1395edo: Difference between revisions

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The 1395 division divides the octave into 1395 steps of 0.8602 cents each. It 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 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 and 14875/14872.

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]]. However, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. 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 ===

{{Harmonics in equal|1395|columns=11|start=12|title=Approximation of prime harmonics in 1395edo (continued)}}

=== Subsets and supersets ===

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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-The 1395 division divides the octave into 1395 steps of 0.8602 cents each. It 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 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 and 14875/14872.
+{{Infobox ET}}
+{{ED intro}}
-{{Primes in edo|1395|prec=3|columns=15}}
+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]]. However, it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat, causing [[23/19]] to become inconsistent, though it remains the only inconsistency up to the [[39-odd-limit]]. 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 ===
+{{Harmonics in equal|1395|columns=11}}
+{{Harmonics in equal|1395|columns=11|start=12|title=Approximation of prime harmonics in 1395edo (continued)}}
+=== Subsets and supersets ===
+Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.