2L 5s (5/3-equivalent)

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Revision as of 03:52, 16 April 2025 by Lériendil (talk | contribs) (Created page with "{{Infobox MOS }} {{MOS intro }} {{MOS scalesig|2L 5s <5/3>}}, in its softer tunings, can be thought of as a MOS generated by a ~4/3 (or equivalently, 5/4), where the small step thereby represents 16/15. This is just at very close to the 3:2 tuning, at 16ed5/3. Tunings softer than that, however, support a 5/3.4/3.7/6-subgroup rank-2 temperament that tempers out 225/224, and therefore equates three 4/3 generators to 10/7 (whose equave c...")
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↖ 1L 4s⟨5/3⟩ ↑ 2L 4s⟨5/3⟩ 3L 4s⟨5/3⟩ ↗
← 1L 5s⟨5/3⟩ 2L 5s (5/3-equivalent) 3L 5s⟨5/3⟩ →
↙ 1L 6s⟨5/3⟩ ↓ 2L 6s⟨5/3⟩ 3L 6s⟨5/3⟩ ↘
Scale structure
Step pattern LssLsss
sssLssL
Equave 5/3 (884.4 ¢)
Period 5/3 (884.4 ¢)
Generator size(ed5/3)
Bright 3\7 to 1\2 (379.0 ¢ to 442.2 ¢)
Dark 1\2 to 4\7 (442.2 ¢ to 505.3 ¢)
Related MOS scales
Parent 2L 3s⟨5/3⟩
Sister 5L 2s⟨5/3⟩
Daughters 7L 2s⟨5/3⟩, 2L 7s⟨5/3⟩
Neutralized 4L 3s⟨5/3⟩
2-Flought 9L 5s⟨5/3⟩, 2L 12s⟨5/3⟩
Equal tunings(ed5/3)
Equalized (L:s = 1:1) 3\7 (379.0 ¢)
Supersoft (L:s = 4:3) 10\23 (384.5 ¢)
Soft (L:s = 3:2) 7\16 (386.9 ¢)
Semisoft (L:s = 5:3) 11\25 (389.1 ¢)
Basic (L:s = 2:1) 4\9 (393.0 ¢)
Semihard (L:s = 5:2) 9\20 (398.0 ¢)
Hard (L:s = 3:1) 5\11 (402.0 ¢)
Superhard (L:s = 4:1) 6\13 (408.2 ¢)
Collapsed (L:s = 1:0) 1\2 (442.2 ¢)
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2L 5s⟨5/3⟩ is a 5/3-equivalent (non-octave) moment of symmetry scale containing 2 large steps and 5 small steps, repeating every interval of 5/3 (884.4 ¢). Generators that produce this scale range from 379 ¢ to 442.2 ¢, or from 442.2 ¢ to 505.3 ¢.

2L 5s⟨5/3⟩, in its softer tunings, can be thought of as a MOS generated by a ~4/3 (or equivalently, 5/4), where the small step thereby represents 16/15. This is just at very close to the 3:2 tuning, at 16ed5/3. Tunings softer than that, however, support a 5/3.4/3.7/6-subgroup rank-2 temperament that tempers out 225/224, and therefore equates three 4/3 generators to 10/7 (whose equave complement is 7/6) and four generators to 8/7. This creates a structure extremely analogous to meantone, where tertian triads form 6:7:8 and its retroversion, which can be considered the primary consonance on equave 5/3.

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 interval regions.
Template:MOS data is deprecated.

Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

List of ed5/3s supporting this scale

Scale tree and tuning spectrum of 2L 5s⟨5/3⟩
Generator(ed5/3) Cents Step ratio Comments
Bright Dark L:s Hardness
3\7 379.011 505.348 1:1 1.000 Equalized 2L 5s⟨5/3⟩
22\51 381.488 502.871 8:7 1.143
19\44 381.882 502.477 7:6 1.167
35\81 382.130 502.228 13:11 1.182
16\37 382.425 501.933 6:5 1.200
45\104 382.655 501.704 17:14 1.214
29\67 382.782 501.577 11:9 1.222
42\97 382.918 501.441 16:13 1.231
13\30 383.222 501.137 5:4 1.250
49\113 383.483 500.876 19:15 1.267
36\83 383.577 500.781 14:11 1.273
59\136 383.656 500.703 23:18 1.278
23\53 383.778 500.580 9:7 1.286
56\129 383.908 500.451 22:17 1.294
33\76 383.998 500.361 13:10 1.300
43\99 384.115 500.243 17:13 1.308
10\23 384.504 499.855 4:3 1.333 Supersoft 2L 5s⟨5/3⟩
47\108 384.860 499.499 19:14 1.357
37\85 384.956 499.403 15:11 1.364
64\147 385.027 499.332 26:19 1.368
27\62 385.124 499.235 11:8 1.375
71\163 385.211 499.147 29:21 1.381
44\101 385.265 499.094 18:13 1.385
61\140 385.328 499.031 25:18 1.389
17\39 385.490 498.869 7:5 1.400
58\133 385.660 498.699 24:17 1.412
41\94 385.731 498.628 17:12 1.417
65\149 385.794 498.565 27:19 1.421
24\55 385.902 498.457 10:7 1.429
55\126 386.030 498.329 23:16 1.438
31\71 386.128 498.230 13:9 1.444
38\87 386.272 498.087 16:11 1.455
7\16 386.907 497.452 3:2 1.500 Soft 2L 5s⟨5/3⟩
39\89 387.528 496.831 17:11 1.545
32\73 387.664 496.695 14:9 1.556
57\130 387.757 496.601 25:16 1.562
25\57 387.877 496.482 11:7 1.571
68\155 387.977 496.382 30:19 1.579
43\98 388.035 496.324 19:12 1.583
61\139 388.100 496.259 27:17 1.588
18\41 388.255 496.104 8:5 1.600
65\148 388.401 495.958 29:18 1.611
47\107 388.457 495.902 21:13 1.615
76\173 388.504 495.854 34:21 1.619
29\66 388.582 495.777 13:8 1.625
69\157 388.667 495.692 31:19 1.632
40\91 388.729 495.630 18:11 1.636
51\116 388.813 495.546 23:14 1.643
11\25 389.118 495.241 5:3 1.667 Semisoft 2L 5s⟨5/3⟩
48\109 389.442 494.916 22:13 1.692
37\84 389.539 494.820 17:10 1.700
63\143 389.613 494.746 29:17 1.706
26\59 389.717 494.641 12:7 1.714
67\152 389.816 494.543 31:18 1.722
41\93 389.879 494.480 19:11 1.727
56\127 389.953 494.405 26:15 1.733
15\34 390.158 494.200 7:4 1.750
49\111 390.393 493.966 23:13 1.769
34\77 390.496 493.863 16:9 1.778
53\120 390.592 493.767 25:14 1.786
19\43 390.763 493.596 9:5 1.800
42\95 390.980 493.379 20:11 1.818
23\52 391.159 493.200 11:6 1.833
27\61 391.437 492.921 13:7 1.857
4\9 393.048 491.310 2:1 2.000 Basic 2L 5s⟨5/3⟩
Scales with tunings softer than this are proper
25\56 394.803 489.556 13:6 2.167
21\47 395.139 489.220 11:5 2.200
38\85 395.360 488.998 20:9 2.222
17\38 395.634 488.725 9:4 2.250
47\105 395.856 488.503 25:11 2.273
30\67 395.982 488.377 16:7 2.286
43\96 396.119 488.240 23:10 2.300
13\29 396.437 487.922 7:3 2.333
48\107 396.722 487.637 26:11 2.364
35\78 396.828 487.531 19:8 2.375
57\127 396.917 487.442 31:13 2.385
22\49 397.059 487.300 12:5 2.400
53\118 397.212 487.147 29:12 2.417
31\69 397.321 487.038 17:7 2.429
40\89 397.465 486.894 22:9 2.444
9\20 397.961 486.397 5:2 2.500 Semihard 2L 5s⟨5/3⟩
41\91 398.447 485.911 23:9 2.556
32\71 398.584 485.775 18:7 2.571
55\122 398.686 485.672 31:12 2.583
23\51 398.828 485.530 13:5 2.600
60\133 398.959 485.400 34:13 2.615
37\82 399.040 485.319 21:8 2.625
51\113 399.135 485.223 29:11 2.636
14\31 399.388 484.971 8:3 2.667
47\104 399.662 484.697 27:10 2.700
33\73 399.779 484.580 19:7 2.714
52\115 399.884 484.475 30:11 2.727
19\42 400.067 484.292 11:4 2.750
43\95 400.289 484.070 25:9 2.778
24\53 400.464 483.894 14:5 2.800
29\64 400.725 483.634 17:6 2.833
5\11 401.981 482.377 3:1 3.000 Hard 2L 5s⟨5/3⟩
26\57 403.392 480.967 16:5 3.200
21\46 403.729 480.630 13:4 3.250
37\81 403.966 480.392 23:7 3.286
16\35 404.278 480.080 10:3 3.333
43\94 404.547 479.812 27:8 3.375
27\59 404.707 479.652 17:5 3.400
38\83 404.887 479.472 24:7 3.429
11\24 405.331 479.028 7:2 3.500
39\85 405.765 478.594 25:7 3.571
28\61 405.935 478.424 18:5 3.600
45\98 406.083 478.276 29:8 3.625
17\37 406.327 478.032 11:3 3.667
40\87 406.602 477.757 26:7 3.714
23\50 406.805 477.554 15:4 3.750
29\63 407.086 477.273 19:5 3.800
6\13 408.166 476.193 4:1 4.000 Superhard 2L 5s⟨5/3⟩
25\54 409.425 474.933 17:4 4.250
19\41 409.825 474.534 13:3 4.333
32\69 410.137 474.221 22:5 4.400
13\28 410.595 473.764 9:2 4.500
33\71 411.040 473.319 23:5 4.600
20\43 411.330 473.029 14:3 4.667
27\58 411.684 472.674 19:4 4.750
7\15 412.701 471.658 5:1 5.000
22\47 413.955 470.404 16:3 5.333
15\32 414.543 469.816 11:2 5.500
23\49 415.107 469.252 17:3 5.667
8\17 416.169 468.190 6:1 6.000
17\36 417.614 466.745 13:2 6.500
9\19 418.907 465.452 7:1 7.000
10\21 421.123 463.236 8:1 8.000
1\2 442.179 442.179 1:0 → ∞ Collapsed 2L 5s⟨5/3⟩
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