1395edo: Difference between revisions

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{~~{EDO intro|1395}~~}

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}.

~~== Theory ==~~

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.

~~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}~~.

=== Prime harmonics ===

~~[[Category:Equal divisions of the octave~~|~~####]] ~~

=== Subsets and supersets ===

~~[[Category:Zeta]]~~

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

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 {{Infobox ET}}
+{{ED intro}}
-{{EDO intro|1395}}
+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}.
-== Theory ==
+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.
-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}.
 === Prime harmonics ===
 {{Harmonics in equal|1395|columns=15}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== Subsets and supersets ===
-[[Category:Zeta]]
+Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.