1L 9s

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1L 9s
Pattern Lsssssssss
Period 2/1
Generator range 9\10 (1,080.0¢) to 1\1 (1,200.0¢)
Parent MOS 1L 8s
Daughter MOSes 10L 1s, 1L 10s
Sister MOS 9L 1s
Equal tunings
Supersoft (L:s = 4:3) 28\31 (1,083.9¢)
Soft (L:s = 3:2) 19\21 (1,085.7¢)
Semisoft (L:s = 5:3) 29\32 (1,087.5¢)
Basic (L:s = 2:1) 10\11 (1,090.9¢)
Semihard (L:s = 5:2) 21\23 (1,095.7¢)
Hard (L:s = 3:1) 11\12 (1,100.0¢)
Superhard (L:s = 4:1) 12\13 (1,107.7¢)

1L 9s is the MOS pattern Lsssssssss with small steps ranging from 0\1 (0¢) to 1\10 (one step of 10edo = 120¢).

This MOS is called the "Happy" decatonic scale in Graham Breed's system, or, potentially, antisinatonic in TAMNAMS by analogy to its sister MOS. It is the simplest MOS which may be used as a complete version of Miracle temperament, which is also its harmonic entropy minimum.

Modes

  • 9|0 Lsssssssss
  • 8|1 sLssssssss
  • 7|2 ssLsssssss
  • 6|3 sssLssssss
  • 5|4 ssssLsssss
  • 4|5 sssssLssss
  • 3|6 ssssssLsss
  • 2|7 sssssssLss
  • 1|8 ssssssssLs
  • 0|9 sssssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)
Small step
(chroma-negative generator)
Cents L s L/s Comments
1\10 120.000 1 1 1.000
5\51 117.647 6 5 1.200
4\41 117.073 5 4 1.250
7\72 116.667 9 7 1.286 Miracle
3\31 116.129 4 3 1.333
8\83 115.663 11 8 1.375
5\52 115.385 7 5 1.400
7\73 115.068 10 7 1.429
2\21 114.286 3 2 1.500
7\74 113.514 11 7 1.571
5\53 113.208 8 5 1.600
8\85 112.941 13 8 1.625 Golden misneb (113.0153¢)
3\32 112.500 5 3 1.667
7\75 112.000 12 7 1.714
4\43 111.628 7 4 1.750
5\54 111.111 9 5 1.800
1\11 109.091 2 1 2.000 Basic 1L 9s
(small steps larger than this are proper)
4\45 106.667 9 4 2.250
3\34 105.882 7 3 2.333
5\57 105.263 12 5 2.400
2\23 104.348 5 2 2.500
5\58 103.448 13 5 2.600 Golden ripple (103.2877¢)
3\35 102.857 8 3 2.667
4\47 102.128 11 4 2.750
1\12 100.000 3 1 3.000 Ripple
3\37 97.297 10 3 3.333 Passion
2\25 96.000 7 2 3.500
3\38 94.737 11 3 3.667
1\13 92.308 4 1 4.000
2\27 88.889 9 2 4.500
1\14 85.714 5 1 5.000
1\15 80.000 6 1 6.000 Valentine
0\1 0.000 1 0 → inf