9L 10s

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↖ 8L 9s ↑ 9L 9s 10L 9s ↗
← 8L 10s 9L 10s 10L 10s →
↙ 8L 11s ↓ 9L 11s 10L 11s ↘ 
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│║│║│║│║│║│║│║│║│║│││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\19 to 1\9 (126.3 ¢ to 133.3 ¢)
Dark 8\9 to 17\19 (1066.7 ¢ to 1073.7 ¢)
TAMNAMS information
Related to 9L 1s (sinatonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 9L 1s
Sister 10L 9s
Daughters 19L 9s, 9L 19s
Neutralized 18L 1s
2-Flought 28L 10s, 9L 29s
Equal tunings
Equalized (L:s = 1:1) 2\19 (126.3 ¢)
Supersoft (L:s = 4:3) 7\66 (127.3 ¢)
Soft (L:s = 3:2) 5\47 (127.7 ¢)
Semisoft (L:s = 5:3) 8\75 (128.0 ¢)
Basic (L:s = 2:1) 3\28 (128.6 ¢)
Semihard (L:s = 5:2) 7\65 (129.2 ¢)
Hard (L:s = 3:1) 4\37 (129.7 ¢)
Superhard (L:s = 4:1) 5\46 (130.4 ¢)
Collapsed (L:s = 1:0) 1\9 (133.3 ¢)

9L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 10 small steps, repeating every octave. 9L 10s is a child scale of 9L 1s, expanding it by 9 tones. Generators that produce this scale range from 126.3 ¢ to 133.3 ¢, or from 1066.7 ¢ to 1073.7 ¢.

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 interval regions.

Intervals

Intervals of 9L 10s
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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 133.3 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 126.3 ¢
Perfect 2-mosstep P2ms L + s 126.3 ¢ to 133.3 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 133.3 ¢ to 189.5 ¢
Major 3-mosstep M3ms 2L + s 189.5 ¢ to 266.7 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 133.3 ¢ to 252.6 ¢
Major 4-mosstep M4ms 2L + 2s 252.6 ¢ to 266.7 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 266.7 ¢ to 315.8 ¢
Major 5-mosstep M5ms 3L + 2s 315.8 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 266.7 ¢ to 378.9 ¢
Major 6-mosstep M6ms 3L + 3s 378.9 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 400.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 4L + 3s 442.1 ¢ to 533.3 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 400.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 4L + 4s 505.3 ¢ to 533.3 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 533.3 ¢ to 568.4 ¢
Major 9-mosstep M9ms 5L + 4s 568.4 ¢ to 666.7 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 533.3 ¢ to 631.6 ¢
Major 10-mosstep M10ms 5L + 5s 631.6 ¢ to 666.7 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 666.7 ¢ to 694.7 ¢
Major 11-mosstep M11ms 6L + 5s 694.7 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 666.7 ¢ to 757.9 ¢
Major 12-mosstep M12ms 6L + 6s 757.9 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 800.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 7L + 6s 821.1 ¢ to 933.3 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 800.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 7L + 7s 884.2 ¢ to 933.3 ¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 933.3 ¢ to 947.4 ¢
Major 15-mosstep M15ms 8L + 7s 947.4 ¢ to 1066.7 ¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 933.3 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 8L + 8s 1010.5 ¢ to 1066.7 ¢
17-mosstep Perfect 17-mosstep P17ms 8L + 9s 1066.7 ¢ to 1073.7 ¢
Augmented 17-mosstep A17ms 9L + 8s 1073.7 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 8L + 10s 1066.7 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 9L + 9s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 9L + 10s 1200.0 ¢

