7L 16s

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↖ 6L 15s ↑ 7L 15s 8L 15s ↗
← 6L 16s 7L 16s 8L 16s →
↙ 6L 17s ↓ 7L 17s 8L 17s ↘ 
┌╥┬┬╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││║│││║││║││║││││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLssLsssLssLssLsss
sssLssLssLsssLssLssLssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 13\23 to 4\7 (678.3¢ to 685.7¢)
Dark 3\7 to 10\23 (514.3¢ to 521.7¢)
TAMNAMS information
Descends from 7L 2s (armotonic)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 7L 9s
Sister 16L 7s
Daughters 23L 7s, 7L 23s
Neutralized 14L 9s
2-Flought 30L 16s, 7L 39s
Equal tunings
Equalized (L:s = 1:1) 13\23 (678.3¢)
Supersoft (L:s = 4:3) 43\76 (678.9¢)
Soft (L:s = 3:2) 30\53 (679.2¢)
Semisoft (L:s = 5:3) 47\83 (679.5¢)
Basic (L:s = 2:1) 17\30 (680.0¢)
Semihard (L:s = 5:2) 38\67 (680.6¢)
Hard (L:s = 3:1) 21\37 (681.1¢)
Superhard (L:s = 4:1) 25\44 (681.8¢)
Collapsed (L:s = 1:0) 4\7 (685.7¢)

7L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 16 small steps, repeating every octave. 7L 16s is a grandchild scale of 7L 2s, expanding it by 14 tones. Generators that produce this scale range from 678.3¢ to 685.7¢, or from 514.3¢ to 521.7¢.

Modes

Modes of 7L 16s
UDP Cyclic
order		 Step
pattern
22|0 1 LssLssLssLsssLssLssLsss
21|1 14 LssLssLsssLssLssLssLsss
20|2 4 LssLssLsssLssLssLsssLss
19|3 17 LssLsssLssLssLssLsssLss
18|4 7 LssLsssLssLssLsssLssLss
17|5 20 LsssLssLssLssLsssLssLss
16|6 10 LsssLssLssLsssLssLssLss
15|7 23 sLssLssLssLsssLssLssLss
14|8 13 sLssLssLsssLssLssLssLss
13|9 3 sLssLssLsssLssLssLsssLs
12|10 16 sLssLsssLssLssLssLsssLs
11|11 6 sLssLsssLssLssLsssLssLs
10|12 19 sLsssLssLssLssLsssLssLs
9|13 9 sLsssLssLssLsssLssLssLs
8|14 22 ssLssLssLssLsssLssLssLs
7|15 12 ssLssLssLsssLssLssLssLs
6|16 2 ssLssLssLsssLssLssLsssL
5|17 15 ssLssLsssLssLssLssLsssL
4|18 5 ssLssLsssLssLssLsssLssL
3|19 18 ssLsssLssLssLssLsssLssL
2|20 8 ssLsssLssLssLsssLssLssL
1|21 21 sssLssLssLssLsssLssLssL
0|22 11 sssLssLssLsssLssLssLssL

