97th-octave temperaments: Difference between revisions

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~~Berkelium is a remarkable high~~-~~limit subgroup temperament with equally remarkable full 31~~-~~limit branchings. It~~ is ~~named after the 97th element, as it divides the octave into~~ 97 ~~equal parts~~.

97th-octave temperaments occur between any equal divisions whose greatest common divisor is 97.

~~Berkelium comes in two variants, berkelium-247, named after the most stable isotope,~~ is ~~described as the 388 & 3395 temperament~~, of ~~which~~ [[388edo]] is consistent in the 37-odd-limit ~~and~~ [[3395edo]] is a zeta edo and a strong 19-limit tuning~~. Another 31~~-limit ~~variety, named berkelium-247 is described as a 388 & 2619 temperament~~, and while [[2619edo]] is not remarkably strong in harmonic approximation, it is consistent in the 33-odd-limit, ~~meaning it~~ is ~~natural for it to be~~ temperament-~~merged with 388edo~~, ~~and the end result~~ is a ~~97th-octave~~ temperament.

Although harmonic quality of 97edo is not visible at first glance, some of its multiples are highly notable large edos. [[388edo]] is the first edo to be consistent in the 37-odd-limit, [[3395edo]] is a zeta edo and a strong 19-limit tuning, having lowest 19-limit relative error than any division before it, and while [[2619edo]] is not remarkably strong in harmonic approximation, it is consistent in the 33-odd-limit.

== Berkelium ==

Berkelium is a remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings. It is named after the 97th element,

Berkelium comes in two variants, berkelium-247, named after the most stable isotope, is described as the 388 & 3395 temperament. Another 31-limit variety, named berkelium-248 is described as a 388 & 2619 temperament.

Different branchings of berkelium also map 1 step of 97edo to drastically different intervals, each of which could be used in a [[comma pump]]. Berkelium-247 maps the period in the higher limits to [[144/143]], the grossma.

~~==Temperament data==~~

Subgroup: 2.3.5.13.17.23.29.31

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Optimal tuning (CTE): ~3/2 = 701.9...

~~Vals:~~ 388, 2619, 3395...

{{Optimal ET sequence|legend=1|388, 2619, 3395}}...

=== Berkelium-248 ===

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Optimal tuning (CTE): ~3/2 = 701.945

~~Vals:~~ {{~~EDOs~~|388, 2619}}, ...

{{Optimal ET sequence|legend=1|388, 2619}}, ...

=== Berkelium-247 ===

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Optimal tuning (CTE): ~3/2 = 701.976

~~[[Category:Rank 2]]~~

@@ Line 1: / Line 1: @@
-Berkelium is a remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings. It is named after the 97th element, as it divides the octave into 97 equal parts.
+{{Infobox fractional-octave|97}}
+th-octave temperaments occur between any equal divisions whose greatest common divisor is 97.
-Berkelium comes in two variants, berkelium-247, named after the most stable isotope, is described as the 388 & 3395 temperament, of which [[388edo]] is consistent in the 37-odd-limit and [[3395edo]] is a zeta edo and a strong 19-limit tuning. Another 31-limit variety, named berkelium-247 is described as a 388 & 2619 temperament, and while [[2619edo]] is not remarkably strong in harmonic approximation, it is consistent in the 33-odd-limit, meaning it is natural for it to be temperament-merged with 388edo, and the end result is a 97th-octave temperament.
+Although harmonic quality of 97edo is not visible at first glance, some of its multiples are highly notable large edos. [[388edo]] is the first edo to be consistent in the 37-odd-limit, [[3395edo]] is a zeta edo and a strong 19-limit tuning, having lowest 19-limit relative error than any division before it, and while [[2619edo]] is not remarkably strong in harmonic approximation, it is consistent in the 33-odd-limit.
+== Berkelium ==
+Berkelium is a remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings. It is named after the 97th element,
+Berkelium comes in two variants, berkelium-247, named after the most stable isotope, is described as the 388 & 3395 temperament. Another 31-limit variety, named berkelium-248 is described as a 388 & 2619 temperament.
 Different branchings of berkelium also map 1 step of 97edo to drastically different intervals, each of which could be used in a [[comma pump]]. Berkelium-247 maps the period in the higher limits to [[144/143]], the grossma.
-==Temperament data==
 Subgroup: 2.3.5.13.17.23.29.31
@@ Line 15: / Line 20: @@
 Optimal tuning (CTE): ~3/2 = 701.9...
-Vals: 388, 2619, 3395...
+{{Optimal ET sequence|legend=1|388, 2619, 3395}}...
 === Berkelium-248 ===
@@ Line 52: / Line 57: @@
 Optimal tuning (CTE): ~3/2 = 701.945
-Vals: {{EDOs|388, 2619}}, ...
+{{Optimal ET sequence|legend=1|388, 2619}}, ...
 === Berkelium-247 ===
@@ Line 111: / Line 116: @@
 Optimal tuning (CTE): ~3/2 = 701.976
-[[Category:Rank 2]]
+{{Navbox fractional-octave}}