1L 9s
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Scale structure
Step pattern
Lsssssssss
sssssssssL
Equave
2/1 (1200.0¢)
Period
1\10 (120.0¢)
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 8s | 2L 8s ↗ | |
| 1L 9s | 2L 9s → | |
| ↓1L 10s | 2L 10s ↘ |
┌╥┬┬┬┬┬┬┬┬┬┐ │║││││││││││ ││││││││││││ └┴┴┴┴┴┴┴┴┴┴┘
sssssssssL
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
| UDP | Rotational 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. |
Scale tree
| 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 | |||||