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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[5-odd-limit]]
* [[5-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 }}
: [{{monzo| 1 0 0 }}, {{monzo| 0 1 0 }}, {{monzo| 2 1/5 0 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 3
: [[Eigenmonzo]]s (unchanged intervals): 2, 3


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~5/4 = [360.000, 400.000] (3\10 to 1\3)
* 5-odd-limit [[diamond monotone]]: ~5/4 = [360.000, 400.000] (3\10 to 1\3)
* [[Diamond tradeoff]] range: ~5/4 = [378.910, 386.314]
* 5-odd-limit [[diamond tradeoff]]: ~5/4 = [378.910, 386.314]
* Diamond monotone and tradeoff: ~5/4 = [378.910, 386.314]
* 5-odd-limit diamond monotone and tradeoff: ~5/4 = [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.
Line 66: Line 65:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
* 7- and [[9-odd-limit]]: ~5/4 = {{monzo| 0 1/5 0 0 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 2 1/5 0 0 }}, {{monzo| -1 12/5 0 0 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 3
: [[Eigenmonzo]]s (unchanged intervals): 2, 3


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~5/4 = [378.947, 381.818] (6\19 to 7\22)
* 7- and 9-odd-limit [[diamond monotone]]: ~5/4 = [378.947, 381.818] (6\19 to 7\22)
* [[Diamond tradeoff]] range: ~5/4 = [378.910, 386.314]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~5/4 = [378.910, 386.314]
* Diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~5/4 = [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.
Line 91: Line 89:


POTE generator: ~5/4 = 380.696
POTE generator: ~5/4 = 380.696
Minimax tuning:
* [[11-odd-limit]]: ~5/4 = {{monzo| 1/3 1/9 0 0 -1/18 }}
: [[Eigenmonzo]]s (unchanged intervals): 2, 11/9


Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~5/4 = [378.947, 381.818] (6\19 to 7\22)
* 11-odd-limit diamond monotone: ~5/4 = [378.947, 381.818] (6\19 to 7\22)
* Diamond tradeoff range: ~5/4 = [378.910, 386.314]
* 11-odd-limit diamond tradeoff: ~5/4 = [378.910, 386.314]
* Diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = [378.947, 381.818]


Vals: {{Val list| 19, 22, 41, 104, 145c }}
Optimal GPV sequence: {{Val list| 19, 22, 41, 104, 145c }}


Badness: 0.020352
Badness: 0.020352
Line 111: Line 113:


Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~5/4 = [378.947, 381.818] (6\19 to 7\22)
* 13- and 15-odd-limit diamond monotone: ~5/4 = [378.947, 381.818] (6\19 to 7\22)
* Diamond tradeoff range: ~5/4 = [378.617, 386.314]
* 13- and 15-odd-limit diamond tradeoff: ~5/4 = [378.617, 386.314]
* 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]


Vals: {{Val list| 19, 22f, 41, 265cdef }}
Optimal GPV sequence: {{Val list| 19, 22f, 41, 265cdef }}


Badness: 0.021509
Badness: 0.021509
Line 128: Line 130:
POTE generator: ~5/4 = 380.477
POTE generator: ~5/4 = 380.477


Tuning ranges:
Optimal GPV sequence: {{Val list| 19, 22, 41f }}
* Diamond monotone range: ~5/4 = 378.947 (6\19)
* Diamond tradeoff range: ~5/4 = [359.472, 386.314]
* Diamond monotone and tradeoff: ~5/4 = 378.947
 
Vals: {{Val list| 19, 22, 41f }}


Badness: 0.025829
Badness: 0.025829
Line 146: Line 143:
POTE generator: ~5/4 = 380.787
POTE generator: ~5/4 = 380.787


Tuning ranges:
Optimal GPV sequence: {{Val list| 19f, 22, 41, 63, 104 }}
* Diamond monotone range: ~5/4 = [380.488, 380.952] (13\41 to 20\63)
* Diamond tradeoff range: ~5/4 = [378.910, 386.314]
* Diamond monotone and tradeoff: ~5/4 = [380.488, 380.952]
 
Vals: {{Val list| 19f, 22, 41, 63, 104 }}


Badness: 0.025275
Badness: 0.025275
Line 164: Line 156:
POTE generator: ~5/4 = 380.508
POTE generator: ~5/4 = 380.508


