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Magic family: Difference between revisions

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m →Magic: Fill in bottom end of optimal ET sequence.
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m Update keys; POTE -> CTE; review comma lists and GPV sequences
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Mapping generators: ~2, ~5/4
Mapping generators: ~2, ~5/4


[[POTE generator]]: ~5/4 = 380.058
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 380.4994


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 33: Line 33:
[[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.


{{Optimal ET sequence|legend=1|3, 13b, 16, 19, 41, 60, 221c, 281c }}
{{Optimal ET sequence|legend=1| 3, 13b, 16, 19, 22, 41 }}


[[Badness]]: 0.039163
[[Badness]]: 0.039163
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{{Multival|legend=1| 5 1 12 -10 5 25 }}
{{Multival|legend=1| 5 1 12 -10 5 25 }}


[[POTE generator]]: ~5/4 = 380.352
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 380.6512


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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[[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.


{{Optimal ET sequence|legend=1| 19, 41, 142cd, 183cd, 224cd }}
{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145c, 186c }}


[[Badness]]: 0.018918
[[Badness]]: 0.018918
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Mapping: [{{val| 1 0 2 -1 6 }}, {{val| 0 5 1 12 -8 }}]
Mapping: [{{val| 1 0 2 -1 6 }}, {{val| 0 5 1 12 -8 }}]


POTE generator: ~5/4 = 380.696
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7200


Minimax tuning:  
Minimax tuning:  
Line 104: Line 104:
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]


{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145c }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41, 104, 145c, 249cce }}


Badness: 0.020352
Badness: 0.020352
Line 115: Line 115:
Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 5 1 12 -8 18 }}]
Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 5 1 12 -8 18 }}]


POTE generator: ~5/4 = 380.427
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.4354


Tuning ranges:  
Tuning ranges:  
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* 13- and 15-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]


{{Optimal ET sequence|legend=1| 19, 22f, 41, 265cdef }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}


Badness: 0.021509
Badness: 0.021509
Line 133: Line 133:
Mapping: [{{val| 1 0 2 -1 6 -2 6 }}, {{val| 0 5 1 12 -8 18 -6 }}]
Mapping: [{{val| 1 0 2 -1 6 -2 6 }}, {{val| 0 5 1 12 -8 18 -6 }}]


POTE generator: ~5/4 = 380.604
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.5103


{{Optimal ET sequence|legend=1| 19, 22f, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}


Badness: 0.020633
Badness: 0.020633
Line 150: Line 150:
POTE generator: ~5/4 = 380.416
POTE generator: ~5/4 = 380.416


{{Optimal ET sequence|legend=1| 19, 22f, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22f, 41 }}


==== Sorcery ====
==== Sorcery ====
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Mapping: [{{val| 1 0 2 -1 6 4 }}, {{val| 0 5 1 12 -8 -1 }}]
Mapping: [{{val| 1 0 2 -1 6 4 }}, {{val| 0 5 1 12 -8 -1 }}]


POTE generator: ~5/4 = 380.477
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.6741


{{Optimal ET sequence|legend=1| 19, 22, 41f }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}


Badness: 0.025829
Badness: 0.025829
Line 172: Line 172:
Mapping: [{{val| 1 0 2 -1 6 4 6 }}, {{val| 0 5 1 12 -8 -1 -6 }}]
Mapping: [{{val| 1 0 2 -1 6 4 6 }}, {{val| 0 5 1 12 -8 -1 -6 }}]


POTE generator: ~5/4 = 380.729
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7839


{{Optimal ET sequence|legend=1| 19, 22, 41f }}
Optimal ET sequence: {{Optimal ET sequence| 19, 22, 41f }}


Badness: 0.023768
Badness: 0.023768
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Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 5 1 12 -8 -23 }}]
Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 5 1 12 -8 -23 }}]


POTE generator: ~5/4 = 380.787
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.7876


{{Optimal ET sequence|legend=1| 19f, 22, 41, 63, 104 }}
Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63, 104 }}


Badness: 0.025275
Badness: 0.025275
Line 198: Line 198:
Mapping: [{{val| 1 0 2 -1 6 11 6 }}, {{val| 0 5 1 12 -8 -23 -6 }}]
Mapping: [{{val| 1 0 2 -1 6 11 6 }}, {{val| 0 5 1 12 -8 -23 -6 }}]


POTE generator: ~5/4 = 380.827
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 380.8373


{{Optimal ET sequence|legend=1| 19f, 22, 41, 63, 104g }}
Optimal ET sequence: {{Optimal ET sequence| 19f, 22, 41, 63, 104g }}


Badness: 0.022032
Badness: 0.022032
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