1395edo: Difference between revisions

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~~== Theory ==~~

1395edo is a strong higher-limit system, being a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

1395edo is a strong higher-limit system, being a [[~~The Riemann~~ zeta ~~function and tuning #Zeta EDO lists~~|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only [[consistent]] through the 21-odd-limit, due to 23 being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {2058/2057, [[2401/2400]], 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 1395 factors into ~~3<sup>2</sup> × 5 × 31~~, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.

Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1395}}
+{{ED intro}}
-== Theory ==
+edo is a strong higher-limit system, being a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.
-edo is a strong higher-limit system, being a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only [[consistent]] through the 21-odd-limit, due to 23 being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {2058/2057, [[2401/2400]], 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.
+Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.
 === Prime harmonics ===
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 === Subsets and supersets ===
-Since 1395 factors into 3<sup>2</sup> × 5 × 31, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.
+Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.