2L 5s (5/3-equivalent)

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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 ¢)

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.

Intervals

Intervals of 2L 5s⟨5/3⟩
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 126.3 ¢
Major 1-mosstep M1ms L 126.3 ¢ to 442.2 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 252.7 ¢
Major 2-mosstep M2ms L + s 252.7 ¢ to 442.2 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 379.0 ¢
Perfect 3-mosstep P3ms L + 2s 379.0 ¢ to 442.2 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 442.2 ¢ to 505.3 ¢
Augmented 4-mosstep A4ms 2L + 2s 505.3 ¢ to 884.4 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 442.2 ¢ to 631.7 ¢
Major 5-mosstep M5ms 2L + 3s 631.7 ¢ to 884.4 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 442.2 ¢ to 758.0 ¢
Major 6-mosstep M6ms 2L + 4s 758.0 ¢ to 884.4 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 884.4 ¢

Generator chain

Generator chain of 2L 5s⟨5/3⟩
Bright gens Scale degree Abbrev.
8 Augmented 3-mosdegree A3md
7 Augmented 0-mosdegree A0md
6 Augmented 4-mosdegree A4md
5 Major 1-mosdegree M1md
4 Major 5-mosdegree M5md
3 Major 2-mosdegree M2md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md
−1 Perfect 4-mosdegree P4md
−2 Minor 1-mosdegree m1md
−3 Minor 5-mosdegree m5md
−4 Minor 2-mosdegree m2md
−5 Minor 6-mosdegree m6md
−6 Diminished 3-mosdegree d3md
−7 Diminished 7-mosdegree d7md
−8 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 2L 5s⟨5/3⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 1 LssLsss Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
5|1 4 LsssLss Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 7 sLssLss Perf. Min. Maj. Perf. Perf. Maj. Maj. Perf.
3|3 3 sLsssLs Perf. Min. Maj. Perf. Perf. Min. Maj. Perf.
2|4 6 ssLssLs Perf. Min. Min. Perf. Perf. Min. Maj. Perf.
1|5 2 ssLsssL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 5 sssLssL Perf. Min. Min. Dim. Perf. Min. Min. Perf.

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⟩
19\44 381.882 502.477 7:6 1.167
16\37 382.425 501.933 6:5 1.200
29\67 382.782 501.577 11:9 1.222
13\30 383.222 501.137 5:4 1.250
36\83 383.577 500.781 14:11 1.273
23\53 383.778 500.580 9:7 1.286
33\76 383.998 500.361 13:10 1.300
10\23 384.504 499.855 4:3 1.333 Supersoft 2L 5s⟨5/3⟩
37\85 384.956 499.403 15:11 1.364
27\62 385.124 499.235 11:8 1.375
44\101 385.265 499.094 18:13 1.385
17\39 385.490 498.869 7:5 1.400
41\94 385.731 498.628 17:12 1.417
24\55 385.902 498.457 10:7 1.429
31\71 386.128 498.230 13:9 1.444
7\16 386.907 497.452 3:2 1.500 Soft 2L 5s⟨5/3⟩
32\73 387.664 496.695 14:9 1.556
25\57 387.877 496.482 11:7 1.571
43\98 388.035 496.324 19:12 1.583
18\41 388.255 496.104 8:5 1.600
47\107 388.457 495.902 21:13 1.615
29\66 388.582 495.777 13:8 1.625
40\91 388.729 495.630 18:11 1.636
11\25 389.118 495.241 5:3 1.667 Semisoft 2L 5s⟨5/3⟩
37\84 389.539 494.820 17:10 1.700
26\59 389.717 494.641 12:7 1.714
41\93 389.879 494.480 19:11 1.727
15\34 390.158 494.200 7:4 1.750
34\77 390.496 493.863 16:9 1.778
19\43 390.763 493.596 9:5 1.800
23\52 391.159 493.200 11:6 1.833
4\9 393.048 491.310 2:1 2.000 Basic 2L 5s⟨5/3⟩
Scales with tunings softer than this are proper
21\47 395.139 489.220 11:5 2.200
17\38 395.634 488.725 9:4 2.250
30\67 395.982 488.377 16:7 2.286
13\29 396.437 487.922 7:3 2.333
35\78 396.828 487.531 19:8 2.375
22\49 397.059 487.300 12:5 2.400
31\69 397.321 487.038 17:7 2.429
9\20 397.961 486.397 5:2 2.500 Semihard 2L 5s⟨5/3⟩
32\71 398.584 485.775 18:7 2.571
23\51 398.828 485.530 13:5 2.600
37\82 399.040 485.319 21:8 2.625
14\31 399.388 484.971 8:3 2.667
33\73 399.779 484.580 19:7 2.714
19\42 400.067 484.292 11:4 2.750
24\53 400.464 483.894 14:5 2.800
5\11 401.981 482.377 3:1 3.000 Hard 2L 5s⟨5/3⟩
21\46 403.729 480.630 13:4 3.250
16\35 404.278 480.080 10:3 3.333
27\59 404.707 479.652 17:5 3.400
11\24 405.331 479.028 7:2 3.500
28\61 405.935 478.424 18:5 3.600
17\37 406.327 478.032 11:3 3.667
23\50 406.805 477.554 15:4 3.750
6\13 408.166 476.193 4:1 4.000 Superhard 2L 5s⟨5/3⟩
19\41 409.825 474.534 13:3 4.333
13\28 410.595 473.764 9:2 4.500
20\43 411.330 473.029 14:3 4.667
7\15 412.701 471.658 5:1 5.000
15\32 414.543 469.816 11:2 5.500
8\17 416.169 468.190 6:1 6.000
9\19 418.907 465.452 7:1 7.000
1\2 442.179 442.179 1:0 → ∞ Collapsed 2L 5s⟨5/3⟩
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