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| {{MOS intro}} | | {{MOS intro}} |
| This MOS is also called the "Happy" decatonic scale in [[Graham Breed's MOS naming scheme|Graham Breed's naming system]]. It is the simplest MOS which may be used as a complete version of [[Miracle]] temperament, which is also its harmonic entropy minimum. | | This scale is the simplest MOS which may be used as a complete version{{Clarify}} of [[Miracle]] temperament, which is also its harmonic entropy minimum. |
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| | This scale is known as the "Happy" decatonic scale in [[Graham Breed's MOS naming scheme|Graham Breed's naming system]]. |
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| == Modes == | | == Modes == |
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| * 0|9 sssssssssL | | * 0|9 sssssssssL |
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| == Scale tree == | | == Scale tree== |
| Generator ranges:
| | {{Scale tree|Comments=9/7: [[Miracle]]; |
| * Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
| | 8/5: [[Misneb]]; |
| * Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)
| | 3/1: [[Ripple]]; |
| | | 13/5: Golden ripple (103.2877¢); |
| {| class="wikitable center-all" | | 10/3: [[Passion]] (generators close to 98.670¢); |
| ! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
| | 6/1: [[Valentine]] (generators close to 78.039¢);}} |
| ! Cents
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| ! L
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| ! s
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| ! L/s
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| ! Comments
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| |-
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| | 1\10 || || || || || || 120.000 || 1 || 1 || 1.000 ||
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| |-
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| | || || || || || 5\51 || 117.647 || 6 || 5 || 1.200 ||
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| |-
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| | || || || || 4\41 || || 117.073 || 5 || 4 || 1.250 ||
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| |-
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| | || || || || || 7\72 || 116.667 || 9 || 7 || 1.286 || [[Miracle]]
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| |-
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| | || || || 3\31 || || || 116.129 || 4 || 3 || 1.333 ||
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| |-
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| | || || || || || 8\83 || 115.663 || 11 || 8 || 1.375 ||
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| |-
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| | || || || || 5\52 || || 115.385 || 7 || 5 || 1.400 ||
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| |-
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| | || || || || || 7\73 || 115.068 || 10 || 7 || 1.429 ||
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| |-
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| | || || 2\21 || || || || 114.286 || 3 || 2 || 1.500 ||
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| |-
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| | || || || || || 7\74 || 113.514 || 11 || 7 || 1.571 ||
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| |-
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| | || || || || 5\53 || || 113.208 || 8 || 5 || 1.600 ||
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| |-
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| | || || || || || 8\85 || 112.941 || 13 || 8 || 1.625 || Golden [[misneb]] (113.0153¢)
| |
| |-
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| | || || || 3\32 || || || 112.500 || 5 || 3 || 1.667 ||
| |
| |-
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| | || || || || || 7\75 || 112.000 || 12 || 7 || 1.714 ||
| |
| |-
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| | || || || || 4\43 || || 111.628 || 7 || 4 || 1.750 ||
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| |-
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| | || || || || || 5\54 || 111.111 || 9 || 5 || 1.800 ||
| |
| |-
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| | || 1\11 || || || || || 109.091 || 2 || 1 || 2.000 || Basic 1L 9s <br>(small steps larger than this are proper)
| |
| |-
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| | || || || || || 4\45 || 106.667 || 9 || 4 || 2.250 ||
| |
| |-
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| | || || || || 3\34 || || 105.882 || 7 || 3 || 2.333 ||
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| |-
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| | || || || || || 5\57 || 105.263 || 12 || 5 || 2.400 ||
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| |-
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| | || || || 2\23 || || || 104.348 || 5 || 2 || 2.500 ||
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| |-
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| | || || || || || 5\58 || 103.448 || 13 || 5 || 2.600 || Golden [[ripple]] (103.2877¢)
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| |-
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| | || || || || 3\35 || || 102.857 || 8 || 3 || 2.667 ||
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| |-
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| | || || || || || 4\47 || 102.128 || 11 || 4 || 2.750 ||
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| |-
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| | || || 1\12 || || || || 100.000 || 3 || 1 || 3.000 || Ripple
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| |-
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| | || || || || || 3\37 || 97.297 || 10 || 3 || 3.333 || [[Passion]]
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| |-
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| | || || || || 2\25 || || 96.000 || 7 || 2 || 3.500 ||
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| |-
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| | || || || || || 3\38 || 94.737 || 11 || 3 || 3.667 ||
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| |-
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| | || || || 1\13 || || || 92.308 || 4 || 1 || 4.000 ||
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| |-
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| | || || || || || 2\27 || 88.889 || 9 || 2 || 4.500 ||
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| |-
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| | || || || || 1\14 || || 85.714 || 5 || 1 || 5.000 ||
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| |-
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| | || || || || || 1\15 || 80.000 || 6 || 1 || 6.000 || [[Valentine]]
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| |-
| |
| | 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
| |
| |}
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| [[Category:10-tone scales]] | | [[Category:10-tone scales]] |