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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* [[Diamond tradeoff]] range: ~3/2 = [694.786, 701.955]
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]


{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}
{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [696.774, 700.000] (18\31 to 7\12)
* 11-odd-limit diamond monotone: ~3/2 = [696.774, 700.000] (18\31 to 7\12)
* Diamond tradeoff range: ~3/2 = [691.202, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]


Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [696.774, 697.674] (18\31 to 25\43)
* 13- and 15-odd-limit diamond monotone: ~3/2 = [696.774, 697.674] (18\31 to 25\43)
* Diamond tradeoff range: ~3/2 = [691.202, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 697.674]


Vals: {{Val list| 12, 19ef, 31, 43, 74 }}
Vals: {{Val list| 12, 19ef, 31, 43, 74 }}
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* 11-odd-limit diamond monotone: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* Diamond tradeoff range: ~3/2 = [691.202, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]


Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* 13- and 15-odd-limit diamond monotone: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* Diamond tradeoff range: ~3/2 = [691.202, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]


Vals: {{Val list| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
Vals: {{Val list| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* 11-odd-limit diamond monotone: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* Diamond tradeoff range: ~3/2 = [682.502, 704.377]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.502, 704.377]
* Diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]


Vals: {{Val list| 7d, 12, 19, 31e, 50ee }}
Vals: {{Val list| 7d, 12, 19, 31e, 50ee }}
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [692.353, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [692.353, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* 11-odd-limit diamond monotone: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* Diamond tradeoff range: ~3/2 = [682.502, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.502, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]


Vals: {{Val list| 7, 19, 26, 45, 71bc, 116bcde }}
Vals: {{Val list| 7, 19, 26, 45, 71bc, 116bcde }}
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* 13- and 15-odd-limit diamond monotone: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* Diamond tradeoff range: ~3/2 = [682.502, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.502, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]


Vals: {{Val list| 7, 19, 26, 45f, 71bcf, 116bcdef }}
Vals: {{Val list| 7, 19, 26, 45f, 71bcf, 116bcdef }}
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~3/2 = [700.000, 720.000] (7\12 to 3\5)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [700.000, 720.000] (7\12 to 3\5)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 715.587]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 715.587]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]
* Diamond monotone and tradeoff: ~3/2 = [700.000, 715.587]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [700.000, 715.587]


{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}
{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }}
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [700.000, 705.882] (7\12 to 10\17)
* 11-odd-limit diamond monotone: ~3/2 = [700.000, 705.882] (7\12 to 10\17)
* Diamond tradeoff range: ~3/2 = [691.202, 715.587]
* 11-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]
* Diamond monotone and tradeoff: ~3/2 = [700.000, 705.882]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [700.000, 705.882]


POTE generator: ~3/2 = 703.254
POTE generator: ~3/2 = 703.254
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Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = 705.882 (10\17)
* 13- and 15-odd-limit diamond monotone: ~3/2 = 705.882 (10\17)
* Diamond tradeoff range: ~3/2 = [691.202, 715.587]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [691.202, 715.587]
* Diamond monotone and tradeoff: ~3/2 = 705.882
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = 705.882


Vals: {{Val list| 12f, 17c, 29cdef }}
Vals: {{Val list| 12f, 17c, 29cdef }}
Line 1,007: Line 1,007:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~7/6 = [240.000, 257.143] (1\5 to 3\14)
* 7- and 9-odd-limit [[diamond monotone]]: ~7/6 = [240.000, 257.143] (1\5 to 3\14)
* [[Diamond tradeoff]] range: ~7/6 = [231.174, 266.871]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~7/6 = [231.174, 266.871]
* Diamond monotone and tradeoff: ~7/6 = [240.000, 257.143]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~7/6 = [240.000, 257.143]


{{Val list|legend=1| 5, 14c, 19 }}
{{Val list|legend=1| 5, 14c, 19 }}
Line 1,027: Line 1,027:


Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~7/6 = [252.632, 257.143] (4\19 to 3\14)
* 11-odd-limit diamond monotone: ~7/6 = [252.632, 257.143] (4\19 to 3\14)
* Diamond tradeoff range: ~7/6 = [231.174, 266.871]
* 11-odd-limit diamond tradeoff: ~7/6 = [231.174, 266.871]
* Diamond monotone and tradeoff: ~7/6 = [252.632, 257.143]
* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [252.632, 257.143]