Intervals

Intervals of 7L 16s
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 52.2¢
Major 1-mosstep M1ms L 52.2¢ to 171.4¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 104.3¢
Major 2-mosstep M2ms L + s 104.3¢ to 171.4¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 156.5¢
Major 3-mosstep M3ms L + 2s 156.5¢ to 171.4¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4¢ to 208.7¢
Major 4-mosstep M4ms 2L + 2s 208.7¢ to 342.9¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4¢ to 260.9¢
Major 5-mosstep M5ms 2L + 3s 260.9¢ to 342.9¢
6-mosstep Minor 6-mosstep m6ms L + 5s 171.4¢ to 313.0¢
Major 6-mosstep M6ms 2L + 4s 313.0¢ to 342.9¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 342.9¢ to 365.2¢
Major 7-mosstep M7ms 3L + 4s 365.2¢ to 514.3¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 342.9¢ to 417.4¢
Major 8-mosstep M8ms 3L + 5s 417.4¢ to 514.3¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 342.9¢ to 469.6¢
Major 9-mosstep M9ms 3L + 6s 469.6¢ to 514.3¢
10-mosstep Perfect 10-mosstep P10ms 3L + 7s 514.3¢ to 521.7¢
Augmented 10-mosstep A10ms 4L + 6s 521.7¢ to 685.7¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 514.3¢ to 573.9¢
Major 11-mosstep M11ms 4L + 7s 573.9¢ to 685.7¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 514.3¢ to 626.1¢
Major 12-mosstep M12ms 4L + 8s 626.1¢ to 685.7¢
13-mosstep Diminished 13-mosstep d13ms 3L + 10s 514.3¢ to 678.3¢
Perfect 13-mosstep P13ms 4L + 9s 678.3¢ to 685.7¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 685.7¢ to 730.4¢
Major 14-mosstep M14ms 5L + 9s 730.4¢ to 857.1¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 685.7¢ to 782.6¢
Major 15-mosstep M15ms 5L + 10s 782.6¢ to 857.1¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 685.7¢ to 834.8¢
Major 16-mosstep M16ms 5L + 11s 834.8¢ to 857.1¢
17-mosstep Minor 17-mosstep m17ms 5L + 12s 857.1¢ to 887.0¢
Major 17-mosstep M17ms 6L + 11s 887.0¢ to 1028.6¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 857.1¢ to 939.1¢
Major 18-mosstep M18ms 6L + 12s 939.1¢ to 1028.6¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 857.1¢ to 991.3¢
Major 19-mosstep M19ms 6L + 13s 991.3¢ to 1028.6¢
20-mosstep Minor 20-mosstep m20ms 6L + 14s 1028.6¢ to 1043.5¢
Major 20-mosstep M20ms 7L + 13s 1043.5¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 6L + 15s 1028.6¢ to 1095.7¢
Major 21-mosstep M21ms 7L + 14s 1095.7¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 6L + 16s 1028.6¢ to 1147.8¢
Major 22-mosstep M22ms 7L + 15s 1147.8¢ to 1200.0¢
23-mosstep Perfect 23-mosstep P23ms 7L + 16s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 7L 16s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\23 678.261 521.739 1:1 1.000 Equalized 7L 16s
69\122 678.689 521.311 6:5 1.200
56\99 678.788 521.212 5:4 1.250
99\175 678.857 521.143 9:7 1.286
43\76 678.947 521.053 4:3 1.333 Supersoft 7L 16s
116\205 679.024 520.976 11:8 1.375
73\129 679.070 520.930 7:5 1.400
103\182 679.121 520.879 10:7 1.429
30\53 679.245 520.755 3:2 1.500 Soft 7L 16s
107\189 679.365 520.635 11:7 1.571
77\136 679.412 520.588 8:5 1.600
124\219 679.452 520.548 13:8 1.625
47\83 679.518 520.482 5:3 1.667 Semisoft 7L 16s
111\196 679.592 520.408 12:7 1.714
64\113 679.646 520.354 7:4 1.750
81\143 679.720 520.280 9:5 1.800
17\30 680.000 520.000 2:1 2.000 Basic 7L 16s
Scales with tunings softer than this are proper
72\127 680.315 519.685 9:4 2.250
55\97 680.412 519.588 7:3 2.333
93\164 680.488 519.512 12:5 2.400
38\67 680.597 519.403 5:2 2.500 Semihard 7L 16s
97\171 680.702 519.298 13:5 2.600
59\104 680.769 519.231 8:3 2.667
80\141 680.851 519.149 11:4 2.750
21\37 681.081 518.919 3:1 3.000 Hard 7L 16s
67\118 681.356 518.644 10:3 3.333
46\81 681.481 518.519 7:2 3.500
71\125 681.600 518.400 11:3 3.667
25\44 681.818 518.182 4:1 4.000 Superhard 7L 16s
54\95 682.105 517.895 9:2 4.500
29\51 682.353 517.647 5:1 5.000
33\58 682.759 517.241 6:1 6.000
4\7 685.714 514.286 1:0 → ∞ Collapsed 7L 16s


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