7L 17s

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↖ 6L 16s ↑ 7L 16s 8L 16s ↗
← 6L 17s 7L 17s 8L 17s →
↙ 6L 18s ↓ 7L 18s 8L 18s ↘
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
Related to 7L 3s (dicoid)
With tunings 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 ¢)
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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.

Notable harmonic entropy minima are mohajira and migration, two alternative extensions of the 2.3.5.11 temperament mohaha to the full 11-limit, merging in 31edo.

Modes

Modes of 7L 17s
UDP Cyclic
order		 Step
pattern
23|0 1 LssLssLsssLssLsssLssLsss
22|1 18 LssLsssLssLssLsssLssLsss
21|2 11 LssLsssLssLsssLssLssLsss
20|3 4 LssLsssLssLsssLssLsssLss
19|4 21 LsssLssLssLsssLssLsssLss
18|5 14 LsssLssLsssLssLssLsssLss
17|6 7 LsssLssLsssLssLsssLssLss
16|7 24 sLssLssLsssLssLsssLssLss
15|8 17 sLssLsssLssLssLsssLssLss
14|9 10 sLssLsssLssLsssLssLssLss
13|10 3 sLssLsssLssLsssLssLsssLs
12|11 20 sLsssLssLssLsssLssLsssLs
11|12 13 sLsssLssLsssLssLssLsssLs
10|13 6 sLsssLssLsssLssLsssLssLs
9|14 23 ssLssLssLsssLssLsssLssLs
8|15 16 ssLssLsssLssLssLsssLssLs
7|16 9 ssLssLsssLssLsssLssLssLs
6|17 2 ssLssLsssLssLsssLssLsssL
5|18 19 ssLsssLssLssLsssLssLsssL
4|19 12 ssLsssLssLsssLssLssLsssL
3|20 5 ssLsssLssLsssLssLsssLssL
2|21 22 sssLssLssLsssLssLsssLssL
1|22 15 sssLssLsssLssLssLsssLssL
0|23 8 sssLssLsssLssLsssLssLssL

Intervals

Intervals of 7L 17s
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 50.0 ¢
Major 1-mosstep M1ms L 50.0 ¢ to 171.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 100.0 ¢
Major 2-mosstep M2ms L + s 100.0 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 150.0 ¢
Major 3-mosstep M3ms L + 2s 150.0 ¢ to 171.4 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 200.0 ¢
Major 4-mosstep M4ms 2L + 2s 200.0 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4 ¢ to 250.0 ¢
Major 5-mosstep M5ms 2L + 3s 250.0 ¢ to 342.9 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 171.4 ¢ to 300.0 ¢
Major 6-mosstep M6ms 2L + 4s 300.0 ¢ to 342.9 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 342.9 ¢ to 350.0 ¢
Augmented 7-mosstep A7ms 3L + 4s 350.0 ¢ to 514.3 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 342.9 ¢ to 400.0 ¢
Major 8-mosstep M8ms 3L + 5s 400.0 ¢ to 514.3 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 342.9 ¢ to 450.0 ¢
Major 9-mosstep M9ms 3L + 6s 450.0 ¢ to 514.3 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 342.9 ¢ to 500.0 ¢
Major 10-mosstep M10ms 3L + 7s 500.0 ¢ to 514.3 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 514.3 ¢ to 550.0 ¢
Major 11-mosstep M11ms 4L + 7s 550.0 ¢ to 685.7 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 514.3 ¢ to 600.0 ¢
Major 12-mosstep M12ms 4L + 8s 600.0 ¢ to 685.7 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 514.3 ¢ to 650.0 ¢
Major 13-mosstep M13ms 4L + 9s 650.0 ¢ to 685.7 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 685.7 ¢ to 700.0 ¢
Major 14-mosstep M14ms 5L + 9s 700.0 ¢ to 857.1 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 685.7 ¢ to 750.0 ¢
Major 15-mosstep M15ms 5L + 10s 750.0 ¢ to 857.1 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 685.7 ¢ to 800.0 ¢
Major 16-mosstep M16ms 5L + 11s 800.0 ¢ to 857.1 ¢
17-mosstep Diminished 17-mosstep d17ms 4L + 13s 685.7 ¢ to 850.0 ¢
Perfect 17-mosstep P17ms 5L + 12s 850.0 ¢ to 857.1 ¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 857.1 ¢ to 900.0 ¢
Major 18-mosstep M18ms 6L + 12s 900.0 ¢ to 1028.6 ¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 857.1 ¢ to 950.0 ¢
Major 19-mosstep M19ms 6L + 13s 950.0 ¢ to 1028.6 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 857.1 ¢ to 1000.0 ¢
Major 20-mosstep M20ms 6L + 14s 1000.0 ¢ to 1028.6 ¢
21-mosstep Minor 21-mosstep m21ms 6L + 15s 1028.6 ¢ to 1050.0 ¢
Major 21-mosstep M21ms 7L + 14s 1050.0 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 6L + 16s 1028.6 ¢ to 1100.0 ¢
Major 22-mosstep M22ms 7L + 15s 1100.0 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 6L + 17s 1028.6 ¢ to 1150.0 ¢
Major 23-mosstep M23ms 7L + 16s 1150.0 ¢ to 1200.0 ¢
24-mosstep Perfect 24-mosstep P24ms 7L + 17s 1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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
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