14348edo: Difference between revisions

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14348edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit [[relative error]] than any lower equal temperaments aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that, it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]], which has to do with its higher limit capability—it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond. The only inconsistent interval pair in the [[69-odd-limit]] is ([[31/29]], [[58/31]]) with 50.2% relative error.

14348edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit [[relative error]] than any lower equal temperaments aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that, it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]], which has to do with its higher limit capability—it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond. The only inconsistent interval pair in the [[69-odd-limit]] is ([[31/29]], [[58/31]]) with 50.2% relative error. Thus the full [[67-limit]] interpretation using the patent val is obvious, though it may be preferable to omit either prime [[29/1|29]] or [[31/1|31]].

An edo of similar size with full consistency to a very high limit ([[57-odd-limit]]) is [[20567edo]].

=== Prime harmonics ===

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=== Subsets and supersets ===

It factors as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all ~~divisors~~.

14348 factors into primes as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all subsets.

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 {{ED intro}}
-edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit [[relative error]] than any lower equal temperaments aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that, it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]], which has to do with its higher limit capability—it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond. The only inconsistent interval pair in the [[69-odd-limit]] is ([[31/29]], [[58/31]]) with 50.2% relative error.
+edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit [[relative error]] than any lower equal temperaments aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that, it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]], which has to do with its higher limit capability—it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond. The only inconsistent interval pair in the [[69-odd-limit]] is ([[31/29]], [[58/31]]) with 50.2% relative error. Thus the full [[67-limit]] interpretation using the patent val is obvious, though it may be preferable to omit either prime [[29/1|29]] or [[31/1|31]].
+An edo of similar size with full consistency to a very high limit ([[57-odd-limit]]) is [[20567edo]].
 === Prime harmonics ===
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 === Subsets and supersets ===
-It factors as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all divisors.
+factors into primes as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all subsets.