1L 9s: Difference between revisions

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This MOS, generated by any interval up to a diatonic semitone of 1/10edo (120 cents), 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.
{{Infobox MOS
{{Infobox MOS
| Name =  
| Name =  
Line 11: Line 9:
}}
}}


{| class="wikitable"
This MOS, generated by any interval up to a diatonic semitone of 1/10edo (120 cents), 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.
|-
! colspan="5" | Generator


(octave fraction)
== Scale tree ==
! | Generator
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)


(cents)
{| class=""wikitable center-all""
! | Comments
! colspan=""6"" | Small step
! 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 ||
|-
|-
| | 0\1
| || || || || 5\53 || || 113.208 || 8 || 5 || 1.600 ||  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 8\85 || 112.941 || 13 || 8 || 1.625 || Golden [[misneb]] (113.0153¢)
| |  
| |  
| |  
| | 1\14
| | 85.714
| style="text-align:center;" |  
|-
|-
| |  
| || || || 3\32 || || || 112.500 || 5 || 3 || 1.667 ||  
| |  
| |  
| | 1\13
| |  
| | 92.308
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 7\75 || 112.000 || 12 || 7 || 1.714 ||  
| |  
| |  
| |  
| | 2\25
| | 96
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 4\43 || || 111.628 || 7 || 4 || 1.750 ||  
| |  
| |  
| |  
| |  
| | 1200/(9+pi)
| |  
|-
|-
| |  
| || || || || || 5\54 || 111.111 || 9 || 5 || 1.800 ||  
| |  
| | 1\12
| |  
| |  
| | 100
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || 1\11 || || || || || 109.091 || 2 || 1 || 2.000 || Basic 1L 9s <br>(small steps larger than this are proper)
| |  
| |  
| |  
| |  
| | 1200/(9+e)
| |
|-
|-
| |  
| || || || || || 4\45 || 106.667 || 9 || 4 || 2.250 ||  
| |  
| |  
| |  
| | 3\35
| | 102.857
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 3\34 || || 105.882 || 7 || 3 || 2.333 ||  
| |  
| |  
| |  
| |  
| | 1200/(10+phi)
| |  
|-
|-
| |  
| || || || || || 5\57 || 105.263 || 12 || 5 || 2.400 ||  
| |  
| |  
| | 2\23
| |  
| | 104.348
| style="text-align:center;" |  
|-
|-
| |  
| || || || 2\23 || || || 104.348 || 5 || 2 || 2.500 ||  
| |  
| |  
| |  
| | 3\34
| | 105.882
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 5\58 || 103.448 || 13 || 5 || 2.600 || Unnamed golden tuning (103.2877¢)
| | 1\11
| |  
| |  
| |  
| | 109.091
| style="text-align:center;" | L/s = 2
|-
|-
| |  
| || || || || 3\35 || || 102.857 || 8 || 3 || 2.667 ||  
| |  
| |  
| |  
| |  
| | 1200/(9+sqrt(3))
| |  
|-
|-
| |  
| || || || || || 4\47 || 102.128 || 11 || 4 || 2.750 ||  
| |  
| |  
| |  
| | 4\43
| | 111.628
| style="text-align:center;" |  
|-
|-
| |  
| || || 1\12 || || || || 100.000 || 3 || 1 || 3.000 || [[Ripple]]
| |  
| |  
| | 3\32
| |  
| | 112.5
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 3\37 || 97.297 || 10 || 3 || 3.333 || [[Passion]]
| |  
| |  
| |  
| |  
| | 1200/(9+phi)
| |  
|-
|-
| |  
| || || || || 2\25 || || 96.000 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| | 5\53
| | 113.2075
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 3\38 || 94.737 || 11 || 3 || 3.667 ||  
| |  
| |  
| |  
| |  
| | 1200/(9+pi/2)
| |  
|-
|-
| |  
| || || || 1\13 || || || 92.308 || 4 || 1 || 4.000 ||  
| |  
| | 2\21
| |  
| |  
| | 114.286
| style="text-align:center;" | L/s = 3/2
|-
|-
| |  
| || || || || || 2\27 || 88.889 || 9 || 2 || 4.500 ||  
| |  
| |  
| |  
| | 5\52
| | 115.385
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 1\14 || || 85.714 || 5 || 1 || 5.000 ||  
| |  
| |  
| | 3\31
| |  
| | 116.129
| style="text-align:center;" | Miracle is in this region
|-
|-
| |  
| || || || || || 1\15 || 80.000 || 6 || 1 || 6.000 || [[Valentine]]
| |  
| |  
| |  
| | 4\41
| | 117.073
| style="text-align:center;" |  
|-
|-
| | 1\10
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| | 120
| style="text-align:center;" |  
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:10-tone scales]]

Revision as of 00:00, 21 February 2022

↑ 1L 8s 2L 8s ↗
1L 9s 2L 9s →
↓ 1L 10s 2L 10s ↘ 
┌╥┬┬┬┬┬┬┬┬┬┐
│║││││││││││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
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 ¢)

This MOS, generated by any interval up to a diatonic semitone of 1/10edo (120 cents), 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.

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 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 Unnamed golden tuning (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
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