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Meantone family: Difference between revisions

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update tuning range links
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autopatrolled, emailconfirmed
5,171 edits
correct per Milne's comments
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [685.714, 720.000] (4\7 to 3\5)
* [[diamond monotone]] range: [685.714, 720.000] (4\7 to 3\5)
* [[diamond pure]] range: [694.786, 701.955] (1/3 comma to Pythagorean)
* [[diamond purer]] range: [694.786, 701.955] (1/3 comma to Pythagorean)
* [[diamond strict]] range: [694.786, 701.955]
* [[diamond nice]] range: [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 }}
Line 71: Line 71:
[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [694.737, 700.000] (11\19 to 7\12)
* [[diamond monotone]] range: [694.737, 700.000] (11\19 to 7\12)
* [[diamond pure]] range: [694.786, 701.955] (1/3 comma to Pythagorean)
* [[diamond purer]] range: [694.786, 701.955] (1/3 comma to Pythagorean)
* [[diamond strict]] range: [694.786, 700.000]
* [[diamond nice]] range: [694.786, 700.000]


[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.
Line 100: Line 100:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [696.774, 700.000] (18\31 to 7\12)
* [[diamond monotone]] range: [696.774, 700.000] (18\31 to 7\12)
* [[diamond pure]] range: [691.202, 701.955]
* [[diamond purer]] range: [691.202, 701.955]
* [[diamond strict]] range: [696.774, 700.000]
* [[diamond nice]] range: [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: [696.774, 700.000] (18\31 to 7\12)
* [[diamond monotone]] range: [696.774, 700.000] (18\31 to 7\12)
* [[diamond pure]] range: [691.202, 701.955]
* [[diamond purer]] range: [691.202, 701.955]
* [[diamond strict]] range: [696.774, 700.000]
* [[diamond nice]] range: [696.774, 700.000]


{{Val list|legend=1| 12, 19ef, 31, 43, 74 }}
{{Val list|legend=1| 12, 19ef, 31, 43, 74 }}
Line 193: Line 193:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31)
* [[diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31)
* [[diamond pure]] range: [691.202, 701.955]
* [[diamond purer]] range: [691.202, 701.955]
* [[diamond strict]] range: [694.737, 696.774]
* [[diamond nice]] range: [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.
Line 220: Line 220:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31)
* [[diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31)
* [[diamond pure]] range: [691.202, 701.955]
* [[diamond purer]] range: [691.202, 701.955]
* [[diamond strict]] range: [694.737, 696.774]
* [[diamond nice]] range: [694.737, 696.774]


{{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
{{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* [[diamond pure]] range: [692.353, 701.955]
* [[diamond purer]] range: [692.353, 701.955]
* [[diamond strict]] range: [692.353, 694.737]
* [[diamond nice]] range: [692.353, 694.737]


Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
Line 530: Line 530:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* [[diamond pure]] range: [682.502, 701.955]
* [[diamond purer]] range: [682.502, 701.955]
* [[diamond strict]] range: [692.308, 694.737]
* [[diamond nice]] range: [692.308, 694.737]


{{Val list|legend=1| 7, 19, 26, 45, 71bc, 116bcde }}
{{Val list|legend=1| 7, 19, 26, 45, 71bc, 116bcde }}
Line 551: Line 551:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* [[diamond pure]] range: [682.502, 701.955]
* [[diamond purer]] range: [682.502, 701.955]
* [[diamond strict]] range: [692.308, 694.737]
* [[diamond nice]] range: [692.308, 694.737]


