Magic family: Difference between revisions

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update tuning range links
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* valid range: [360.000, 400.000] (3\10 to 1\3)
* [[diamond monotone]] range: [360.000, 400.000] (3\10 to 1\3)
* nice range: [378.910, 386.314]
* [[diamond pure]] range: [378.910, 386.314]
* strict range: [378.910, 386.314]
* [[diamond strict]] range: [378.910, 386.314]


[[Algebraic generator]]: Terzbirat, the positive root of 9''x''<sup>2</sup> - 8''x'' - 4 = (4 + 2√13)/9; approximately 380.3175 [[cent]]s.
[[Algebraic generator]]: Terzbirat, the positive root of 9''x''<sup>2</sup> - 8''x'' - 4 = (4 + 2√13)/9; approximately 380.3175 [[cent]]s.
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* valid range: [378.947, 381.818] (6\19 to 7\22)
* [[diamond monotone]] range: [378.947, 381.818] (6\19 to 7\22)
* nice range: [378.910, 386.314]
* [[diamond pure]] range: [378.910, 386.314]
* strict range: [378.947, 381.818]
* [[diamond strict]] range: [378.947, 381.818]


[[Algebraic generator]]: Tirzbirat or Septimage, the real root of 5''x''<sup>5</sup> + 4''x'' - 20, 380.7604 cents.
[[Algebraic generator]]: Tirzbirat or Septimage, the real root of 5''x''<sup>5</sup> + 4''x'' - 20, 380.7604 cents.
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Tuning ranges:  
Tuning ranges:  
* valid range: [378.947, 381.818] (6\19 to 7\22)
* [[diamond monotone]] range: [378.947, 381.818] (6\19 to 7\22)
* nice range: [378.910, 386.314]
* [[diamond pure]] range: [378.910, 386.314]
* strict range: [378.947, 381.818]
* [[diamond strict]] range: [378.947, 381.818]


Vals: {{Val list| 19, 22, 41, 104, 145c }}
Vals: {{Val list| 19, 22, 41, 104, 145c }}
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Tuning ranges:  
Tuning ranges:  
* valid range: [378.947, 381.818] (6\19 to 7\22)
* [[diamond monotone]] range: [378.947, 381.818] (6\19 to 7\22)
* nice range: [378.617, 386.314]
* [[diamond pure]] range: [378.617, 386.314]
* strict range: [378.947, 381.818]
* [[diamond strict]] range: [378.947, 381.818]


Vals: {{Val list| 19, 22f, 41, 265cdef }}
Vals: {{Val list| 19, 22f, 41, 265cdef }}
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Tuning ranges:  
Tuning ranges:  
* valid range: 378.947 (6\19)
* [[diamond monotone]] range: 378.947 (6\19)
* nice range: [359.472, 386.314]
* [[diamond pure]] range: [359.472, 386.314]
* strict range: 378.947
* [[diamond strict]] range: 378.947


Vals: {{Val list| 19, 22, 41f }}
Vals: {{Val list| 19, 22, 41f }}
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Tuning ranges:  
Tuning ranges:  
* valid range: [380.488, 380.952] (13\41 to 20\63)
* [[diamond monotone]] range: [380.488, 380.952] (13\41 to 20\63)
* nice range: [378.910, 386.314]
* [[diamond pure]] range: [378.910, 386.314]
* strict range: [380.488, 380.952]
* [[diamond strict]] range: [380.488, 380.952]


Vals: {{Val list| 19f, 22, 41, 63, 104 }}
Vals: {{Val list| 19f, 22, 41, 63, 104 }}