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

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

Template:Scale tree

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