 Semisoft 17L 5s
98\239 492.050 707.950 12:7 1.714
57\139 492.086 707.914 7:4 1.750
73\178 492.135 707.865 9:5 1.800
16\39 492.308 707.692 2:1 2.000 Basic 17L 5s
Scales with tunings softer than this are proper
71\173 492.486 707.514 9:4 2.250
55\134 492.537 707.463 7:3 2.333
94\229 492.576 707.424 12:5 2.400
39\95 492.632 707.368 5:2 2.500 Semihard 17L 5s
101\246 492.683 707.317 13:5 2.600
62\151 492.715 707.285 8:3 2.667
85\207 492.754 707.246 11:4 2.750
23\56 492.857 707.143 3:1 3.000 Hard 17L 5s
76\185 492.973 707.027 10:3 3.333
53\129 493.023 706.977 7:2 3.500
83\202 493.069 706.931 11:3 3.667
30\73 493.151 706.849 4:1 4.000 Superhard 17L 5s
Archagall
67\163 493.252 706.748 9:2 4.500
37\90 493.333 706.667 5:1 5.000
44\107 493.458 706.542 6:1 6.000
7\17 494.118 705.882 1:0 → ∞ Collapsed 17L 5s