Vals: {{Val list| 22, 60, 82 }}
Optimal GPV sequence: {{Val list| 22, 60, 82 }}


Badness: 0.055443
Badness: 0.055443
Line 177: Line 169:
POTE generator: ~5/4 = 381.019
POTE generator: ~5/4 = 381.019


Vals: {{Val list| 19e, 22, 41e, 63e }}
Optimal GPV sequence: {{Val list| 19e, 22, 41e, 63e }}


Badness: 0.027109
Badness: 0.027109
Line 190: Line 182:
POTE generator: ~5/4 = 380.520
POTE generator: ~5/4 = 380.520


Vals: {{Val list| 19e, 22, 41ef }}
Optimal GPV sequence: {{Val list| 19e, 22, 41ef }}


Badness: 0.025522
Badness: 0.025522
Line 203: Line 195:
POTE generator: ~5/4 = 379.642
POTE generator: ~5/4 = 379.642


Vals: {{Val list| 3de, 19, 41ee, 60ee }}
Optimal GPV sequence: {{Val list| 3de, 19, 41ee, 60ee }}


Badness: 0.039282
Badness: 0.039282
Line 216: Line 208:
POTE generator: ~5/4 = 379.791
POTE generator: ~5/4 = 379.791


Vals: {{Val list| 3def, 19, 41ee, 60ee }}
Optimal GPV sequence: {{Val list| 3def, 19, 41ee, 60ee }}


Badness: 0.031938
Badness: 0.031938
Line 229: Line 221:
POTE generator: ~5/4 = 379.116
POTE generator: ~5/4 = 379.116


Vals: {{Val list| 3de, 19 }}
Optimal GPV sequence: {{Val list| 3de, 19 }}


Badness: 0.033317
Badness: 0.033317
Line 242: Line 234:
POTE generator: ~5/4 = 380.232
POTE generator: ~5/4 = 380.232


Vals: {{Val list| 41, 60e, 101cd, 243cde }}
Optimal GPV sequence: {{Val list| 41, 60e, 101cd, 243cde }}


Badness: 0.030706
Badness: 0.030706
Line 255: Line 247:
POTE generator: ~5/4 = 380.189
POTE generator: ~5/4 = 380.189


Vals: {{Val list| 41, 60e, 101cd }}
Optimal GPV sequence: {{Val list| 41, 60e, 101cd }}


Badness: 0.023547
Badness: 0.023547
Line 268: Line 260:
POTE generator: ~5/4 = 380.233
POTE generator: ~5/4 = 380.233


Vals: {{Val list| 22, 38d, 60e, 142cde }}
Optimal GPV sequence: {{Val list| 22, 38d, 60e, 142cde }}


Badness: 0.035864
Badness: 0.035864
Line 281: Line 273:
POTE generator: ~5/4 = 379.920
POTE generator: ~5/4 = 379.920


Vals: {{Val list| 22f, 60e }}
Optimal GPV sequence: {{Val list| 22f, 60e }}


Badness: 0.034551
Badness: 0.034551
Line 294: Line 286:
POTE generator: ~14/11 = 409.910
POTE generator: ~14/11 = 409.910


Vals: {{Val list| 38d, 41, 120cd, 161cd, 202cd }}
Optimal GPV sequence: {{Val list| 38d, 41, 120cd, 161cd, 202cd }}


Badness: 0.038519
Badness: 0.038519
Line 307: Line 299:
POTE generator: ~14/11 = 410.004
POTE generator: ~14/11 = 410.004


Vals: {{Val list| 41, 79d, 120cd }}
Optimal GPV sequence: {{Val list| 41, 79d, 120cd }}


Badness: 0.030280
Badness: 0.030280
Line 323: Line 315:


[[POTE generator]]: ~5/4 = 378.479
[[POTE generator]]: ~5/4 = 378.479
[[Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~5/4 = [375.000, 378.947] (5\16 to 6\19)
* 9-odd-limit diamond monotone: ~5/4 = 378.947 (6\19)
* 7- and 9-odd-limit [[diamond tradeoff]]: ~5/4 = [375.882, 386.314]
* 7-odd-limit diamond monotone and tradeoff: ~5/4 = [375.882, 378.947]
* 9-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947


{{Val list|legend=1| 16, 19, 73bcd, 92bcd }}
{{Val list|legend=1| 16, 19, 73bcd, 92bcd }}
Line 337: Line 336:
POTE generator: ~5/4 = 377.724
POTE generator: ~5/4 = 377.724


