1578edo: Difference between revisions

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1578edo is a very strong higher limit system, and is a [[~~The Riemann~~ zeta ~~function and tuning #Zeta EDO lists~~|zeta peak, peak integer, integral and gap edo]]. It is ~~distinctly~~ [[consistent]] through the [[29-odd-limit]], and is the first [[edo]] past [[311edo]] with a lower 29-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It is also the lowest past 311edo in the [[31-limit]], the lowest past [[581edo]] in the [[23-limit]], and the lowest past [[1178edo]] in the [[19-limit]]. It is also quite strong taken just as an [[11-limit]] system; the only smaller edo with a lower 11-limit relative error is [[342edo]].

1578edo is a very strong higher limit system, and is a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. It is [[consistency|distinctly consistent]] through the [[29-odd-limit]], and is the first [[edo]] past [[311edo]] with a lower 29-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It is also the lowest past 311edo in the [[31-limit]], the lowest past [[581edo]] in the [[23-limit]], and the lowest past [[1178edo]] in the [[19-limit]]. It is also quite strong taken just as an [[11-limit]] system; the only smaller edo with a lower 11-limit relative error is [[342edo]].

It is also the most accurate edo below 10000 to approximate [[quarter-comma meantone]], with its approximation of {{monzo| 0 0 1/4 }} with a relative error of only 0.06%.

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=== ~~Divisors~~ ===

=== Subsets and supersets ===

Since 1578 factors into ~~2 × 3 × 263~~, 1578edo has subset edos 2, 3, 6, 263, 526, and 789.

Since 1578 factors into {{factorization|1578}}, 1578edo has subset edos 2, 3, 6, 263, 526, and 789.

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 {{EDO intro|1578}}
-edo is a very strong higher limit system, and is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, peak integer, integral and gap edo]]. It is distinctly [[consistent]] through the [[29-odd-limit]], and is the first [[edo]] past [[311edo]] with a lower 29-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It is also the lowest past 311edo in the [[31-limit]], the lowest past [[581edo]] in the [[23-limit]], and the lowest past [[1178edo]] in the [[19-limit]]. It is also quite strong taken just as an [[11-limit]] system; the only smaller edo with a lower 11-limit relative error is [[342edo]].
+edo is a very strong higher limit system, and is a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. It is [[consistency|distinctly consistent]] through the [[29-odd-limit]], and is the first [[edo]] past [[311edo]] with a lower 29-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It is also the lowest past 311edo in the [[31-limit]], the lowest past [[581edo]] in the [[23-limit]], and the lowest past [[1178edo]] in the [[19-limit]]. It is also quite strong taken just as an [[11-limit]] system; the only smaller edo with a lower 11-limit relative error is [[342edo]].
 It is also the most accurate edo below 10000 to approximate [[quarter-comma meantone]], with its approximation of {{monzo| 0 0 1/4 }} with a relative error of only 0.06%.
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 {{Harmonics in equal|1578|columns=11}}
-=== Divisors ===
+=== Subsets and supersets ===
-Since 1578 factors into 2 × 3 × 263, 1578edo has subset edos 2, 3, 6, 263, 526, and 789.
+Since 1578 factors into {{factorization|1578}}, 1578edo has subset edos 2, 3, 6, 263, 526, and 789.