5L 2s (8/3-equivalent)

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↖ 4L 1s⟨8/3⟩ ↑ 5L 1s⟨8/3⟩ 6L 1s⟨8/3⟩ ↗
← 4L 2s⟨8/3⟩ 5L 2s (8/3-equivalent) 6L 2s⟨8/3⟩ →
↙ 4L 3s⟨8/3⟩ ↓ 5L 3s⟨8/3⟩ 6L 3s⟨8/3⟩ ↘ 
┌╥╥╥┬╥╥┬┐
│║║║│║║││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLs
sLLsLLL
Equave 8/3 (1698.0 ¢)
Period 8/3 (1698.0 ¢)
Generator size(ed8/3)
Bright 4\7 to 3\5 (970.3 ¢ to 1018.8 ¢)
Dark 2\5 to 3\7 (679.2 ¢ to 727.7 ¢)
Related MOS scales
Parent 2L 3s⟨8/3⟩
Sister 2L 5s⟨8/3⟩
Daughters 7L 5s⟨8/3⟩, 5L 7s⟨8/3⟩
Neutralized 3L 4s⟨8/3⟩
2-Flought 12L 2s⟨8/3⟩, 5L 9s⟨8/3⟩
Equal tunings(ed8/3)
Equalized (L:s = 1:1) 4\7 (970.3 ¢)
Supersoft (L:s = 4:3) 15\26 (979.6 ¢)
Soft (L:s = 3:2) 11\19 (983.1 ¢)
Semisoft (L:s = 5:3) 18\31 (986.0 ¢)
Basic (L:s = 2:1) 7\12 (990.5 ¢)
Semihard (L:s = 5:2) 17\29 (995.4 ¢)
Hard (L:s = 3:1) 10\17 (998.8 ¢)
Superhard (L:s = 4:1) 13\22 (1003.4 ¢)
Collapsed (L:s = 1:0) 3\5 (1018.8 ¢)

5L 2s⟨8/3⟩ is a 8/3-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every interval of 8/3 (1698.0 ¢). Generators that produce this scale range from 970.3 ¢ to 1018.8 ¢, or from 679.2 ¢ to 727.7 ¢.

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 5L 2s⟨8/3⟩
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 242.6 ¢
Major 1-mosstep M1ms L 242.6 ¢ to 339.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 339.6 ¢ to 485.2 ¢
Major 2-mosstep M2ms 2L 485.2 ¢ to 679.2 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 679.2 ¢ to 727.7 ¢
Augmented 3-mosstep A3ms 3L 727.7 ¢ to 1018.8 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 679.2 ¢ to 970.3 ¢
Perfect 4-mosstep P4ms 3L + s 970.3 ¢ to 1018.8 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 1018.8 ¢ to 1212.9 ¢
Major 5-mosstep M5ms 4L + s 1212.9 ¢ to 1358.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 1358.4 ¢ to 1455.5 ¢
Major 6-mosstep M6ms 5L + s 1455.5 ¢ to 1698.0 ¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 1698.0 ¢

Generator chain

Generator chain of 5L 2s⟨8/3⟩
Bright gens Scale degree Abbrev.
11 Augmented 2-mosdegree A2md
10 Augmented 5-mosdegree A5md
9 Augmented 1-mosdegree A1md
8 Augmented 4-mosdegree A4md
7 Augmented 0-mosdegree A0md
6 Augmented 3-mosdegree A3md
5 Major 6-mosdegree M6md
4 Major 2-mosdegree M2md
3 Major 5-mosdegree M5md
2 Major 1-mosdegree M1md
1 Perfect 4-mosdegree P4md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 2-mosdegree m2md
−4 Minor 5-mosdegree m5md
−5 Minor 1-mosdegree m1md
−6 Diminished 4-mosdegree d4md
−7 Diminished 7-mosdegree d7md
−8 Diminished 3-mosdegree d3md
−9 Diminished 6-mosdegree d6md
−10 Diminished 2-mosdegree d2md
−11 Diminished 5-mosdegree d5md

Modes

Scale degrees of the modes of 5L 2s⟨8/3⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 5L 2s⟨8/3⟩
Generator(ed8/3) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 970.311 727.734 1:1 1.000 Equalized 5L 2s⟨8/3⟩
23\40 976.376 721.669 6:5 1.200
19\33 977.662 720.383 5:4 1.250
34\59 978.534 719.511 9:7 1.286
15\26 979.641 718.404 4:3 1.333 Supersoft 5L 2s⟨8/3⟩
41\71 980.561 717.484 11:8 1.375
26\45 981.093 716.952 7:5 1.400
37\64 981.682 716.363 10:7 1.429
11\19 983.079 714.966 3:2 1.500 Soft 5L 2s⟨8/3⟩
40\69 984.374 713.671 11:7 1.571
29\50 984.866 713.179 8:5 1.600
47\81 985.285 712.760 13:8 1.625
18\31 985.962 712.083 5:3 1.667 Semisoft 5L 2s⟨8/3⟩
43\74 986.702 711.343 12:7 1.714
25\43 987.235 710.810 7:4 1.750
32\55 987.953 710.092 9:5 1.800
7\12 990.526 707.519 2:1 2.000 Basic 5L 2s⟨8/3⟩
Scales with tunings softer than this are proper
31\53 993.196 704.849 9:4 2.250
24\41 993.978 704.067 7:3 2.333
41\70 994.569 703.476 12:5 2.400
17\29 995.406 702.639 5:2 2.500 Semihard 5L 2s⟨8/3⟩
44\75 996.186 701.859 13:5 2.600
27\46 996.679 701.366 8:3 2.667
37\63 997.265 700.780 11:4 2.750
10\17 998.850 699.195 3:1 3.000 Hard 5L 2s⟨8/3⟩
33\56 1000.634 697.411 10:3 3.333
23\39 1001.411 696.634 7:2 3.500
36\61 1002.125 695.920 11:3 3.667
13\22 1003.390 694.655 4:1 4.000 Superhard 5L 2s⟨8/3⟩
29\49 1004.965 693.080 9:2 4.500
16\27 1006.249 691.796 5:1 5.000
19\32 1008.214 689.831 6:1 6.000
3\5 1018.827 679.218 1:0 → ∞ Collapsed 5L 2s⟨8/3⟩
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