2L 15s

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↖ 1L 14s ↑ 2L 14s 3L 14s ↗
← 1L 15s 2L 15s 3L 15s →
↙ 1L 16s ↓ 2L 16s 3L 16s ↘ 
┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┐
│║│││││││║│││││││││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssssLssssssss
ssssssssLsssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\17 to 1\2 (564.7 ¢ to 600.0 ¢)
Dark 1\2 to 9\17 (600.0 ¢ to 635.3 ¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Ancestor's step ratio range 5:1 to 1:0
Related MOS scales
Parent 2L 13s
Sister 15L 2s
Daughters 17L 2s, 2L 17s
Neutralized 4L 13s
2-Flought 19L 15s, 2L 32s
Equal tunings
Equalized (L:s = 1:1) 8\17 (564.7 ¢)
Supersoft (L:s = 4:3) 25\53 (566.0 ¢)
Soft (L:s = 3:2) 17\36 (566.7 ¢)
Semisoft (L:s = 5:3) 26\55 (567.3 ¢)
Basic (L:s = 2:1) 9\19 (568.4 ¢)
Semihard (L:s = 5:2) 19\40 (570.0 ¢)
Hard (L:s = 3:1) 10\21 (571.4 ¢)
Superhard (L:s = 4:1) 11\23 (573.9 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 15 small steps, repeating every octave. 2L 15s is related to 2L 7s, expanding it by 8 tones. Generators that produce this scale range from 564.7 ¢ to 600 ¢, or from 600 ¢ to 635.3 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

Intervals of 2L 15s
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 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 141.2 ¢
Major 2-mosstep M2ms L + s 141.2 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms L + 2s 211.8 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms L + 3s 282.4 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms L + 4s 352.9 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms L + 5s 423.5 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms L + 6s 494.1 ¢ to 600.0 ¢
8-mosstep Diminished 8-mosstep d8ms 8s 0.0 ¢ to 564.7 ¢
Perfect 8-mosstep P8ms L + 7s 564.7 ¢ to 600.0 ¢
9-mosstep Perfect 9-mosstep P9ms L + 8s 600.0 ¢ to 635.3 ¢
Augmented 9-mosstep A9ms 2L + 7s 635.3 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 600.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 2L + 8s 705.9 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 600.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 2L + 9s 776.5 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 600.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 2L + 10s 847.1 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 2L + 11s 917.6 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 2L + 12s 988.2 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms L + 14s 600.0 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 2L + 13s 1058.8 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms L + 15s 600.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 2L + 14s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 2L + 15s 1200.0 ¢

Generator chain

Generator chain of 2L 15s
Bright gens Scale degree Abbrev.
18 Augmented 8-mosdegree A8md
17 Augmented 0-mosdegree A0md
16 Augmented 9-mosdegree A9md
15 Major 1-mosdegree M1md
14 Major 10-mosdegree M10md
13 Major 2-mosdegree M2md
12 Major 11-mosdegree M11md
11 Major 3-mosdegree M3md
10 Major 12-mosdegree M12md
9 Major 4-mosdegree M4md
8 Major 13-mosdegree M13md
7 Major 5-mosdegree M5md
6 Major 14-mosdegree M14md
5 Major 6-mosdegree M6md
4 Major 15-mosdegree M15md
3 Major 7-mosdegree M7md
2 Major 16-mosdegree M16md
1 Perfect 8-mosdegree P8md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 9-mosdegree P9md
−2 Minor 1-mosdegree m1md
−3 Minor 10-mosdegree m10md
−4 Minor 2-mosdegree m2md
−5 Minor 11-mosdegree m11md
−6 Minor 3-mosdegree m3md
−7 Minor 12-mosdegree m12md
−8 Minor 4-mosdegree m4md
−9 Minor 13-mosdegree m13md
−10 Minor 5-mosdegree m5md
−11 Minor 14-mosdegree m14md
−12 Minor 6-mosdegree m6md
−13 Minor 15-mosdegree m15md
−14 Minor 7-mosdegree m7md
−15 Minor 16-mosdegree m16md
−16 Diminished 8-mosdegree d8md
−17 Diminished 17-mosdegree d17md
−18 Diminished 9-mosdegree d9md