Vals: {{Val list| 16, 19, 35, 54bd }}
Tuning ranges:
* 11-odd-limit diamond monotone: ~5/4 = 378.947 (6\19)
* 11-odd-limit diamond tradeoff: ~5/4 = [347.408, 386.314]
* 11-odd-limit diamond monotone and tradeoff: ~5/4 = 378.947
 
Optimal GPV sequence: {{Val list| 16, 19, 35, 54bd }}


Badness: 0.048038
Badness: 0.048038
Line 350: Line 354:
POTE generator: ~5/4 = 377.724
POTE generator: ~5/4 = 377.724


Vals: {{Val list| 16, 19, 35f, 54bdf }}
Optimal GPV sequence: {{Val list| 16, 19, 35f, 54bdf }}


Badness: 0.030386
Badness: 0.030386
Line 378: Line 382:
POTE generator: ~5/4 = 380.530
POTE generator: ~5/4 = 380.530


Vals: {{Val list| 6, 16, 22, 60de, 82de }}
Optimal GPV sequence: {{Val list| 6, 16, 22, 60de, 82de }}


Badness: 0.039151
Badness: 0.039151
Line 391: Line 395:
POTE generator: ~5/4 = 379.787
POTE generator: ~5/4 = 379.787


Vals: {{Val list| 6, 16, 22, 38f }}
Optimal GPV sequence: {{Val list| 6, 16, 22, 38f }}


Badness: 0.034376
Badness: 0.034376
Line 407: Line 411:
POTE generator: ~5/4 = 379.837
POTE generator: ~5/4 = 379.837


Vals: {{Val list| 16, 22f, 38 }}
Optimal GPV sequence: {{Val list| 16, 22f, 38 }}


Badness: 0.035284
Badness: 0.035284
Line 437: Line 441:
POTE generator: ~11/10 = 190.285
POTE generator: ~11/10 = 190.285


Vals: {{Val list| 6, 19, 44de, 63dee, 82ddee }}
Optimal GPV sequence: {{Val list| 6, 19, 44de, 63dee, 82ddee }}


Badness: 0.059791
Badness: 0.059791
Line 450: Line 454:
POTE generator: ~11/10 = 189.928
POTE generator: ~11/10 = 189.928


Vals: {{Val list| 6, 19, 82ddeeff }}
Optimal GPV sequence: {{Val list| 6, 19, 82ddeeff }}


Badness: 0.045591
Badness: 0.045591
Line 463: Line 467:
POTE generator: ~11/10 = 190.360
POTE generator: ~11/10 = 190.360


Vals: {{Val list| 19, 44de, 63dee, 82ddee }}
Optimal GPV sequence: {{Val list| 19, 44de, 63dee, 82ddee }}


Badness: 0.041603
Badness: 0.041603
Line 506: Line 510:
Mapping: [{{val| 1 10 4 0 13 }}, {{val| 0 -15 -3 5 -17 }}]
Mapping: [{{val| 1 10 4 0 13 }}, {{val| 0 -15 -3 5 -17 }}]


Vals: {{Val list| 16, 25e, 41, 98c, 139c, 180c }}
Optimal GPV sequence: {{Val list| 16, 25e, 41, 98c, 139c, 180c }}


Badness: 0.045623
Badness: 0.045623
Line 519: Line 523:
POTE generator: ~22/15 = 673.359
POTE generator: ~22/15 = 673.359


Vals: {{Val list| 16, 25e, 41, 98c, 139cf }}
Optimal GPV sequence: {{Val list| 16, 25e, 41, 98c, 139cf }}


Badness: 0.033081
Badness: 0.033081
Line 547: Line 551:
POTE generator: ~28/25 = 204.956
POTE generator: ~28/25 = 204.956


Vals: {{Val list| 6, 35, 41, 199cde, 240cde, 281cde }}
Optimal GPV sequence: {{Val list| 6, 35, 41, 199cde, 240cde, 281cde }}


Badness: 0.061572
Badness: 0.061572
Line 560: Line 564:
POTE generator: ~28/25 = 205.028
POTE generator: ~28/25 = 205.028


Vals: {{Val list| 41, 117c, 158cd, 199cdef }}
Optimal GPV sequence: {{Val list| 41, 117c, 158cd, 199cdef }}


Badness: 0.044047
Badness: 0.044047
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