17L 5s
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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)
Ancestor's 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
2-Flought
39L 5s, 17L 27s
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¢)
↖ 16L 4s | ↑ 17L 4s | 18L 4s ↗ |
← 16L 5s | 17L 5s | 18L 5s → |
↙ 16L 6s | ↓ 17L 6s | 18L 6s ↘ |
┌╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║║│║║║│║║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLsLLLLsLLLsLLLL
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
UDP | Cyclic 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
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 |