1L 9s: Difference between revisions
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This MOS is called the "Happy" decatonic scale in Graham Breed's system, or, potentially, antisinatonic in [[TAMNAMS]] by analogy to its sister MOS. It is the simplest MOS which may be used as a complete version of [[Miracle]] temperament, which is also its harmonic entropy minimum. | This MOS is called the "Happy" decatonic scale in Graham Breed's system, or, potentially, antisinatonic in [[TAMNAMS]] by analogy to its sister MOS. It is the simplest MOS which may be used as a complete version of [[Miracle]] temperament, which is also its harmonic entropy minimum. | ||
Revision as of 23:47, 31 May 2023
| ↑ 1L 8s | 2L 8s ↗ | |
| 1L 9s | 2L 9s → | |
| ↓ 1L 10s | 2L 10s ↘ |
┌╥┬┬┬┬┬┬┬┬┬┐ │║││││││││││ ││││││││││││ └┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sssssssssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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 MOS is called the "Happy" decatonic scale in Graham Breed's system, or, potentially, antisinatonic in TAMNAMS by analogy to its sister MOS. It is the simplest MOS which may be used as a complete version of Miracle temperament, which is also its harmonic entropy minimum.
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
Generator ranges:
- Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
- Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)
| Small step (chroma-negative generator) |
Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1\10 | 120.000 | 1 | 1 | 1.000 | ||||||
| 5\51 | 117.647 | 6 | 5 | 1.200 | ||||||
| 4\41 | 117.073 | 5 | 4 | 1.250 | ||||||
| 7\72 | 116.667 | 9 | 7 | 1.286 | Miracle | |||||
| 3\31 | 116.129 | 4 | 3 | 1.333 | ||||||
| 8\83 | 115.663 | 11 | 8 | 1.375 | ||||||
| 5\52 | 115.385 | 7 | 5 | 1.400 | ||||||
| 7\73 | 115.068 | 10 | 7 | 1.429 | ||||||
| 2\21 | 114.286 | 3 | 2 | 1.500 | ||||||
| 7\74 | 113.514 | 11 | 7 | 1.571 | ||||||
| 5\53 | 113.208 | 8 | 5 | 1.600 | ||||||
| 8\85 | 112.941 | 13 | 8 | 1.625 | Golden misneb (113.0153¢) | |||||
| 3\32 | 112.500 | 5 | 3 | 1.667 | ||||||
| 7\75 | 112.000 | 12 | 7 | 1.714 | ||||||
| 4\43 | 111.628 | 7 | 4 | 1.750 | ||||||
| 5\54 | 111.111 | 9 | 5 | 1.800 | ||||||
| 1\11 | 109.091 | 2 | 1 | 2.000 | Basic 1L 9s (small steps larger than this are proper) | |||||
| 4\45 | 106.667 | 9 | 4 | 2.250 | ||||||
| 3\34 | 105.882 | 7 | 3 | 2.333 | ||||||
| 5\57 | 105.263 | 12 | 5 | 2.400 | ||||||
| 2\23 | 104.348 | 5 | 2 | 2.500 | ||||||
| 5\58 | 103.448 | 13 | 5 | 2.600 | Golden ripple (103.2877¢) | |||||
| 3\35 | 102.857 | 8 | 3 | 2.667 | ||||||
| 4\47 | 102.128 | 11 | 4 | 2.750 | ||||||
| 1\12 | 100.000 | 3 | 1 | 3.000 | Ripple | |||||
| 3\37 | 97.297 | 10 | 3 | 3.333 | Passion | |||||
| 2\25 | 96.000 | 7 | 2 | 3.500 | ||||||
| 3\38 | 94.737 | 11 | 3 | 3.667 | ||||||
| 1\13 | 92.308 | 4 | 1 | 4.000 | ||||||
| 2\27 | 88.889 | 9 | 2 | 4.500 | ||||||
| 1\14 | 85.714 | 5 | 1 | 5.000 | ||||||
| 1\15 | 80.000 | 6 | 1 | 6.000 | Valentine | |||||
| 0\1 | 0.000 | 1 | 0 | → inf | ||||||