5L 2s/Temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) update tuning range links |
Cmloegcmluin (talk | contribs) correct per Milne's comments |
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* [[diamond monotone]] range: [685.714, 720.000] (7 to 5) | * [[diamond monotone]] range: [685.714, 720.000] (7 to 5) | ||
* [[diamond | * [[diamond purer]] range: [694.786, 701.955] (1/3 comma to Pythagorean) | ||
* [[diamond | * [[diamond nice]] range: [694.786, 701.955] | ||
{{Vals|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | {{Vals|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | ||
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[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* [[diamond monotone]] range: [692.308, 694.737] (26 to 19) | * [[diamond monotone]] range: [692.308, 694.737] (26 to 19) | ||
* [[diamond | * [[diamond purer]] range: [692.353, 701.955] | ||
* [[diamond | * [[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. | ||
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[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* [[diamond monotone]] range: [694.737, 700.000] (19 to 12) | * [[diamond monotone]] range: [694.737, 700.000] (19 to 12) | ||
* [[diamond | * [[diamond purer]] range: [694.786, 701.955] | ||
* [[diamond | * [[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, which comes to 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, which comes to 503.4257 cents. The recurrence converges quickly. | ||
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Tuning ranges: | Tuning ranges: | ||
* [[diamond monotone]] range: [694.737, 696.774] (19 to 31) | * [[diamond monotone]] range: [694.737, 696.774] (19 to 31) | ||
* [[diamond | * [[diamond purer]] range: [691.202, 701.955] | ||
* [[diamond | * [[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. | ||
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Tuning ranges: | Tuning ranges: | ||
* [[diamond monotone]] range: [696.774, 700.000] (31 to 12) | * [[diamond monotone]] range: [696.774, 700.000] (31 to 12) | ||
* [[diamond | * [[diamond purer]] range: [691.202, 701.955] | ||
* [[diamond | * [[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. | ||