1L 9s

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↑1L 8s 2L 8s ↗
1L 9s 2L 9s →
↓1L 10s 2L 10s ↘
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│║││││││││││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lsssssssss
sssssssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 9\10 to 1\1 (1080.0¢ to 1200.0¢)
Dark 0\1 to 1\10 (0.0¢ to 120.0¢)
TAMNAMS information
Name antisinatonic
Prefix asina-
Abbrev. asi
Related MOS scales
Parent 1L 8s
Sister 9L 1s
Daughters 10L 1s, 1L 10s
Neutralized 2L 8s
Equal tunings
Equalized (L:s = 1:1) 9\10 (1080.0¢)
Supersoft (L:s = 4:3) 28\31 (1083.9¢)
Soft (L:s = 3:2) 19\21 (1085.7¢)
Semisoft (L:s = 5:3) 29\32 (1087.5¢)
Basic (L:s = 2:1) 10\11 (1090.9¢)
Semihard (L:s = 5:2) 21\23 (1095.7¢)
Hard (L:s = 3:1) 11\12 (1100.0¢)
Superhard (L:s = 4:1) 12\13 (1107.7¢)
Collapsed (L:s = 1:0) 1\1 (1200.0¢)

1L 9s, named antisinatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 9 small steps, repeating every octave. Generators that produce this scale range from 1080¢ to 1200¢, or from 0¢ to 120¢. This scale is the simplest MOS which may be used as a complete version[clarification needed] of Miracle temperament, which is also its harmonic entropy minimum.

This scale is known as the "Happy" decatonic scale in Graham Breed's naming system.

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

Scale Tree and Tuning Spectrum of 1L 9s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
9\10 1080.000 120.000 1:1 1.000 Equalized 1L 9s
46\51 1082.353 117.647 6:5 1.200
37\41 1082.927 117.073 5:4 1.250
65\72 1083.333 116.667 9:7 1.286 Miracle
28\31 1083.871 116.129 4:3 1.333 Supersoft 1L 9s
75\83 1084.337 115.663 11:8 1.375
47\52 1084.615 115.385 7:5 1.400
66\73 1084.932 115.068 10:7 1.429
19\21 1085.714 114.286 3:2 1.500 Soft 1L 9s
67\74 1086.486 113.514 11:7 1.571
48\53 1086.792 113.208 8:5 1.600 Misneb
77\85 1087.059 112.941 13:8 1.625
29\32 1087.500 112.500 5:3 1.667 Semisoft 1L 9s
68\75 1088.000 112.000 12:7 1.714
39\43 1088.372 111.628 7:4 1.750
49\54 1088.889 111.111 9:5 1.800
10\11 1090.909 109.091 2:1 2.000 Basic 1L 9s
Scales with tunings softer than this are proper
41\45 1093.333 106.667 9:4 2.250
31\34 1094.118 105.882 7:3 2.333
52\57 1094.737 105.263 12:5 2.400
21\23 1095.652 104.348 5:2 2.500 Semihard 1L 9s
53\58 1096.552 103.448 13:5 2.600 Golden ripple (103.2877¢)
32\35 1097.143 102.857 8:3 2.667
43\47 1097.872 102.128 11:4 2.750
11\12 1100.000 100.000 3:1 3.000 Hard 1L 9s
Ripple
34\37 1102.703 97.297 10:3 3.333 Passion (generators close to 98.670¢)
23\25 1104.000 96.000 7:2 3.500
35\38 1105.263 94.737 11:3 3.667
12\13 1107.692 92.308 4:1 4.000 Superhard 1L 9s
25\27 1111.111 88.889 9:2 4.500
13\14 1114.286 85.714 5:1 5.000
14\15 1120.000 80.000 6:1 6.000 Valentine (generators close to 78.039¢)
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 9s