9L 8s (3/1-equivalent)

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↖ 8L 7s⟨3/1⟩ ↑ 9L 7s⟨3/1⟩ 10L 7s⟨3/1⟩ ↗
← 8L 8s⟨3/1⟩ 9L 8s (3/1-equivalent) 10L 8s⟨3/1⟩ →
↙ 8L 9s⟨3/1⟩ ↓ 9L 9s⟨3/1⟩ 10L 9s⟨3/1⟩ ↘ 
┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐
│║║│║│║│║│║│║│║│║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLL
Equave 3/1 (1902.0¢)
Period 3/1 (1902.0¢)
Generator size(edt)
Bright 15\17 to 8\9 (1678.2¢ to 1690.6¢)
Dark 1\9 to 2\17 (211.3¢ to 223.8¢)
Related MOS scales
Parent 8L 1s⟨3/1⟩
Sister 8L 9s⟨3/1⟩
Daughters 17L 9s⟨3/1⟩, 9L 17s⟨3/1⟩
Neutralized 1L 16s⟨3/1⟩
2-Flought 26L 8s⟨3/1⟩, 9L 25s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 15\17 (1678.2¢)
Supersoft (L:s = 4:3) 53\60 (1680.1¢)
Soft (L:s = 3:2) 38\43 (1680.8¢)
Semisoft (L:s = 5:3) 61\69 (1681.4¢)
Basic (L:s = 2:1) 23\26 (1682.5¢)
Semihard (L:s = 5:2) 54\61 (1683.7¢)
Hard (L:s = 3:1) 31\35 (1684.6¢)
Superhard (L:s = 4:1) 39\44 (1685.8¢)
Collapsed (L:s = 1:0) 8\9 (1690.6¢)

9L 8s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 9 large steps and 8 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1678.2¢ to 1690.6¢, or from 211.3¢ to 223.8¢.

Theory

Modes

Modes of 9L 8s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
16|0 1 LLsLsLsLsLsLsLsLs
15|1 16 LsLLsLsLsLsLsLsLs
14|2 14 LsLsLLsLsLsLsLsLs
13|3 12 LsLsLsLLsLsLsLsLs
12|4 10 LsLsLsLsLLsLsLsLs
11|5 8 LsLsLsLsLsLLsLsLs
10|6 6 LsLsLsLsLsLsLLsLs
9|7 4 LsLsLsLsLsLsLsLLs
8|8 2 LsLsLsLsLsLsLsLsL
7|9 17 sLLsLsLsLsLsLsLsL
6|10 15 sLsLLsLsLsLsLsLsL
5|11 13 sLsLsLLsLsLsLsLsL
4|12 11 sLsLsLsLLsLsLsLsL
3|13 9 sLsLsLsLsLLsLsLsL
2|14 7 sLsLsLsLsLsLLsLsL
1|15 5 sLsLsLsLsLsLsLLsL
0|16 3 sLsLsLsLsLsLsLsLL

Temperament interpretations

Icon-Todo.png Todo: expand

Intervals

Intervals of 9L 8s⟨3/1⟩
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 111.9¢
Major 1-mosstep M1ms L 111.9¢ to 211.3¢
2-mosstep Perfect 2-mosstep P2ms L + s 211.3¢ to 223.8¢
Augmented 2-mosstep A2ms 2L 223.8¢ to 422.7¢
3-mosstep Minor 3-mosstep m3ms L + 2s 211.3¢ to 335.6¢
Major 3-mosstep M3ms 2L + s 335.6¢ to 422.7¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 422.7¢ to 447.5¢
Major 4-mosstep M4ms 3L + s 447.5¢ to 634.0¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 422.7¢ to 559.4¢
Major 5-mosstep M5ms 3L + 2s 559.4¢ to 634.0¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 634.0¢ to 671.3¢
Major 6-mosstep M6ms 4L + 2s 671.3¢ to 845.3¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 634.0¢ to 783.2¢
Major 7-mosstep M7ms 4L + 3s 783.2¢ to 845.3¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 845.3¢ to 895.0¢
Major 8-mosstep M8ms 5L + 3s 895.0¢ to 1056.6¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 845.3¢ to 1006.9¢
Major 9-mosstep M9ms 5L + 4s 1006.9¢ to 1056.6¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 1056.6¢ to 1118.8¢
Major 10-mosstep M10ms 6L + 4s 1118.8¢ to 1268.0¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 1056.6¢ to 1230.7¢
Major 11-mosstep M11ms 6L + 5s 1230.7¢ to 1268.0¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 1268.0¢ to 1342.6¢
Major 12-mosstep M12ms 7L + 5s 1342.6¢ to 1479.3¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 1268.0¢ to 1454.4¢
Major 13-mosstep M13ms 7L + 6s 1454.4¢ to 1479.3¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 1479.3¢ to 1566.3¢
Major 14-mosstep M14ms 8L + 6s 1566.3¢ to 1690.6¢
15-mosstep Diminished 15-mosstep d15ms 7L + 8s 1479.3¢ to 1678.2¢
Perfect 15-mosstep P15ms 8L + 7s 1678.2¢ to 1690.6¢
16-mosstep Minor 16-mosstep m16ms 8L + 8s 1690.6¢ to 1790.1¢
Major 16-mosstep M16ms 9L + 7s 1790.1¢ to 1902.0¢
17-mosstep Perfect 17-mosstep P17ms 9L + 8s 1902.0¢