Modes

Scale degrees of the modes of 2L 15s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
16|0 1 LsssssssLssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|1 9 LssssssssLsssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|2 17 sLsssssssLsssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|3 8 sLssssssssLssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|4 16 ssLsssssssLssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
11|5 7 ssLssssssssLsssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
10|6 15 sssLsssssssLsssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
9|7 6 sssLssssssssLssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
8|8 14 ssssLsssssssLssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
7|9 5 ssssLssssssssLsss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
6|10 13 sssssLsssssssLsss Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
5|11 4 sssssLssssssssLss Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf.
4|12 12 ssssssLsssssssLss Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf.
3|13 3 ssssssLssssssssLs Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf.
2|14 11 sssssssLsssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf.
1|15 2 sssssssLssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
0|16 10 ssssssssLsssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Dim. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 15s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\17 564.706 635.294 1:1 1.000 Equalized 2L 15s
57\121 565.289 634.711 8:7 1.143
49\104 565.385 634.615 7:6 1.167
90\191 565.445 634.555 13:11 1.182
41\87 565.517 634.483 6:5 1.200
115\244 565.574 634.426 17:14 1.214
74\157 565.605 634.395 11:9 1.222
107\227 565.639 634.361 16:13 1.231
33\70 565.714 634.286 5:4 1.250
124\263 565.779 634.221 19:15 1.267
91\193 565.803 634.197 14:11 1.273
149\316 565.823 634.177 23:18 1.278
58\123 565.854 634.146 9:7 1.286
141\299 565.886 634.114 22:17 1.294
83\176 565.909 634.091 13:10 1.300
108\229 565.939 634.061 17:13 1.308
25\53 566.038 633.962 4:3 1.333 Supersoft 2L 15s
Tricot
117\248 566.129 633.871 19:14 1.357
92\195 566.154 633.846 15:11 1.364
159\337 566.172 633.828 26:19 1.368
67\142 566.197 633.803 11:8 1.375
176\373 566.220 633.780 29:21 1.381
109\231 566.234 633.766 18:13 1.385
151\320 566.250 633.750 25:18 1.389
42\89 566.292 633.708 7:5 1.400
143\303 566.337 633.663 24:17 1.412
101\214 566.355 633.645 17:12 1.417
160\339 566.372 633.628 27:19 1.421
59\125 566.400 633.600 10:7 1.429
135\286 566.434 633.566 23:16 1.438
76\161 566.460 633.540 13:9 1.444
93\197 566.497 633.503 16:11 1.455
17\36 566.667 633.333 3:2 1.500 Soft 2L 15s
94\199 566.834 633.166 17:11 1.545
77\163 566.871 633.129 14:9 1.556
137\290 566.897 633.103 25:16 1.562
60\127 566.929 633.071 11:7 1.571
163\345 566.957 633.043 30:19 1.579
103\218 566.972 633.028 19:12 1.583
146\309 566.990 633.010 27:17 1.588
43\91 567.033 632.967 8:5 1.600 Liesel
155\328 567.073 632.927 29:18 1.611
112\237 567.089 632.911 21:13 1.615
181\383 567.102 632.898 34:21 1.619
