60th-octave temperaments - Revision history

FloraC: - minutes and neodymium (addressed in landscape microtemps)

2026-04-24T13:22:37Z

- minutes and neodymium (addressed in landscape microtemps)

@@ Line 1: / Line 1: @@
 {{Infobox fractional-octave|60}}
-[[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo.
+[[60edo]] is a [[highly composite edo]], and some its multiples are notable for their consistency limits, such as [[2460edo]], which is a [[The Riemann zeta function and tuning #Zeta edo lists|zeta record edo]].
-== Minutes ==
+See [[minutes]] and [[neodymium]].
 == Magnetismic microtemperaments ==
 All these temperaments temper out the [[magnetisma]], a 2.3.29.43 subgroup comma which when tempered sets the [[87/86]] interval to 1/60th of the octave, and thus all these temperaments have a period that maps to 87/86.
-===Neodymium magnet===
+=== Neodymium magnet ===
-An extension of neodymium. Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that [[87/86]] is very close to 1/60th of the octave.  and thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.
+An extension of neodymium. Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that [[87/86]] is very close to 1/60th of the octave. And thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.
 Subgroup: 2.3.5.29.43

ArrowHead294 at 03:40, 14 February 2025

2025-02-14T03:40:31Z

← Older revision		Revision as of 03:40, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|60}}		{{Infobox fractional-octave\|60}}
	[[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo.		[[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo.
	==Minutes==
			== Minutes ==
	Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the [[Kirnberger's atom]], and in the limits below 13, it's a contorted atomic temperament.		Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the [[Kirnberger's atom]], and in the limits below 13, it's a contorted atomic temperament.

MisterShafXen: /* 19-limit */

2024-12-16T23:44:15Z

19-limit

← Older revision		Revision as of 23:44, 16 December 2024
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	=== 19-limit ===		=== 19-limit ===
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17.19

	Comma list: 9801/9800, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 23409/23408		Comma list: 9801/9800, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 23409/23408

BudjarnLambeth at 07:45, 5 December 2024

2024-12-05T07:45:36Z

← Older revision		Revision as of 07:45, 5 December 2024
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	[[Category:60edo]]		[[Category:60edo]]
	~~[[Category:Temperament collections]]~~

BudjarnLambeth: navbox

2024-12-05T07:38:26Z

navbox

← Older revision		Revision as of 07:38, 5 December 2024
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	Optimal tuning (CTE): ~216/175 = 364.385		Optimal tuning (CTE): ~216/175 = 364.385

			{{Navbox fractional-octave}}

	[[Category:60edo]]		[[Category:60edo]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Eliora at 12:21, 21 September 2023

2023-09-21T12:21:20Z

← Older revision		Revision as of 12:21, 21 September 2023
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	[[Category:60edo]]		[[Category:60edo]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Rank 2]]~~

Eliora at 22:36, 14 July 2023

2023-07-14T22:36:25Z

← Older revision		Revision as of 22:36, 14 July 2023
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			{{Fractional-octave navigation\|60}}
	[[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo.		[[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo.
	==Minutes==		==Minutes==

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

2023-05-07T20:07:19Z

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

← Older revision		Revision as of 20:07, 7 May 2023
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	Optimal tuning (CTE): ~216/175 = 364.387		Optimal tuning (CTE): ~216/175 = 364.387

	~~Vals:~~ {{~~EDOs~~\|540, 1380, 1920, 2460, 3000, 3840, 4380, 4920, 6300, 6840e}}		{{Optimal ET sequence\|legend=1\|540, 1380, 1920, 2460, 3000, 3840, 4380, 4920, 6300, 6840e}}

	=== 19-limit ===		=== 19-limit ===
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	Optimal tuning (CTE): ~7533637632/6103515625 = 364.385		Optimal tuning (CTE): ~7533637632/6103515625 = 364.385

	~~Vals:~~ {{~~EDOs~~\|540jn, 1380jn, 1920, 2460, 3000jjnn, 3840jn, 4920jn 4380, 6300, 6840}}		{{Optimal ET sequence\|legend=1\|540jn, 1380jn, 1920, 2460, 3000jjnn, 3840jn, 4920jn 4380, 6300, 6840}}

	==== 2.3.5.7.29.43 subgroup ====		==== 2.3.5.7.29.43 subgroup ====

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

2023-05-07T17:49:47Z

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

← Older revision		Revision as of 17:49, 7 May 2023
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	Optimal tuning (CTE): ~3/2 = 701.948		Optimal tuning (CTE): ~3/2 = 701.948

	Optimal ~~GPV~~ sequence~~: {{EDOs~~\|1860, 2460, 6780, 7380}}		{{Optimal ET sequence\|legend=1\|1860, 2460, 6780, 7380}}

	=== 17-limit ===		=== 17-limit ===

Eliora: /* Minutes */ improve optimal gpv, it can be worked out manually if all the patent vals are known

2023-05-04T20:02:19Z

Minutes: improve optimal gpv, it can be worked out manually if all the patent vals are known

← Older revision		Revision as of 20:02, 4 May 2023
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	Optimal tuning (CTE): ~3/2 = 701.948		Optimal tuning (CTE): ~3/2 = 701.948

	~~Vals~~: {{EDOs\|~~600e,~~ 1860, 2460, ~~3060de, 3720de, 4320, 4920, 6180de,~~ 6780, ~~7380e,~~ }}		Optimal GPV sequence: {{EDOs\|1860, 2460, 6780, 7380}}

	=== 17-limit ===		=== 17-limit ===
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	Optimal tuning (CTE): ~3/2 = 701.948		Optimal tuning (CTE): ~3/2 = 701.948

	==Neodymium==		==Neodymium==
	Starts with the 17-limit since it is contorted in 13-limit and below, can be expressed as as 1920 & 4380 or 1920 & 2460.		Starts with the 17-limit since it is contorted in 13-limit and below, can be expressed as as 1920 & 4380 or 1920 & 2460.