5L 2s/Temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955] | * 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955] | ||
{{ | {{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | ||
[[Badness]]: 0.007381 | [[Badness]]: 0.007381 | ||
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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. | ||
{{ | {{Optimal ET sequence|legend=1| 7, 19, 26, 45f }} | ||
[[Tp_tuning#T2 tuning|RMS error]]: 1.742 cents | [[Tp_tuning#T2 tuning|RMS error]]: 1.742 cents | ||
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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. | ||
{{ | {{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }} | ||
[[Badness]]: 0.013707 | [[Badness]]: 0.013707 | ||
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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. | ||
{{ | {{Optimal ET sequence|legend=1| 12e, 19, 31, 81 }} | ||
[[Badness]]: 0.021543 | [[Badness]]: 0.021543 | ||
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[[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. | ||
{{ | {{Optimal ET sequence|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }} | ||
[[Badness]]: 0.017027 | [[Badness]]: 0.017027 | ||