97th-octave temperaments - Revision history

ArrowHead294 at 03:42, 14 February 2025

2025-02-14T03:42:50Z

← Older revision		Revision as of 03:42, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|97}}		{{Infobox fractional-octave\|97}}
	97th-octave temperaments occur between any equal divisions whose greatest common divisor is 97.		97th-octave temperaments occur between any equal divisions whose greatest common divisor is 97.

BudjarnLambeth: navbox

2024-12-05T07:42:40Z

navbox

← Older revision		Revision as of 07:42, 5 December 2024
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	Optimal tuning (CTE): ~3/2 = 701.976		Optimal tuning (CTE): ~3/2 = 701.976

			{{Navbox fractional-octave}}

Eliora: /* 19-limit */

2023-09-21T12:46:26Z

19-limit

← Older revision		Revision as of 12:46, 21 September 2023
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	Optimal tuning (CTE): ~3/2 = 701.976		Optimal tuning (CTE): ~3/2 = 701.976

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

Eliora at 22:35, 14 July 2023

2023-07-14T22:35:00Z

← Older revision		Revision as of 22:35, 14 July 2023
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			{{Fractional-octave navigation\|97}}
	97th-octave temperaments occur between any equal divisions whose greatest common divisor is 97.		97th-octave temperaments occur between any equal divisions whose greatest common divisor is 97.

Eliora: rewrite

2023-06-17T20:36:15Z

rewrite

← Older revision		Revision as of 20:36, 17 June 2023
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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-248 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.		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.

Eliora: oops

2023-06-17T20:33:37Z

oops

← Older revision		Revision as of 20:33, 17 June 2023
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	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.		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		Subgroup: 2.3.5.13.17.23.29.31

Eliora: Eliora moved page Berkelium to 97th-octave temperaments: given the restructuring of the fractional-octave temperaments page and the fact that each period will have its own page and some pages have just one temperament, renaming

2023-06-17T20:33:16Z

Eliora moved page Berkelium to 97th-octave temperaments: given the restructuring of the fractional-octave temperaments page and the fact that each period will have its own page and some pages have just one temperament, renaming

← Older revision	Revision as of 20:33, 17 June 2023
(No difference)

Eliora at 23:24, 17 May 2023

2023-05-17T23:24:45Z

← Older revision		Revision as of 23:24, 17 May 2023
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	~~ŃBerkelium~~ 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.		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.

	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-248 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.		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-248 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.

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T20:06:39Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 20:06, 7 May 2023
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	Optimal tuning (CTE): ~3/2 = 701.9...		Optimal tuning (CTE): ~3/2 = 701.9...

	~~Vals:~~ 388, 2619, 3395...		{{Optimal ET sequence\|legend=1\|388, 2619, 3395}}...

	=== Berkelium-248 ===		=== Berkelium-248 ===
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	Optimal tuning (CTE): ~3/2 = 701.945		Optimal tuning (CTE): ~3/2 = 701.945

	~~Vals:~~ {{~~EDOs~~\|388, 2619}}, ...		{{Optimal ET sequence\|legend=1\|388, 2619}}, ...

	=== Berkelium-247 ===		=== Berkelium-247 ===

Eliora: oops

2023-03-24T21:56:22Z

oops

← Older revision		Revision as of 21:56, 24 March 2023
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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.		ŃBerkelium 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.

	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.		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-248 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.

	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.		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.