2L 9s (3/1-equivalent)
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Scale structure
Step pattern
LssssLsssss
sssssLssssL
Equave
3/1 (1902.0¢)
Period
3/1 (1902.0¢)
Generator size(edt)
Bright
5\11 to 1\2 (864.5¢ to 951.0¢)
Dark
1\2 to 6\11 (951.0¢ to 1037.4¢)
Related MOS scales
Parent
2L 7s⟨3/1⟩
Sister
9L 2s⟨3/1⟩
Daughters
11L 2s⟨3/1⟩, 2L 11s⟨3/1⟩
Neutralized
4L 7s⟨3/1⟩
2-Flought
13L 9s⟨3/1⟩, 2L 20s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)
5\11 (864.5¢)
Supersoft (L:s = 4:3)
16\35 (869.5¢)
Soft (L:s = 3:2)
11\24 (871.7¢)
Semisoft (L:s = 5:3)
17\37 (873.9¢)
Basic (L:s = 2:1)
6\13 (877.8¢)
Semihard (L:s = 5:2)
13\28 (883.1¢)
Hard (L:s = 3:1)
7\15 (887.6¢)
Superhard (L:s = 4:1)
8\17 (895.0¢)
Collapsed (L:s = 1:0)
1\2 (951.0¢)
↖ 1L 8s⟨3/1⟩ | ↑ 2L 8s⟨3/1⟩ | 3L 8s⟨3/1⟩ ↗ |
← 1L 9s⟨3/1⟩ | 2L 9s (3/1-equivalent) | 3L 9s⟨3/1⟩ → |
↙ 1L 10s⟨3/1⟩ | ↓ 2L 10s⟨3/1⟩ | 3L 10s⟨3/1⟩ ↘ |
┌╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
sssssLssssL
2L 9s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 9 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 864.5¢ to 951¢, or from 951¢ to 1037.4¢.
The generators of this scale in the hard-of-basic region approximate 5/3. It is a scale of the Arcturus temperament.
Modes
UDP | Cyclic order |
Step pattern |
---|---|---|
10|0 | 1 | LssssLsssss |
9|1 | 6 | LsssssLssss |
8|2 | 11 | sLssssLssss |
7|3 | 5 | sLsssssLsss |
6|4 | 10 | ssLssssLsss |
5|5 | 4 | ssLsssssLss |
4|6 | 9 | sssLssssLss |
3|7 | 3 | sssLsssssLs |
2|8 | 8 | ssssLssssLs |
1|9 | 2 | ssssLsssssL |
0|10 | 7 | sssssLssssL |
Intervals
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 172.9¢ |
Major 1-mosstep | M1ms | L | 172.9¢ to 951.0¢ | |
2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 345.8¢ |
Major 2-mosstep | M2ms | L + s | 345.8¢ to 951.0¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 518.7¢ |
Major 3-mosstep | M3ms | L + 2s | 518.7¢ to 951.0¢ | |
4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 691.6¢ |
Major 4-mosstep | M4ms | L + 3s | 691.6¢ to 951.0¢ | |
5-mosstep | Diminished 5-mosstep | d5ms | 5s | 0.0¢ to 864.5¢ |
Perfect 5-mosstep | P5ms | L + 4s | 864.5¢ to 951.0¢ | |
6-mosstep | Perfect 6-mosstep | P6ms | L + 5s | 951.0¢ to 1037.4¢ |
Augmented 6-mosstep | A6ms | 2L + 4s | 1037.4¢ to 1902.0¢ | |
7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 951.0¢ to 1210.3¢ |
Major 7-mosstep | M7ms | 2L + 5s | 1210.3¢ to 1902.0¢ | |
