17L 5s

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↖ 16L 4s ↑ 17L 4s 18L 4s ↗
← 16L 5s 17L 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)
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¢)

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 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

Intervals

Intervals of 17L 5s
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 54.5¢
Major 1-mosstep M1ms L 54.5¢ to 70.6¢
2-mosstep Minor 2-mosstep m2ms L + s 70.6¢ to 109.1¢
Major 2-mosstep M2ms 2L 109.1¢ to 141.2¢
3-mosstep Minor 3-mosstep m3ms 2L + s 141.2¢ to 163.6¢
Major 3-mosstep M3ms 3L 163.6¢ to 211.8¢
4-mosstep Minor 4-mosstep m4ms 3L + s 211.8¢ to 218.2¢
Major 4-mosstep M4ms 4L 218.2¢ to 282.4¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 211.8¢ to 272.7¢
Major 5-mosstep M5ms 4L + s 272.7¢ to 282.4¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 282.4¢ to 327.3¢
Major 6-mosstep M6ms 5L + s 327.3¢ to 352.9¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 352.9¢ to 381.8¢
Major 7-mosstep M7ms 6L + s 381.8¢ to 423.5¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 423.5¢ to 436.4¢
Major 8-mosstep M8ms 7L + s 436.4¢ to 494.1¢
9-mosstep Diminished 9-mosstep d9ms 6L + 3s 423.5¢ to 490.9¢
Perfect 9-mosstep P9ms 7L + 2s 490.9¢ to 494.1¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 494.1¢ to 545.5¢
Major 10-mosstep M10ms 8L + 2s 545.5¢ to 564.7¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 564.7¢ to 600.0¢
Major 11-mosstep M11ms 9L + 2s 600.0¢ to 635.3¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 635.3¢ to 654.5¢
Major 12-mosstep M12ms 10L + 2s 654.5¢ to 705.9¢
13-mosstep Perfect 13-mosstep P13ms 10L + 3s 705.9¢ to 709.1¢
Augmented 13-mosstep A13ms 11L + 2s 709.1¢ to 776.5¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 705.9¢ to 763.6¢
Major 14-mosstep M14ms 11L + 3s 763.6¢ to 776.5¢
15-mosstep Minor 15-mosstep m15ms 11L + 4s 776.5¢ to 818.2¢
Major 15-mosstep M15ms 12L + 3s 818.2¢ to 847.1¢
16-mosstep Minor 16-mosstep m16ms 12L + 4s 847.1¢ to 872.7¢
Major 16-mosstep M16ms 13L + 3s 872.7¢ to 917.6¢
17-mosstep Minor 17-mosstep m17ms 13L + 4s 917.6¢ to 927.3¢
Major 17-mosstep M17ms 14L + 3s 927.3¢ to 988.2¢
18-mosstep Minor 18-mosstep m18ms 13L + 5s 917.6¢ to 981.8¢
Major 18-mosstep M18ms 14L + 4s 981.8¢ to 988.2¢
19-mosstep Minor 19-mosstep m19ms 14L + 5s 988.2¢ to 1036.4¢
Major 19-mosstep M19ms 15L + 4s 1036.4¢ to 1058.8¢
20-mosstep Minor 20-mosstep m20ms 15L + 5s 1058.8¢ to 1090.9¢
Major 20-mosstep M20ms 16L + 4s 1090.9¢ to 1129.4¢
21-mosstep Minor 21-mosstep m21ms 16L + 5s 1129.4¢ to 1145.5¢
Major 21-mosstep M21ms 17L + 4s 1145.5¢ to 1200.0¢
22-mosstep Perfect 22-mosstep P22ms 17L + 5s 1200.0¢

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
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