8L 9s

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↖ 7L 8s ↑ 8L 8s 9L 8s ↗
← 7L 9s 8L 9s 9L 9s →
↙ 7L 10s ↓ 8L 10s 9L 10s ↘ 
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│║│║│║│║│││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\17 to 1\8 (141.2 ¢ to 150.0 ¢)
Dark 7\8 to 15\17 (1050.0 ¢ to 1058.8 ¢)
TAMNAMS information
Related to 8L 1s (subneutralic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 8L 1s
Sister 9L 8s
Daughters 17L 8s, 8L 17s
Neutralized 16L 1s
2-Flought 25L 9s, 8L 26s
Equal tunings
Equalized (L:s = 1:1) 2\17 (141.2 ¢)
Supersoft (L:s = 4:3) 7\59 (142.4 ¢)
Soft (L:s = 3:2) 5\42 (142.9 ¢)
Semisoft (L:s = 5:3) 8\67 (143.3 ¢)
Basic (L:s = 2:1) 3\25 (144.0 ¢)
Semihard (L:s = 5:2) 7\58 (144.8 ¢)
Hard (L:s = 3:1) 4\33 (145.5 ¢)
Superhard (L:s = 4:1) 5\41 (146.3 ¢)
Collapsed (L:s = 1:0) 1\8 (150.0 ¢)

8L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 9 small steps, repeating every octave. 8L 9s is a child scale of 8L 1s, expanding it by 8 tones. Generators that produce this scale range from 141.2 ¢ to 150 ¢, or from 1050 ¢ to 1058.8 ¢.

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 diatonic interval categories.

Intervals

Intervals of 8L 9s
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 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 150.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 141.2 ¢
Perfect 2-mosstep P2ms L + s 141.2 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms 2L + s 211.8 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms 2L + 2s 282.4 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 300.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms 3L + 2s 352.9 ¢ to 450.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 300.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms 3L + 3s 423.5 ¢ to 450.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 450.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms 4L + 3s 494.1 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 450.0 ¢ to 564.7 ¢
Major 8-mosstep M8ms 4L + 4s 564.7 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 600.0 ¢ to 635.3 ¢
Major 9-mosstep M9ms 5L + 4s 635.3 ¢ to 750.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 600.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 5L + 5s 705.9 ¢ to 750.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 750.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 6L + 5s 776.5 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 750.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 6L + 6s 847.1 ¢ to 900.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 900.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 7L + 6s 917.6 ¢ to 1050.0 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 900.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 7L + 7s 988.2 ¢ to 1050.0 ¢
15-mosstep Perfect 15-mosstep P15ms 7L + 8s 1050.0 ¢ to 1058.8 ¢
Augmented 15-mosstep A15ms 8L + 7s 1058.8 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 1050.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 8L + 8s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 8L + 9s 1200.0 ¢

Generator chain

Generator chain of 8L 9s
Bright gens Scale degree Abbrev.
24 Augmented 14-mosdegree A14md
23 Augmented 12-mosdegree A12md
22 Augmented 10-mosdegree A10md
21 Augmented 8-mosdegree A8md
20 Augmented 6-mosdegree A6md
19 Augmented 4-mosdegree A4md
18 Augmented 2-mosdegree A2md
17 Augmented 0-mosdegree A0md
16 Augmented 15-mosdegree A15md
15 Major 13-mosdegree M13md
14 Major 11-mosdegree M11md
13 Major 9-mosdegree M9md
12 Major 7-mosdegree M7md
11 Major 5-mosdegree M5md
10 Major 3-mosdegree M3md
9 Major 1-mosdegree M1md
8 Major 16-mosdegree M16md
7 Major 14-mosdegree M14md
6 Major 12-mosdegree M12md
5 Major 10-mosdegree M10md
4 Major 8-mosdegree M8md
3 Major 6-mosdegree M6md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 15-mosdegree P15md
−2 Minor 13-mosdegree m13md
−3 Minor 11-mosdegree m11md
−4 Minor 9-mosdegree m9md
−5 Minor 7-mosdegree m7md
−6 Minor 5-mosdegree m5md
−7 Minor 3-mosdegree m3md
−8 Minor 1-mosdegree m1md
−9 Minor 16-mosdegree m16md
−10 Minor 14-mosdegree m14md
−11 Minor 12-mosdegree m12md
−12 Minor 10-mosdegree m10md
−13 Minor 8-mosdegree m8md
−14 Minor 6-mosdegree m6md
−15 Minor 4-mosdegree m4md
−16 Diminished 2-mosdegree d2md
−17 Diminished 17-mosdegree d17md
−18 Diminished 15-mosdegree d15md
−19 Diminished 13-mosdegree d13md
−20 Diminished 11-mosdegree d11md
−21 Diminished 9-mosdegree d9md
−22 Diminished 7-mosdegree d7md
−23 Diminished 5-mosdegree d5md
−24 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 8L 9s
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 LsLsLsLsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
15|1 3 LsLsLsLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
14|2 5 LsLsLsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
13|3 7 LsLsLsLsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
12|4 9 LsLsLsLssLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
11|5 11 LsLsLssLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
10|6 13 LsLssLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
9|7 15 LssLsLsLsLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|8 17 sLsLsLsLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
7|9 2 sLsLsLsLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
6|10 4 sLsLsLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
5|11 6 sLsLsLsLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
4|12 8 sLsLsLsLssLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
3|13 10 sLsLsLssLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
2|14 12 sLsLssLsLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
1|15 14 sLssLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|16 16 ssLsLsLsLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\17 141.176 1058.824 1:1 1.000 Equalized 8L 9s
11\93 141.935 1058.065 6:5 1.200
9\76 142.105 1057.895 5:4 1.250
16\135 142.222 1057.778 9:7 1.286
7\59 142.373 1057.627 4:3 1.333 Supersoft 8L 9s
19\160 142.500 1057.500 11:8 1.375
12\101 142.574 1057.426 7:5 1.400
17\143 142.657 1057.343 10:7 1.429
5\42 142.857 1057.143 3:2 1.500 Soft 8L 9s
18\151 143.046 1056.954 11:7 1.571
13\109 143.119 1056.881 8:5 1.600
21\176 143.182 1056.818 13:8 1.625
8\67 143.284 1056.716 5:3 1.667 Semisoft 8L 9s
19\159 143.396 1056.604 12:7 1.714
11\92 143.478 1056.522 7:4 1.750
14\117 143.590 1056.410 9:5 1.800
3\25 144.000 1056.000 2:1 2.000 Basic 8L 9s
Scales with tunings softer than this are proper
13\108 144.444 1055.556 9:4 2.250
10\83 144.578 1055.422 7:3 2.333
17\141 144.681 1055.319 12:5 2.400
7\58 144.828 1055.172 5:2 2.500 Semihard 8L 9s
18\149 144.966 1055.034 13:5 2.600
11\91 145.055 1054.945 8:3 2.667
15\124 145.161 1054.839 11:4 2.750
4\33 145.455 1054.545 3:1 3.000 Hard 8L 9s
13\107 145.794 1054.206 10:3 3.333
9\74 145.946 1054.054 7:2 3.500
14\115 146.087 1053.913 11:3 3.667
5\41 146.341 1053.659 4:1 4.000 Superhard 8L 9s
Bohpier
11\90 146.667 1053.333 9:2 4.500
6\49 146.939 1053.061 5:1 5.000
7\57 147.368 1052.632 6:1 6.000 Indium
1\8 150.000 1050.000 1:0 → ∞ Collapsed 8L 9s
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