8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 951.0¢ to 1383.2¢ |
Major 8-mosstep | M8ms | 2L + 6s | 1383.2¢ to 1902.0¢ | |
9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 951.0¢ to 1556.1¢ |
Major 9-mosstep | M9ms | 2L + 7s | 1556.1¢ to 1902.0¢ | |
10-mosstep | Minor 10-mosstep | m10ms | L + 9s | 951.0¢ to 1729.1¢ |
Major 10-mosstep | M10ms | 2L + 8s | 1729.1¢ to 1902.0¢ | |
11-mosstep | Perfect 11-mosstep | P11ms | 2L + 9s | 1902.0¢ |
Scale tree
Generator(edt) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
5\11 | 864.525 | 1037.430 | 1:1 | 1.000 | Equalized 2L 9s⟨3/1⟩ | |||||
26\57 | 867.558 | 1034.397 | 6:5 | 1.200 | ||||||
21\46 | 868.284 | 1033.671 | 5:4 | 1.250 | ||||||
37\81 | 868.794 | 1033.161 | 9:7 | 1.286 | ||||||
16\35 | 869.465 | 1032.490 | 4:3 | 1.333 | Supersoft 2L 9s⟨3/1⟩ | |||||
43\94 | 870.043 | 1031.912 | 11:8 | 1.375 | ||||||
27\59 | 870.386 | 1031.569 | 7:5 | 1.400 | ||||||
38\83 | 870.775 | 1031.180 | 10:7 | 1.429 | ||||||
11\24 | 871.729 | 1030.226 | 3:2 | 1.500 | Soft 2L 9s⟨3/1⟩ | |||||
39\85 | 872.662 | 1029.293 | 11:7 | 1.571 | ||||||
28\61 | 873.029 | 1028.926 | 8:5 | 1.600 | ||||||
45\98 | 873.347 | 1028.608 | 13:8 | 1.625 | ||||||
17\37 | 873.871 | 1028.084 | 5:3 | 1.667 | Semisoft 2L 9s⟨3/1⟩ | |||||
40\87 | 874.462 | 1027.493 | 12:7 | 1.714 | ||||||
23\50 | 874.899 | 1027.056 | 7:4 | 1.750 | ||||||
29\63 | 875.503 | 1026.452 | 9:5 | 1.800 | ||||||
6\13 | 877.825 | 1024.130 | 2:1 | 2.000 | Basic 2L 9s⟨3/1⟩ Scales with tunings softer than this are proper | |||||
25\54 | 880.535 | 1021.420 | 9:4 | 2.250 | ||||||
19\41 | 881.394 | 1020.561 | 7:3 | 2.333 | ||||||
32\69 | 882.066 | 1019.889 | 12:5 | 2.400 | ||||||
13\28 | 883.051 | 1018.904 | 5:2 | 2.500 | Semihard 2L 9s⟨3/1⟩ Arcturus is around here | |||||
33\71 | 884.007 | 1017.948 | 13:5 | 2.600 | ||||||
20\43 | 884.630 | 1017.325 | 8:3 | 2.667 | 5/3-Pythagorean is around here | |||||
27\58 | 885.393 | 1016.562 | 11:4 | 2.750 | ||||||
7\15 | 887.579 | 1014.376 | 3:1 | 3.000 | Hard 2L 9s⟨3/1⟩ | |||||
22\47 | 890.277 | 1011.678 | 10:3 | 3.333 | ||||||
15\32 | 891.541 | 1010.414 | 7:2 | 3.500 | ||||||
23\49 | 892.754 | 1009.201 | 11:3 | 3.667 | ||||||
8\17 | 895.038 | 1006.917 | 4:1 | 4.000 | Superhard 2L 9s⟨3/1⟩ | |||||
17\36 | 898.145 | 1003.810 | 9:2 | 4.500 | ||||||
9\19 | 900.926 | 1001.029 | 5:1 | 5.000 | ||||||
10\21 | 905.693 | 996.262 | 6:1 | 6.000 | ||||||
1\2 | 950.978 | 950.978 | 1:0 | → ∞ | Collapsed 2L 9s⟨3/1⟩ |