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
2-Flought 11L 9s, 1L 19s
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

Modes of 1L 9s
UDP Cyclic
order		 Step
pattern
9|0 1 Lsssssssss
8|1 10 sLssssssss
7|2 9 ssLsssssss
6|3 8 sssLssssss
5|4 7 ssssLsssss
4|5 6 sssssLssss
3|6 5 ssssssLsss
2|7 4 sssssssLss
1|8 3 ssssssssLs
0|9 2 sssssssssL

Degrees

Scale degrees of the modes of 1L 9s 
UDP Cyclic
order		 Step
pattern		 Scale degree (asinadegree)
0 1 2 3 4 5 6 7 8 9 10
9|0 1 Lsssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
8|1 10 sLssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|2 9 ssLsssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|3 8 sssLssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|4 7 ssssLsssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|5 6 sssssLssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|6 5 ssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|7 4 sssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|8 3 ssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|9 2 sssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Intervals

Intervals of 1L 9s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-asinastep Perfect 0-asinastep P0asis 0 0.0¢
1-asinastep Perfect 1-asinastep P1asis s 0.0¢ to 120.0¢
Augmented 1-asinastep A1asis L 120.0¢ to 1200.0¢
2-asinastep Minor 2-asinastep m2asis 2s 0.0¢ to 240.0¢
Major 2-asinastep M2asis L + s 240.0¢ to 1200.0¢
3-asinastep Minor 3-asinastep m3asis 3s 0.0¢ to 360.0¢
Major 3-asinastep M3asis L + 2s 360.0¢ to 1200.0¢
4-asinastep Minor 4-asinastep m4asis 4s 0.0¢ to 480.0¢
Major 4-asinastep M4asis L + 3s 480.0¢ to 1200.0¢
5-asinastep Minor 5-asinastep m5asis 5s 0.0¢ to 600.0¢
Major 5-asinastep M5asis L + 4s 600.0¢ to 1200.0¢
6-asinastep Minor 6-asinastep m6asis 6s 0.0¢ to 720.0¢
Major 6-asinastep M6asis L + 5s 720.0¢ to 1200.0¢
7-asinastep Minor 7-asinastep m7asis 7s 0.0¢ to 840.0¢
Major 7-asinastep M7asis L + 6s 840.0¢ to 1200.0¢
8-asinastep Minor 8-asinastep m8asis 8s 0.0¢ to 960.0¢
Major 8-asinastep M8asis L + 7s 960.0¢ to 1200.0¢
9-asinastep Diminished 9-asinastep d9asis 9s 0.0¢ to 1080.0¢
Perfect 9-asinastep P9asis L + 8s 1080.0¢ to 1200.0¢
10-asinastep Perfect 10-asinastep P10asis L + 9s 1200.0¢

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 (103.288¢)
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
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 Nautilus, nuke, ↓valentine
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 9s
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