69\146 567.123 632.877 13:8 1.625
164\347 567.147 632.853 31:19 1.632
95\201 567.164 632.836 18:11 1.636
121\256 567.188 632.812 23:14 1.643
26\55 567.273 632.727 5:3 1.667 Semisoft 2L 15s
113\239 567.364 632.636 22:13 1.692
87\184 567.391 632.609 17:10 1.700
148\313 567.412 632.588 29:17 1.706
61\129 567.442 632.558 12:7 1.714
157\332 567.470 632.530 31:18 1.722
96\203 567.488 632.512 19:11 1.727
131\277 567.509 632.491 26:15 1.733
35\74 567.568 632.432 7:4 1.750
114\241 567.635 632.365 23:13 1.769
79\167 567.665 632.335 16:9 1.778
123\260 567.692 632.308 25:14 1.786
44\93 567.742 632.258 9:5 1.800 Pycnic
97\205 567.805 632.195 20:11 1.818
53\112 567.857 632.143 11:6 1.833
62\131 567.939 632.061 13:7 1.857
9\19 568.421 631.579 2:1 2.000 Basic 2L 15s
Scales with tunings softer than this are proper
55\116 568.966 631.034 13:6 2.167 Lisa
46\97 569.072 630.928 11:5 2.200
83\175 569.143 630.857 20:9 2.222
37\78 569.231 630.769 9:4 2.250
102\215 569.302 630.698 25:11 2.273
65\137 569.343 630.657 16:7 2.286
93\196 569.388 630.612 23:10 2.300
28\59 569.492 630.508 7:3 2.333
103\217 569.585 630.415 26:11 2.364
75\158 569.620 630.380 19:8 2.375
122\257 569.650 630.350 31:13 2.385
47\99 569.697 630.303 12:5 2.400
113\238 569.748 630.252 29:12 2.417
66\139 569.784 630.216 17:7 2.429
85\179 569.832 630.168 22:9 2.444
19\40 570.000 630.000 5:2 2.500 Semihard 2L 15s
86\181 570.166 629.834 23:9 2.556
67\141 570.213 629.787 18:7 2.571
115\242 570.248 629.752 31:12 2.583
48\101 570.297 629.703 13:5 2.600
125\263 570.342 629.658 34:13 2.615
77\162 570.370 629.630 21:8 2.625
106\223 570.404 629.596 29:11 2.636
29\61 570.492 629.508 8:3 2.667
97\204 570.588 629.412 27:10 2.700
68\143 570.629 629.371 19:7 2.714
107\225 570.667 629.333 30:11 2.727
39\82 570.732 629.268 11:4 2.750
88\185 570.811 629.189 25:9 2.778
49\103 570.874 629.126 14:5 2.800
59\124 570.968 629.032 17:6 2.833
10\21 571.429 628.571 3:1 3.000 Hard 2L 15s
51\107 571.963 628.037 16:5 3.200
41\86 572.093 627.907 13:4 3.250
72\151 572.185 627.815 23:7 3.286
31\65 572.308 627.692 10:3 3.333
83\174 572.414 627.586 27:8 3.375
52\109 572.477 627.523 17:5 3.400
73\153 572.549 627.451 24:7 3.429
21\44 572.727 627.273 7:2 3.500
74\155 572.903 627.097 25:7 3.571
53\111 572.973 627.027 18:5 3.600
85\178 573.034 626.966 29:8 3.625
32\67 573.134 626.866 11:3 3.667
75\157 573.248 626.752 26:7 3.714
43\90 573.333 626.667 15:4 3.750
54\113 573.451 626.549 19:5 3.800
11\23 573.913 626.087 4:1 4.000 Superhard 2L 15s
45\94 574.468 625.532 17:4 4.250
34\71 574.648 625.352 13:3 4.333
57\119 574.790 625.210 22:5 4.400
23\48 575.000 625.000 9:2 4.500
58\121 575.207 624.793 23:5 4.600
35\73 575.342 624.658 14:3 4.667
47\98 575.510 624.490 19:4 4.750
12\25 576.000 624.000 5:1 5.000
37\77 576.623 623.377 16:3 5.333
25\52 576.923 623.077 11:2 5.500
38\79 577.215 622.785 17:3 5.667
13\27 577.778 622.222 6:1 6.000 Fervor, Tritonic ↓
27\56 578.571 621.429 13:2 6.500
14\29 579.310 620.690 7:1 7.000
15\31 580.645 619.355 8:1 8.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 15s
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