Generator chain

Generator chain of 9L 10s
Bright gens Scale degree Abbrev.
27 Augmented 16-mosdegree A16md
26 Augmented 14-mosdegree A14md
25 Augmented 12-mosdegree A12md
24 Augmented 10-mosdegree A10md
23 Augmented 8-mosdegree A8md
22 Augmented 6-mosdegree A6md
21 Augmented 4-mosdegree A4md
20 Augmented 2-mosdegree A2md
19 Augmented 0-mosdegree A0md
18 Augmented 17-mosdegree A17md
17 Major 15-mosdegree M15md
16 Major 13-mosdegree M13md
15 Major 11-mosdegree M11md
14 Major 9-mosdegree M9md
13 Major 7-mosdegree M7md
12 Major 5-mosdegree M5md
11 Major 3-mosdegree M3md
10 Major 1-mosdegree M1md
9 Major 18-mosdegree M18md
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 19-mosdegree		 P0md
P19md
−1 Perfect 17-mosdegree P17md
−2 Minor 15-mosdegree m15md
−3 Minor 13-mosdegree m13md
−4 Minor 11-mosdegree m11md
−5 Minor 9-mosdegree m9md
−6 Minor 7-mosdegree m7md
−7 Minor 5-mosdegree m5md
−8 Minor 3-mosdegree m3md
−9 Minor 1-mosdegree m1md
−10 Minor 18-mosdegree m18md
−11 Minor 16-mosdegree m16md
−12 Minor 14-mosdegree m14md
−13 Minor 12-mosdegree m12md
−14 Minor 10-mosdegree m10md
−15 Minor 8-mosdegree m8md
−16 Minor 6-mosdegree m6md
−17 Minor 4-mosdegree m4md
−18 Diminished 2-mosdegree d2md
−19 Diminished 19-mosdegree d19md
−20 Diminished 17-mosdegree d17md
−21 Diminished 15-mosdegree d15md
−22 Diminished 13-mosdegree d13md
−23 Diminished 11-mosdegree d11md
−24 Diminished 9-mosdegree d9md
−25 Diminished 7-mosdegree d7md
−26 Diminished 5-mosdegree d5md
−27 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 9L 10s
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 18 19
18|0 1 LsLsLsLsLsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
17|1 3 LsLsLsLsLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
16|2 5 LsLsLsLsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
15|3 7 LsLsLsLsLsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
14|4 9 LsLsLsLsLssLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
13|5 11 LsLsLsLssLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
12|6 13 LsLsLssLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
11|7 15 LsLssLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
10|8 17 LssLsLsLsLsLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
9|9 19 sLsLsLsLsLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|10 2 sLsLsLsLsLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
7|11 4 sLsLsLsLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
6|12 6 sLsLsLsLsLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
5|13 8 sLsLsLsLsLssLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
4|14 10 sLsLsLsLssLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
3|15 12 sLsLsLssLsLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
2|16 14 sLsLssLsLsLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
1|17 16 sLssLsLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|18 18 ssLsLsLsLsLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\19 126.316 1073.684 1:1 1.000 Equalized 9L 10s
11\104 126.923 1073.077 6:5 1.200
9\85 127.059 1072.941 5:4 1.250
16\151 127.152 1072.848 9:7 1.286
7\66 127.273 1072.727 4:3 1.333 Supersoft 9L 10s
19\179 127.374 1072.626 11:8 1.375
12\113 127.434 1072.566 7:5 1.400
17\160 127.500 1072.500 10:7 1.429
5\47 127.660 1072.340 3:2 1.500 Soft 9L 10s
18\169 127.811 1072.189 11:7 1.571
13\122 127.869 1072.131 8:5 1.600
21\197 127.919 1072.081 13:8 1.625
8\75 128.000 1072.000 5:3 1.667 Semisoft 9L 10s
19\178 128.090 1071.910 12:7 1.714
11\103 128.155 1071.845 7:4 1.750
14\131 128.244 1071.756 9:5 1.800
3\28 128.571 1071.429 2:1 2.000 Basic 9L 10s
Scales with tunings softer than this are proper
13\121 128.926 1071.074 9:4 2.250
10\93 129.032 1070.968 7:3 2.333
17\158 129.114 1070.886 12:5 2.400
7\65 129.231 1070.769 5:2 2.500 Semihard 9L 10s
18\167 129.341 1070.659 13:5 2.600
11\102 129.412 1070.588 8:3 2.667
15\139 129.496 1070.504 11:4 2.750
4\37 129.730 1070.270 3:1 3.000 Hard 9L 10s
13\120 130.000 1070.000 10:3 3.333
9\83 130.120 1069.880 7:2 3.500
14\129 130.233 1069.767 11:3 3.667
5\46 130.435 1069.565 4:1 4.000 Superhard 9L 10s
11\101 130.693 1069.307 9:2 4.500
6\55 130.909 1069.091 5:1 5.000
7\64 131.250 1068.750 6:1 6.000
1\9 133.333 1066.667 1:0 → ∞ Collapsed 9L 10s
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