2684edo: Difference between revisions
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Cmloegcmluin (talk | contribs) I've asked for the clutter of pages of different forms for the words defactor and enfactor to be deleted, so now pages that linked to them need to be updated to use the remaining working link |
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The '''2684 equal divisions of the octave''' divides the octave into 2684 equal parts of 0.4471 [[cent]]s each. It is a very strong 13-limit tuning, with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until we reach [[5585edo]]. It is distinctly consistent through the [[17-odd-limit]], and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta integral edo]]. It is [[enfactored]] in the 5-limit, with the same tuning as [[1342edo]], tempering out kwazy, {{monzo| -53 10 16 }}, senior, {{monzo| -17 62 -35 }} and egads, {{monzo| -36 52 51 }}. A basis for its 13-limit commas is {9801/9800, 10648/10647, 140625/140608, 196625/196608, 823680/823543}; it also tempers out 123201/123200. It factors as 2<sup>2</sup> × 11 × 61, with divisors 2, 4, 11, 22, 44, 61, 122, 244, 671, and 1342. | The '''2684 equal divisions of the octave''' divides the octave into 2684 equal parts of 0.4471 [[cent]]s each. It is a very strong 13-limit tuning, with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until we reach [[5585edo]]. It is distinctly consistent through the [[17-odd-limit]], and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta integral edo]]. It is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[1342edo]], tempering out kwazy, {{monzo| -53 10 16 }}, senior, {{monzo| -17 62 -35 }} and egads, {{monzo| -36 52 51 }}. A basis for its 13-limit commas is {9801/9800, 10648/10647, 140625/140608, 196625/196608, 823680/823543}; it also tempers out 123201/123200. It factors as 2<sup>2</sup> × 11 × 61, with divisors 2, 4, 11, 22, 44, 61, 122, 244, 671, and 1342. | ||
{{Primes in edo|2684}} | {{Primes in edo|2684}} | ||
Revision as of 22:47, 13 January 2022
The 2684 equal divisions of the octave divides the octave into 2684 equal parts of 0.4471 cents each. It is a very strong 13-limit tuning, with a lower 13-limit relative error than any division until we reach 5585edo. It is distinctly consistent through the 17-odd-limit, and is both a zeta peak and zeta integral edo. It is enfactored in the 5-limit, with the same tuning as 1342edo, tempering out kwazy, [-53 10 16⟩, senior, [-17 62 -35⟩ and egads, [-36 52 51⟩. A basis for its 13-limit commas is {9801/9800, 10648/10647, 140625/140608, 196625/196608, 823680/823543}; it also tempers out 123201/123200. It factors as 22 × 11 × 61, with divisors 2, 4, 11, 22, 44, 61, 122, 244, 671, and 1342.
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