{{Val list|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }}
{{Val list|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }}
Line 576: Line 576:
[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [700.000, 720.000] (7\12 to 3\5)
* [[diamond monotone]] range: [700.000, 720.000] (7\12 to 3\5)
* [[diamond pure]] range: [694.786, 715.587]
* [[diamond purer]] range: [694.786, 715.587]
* [[diamond strict]] range: [700.000, 715.587]
* [[diamond nice]] range: [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: [700.000, 705.882] (7\12 to 10\17)
* [[diamond monotone]] range: [700.000, 705.882] (7\12 to 10\17)
* [[diamond pure]] range: [691.202, 715.587]
* [[diamond purer]] range: [691.202, 715.587]
* [[diamond strict]] range: [700.000, 705.882]
* [[diamond nice]] range: [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: 705.882 (10\17)
* [[diamond monotone]] range: 705.882 (10\17)
* [[diamond pure]] range: [691.202, 715.587]
* [[diamond purer]] range: [691.202, 715.587]
* [[diamond strict]] range: 705.882
* [[diamond nice]] range: 705.882


{{Val list|legend=1| 12f, 17c, 29cdef }}
{{Val list|legend=1| 12f, 17c, 29cdef }}
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [240.000, 257.143] (1\5 to 3\14)
* [[diamond monotone]] range: [240.000, 257.143] (1\5 to 3\14)
* [[diamond pure]] range: [231.174, 266.871]
* [[diamond purer]] range: [231.174, 266.871]
* [[diamond strict]] range: [240.000, 257.143]
* [[diamond nice]] range: [240.000, 257.143]


{{Val list|legend=1| 5, 14c, 19 }}
{{Val list|legend=1| 5, 14c, 19 }}
Line 931: Line 931:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [252.632, 257.143] (4\19 to 3\14)
* [[diamond monotone]] range: [252.632, 257.143] (4\19 to 3\14)
* [[diamond pure]] range: [231.174, 266.871]
* [[diamond purer]] range: [231.174, 266.871]
* [[diamond strict]] range: [252.632, 257.143]
* [[diamond nice]] range: [252.632, 257.143]


{{Val list|legend=1| 14c, 19, 33cd, 52cd }}
{{Val list|legend=1| 14c, 19, 33cd, 52cd }}
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Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: 694.737 (4\19)
* [[diamond monotone]] range: 694.737 (4\19)
* [[diamond pure]] range: [621.581, 737.652]
* [[diamond purer]] range: [621.581, 737.652]
* [[diamond strict]] range: 694.737
* [[diamond nice]] range: 694.737


{{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }}
{{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }}
Line 1,041: Line 1,041:
[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[diamond monotone]] range: [685.714, 700.000] (8\14 to 7\12)
* [[diamond monotone]] range: [685.714, 700.000] (8\14 to 7\12)
* [[diamond pure]] range: [688.957, 701.955]
* [[diamond purer]] range: [688.957, 701.955]
* [[diamond strict]] range: [688.957, 700.000]
* [[diamond nice]] range: [688.957, 700.000]


{{Multival|legend=1| 2 8 8 8 7 -4 }}
{{Multival|legend=1| 2 8 8 8 7 -4 }}
Line 1,067: Line 1,067:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: [685.714, 700.000] (8\14 to 7\12)
* [[diamond monotone]] range: [685.714, 700.000] (8\14 to 7\12)
* [[diamond pure]] range: [682.458, 701.955]
* [[diamond purer]] range: [682.458, 701.955]
* [[diamond strict]] range: [685.714, 700.000]
* [[diamond nice]] range: [685.714, 700.000]


{{Val list|legend=1| 12, 14c, 26, 90bce, 116bcce }}
{{Val list|legend=1| 12, 14c, 26, 90bce, 116bcce }}
Line 1,088: Line 1,088:
Tuning ranges:  
Tuning ranges:  
* [[diamond monotone]] range: 692.308 (15\26)
* [[diamond monotone]] range: 692.308 (15\26)
* [[diamond pure]] range: [682.458, 701.955]
* [[diamond purer]] range: [682.458, 701.955]
* [[diamond strict]] range: 692.308 (15\26)
* [[diamond nice]] range: 692.308 (15\26)


{{Val list|legend=1| 12f, 14cf, 26, 38e }}
{{Val list|legend=1| 12f, 14cf, 26, 38e }}
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