1448edo - Revision history

Overthink: wording

2026-03-27T04:09:51Z

wording

← Older revision		Revision as of 04:09, 27 March 2026
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	The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.		The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.

	Notably, it is the first edo to be [[diamond monotone]] to the [[95-odd-limit]], completing the first five octaves and a fifth of the [[harmonic series]], in fact by the [[patent val]]. It is thus usable in the full [[89-limit]], where prime 89 is ~~right before~~ a record {{W\|prime gap}} from 89 to 97.		Notably, it is the first edo to be [[diamond monotone]] to the [[95-odd-limit]], completing the first five octaves and a fifth of the [[harmonic series]], in fact by the [[patent val]]. It is thus usable in the full [[89-limit]], where prime 89 is the start of a record {{W\|prime gap}} from 89 to 97.

	=== Prime harmonics ===		=== Prime harmonics ===

Overthink: 89-limit usability

2026-03-25T03:17:03Z

89-limit usability

← Older revision		Revision as of 03:17, 25 March 2026
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	The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.		The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.

			Notably, it is the first edo to be [[diamond monotone]] to the [[95-odd-limit]], completing the first five octaves and a fifth of the [[harmonic series]], in fact by the [[patent val]]. It is thus usable in the full [[89-limit]], where prime 89 is right before a record {{W\|prime gap}} from 89 to 97.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1448}}		{{Harmonics in equal\|1448\|columns=12}}
			{{Harmonics in equal\|1448\|columns=12\|start=13\|collapsed=1\|title=Approximation of prime harmonics in 1448edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 17:04, 18 February 2025

2025-02-18T17:04:48Z

← Older revision		Revision as of 17:04, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1448~~}}		{{ED intro}}

	The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.		The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-31T09:07:57Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 09:07, 31 October 2023
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	{{EDO intro\|1448}}		{{EDO intro\|1448}}

	The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[~~The Riemann zeta function and tuning #Zeta EDO lists\|~~zeta peak]] ~~edo~~, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit ~~commas~~ is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.		The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1448}}		{{Harmonics in equal\|1448}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	Since 1448 factors into ~~2<sup>3</sup> × 181~~, it has subset edos 2, 4, 8, 181, 362, and 724.		Since 1448 factors into {{factorization\|1448}}, it has subset edos 2, 4, 8, 181, 362, and 724.

	[[Category:Thor]]		[[Category:Thor]]
	[[Category:Donar]]		[[Category:Donar]]

BudjarnLambeth at 06:54, 9 July 2023

2023-07-09T06:54:04Z

← Older revision		Revision as of 06:54, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1448}}		{{EDO intro\|1448}}

BudjarnLambeth at 05:09, 9 July 2023

2023-07-09T05:09:04Z

← Older revision		Revision as of 05:09, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1448}}		{{EDO intro\|1448}}

Eliora: remove overly informal / expressionate language

2023-04-08T16:22:58Z

remove overly informal / expressionate language

← Older revision		Revision as of 16:22, 8 April 2023
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	{{EDO intro\|1448}}		{{EDO intro\|1448}}

	The 1448edo is a strong 13-limit system, and ~~if you do not care about 17, a terrific~~ 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.		The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Improve intro and +divisors

2023-01-08T04:32:57Z

Improve intro and +divisors

← Older revision		Revision as of 04:32, 8 January 2023
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	{{Infobox ET}}		{{Infobox ET}}
	The ~~1448 division divides the octave into 1448 equal parts of 0.8287 cents each. It~~ is a strong 13-limit system, and if you ~~don't~~ care about 17, a terrific 2.3.5.7.11.13.19.23 system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {3025/3024, 4225/4224, 4375/4374, 140625/140608, 823680/823543}.		{{EDO intro\|1448}}

			The 1448edo is a strong 13-limit system, and if you do not care about 17, a terrific 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1448}}		{{Harmonics in equal\|1448}}

	[[Category:~~Equal divisions of the octave\|####~~]] ~~<!-- 4-digit number -->~~		=== Divisors ===
			Since 1448 factors into 2<sup>3</sup> × 181, it has subset edos 2, 4, 8, 181, 362, and 724.

			[[Category:Thor]]
			[[Category:Donar]]

Plumtree: Infobox ET added

2022-10-04T22:10:08Z

Infobox ET added

← Older revision		Revision as of 22:10, 4 October 2022
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			{{Infobox ET}}
	The 1448 division divides the octave into 1448 equal parts of 0.8287 cents each. It is a strong 13-limit system, and if you don't care about 17, a terrific 2.3.5.7.11.13.19.23 system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {3025/3024, 4225/4224, 4375/4374, 140625/140608, 823680/823543}.		The 1448 division divides the octave into 1448 equal parts of 0.8287 cents each. It is a strong 13-limit system, and if you don't care about 17, a terrific 2.3.5.7.11.13.19.23 system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {3025/3024, 4225/4224, 4375/4374, 140625/140608, 823680/823543}.

Fredg999 category edits: Sort key

2022-07-04T01:16:35Z

Sort key

← Older revision		Revision as of 01:16, 4 July 2022
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	{{Harmonics in equal\|1448}}		{{Harmonics in equal\|1448}}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->