1L 10s

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Todo: review
Adopt scale tree template, review entries
↑1L 9s 2L 9s ↗
1L 10s 2L 10s →
↓1L 11s 2L 11s ↘
┌╥┬┬┬┬┬┬┬┬┬┬┐
│║│││││││││││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssssssss
ssssssssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 10\11 to 1\1 (1090.9¢ to 1200.0¢)
Dark 0\1 to 1\11 (0.0¢ to 109.1¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Required step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 1L 9s
Sister 10L 1s
Daughters 11L 1s, 1L 11s
Neutralized 2L 9s
2-Flought 12L 10s, 1L 21s
Equal tunings
Equalized (L:s = 1:1) 10\11 (1090.9¢)
Supersoft (L:s = 4:3) 31\34 (1094.1¢)
Soft (L:s = 3:2) 21\23 (1095.7¢)
Semisoft (L:s = 5:3) 32\35 (1097.1¢)
Basic (L:s = 2:1) 11\12 (1100.0¢)
Semihard (L:s = 5:2) 23\25 (1104.0¢)
Hard (L:s = 3:1) 12\13 (1107.7¢)
Superhard (L:s = 4:1) 13\14 (1114.3¢)
Collapsed (L:s = 1:0) 1\1 (1200.0¢)

1L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 10 small steps, repeating every octave. 1L 10s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 1090.9¢ to 1200¢, or from 0¢ to 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