Scale degrees

Scale degrees of the modes of 9L 8s⟨3/1⟩ 
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
16|0 1 LLsLsLsLsLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
15|1 16 LsLLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
14|2 14 LsLsLLsLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
13|3 12 LsLsLsLLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
12|4 10 LsLsLsLsLLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
11|5 8 LsLsLsLsLsLLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
10|6 6 LsLsLsLsLsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf.
9|7 4 LsLsLsLsLsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf.
8|8 2 LsLsLsLsLsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
7|9 17 sLLsLsLsLsLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
6|10 15 sLsLLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
5|11 13 sLsLsLLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
4|12 11 sLsLsLsLLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
3|13 9 sLsLsLsLsLLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
2|14 7 sLsLsLsLsLsLLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf.
1|15 5 sLsLsLsLsLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|16 3 sLsLsLsLsLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Perf.

Scale tree

Scale Tree and Tuning Spectrum of 9L 8s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
15\17 1678.196 223.759 1:1 1.000 Equalized 9L 8s⟨3/1⟩
83\94 1679.386 222.569 6:5 1.200
68\77 1679.649 222.306 5:4 1.250
121\137 1679.829 222.126 9:7 1.286
53\60 1680.060 221.895 4:3 1.333 Supersoft 9L 8s⟨3/1⟩
144\163 1680.255 221.700 11:8 1.375
91\103 1680.368 221.587 7:5 1.400
129\146 1680.494 221.461 10:7 1.429
38\43 1680.797 221.158 3:2 1.500 Soft 9L 8s⟨3/1⟩
137\155 1681.083 220.872 11:7 1.571
99\112 1681.192 220.763 8:5 1.600
160\181 1681.286 220.669 13:8 1.625
61\69 1681.438 220.517 5:3 1.667 Semisoft 9L 8s⟨3/1⟩
145\164 1681.607 220.348 12:7 1.714
84\95 1681.729 220.226 7:4 1.750
107\121 1681.894 220.061 9:5 1.800
23\26 1682.499 219.456 2:1 2.000 Basic 9L 8s⟨3/1⟩
Scales with tunings softer than this are proper
100\113 1683.146 218.809 9:4 2.250
77\87 1683.339 218.616 7:3 2.333
131\148 1683.487 218.468 12:5 2.400
54\61 1683.698 218.257 5:2 2.500 Semihard 9L 8s⟨3/1⟩
139\157 1683.896 218.059 13:5 2.600
85\96 1684.023 217.932 8:3 2.667
116\131 1684.174 217.781 11:4 2.750
31\35 1684.589 217.366 3:1 3.000 Hard 9L 8s⟨3/1⟩
101\114 1685.065 216.890 10:3 3.333
70\79 1685.277 216.678 7:2 3.500
109\123 1685.472 216.483 11:3 3.667
39\44 1685.824 216.131 4:1 4.000 Superhard 9L 8s⟨3/1⟩
86\97 1686.269 215.686 9:2 4.500
47\53 1686.639 215.316 5:1 5.000
55\62 1687.218 214.737 6:1 6.000
8\9 1690.627 211.328 1:0 → ∞ Collapsed 9L 8s⟨3/1⟩
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