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| | nSmallSteps = 9 | | | nSmallSteps = 9 |
| | Equalized = 9 | | | Equalized = 9 |
| | Paucitonic = 1 | | | Collapsed = 1 |
| | Pattern = Lsssssssss | | | Pattern = Lsssssssss |
| }} | | }} |
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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.
| | {{MOS intro}} |
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| == Modes ==
| | 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. |
| * 9|0 Lsssssssss
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| * 8|1 sLssssssss
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| * 7|2 ssLsssssss
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| * 6|3 sssLssssss
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| * 5|4 ssssLsssss
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| * 4|5 sssssLssss
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| * 3|6 ssssssLsss
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| * 2|7 sssssssLss
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| * 1|8 ssssssssLs
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| * 0|9 sssssssssL
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| == Scale tree ==
| | This scale is known as the '''Happy decatonic scale''' in [[Graham Breed's MOS naming scheme|Graham Breed's naming system]]. |
| Generator ranges:
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| * Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
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| * Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)
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| {| class="wikitable center-all"
| | == Scale properties == |
| ! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
| | {{TAMNAMS use}} |
| ! Cents
| | |
| ! L
| | === Intervals === |
| ! s
| | {{MOS intervals}} |
| ! L/s
| | |
| ! Comments
| | === Generator chain === |
| |-
| | {{MOS genchain}} |
| | 1\10 || || || || || || 120.000 || 1 || 1 || 1.000 ||
| | |
| |-
| | === Modes === |
| | || || || || || 5\51 || 117.647 || 6 || 5 || 1.200 ||
| | {{MOS mode degrees}} |
| |-
| | |
| | || || || || 4\41 || || 117.073 || 5 || 4 || 1.250 ||
| | == Scale tree== |
| |-
| | {{MOS tuning spectrum |
| | || || || || || 7\72 || 116.667 || 9 || 7 || 1.286 || [[Miracle]]
| | | 9/7 = [[Miracle]] |
| |-
| | | 8/5 = [[Misneb]] |
| | || || || 3\31 || || || 116.129 || 4 || 3 || 1.333 ||
| | | 3/1 = [[Ripple]] |
| |-
| | | 13/5 = Golden ripple (103.288¢) |
| | || || || || || 8\83 || 115.663 || 11 || 8 || 1.375 ||
| | | 10/3 = [[Passion]] |
| |-
| | | 6/1 = [[Nautilus]], [[nuke]], ↓[[valentine]] |
| | || || || || 5\52 || || 115.385 || 7 || 5 || 1.400 ||
| | }} |
| |-
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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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| |-
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| | || || || 3\32 || || || 112.500 || 5 || 3 || 1.667 ||
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| |-
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| | || || || || || 7\75 || 112.000 || 12 || 7 || 1.714 ||
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| |-
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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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| |-
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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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| |-
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| | || || || || || 4\45 || 106.667 || 9 || 4 || 2.250 ||
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| |-
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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 || Unnamed golden tuning (103.2877¢)
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| |- | |
| | || || || || 3\35 || || 102.857 || 8 || 3 || 2.667 ||
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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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| |-
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| | 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
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| |}
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| [[Category:Abstract MOS patterns]]
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| [[Category:10-tone scales]] | | [[Category:10-tone scales]] |