2L 17s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖1L 16s ↑2L 16s 3L 16s↗
←1L 17s2L 17s 3L 17s→
↙1L 18s ↓2L 18s 3L 18s↘
┌╥┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┐
│║││││││││║││││││││││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssssLsssssssss
sssssssssLssssssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\19 to 1\2 (63.2¢ to 600.0¢)
Small 0\2 to 1\19 (0.0¢ to 63.2¢)
Generator size
Bright 9\19 to 1\2 (568.4¢ to 600.0¢)
Dark 1\2 to 10\19 (600.0¢ to 631.6¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Related MOS scales
Parent 2L 15s
Sister 17L 2s
Daughters 19L 2s
2L 19s
Equal tunings
Equalized (L:s = 1:1) 9\19 (568.4¢)
Supersoft (L:s = 4:3) 28\59 (569.5¢)
Soft (L:s = 3:2) 19\40 (570.0¢)
Semisoft (L:s = 5:3) 29\61 (570.5¢)
Basic (L:s = 2:1) 10\21 (571.4¢)
Semihard (L:s = 5:2) 21\44 (572.7¢)
Hard (L:s = 3:1) 11\23 (573.9¢)
Superhard (L:s = 4:1) 12\25 (576.0¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

2L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 17 small steps, repeating every octave. 2L 17s is related to 2L 7s, expanding it by 10 tones. Generators that produce this scale range from 568.4¢ to 600¢, or from 600¢ to 631.6¢.

This is the MOS where the small steps divide 9-8 between the large steps. The generator is a tritone of no less than 9/19edo (568.421 cents), having minimum harmonic entropy at 7/5.

Scale tree and tuning spectrum of 2L 17s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\19 568.421 631.579 1:1 1.000 Equalized 2L 17s
46\97 569.072 630.928 6:5 1.200
37\78 569.231 630.769 5:4 1.250
65\137 569.343 630.657 9:7 1.286
28\59 569.492 630.508 4:3 1.333 Supersoft 2L 17s
75\158 569.620 630.380 11:8 1.375
47\99 569.697 630.303 7:5 1.400
66\139 569.784 630.216 10:7 1.429
19\40 570.000 630.000 3:2 1.500 Soft 2L 17s
67\141 570.213 629.787 11:7 1.571
48\101 570.297 629.703 8:5 1.600
77\162 570.370 629.630 13:8 1.625
29\61 570.492 629.508 5:3 1.667 Semisoft 2L 17s
68\143 570.629 629.371 12:7 1.714
39\82 570.732 629.268 7:4 1.750
49\103 570.874 629.126 9:5 1.800
10\21 571.429 628.571 2:1 2.000 Basic 2L 17s
Scales with tunings softer than this are proper
41\86 572.093 627.907 9:4 2.250
31\65 572.308 627.692 7:3 2.333
52\109 572.477 627.523 12:5 2.400
21\44 572.727 627.273 5:2 2.500 Semihard 2L 17s
53\111 572.973 627.027 13:5 2.600
32\67 573.134 626.866 8:3 2.667
43\90 573.333 626.667 11:4 2.750
11\23 573.913 626.087 3:1 3.000 Hard 2L 17s
34\71 574.648 625.352 10:3 3.333
23\48 575.000 625.000 7:2 3.500
35\73 575.342 624.658 11:3 3.667
12\25 576.000 624.000 4:1 4.000 Superhard 2L 17s
25\52 576.923 623.077 9:2 4.500
13\27 577.778 622.222 5:1 5.000
14\29 579.310 620.690 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 17s