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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 =  
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}}
}}


{| 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]]
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