7L 17s

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↖ 6L 16s ↑7L 16s 8L 16s ↗
← 6L 17s7L 17s 8L 17s →
↙ 6L 18s ↓7L 18s 8L 18s ↘
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐
│║││║││║│││║││║│││║││║││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsssLssLsssLssLsss
sssLssLsssLssLsssLssLssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 17\24 to 5\7 (850.0¢ to 857.1¢)
Dark 2\7 to 7\24 (342.9¢ to 350.0¢)
TAMNAMS information
Descends from 7L 3s (dicoid)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 7L 10s
Sister 17L 7s
Daughters 24L 7s, 7L 24s
Neutralized 14L 10s
2-Flought 31L 17s, 7L 41s
Equal tunings
Equalized (L:s = 1:1) 17\24 (850.0¢)
Supersoft (L:s = 4:3) 56\79 (850.6¢)
Soft (L:s = 3:2) 39\55 (850.9¢)
Semisoft (L:s = 5:3) 61\86 (851.2¢)
Basic (L:s = 2:1) 22\31 (851.6¢)
Semihard (L:s = 5:2) 49\69 (852.2¢)
Hard (L:s = 3:1) 27\38 (852.6¢)
Superhard (L:s = 4:1) 32\45 (853.3¢)
Collapsed (L:s = 1:0) 5\7 (857.1¢)

7L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 17 small steps, repeating every octave. 7L 17s is a grandchild scale of 7L 3s, expanding it by 14 tones. Generators that produce this scale range from 850¢ to 857.1¢, or from 342.9¢ to 350¢. The dark generator serves as an approximate 11/9 (347¢), with 11\38 – the low estimate for the boundary of "practicality" – giving this ratio almost exactly.

Scale Tree and Tuning Spectrum of 7L 17s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
17\24 850.000 350.000 1:1 1.000 Equalized 7L 17s
90\127 850.394 349.606 6:5 1.200
73\103 850.485 349.515 5:4 1.250
129\182 850.549 349.451 9:7 1.286
56\79 850.633 349.367 4:3 1.333 Supersoft 7L 17s
151\213 850.704 349.296 11:8 1.375
95\134 850.746 349.254 7:5 1.400
134\189 850.794 349.206 10:7 1.429
39\55 850.909 349.091 3:2 1.500 Soft 7L 17s
139\196 851.020 348.980 11:7 1.571
100\141 851.064 348.936 8:5 1.600
161\227 851.101 348.899 13:8 1.625
61\86 851.163 348.837 5:3 1.667 Semisoft 7L 17s
144\203 851.232 348.768 12:7 1.714
83\117 851.282 348.718 7:4 1.750
105\148 851.351 348.649 9:5 1.800
22\31 851.613 348.387 2:1 2.000 Basic 7L 17s
Scales with tunings softer than this are proper
93\131 851.908 348.092 9:4 2.250
71\100 852.000 348.000 7:3 2.333
120\169 852.071 347.929 12:5 2.400
49\69 852.174 347.826 5:2 2.500 Semihard 7L 17s
125\176 852.273 347.727 13:5 2.600
76\107 852.336 347.664 8:3 2.667
103\145 852.414 347.586 11:4 2.750
27\38 852.632 347.368 3:1 3.000 Hard 7L 17s
86\121 852.893 347.107 10:3 3.333
59\83 853.012 346.988 7:2 3.500
91\128 853.125 346.875 11:3 3.667
32\45 853.333 346.667 4:1 4.000 Superhard 7L 17s
69\97 853.608 346.392 9:2 4.500
37\52 853.846 346.154 5:1 5.000
42\59 854.237 345.763 6:1 6.000
5\7 857.143 342.857 1:0 → ∞ Collapsed 7L 17s