20th-octave temperaments - Revision history

Overthink: + links

2025-12-06T18:51:09Z

+ links

← Older revision		Revision as of 18:51, 6 December 2025
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	[[20edo]] (in isolation) is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.		[[20edo]] (in isolation) is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.

	In the 17-limit, one step of 20edo is extremely close to 88/85, which serves as a period in two of these temperaments – Soviet Ferris wheel and calcium.		In the [[17-limit]], one step of 20edo is extremely close to [[88/85]], which serves as a period in two of these temperaments – Soviet Ferris wheel and calcium.

	Temperaments discussed elsewhere include		Temperaments discussed elsewhere include

ArrowHead294 at 03:40, 14 February 2025

2025-02-14T03:40:10Z

← Older revision		Revision as of 03:40, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|20}}		{{Infobox fractional-octave\|20}}
	[[20edo]] (in isolation) is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.		[[20edo]] (in isolation) is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.

BudjarnLambeth: navbox

2024-12-05T07:19:42Z

navbox

← Older revision		Revision as of 07:19, 5 December 2024
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	{{Optimal ET sequence\|legend=1\|460, 2000, 2460}}		{{Optimal ET sequence\|legend=1\|460, 2000, 2460}}

			{{Navbox fractional-octave}}

	[[Category:20edo]]		[[Category:20edo]]
	~~[[Category:Temperament collections]]~~

Godtone: note importance of Degrees

2024-08-27T16:01:19Z

note importance of Degrees

← Older revision		Revision as of 16:01, 27 August 2024
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	{{Fractional-octave navigation\|20}}		{{Fractional-octave navigation\|20}}
	[[20edo]] is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments.		[[20edo]] (in isolation) is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments. It's worth noting that [[Degrees]] (discussed elsewhere) is a no-31's [[41-limit]] temperament which serves as a well-temperament of [[80edo]] in the corresponding subgroup, as a 60L 20s MOS is sufficient for finding all its primes.

	In the 17-limit, one step of 20edo is extremely close to 88/85, which serves as a period in two of these temperaments – Soviet Ferris wheel and calcium.		In the 17-limit, one step of 20edo is extremely close to 88/85, which serves as a period in two of these temperaments – Soviet Ferris wheel and calcium.

Eliora at 15:10, 7 July 2023

2023-07-07T15:10:49Z

← Older revision		Revision as of 15:10, 7 July 2023
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			{{Fractional-octave navigation\|20}}
	[[20edo]] is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments.		[[20edo]] is not a particularly harmonically interesting edo, but some of its multiples have high consistency limits (17-odd-limit and higher), and therefore are worthy of being considered in terms of rank-2 temperaments.

Eliora: /* Calcium */ that is notable

2023-06-07T20:53:30Z

Calcium: that is notable

← Older revision		Revision as of 20:53, 7 June 2023
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	=== 19-limit ===		=== 19-limit ===
	Both [[11/7]] and [[19/16]] are reached in eight generator steps.		2000edo and 2460edo are adjacent members of a sequence of tunings with progressively less error in 19-limit. Both [[11/7]] and [[19/16]] are reached in eight generator steps.

	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

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

2023-05-07T19:38:36Z

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

← Older revision		Revision as of 19:38, 7 May 2023
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	Optimal tuning (CTE): ~208568572998046875/144115188075855872 = 633.970		Optimal tuning (CTE): ~208568572998046875/144115188075855872 = 633.970

	~~Vals:~~ {{~~EDOs~~\|40, 140, 180, 320, 460, 600, 740, 780, 1060, 1240, 1520}}, ...		{{Optimal ET sequence\|legend=1\|40, 140, 180, 320, 460, 600, 740, 780, 1060, 1240, 1520}}, ...

	=== 7-limit ===		=== 7-limit ===
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	Optimal tuning (CTE): ~238/165 = 633.913		Optimal tuning (CTE): ~238/165 = 633.913

	~~Vals:~~ 140, 320, 460		{{Optimal ET sequence\|legend=1\|140, 320, 460}}
	===19-limit===		===19-limit===
	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19
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	Optimal tuning (CTE): ~238/165 = 633.913		Optimal tuning (CTE): ~238/165 = 633.913

	~~Vals:~~ {{~~EDOs~~\|140, 320, 460}}		{{Optimal ET sequence\|legend=1\|140, 320, 460}}

	==Calcium==		==Calcium==
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	Optimal tuning (CTE): ~169/153 = 172.196		Optimal tuning (CTE): ~169/153 = 172.196

	~~Vals:~~ 460, 2000, 2460		{{Optimal ET sequence\|legend=1\|460, 2000, 2460}}

	===23-limit===		===23-limit===
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	Optimal tuning (CTE): ~11875/10752 = 172.196		Optimal tuning (CTE): ~11875/10752 = 172.196

	~~Vals:~~ {{~~EDOs~~\|460, 2000, 2460}}		{{Optimal ET sequence\|legend=1\|460, 2000, 2460}}

	[[Category:20edo]]		[[Category:20edo]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Eliora: /* Soviet Ferris wheel */

2023-05-03T13:03:35Z

Soviet Ferris wheel

← Older revision		Revision as of 13:03, 3 May 2023
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	== Soviet Ferris wheel ==		== Soviet Ferris wheel ==
	Defined as the 320 & 460 temperament, and named because it's a period-20 temperament, and there are 20 cabins on a standard ferris wheel found throughout most of Eastern Europe and Central Asia (as in abandoned Pripyat wheel, for example).		Defined as the 320 & 460 temperament, and named because it's a period-20 temperament, and there are 20 cabins on a standard ferris wheel found throughout most of Eastern Europe and Central Asia (as in abandoned Pripyat wheel, for example).

			The 5-limit comma is an interval which can also be produced by closing 20 [[375/256]]'s at 11 octaves, tempering this interval to 11\20.

	Subgroup: 2.3.5		Subgroup: 2.3.5

Eliora: /* Soviet Ferris wheel */ +5-limit, +7-limit

2023-05-03T12:58:06Z

Soviet Ferris wheel: +5-limit, +7-limit

@@ Line 8: / Line 8: @@
 == Soviet Ferris wheel ==
 Defined as the 320 & 460 temperament, and named because it's a period-20 temperament, and there are 20 cabins on a standard ferris wheel found throughout most of Eastern Europe and Central Asia (as in abandoned Pripyat wheel, for example).
 Subgroup: 2.3.5.7.11
@@ Line 54: / Line 80: @@
 Vals: {{EDOs|140, 320, 460}}
 ==Calcium==
 A highly precise and high-limit 2000 & 2460 temperament, named after the 20th element following the convention of naming some fractional-octave temperaments after chemical elements.

Eliora: /* 19-limit */ facts

2023-01-11T21:11:27Z

19-limit: facts

← Older revision		Revision as of 21:11, 11 January 2023
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	=== 17-limit ===		=== 17-limit ===
	Both [[5/3]] and [[17/13]] are reached in two generator steps~~, and are set 13 steps of 20edo apart~~.		Both [[5/3]] and [[17/13]] are reached in two generator steps.

	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17
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	=== 19-limit ===		=== 19-limit ===
			Both [[11/7]] and [[19/16]] are reached in eight generator steps.

	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19