Vals: {{Val list| 14c, 19, 33cd, 52cd }}
Vals: {{Val list| 14c, 19, 33cd, 52cd }}
Line 1,047: Line 1,047:


Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~7/6 = 252.632 (4\19)
* 13- and 15-odd-limit diamond monotone: ~7/6 = 252.632 (4\19)
* Diamond tradeoff range: ~7/6 = [231.174, 289.210]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [231.174, 289.210]
* Diamond monotone and tradeoff: ~7/6 = 252.632
* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = 252.632


Vals: {{Val list| 14cf, 19, 33cdff, 52cdff }}
Vals: {{Val list| 14cf, 19, 33cdff, 52cdff }}
Line 1,133: Line 1,133:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: ~3/2 = [685.714, 700.000] (8\14 to 7\12)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 700.000] (8\14 to 7\12)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [688.957, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [688.957, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
Line 1,158: Line 1,158:


Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = [685.714, 700.000] (8\14 to 7\12)
* 11-odd-limit diamond monotone: ~3/2 = [685.714, 700.000] (8\14 to 7\12)
* Diamond tradeoff range: ~3/2 = [682.458, 701.955]
* 11-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* Diamond monotone and tradeoff: ~3/2 = [685.714, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [685.714, 700.000]


Vals: {{Val list| 12, 14c, 26, 90bce, 116bcce }}
Vals: {{Val list| 12, 14c, 26, 90bce, 116bcce }}
Line 1,178: Line 1,178:


Tuning ranges:  
Tuning ranges:  
* Diamond monotone range: ~3/2 = 692.308 (15\26)
* 13- and 15-odd-limit diamond monotone: ~3/2 = 692.308 (15\26)
* Diamond tradeoff range: ~3/2 = [682.458, 701.955]
* 13- and 15-odd-limit diamond tradeoff: ~3/2 = [682.458, 701.955]
* Diamond monotone and tradeoff: ~3/2 = 692.308
* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = 692.308


Vals: {{Val list| 12f, 14cf, 26, 38e }}
Vals: {{Val list| 12f, 14cf, 26, 38e }}
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[[Tuning ranges]]:
[[Tuning ranges]]:
* [[Diamond monotone]] range: ~128/105 = [347.368, 350.000] (11\38 to 7\24)
* 7- and 9-odd-limit [[diamond monotone]]: ~128/105 = [347.368, 350.000] (11\38 to 7\24)
* 7-odd-limit [[diamond tradeoff]]: ~128/105 = [347.393, 350.978]
* 7-odd-limit [[diamond tradeoff]]: ~128/105 = [347.393, 350.978]
* 9-odd-limit [[diamond tradeoff]]: ~128/105 = [345.601, 350.978]
* 9-odd-limit [[diamond tradeoff]]: ~128/105 = [345.601, 350.978]
Line 1,327: Line 1,327:


[[Tuning ranges]]:
[[Tuning ranges]]:
* Diamond monotone range: ~11/9 = [348.387, 350.000] (9\31 to 7\24)
* 11-odd-limit diamond monotone: ~11/9 = [348.387, 350.000] (9\31 to 7\24)
* Diamond tradeoff range: ~11/9 = [344.999, 350.978]
* 11-odd-limit diamond tradeoff: ~11/9 = [344.999, 350.978]
* Diamond monotone and tradeoff: ~11/9 = [348.387, 350.000]
* 11-odd-limit diamond monotone and tradeoff: ~11/9 = [348.387, 350.000]


Vals: {{Val list| 7, 24, 31 }}
Vals: {{Val list| 7, 24, 31 }}
Line 2,016: Line 2,016:
POTE generator: ~8/7 = 233.486
POTE generator: ~8/7 = 233.486


{{Val list|legend=1| 19, 38, 57, 76 }}
Vals: {{Val list| 19, 38, 57, 76 }}


Badness: 0.066829
Badness: 0.066829
Line 2,031: Line 2,031:
POTE generator: ~8/7 = 234.890
POTE generator: ~8/7 = 234.890


{{Val list|legend=1| 19, 38, 57, 76 }}
Vals: {{Val list| 19, 38, 57, 76 }}


Badness: 0.045844
Badness: 0.045844
Line 2,048: Line 2,048:
{{Val list|legend=1| 19, 38d }}
{{Val list|legend=1| 19, 38d }}


Badness: 0.036387
[[Badness]]: 0.036387


=== 13-limit ===
=== 13-limit ===
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