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Semicomma family: Difference between revisions

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The 5-limit parent comma for the '''semicomma family''' is the [[semicomma]], 2109375/2097152 = {{monzo| -21 3 7 }}. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths.  
The 5-limit parent comma for the '''semicomma family''' is the [[semicomma]], 2109375/2097152 = {{monzo| -21 3 7 }}. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor sixths.


= Orson =
= Orson =
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[[POTE generator]]: ~75/64 = 271.627
[[POTE generator]]: ~75/64 = 271.627


[[Tuning ranges]]:  
[[Tuning ranges]]:
* valid range: [257.143, 276.923] (3\14 to 3\13)
* [[diamond montone]] range: [257.143, 276.923] (3\14 to 3\13)
* nice range: [271.229, 271.708]
* [[diamond pure]] range: [271.229, 271.708]
* strict range: [271.229, 271.708]
* [[diamond strict]] range: [271.229, 271.708]


{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
{{Val list|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
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== Seven limit children ==
== Seven limit children ==
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65625/65536 (or 225/224) leads to orwell, but we could also add
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65625/65536 (or 225/224) leads to orwell, but we could also add
* 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or  
* 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or
* 2401/2400, giving the 31&243 temperament (quadrawell) with wedgie {{multival| 28 -12 1 -84 -77 36 }}, or  
* 2401/2400, giving the 31&243 temperament (quadrawell) with wedgie {{multival| 28 -12 1 -84 -77 36 }}, or
* 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}.
* 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}.


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[[POTE generator]]: ~7/6 = 271.509
[[POTE generator]]: ~7/6 = 271.509


[[Minimax tuning]]:  
[[Minimax tuning]]:
* [[7-odd-limit]]
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 }}, {{monzo| 27/11 0 3/11 -3/11 }}, {{monzo| 27/11 0 -8/11 8/11 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 }}, {{monzo| 27/11 0 3/11 -3/11 }}, {{monzo| 27/11 0 -8/11 8/11 }}]
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: [[Eigenmonzo]]s: 2, 10/9
: [[Eigenmonzo]]s: 2, 10/9


[[Tuning ranges]]:  
[[Tuning ranges]]:
* valid range: [266.667, 272.727] (2\9 to 5\22)
* [[diamond montone]] range: [266.667, 272.727] (2\9 to 5\22)
* nice range: [266.871, 271.708]
* [[diamond pure]] range: [266.871, 271.708]
* strict range: [266.871, 271.708]
* [[diamond strict]] range: [266.871, 271.708]


[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
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POTE generator: ~7/6 = 271.426
POTE generator: ~7/6 = 271.426


Minimax tuning:  
Minimax tuning:
* 11-odd-limit
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 0 }}, {{monzo| 27/11 0 3/11 -3/11 0 }}, {{monzo| 27/11 0 -8/11 8/11 0 }}, {{monzo| 37/11 0 -2/11 2/11 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 14/11 0 -7/11 7/11 0 }}, {{monzo| 27/11 0 3/11 -3/11 0 }}, {{monzo| 27/11 0 -8/11 8/11 0 }}, {{monzo| 37/11 0 -2/11 2/11 0 }}]
: Eigenmonzos: 2, 7/5
: Eigenmonzos: 2, 7/5


Tuning ranges:  
Tuning ranges:
* valid range: [270.968, 272.727] (7\31 to 5\22)
* [[diamond montone]] range: [270.968, 272.727] (7\31 to 5\22)
* nice range: [266.871, 275.659]
* [[diamond pure]] range: [266.871, 275.659]
* strict range: [270.968, 272.727]
* [[diamond strict]] range: [270.968, 272.727]


Vals: {{Val list| 9, 22, 31, 53, 84e }}
Vals: {{Val list| 9, 22, 31, 53, 84e }}
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POTE generator: ~7/6 = 271.546
POTE generator: ~7/6 = 271.546


Tuning ranges:  
Tuning ranges:
* valid range: [270.968, 271.698] (7\31 to 12\53)
* [[diamond montone]] range: [270.968, 271.698] (7\31 to 12\53)
* nice range: [266.871, 275.659]
* [[diamond pure]] range: [266.871, 275.659]
* strict range: [270.968, 271.698]
* [[diamond strict]] range: [270.968, 271.698]


Vals: {{Val list| 22, 31, 53, 84e, 137e }}
Vals: {{Val list| 22, 31, 53, 84e, 137e }}
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POTE generator: ~7/6 = 271.088
POTE generator: ~7/6 = 271.088


Tuning ranges:  
Tuning ranges:
* valid range: [270.968, 272.727] (7\31 to 5\22)
* [[diamond montone]] range: [270.968, 272.727] (7\31 to 5\22)
* nice range: [266.871, 281.691]
* [[diamond pure]] range: [266.871, 281.691]
* strict range: [270.968, 272.727]
* [[diamond strict]] range: [270.968, 272.727]


Vals: {{Val list| 22f, 31 }}
Vals: {{Val list| 22f, 31 }}
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POTE generator: ~13/12 = 135.723
POTE generator: ~13/12 = 135.723


Tuning ranges:  
Tuning ranges:
* valid range: [135.484, 136.364] (7\62 to 5\44)
* [[diamond montone]] range: [135.484, 136.364] (7\62 to 5\44)
* nice range: [128.298, 138.573]
* [[diamond pure]] range: [128.298, 138.573]
* strict range: [135.484, 136.364]
* [[diamond strict]] range: [135.484, 136.364]


Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
Vals: {{Val list| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
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POTE generator: ~7/6 = 271.288
POTE generator: ~7/6 = 271.288


Tuning ranges:  
Tuning ranges:
* valid range: [270.968, 271.698] (7\31 to 12\53)
* [[diamond montone]] range: [270.968, 271.698] (7\31 to 12\53)
* nice range: [266.871, 272.514]
* [[diamond pure]] range: [266.871, 272.514]
* strict range: [270.968, 271.698]
* [[diamond strict]] range: [270.968, 271.698]


Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}
Vals: {{Val list| 31, 84, 115, 376b, 491bd, 606bde }}
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