7315edo: Difference between revisions

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~~== Theory ==~~

7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1|3]] with [[665edo]]. It notably demonstrates 3-2 [[telicity]], and is in fact the largest multiple of 665edo to do so. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.

~~This EDO~~ is consistent up to the 27-odd-limit, ~~which~~ is ~~rather impressive~~.

~~{{Harmonics~~ in ~~equal|7315}}~~

It can be used in higher limits, notably the [[31-odd-limit]], and even the no-41 [[59-odd-limit]], due to a large number of the harmonics being either sharp, or not too negative. The inconsistencies here largely happen with primes 29, 37, and 43, which are slightly flat; namely: 49/29, 49/37, 49/43, 29/19, 37/19, 43/38, 59/58, 59/37, 59/43, and [[octave complement]]<nowiki/>s.

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

=== Prime harmonics ===

{{Harmonics in equal|7315}}{{Harmonics in equal|7315|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 7315edo (continued)}}

=== Subsets and supersets ===

Since 7315 factors into {{factorization|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|7315}}
+{{ED intro}}
-== Theory ==
+edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1|3]] with [[665edo]]. It notably demonstrates 3-2 [[telicity]], and is in fact the largest multiple of 665edo to do so. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.
-This EDO is consistent up to the 27-odd-limit, which is rather impressive.
-{{Harmonics in equal|7315}}
+It can be used in higher limits, notably the [[31-odd-limit]], and even the no-41 [[59-odd-limit]], due to a large number of the harmonics being either sharp, or not too negative. The inconsistencies here largely happen with primes 29, 37, and 43, which are slightly flat; namely: 49/29, 49/37, 49/43, 29/19, 37/19, 43/38, 59/58, 59/37, 59/43, and [[octave complement]]<nowiki/>s.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|7315}}{{Harmonics in equal|7315|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 7315edo (continued)}}
+=== Subsets and supersets ===
+Since 7315 factors into {{factorization|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.