1L 10s

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1L 10s
Pattern Lssssssssss
Period 2/1
Generator range 10\11 (1,090.9¢) to 1\1 (1,200.0¢)
Parent MOS 1L 9s
Daughter MOSes 11L 1s, 1L 11s
Sister MOS 10L 1s
Equal tunings
Supersoft (L:s = 4:3) 31\34 (1,094.1¢)
Soft (L:s = 3:2) 21\23 (1,095.7¢)
Semisoft (L:s = 5:3) 32\35 (1,097.1¢)
Basic (L:s = 2:1) 11\12 (1,100.0¢)
Semihard (L:s = 5:2) 23\25 (1,104.0¢)
Hard (L:s = 3:1) 12\13 (1,107.7¢)
Superhard (L:s = 4:1) 13\14 (1,114.3¢)

1L 10s is the MOS pattern Lssssssssss with small steps ranging from 0\1 (0¢) to 1\11 (one step of 11edo = 109.1¢).

This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).

Modes

  • 10|0 Lssssssssss
  • 9|1 sLsssssssss
  • 8|2 ssLssssssss
  • 7|3 sssLsssssss
  • 6|4 ssssLssssss
  • 5|5 sssssLsssss
  • 4|6 ssssssLssss
  • 3|7 sssssssLsss
  • 2|8 ssssssssLss
  • 1|9 sssssssssLs
  • 0|10 ssssssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)
Small step
(chroma-negative generator)
Cents L s L/s Comments
1\11 109.091 1 1 1.000
5\56 107.143 6 5 1.200
4\45 106.667 5 4 1.250
7\79 106.329 9 7 1.286
3\34 105.882 4 3 1.333
8\91 105.495 11 8 1.375
5\57 105.263 7 5 1.400
7\80 105.000 10 7 1.429 Septendesemi
2\23 104.348 3 2 1.500
7\81 103.704 11 7 1.571
5\58 103.448 8 5 1.600
8\93 103.226 13 8 1.625 Golden ripple (103.2877¢)
3\35 102.857 5 3 1.667
7\82 102.439 12 7 1.714
4\47 102.128 7 4 1.750
5\59 101.695 9 5 1.800
1\12 100.000 2 1 2.000 Basic 1L 10s
(small steps larger than this are proper)
4\49 97.959 9 4 2.250
3\37 97.297 7 3 2.333 Passion
5\62 96.774 12 5 2.400
2\25 96.000 5 2 2.500
5\63 95.238 13 5 2.600 Unnamed golden tuning (95.102¢)
3\38 94.737 8 3 2.667
4\51 94.118 11 4 2.750
1\13 92.308 3 1 3.000
3\40 90.000 10 3 3.333
2\27 88.889 7 2 3.500
3\41 87.805 11 3 3.667 Octacot
1\14 85.714 4 1 4.000
2\29 82.759 9 2 4.500
1\15 80.000 5 1 5.000 Valentine
1\16 75.000 6 1 6.000
0\1 0.000 1 0 → inf