9L 10s

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↖ 8L 9s ↑ 9L 9s 10L 9s ↗
← 8L 10s 9L 10s 10L 10s →
↙ 8L 11s ↓ 9L 11s 10L 11s ↘ 
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│║│║│║│║│║│││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Descends from 9L 1s (sinatonic)
Ancestor's step ratio range 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¢.

Modes

Modes of 9L 10s
UDP Cyclic
order		 Step
pattern
18|0 1 LsLsLsLsLsLsLsLsLss
17|1 3 LsLsLsLsLsLsLsLssLs
16|2 5 LsLsLsLsLsLsLssLsLs
15|3 7 LsLsLsLsLsLssLsLsLs
14|4 9 LsLsLsLsLssLsLsLsLs
13|5 11 LsLsLsLssLsLsLsLsLs
12|6 13 LsLsLssLsLsLsLsLsLs
11|7 15 LsLssLsLsLsLsLsLsLs
10|8 17 LssLsLsLsLsLsLsLsLs
9|9 19 sLsLsLsLsLsLsLsLsLs
8|10 2 sLsLsLsLsLsLsLsLssL
7|11 4 sLsLsLsLsLsLsLssLsL
6|12 6 sLsLsLsLsLsLssLsLsL
5|13 8 sLsLsLsLsLssLsLsLsL
4|14 10 sLsLsLsLssLsLsLsLsL
3|15 12 sLsLsLssLsLsLsLsLsL
2|16 14 sLsLssLsLsLsLsLsLsL
1|17 16 sLssLsLsLsLsLsLsLsL
0|18 18 ssLsLsLsLsLsLsLsLsL

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¢

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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