8L 1s (3/1-equivalent)

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← 7L 1s⟨3/1⟩ 8L 1s (3/1-equivalent) 9L 1s⟨3/1⟩ →
↙ 7L 2s⟨3/1⟩ ↓ 8L 2s⟨3/1⟩ 9L 2s⟨3/1⟩ ↘
Scale structure
Step pattern LLLLLLLLs
sLLLLLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 1\9 to 1\8 (211.3 ¢ to 237.7 ¢)
Dark 7\8 to 8\9 (1664.2 ¢ to 1690.6 ¢)
Related MOS scales
Parent 1L 7s⟨3/1⟩
Sister 1L 8s⟨3/1⟩
Daughters 9L 8s⟨3/1⟩, 8L 9s⟨3/1⟩
Neutralized 7L 2s⟨3/1⟩
2-Flought 17L 1s⟨3/1⟩, 8L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 1\9 (211.3 ¢)
Supersoft (L:s = 4:3) 4\35 (217.4 ¢)
Soft (L:s = 3:2) 3\26 (219.5 ¢)
Semisoft (L:s = 5:3) 5\43 (221.2 ¢)
Basic (L:s = 2:1) 2\17 (223.8 ¢)
Semihard (L:s = 5:2) 5\42 (226.4 ¢)
Hard (L:s = 3:1) 3\25 (228.2 ¢)
Superhard (L:s = 4:1) 4\33 (230.5 ¢)
Collapsed (L:s = 1:0) 1\8 (237.7 ¢)
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8L 1s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 8 large steps and 1 small step, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 211.3 ¢ to 237.7 ¢, or from 1664.2 ¢ to 1690.6 ¢. Scales of this form are always proper because there is only one small step.

Theory

Modes

Modes of 8L 1s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
8|0 1 LLLLLLLLs
7|1 2 LLLLLLLsL
6|2 3 LLLLLLsLL
5|3 4 LLLLLsLLL
4|4 5 LLLLsLLLL
3|5 6 LLLsLLLLL
2|6 7 LLsLLLLLL
1|7 8 LsLLLLLLL
0|8 9 sLLLLLLLL

Temperament interpretations

Todo: expand

Intervals

Intervals of 8L 1s⟨3/1⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 211.3 ¢
Perfect 1-mosstep P1ms L 211.3 ¢ to 237.7 ¢
2-mosstep Minor 2-mosstep m2ms L + s 237.7 ¢ to 422.7 ¢
Major 2-mosstep M2ms 2L 422.7 ¢ to 475.5 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 475.5 ¢ to 634.0 ¢
Major 3-mosstep M3ms 3L 634.0 ¢ to 713.2 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 713.2 ¢ to 845.3 ¢
Major 4-mosstep M4ms 4L 845.3 ¢ to 951.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 951.0 ¢ to 1056.6 ¢
Major 5-mosstep M5ms 5L 1056.6 ¢ to 1188.7 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 1188.7 ¢ to 1268.0 ¢
Major 6-mosstep M6ms 6L 1268.0 ¢ to 1426.5 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 1426.5 ¢ to 1479.3 ¢
Major 7-mosstep M7ms 7L 1479.3 ¢ to 1664.2 ¢
8-mosstep Perfect 8-mosstep P8ms 7L + s 1664.2 ¢ to 1690.6 ¢
Augmented 8-mosstep A8ms 8L 1690.6 ¢ to 1902.0 ¢
9-mosstep Perfect 9-mosstep P9ms 8L + s 1902.0 ¢

Scale degrees

Scale degrees of the modes of 8L 1s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLLLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf.
7|1 2 LLLLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|2 3 LLLLLLsLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf.
5|3 4 LLLLLsLLL Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf.
4|4 5 LLLLsLLLL Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Perf.
3|5 6 LLLsLLLLL Perf. Perf. Maj. Maj. Min. Min. Min. Min. Perf. Perf.
2|6 7 LLsLLLLLL Perf. Perf. Maj. Min. Min. Min. Min. Min. Perf. Perf.
1|7 8 LsLLLLLLL Perf. Perf. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|8 9 sLLLLLLLL Perf. Dim. Min. Min. Min. Min. Min. Min. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 1s⟨3/1⟩
Generator(edt) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\9 211.328 1690.627 1:1 1.000 Equalized 8L 1s⟨3/1⟩
6\53 215.316 1686.639 6:5 1.200
5\44 216.131 1685.824 5:4 1.250
9\79 216.678 1685.277 9:7 1.286 Just 17/15 generator
4\35 217.366 1684.589 4:3 1.333 Supersoft 8L 1s⟨3/1⟩
11\96 217.932 1684.023 11:8 1.375
7\61 218.257 1683.698 7:5 1.400
10\87 218.616 1683.339 10:7 1.429
3\26 219.456 1682.499 3:2 1.500 Soft 8L 1s⟨3/1⟩
11\95 220.226 1681.729 11:7 1.571 Dubhe is around here
8\69 220.517 1681.438 8:5 1.600
13\112 220.763 1681.192 13:8 1.625
5\43 221.158 1680.797 5:3 1.667 Semisoft 8L 1s⟨3/1⟩
12\103 221.587 1680.368 12:7 1.714
7\60 221.895 1680.060 7:4 1.750
9\77 222.306 1679.649 9:5 1.800
2\17 223.759 1678.196 2:1 2.000 Basic 8L 1s⟨3/1⟩
9\76 225.232 1676.723 9:4 2.250
7\59 225.656 1676.299 7:3 2.333
12\101 225.975 1675.980 12:5 2.400
5\42 226.423 1675.532 5:2 2.500 Semihard 8L 1s⟨3/1⟩
13\109 226.839 1675.116 13:5 2.600
8\67 227.099 1674.856 8:3 2.667
11\92 227.408 1674.547 11:4 2.750
3\25 228.235 1673.720 3:1 3.000 Hard 8L 1s⟨3/1⟩
10\83 229.151 1672.804 10:3 3.333
7\58 229.546 1672.409 7:2 3.500
11\91 229.907 1672.048 11:3 3.667
4\33 230.540 1671.415 4:1 4.000 Superhard 8L 1s⟨3/1⟩
9\74 231.319 1670.636 9:2 4.500
5\41 231.946 1670.009 5:1 5.000
6\49 232.892 1669.063 6:1 6.000
1\8 237.744 1664.211 1:0 → ∞ Collapsed 8L 1s⟨3/1⟩
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