2684edo: Difference between revisions

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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.

Revision as of 11:04, 23 October 2021 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 18,308 edits +5-limit commas ← Older edit		Revision as of 22:47, 13 January 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled 5,160 edits 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 Newer edit →
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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}}