User:Aura/4191814edo - Revision history

FloraC: Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}"

2025-08-20T16:53:44Z

Text replacement - "{{Infobox ET}}" to "{{Infobox ET|debug=1}}"

← Older revision		Revision as of 16:53, 20 August 2025
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	{{Mathematical interest}}		{{Mathematical interest}}
	{{Infobox ET}}		{{Infobox ET\|debug=1}}
	{{ED intro}}		{{ED intro}}

Fredg999: Fredg999 moved page 4191814edo to User:Aura/4191814edo without leaving a redirect: XW:NG

2025-08-14T21:54:05Z

Fredg999 moved page 4191814edo to User:Aura/4191814edo without leaving a redirect: XW:NG

← Older revision	Revision as of 21:54, 14 August 2025
(No difference)

BudjarnLambeth: Mathematical interest

2025-08-10T22:31:48Z

Mathematical interest

← Older revision		Revision as of 22:31, 10 August 2025
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	{{~~Niche~~}}		{{Mathematical interest}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

FloraC: Mark as niche. Cleanup. Wrap the harmonics table

2025-07-31T14:33:19Z

Mark as niche. Cleanup. Wrap the harmonics table

← Older revision		Revision as of 14:33, 31 July 2025
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			{{Niche}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

	~~== Theory ==~~		This edo has a [[consistency]] limit of 21, which is the most impressive out of all the 3-2 [[telicity\|telic]] multiples of [[190537edo]]. It tempers out the [[archangelic comma]] in the [[3-limit]], and though this system's 5-limit and 7-limit are rather lackluster for an edo this size, the representation of the prime [[11/1\|11]] is a bit better, and the representations of the [[13/1\|13]], [[17/1\|17]], and [[19/1\|19]] are excellent, all which help to bridge the lackluster [[5/1\|5]] and [[7/1\|7]]. Thus, this system is worthy of a great deal of further exploration in the [[19-limit]].
	This ~~EDO~~ has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity\|telic]] multiples of [[190537edo]]. It tempers out the [[~~Archangelic~~ comma]] in the 3-limit, and though this system's 5-limit and 7-limit are rather lackluster for an ~~EDO~~ this size, the representation of the 11~~-prime~~ is a bit better, and the representations of the 13~~-prime~~, 17~~-prime~~, and 19~~-prime~~ are excellent, all which help to bridge the lackluster 5~~-prime~~ and 7~~-prime~~. Thus, this system is worthy of a great deal of further exploration in the [[19-limit]].

	In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system, but also [[metatemperament]]s to [[~~Yarman~~ I]] and [[~~Yarman~~ II]].		In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2<sup>4</sup>, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system, but also [[metatemperament]]s to [[yarman I]] and [[yarman II]].

	{{Harmonics in equal\|4191814\|columns=12}}		=== Prime harmonics ===
			{{Harmonics in equal\|4191814\|columns=9}}
	~~[[Category:Equal divisions~~ of ~~the octave\|#######]] <!-- 7-digit number -->~~		{{Harmonics in equal\|4191814\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 4191814edo (continued)}}

Francium: changed EDO intro to ED intro

2025-02-20T17:01:03Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:01, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|4191814~~}}		{{ED intro}}

	== Theory ==		== Theory ==

BudjarnLambeth at 07:22, 9 July 2023

2023-07-09T07:22:01Z

← Older revision		Revision as of 07:22, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|4191814}}		{{EDO intro\|4191814}}

BudjarnLambeth at 03:56, 9 July 2023

2023-07-09T03:56:50Z

← Older revision		Revision as of 03:56, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|4191814}}		{{EDO intro\|4191814}}

Aura at 16:45, 23 December 2022

2022-12-23T16:45:23Z

← Older revision		Revision as of 16:45, 23 December 2022
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	This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity\|telic]] multiples of [[190537edo]]. It tempers out the [[Archangelic comma]] in the 3-limit, and though this system's 5-limit and 7-limit are rather lackluster for an EDO this size, the representation of the 11-prime is a bit better, and the representations of the 13-prime, 17-prime, and 19-prime are excellent, all which help to bridge the lackluster 5-prime and 7-prime. Thus, this system is worthy of a great deal of further exploration in the [[19-limit]].		This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity\|telic]] multiples of [[190537edo]]. It tempers out the [[Archangelic comma]] in the 3-limit, and though this system's 5-limit and 7-limit are rather lackluster for an EDO this size, the representation of the 11-prime is a bit better, and the representations of the 13-prime, 17-prime, and 19-prime are excellent, all which help to bridge the lackluster 5-prime and 7-prime. Thus, this system is worthy of a great deal of further exploration in the [[19-limit]].

	In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system, but also a [[metatemperament]] to [[~~yarman~~]].		In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system, but also [[metatemperament]]s to [[Yarman I]] and [[Yarman II]].

	{{Harmonics in equal\|4191814\|columns=12}}		{{Harmonics in equal\|4191814\|columns=12}}

	[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->		[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->

Aura at 16:44, 23 December 2022

2022-12-23T16:44:02Z

← Older revision		Revision as of 16:44, 23 December 2022
Line 5:		Line 5:
	This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity\|telic]] multiples of [[190537edo]]. It tempers out the [[Archangelic comma]] in the 3-limit, and though this system's 5-limit and 7-limit are rather lackluster for an EDO this size, the representation of the 11-prime is a bit better, and the representations of the 13-prime, 17-prime, and 19-prime are excellent, all which help to bridge the lackluster 5-prime and 7-prime. Thus, this system is worthy of a great deal of further exploration in the [[19-limit]].		This EDO has a consistency limit of 21, which is the most impressive out of all the 3-2 [[telicity\|telic]] multiples of [[190537edo]]. It tempers out the [[Archangelic comma]] in the 3-limit, and though this system's 5-limit and 7-limit are rather lackluster for an EDO this size, the representation of the 11-prime is a bit better, and the representations of the 13-prime, 17-prime, and 19-prime are excellent, all which help to bridge the lackluster 5-prime and 7-prime. Thus, this system is worthy of a great deal of further exploration in the [[19-limit]].

	In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system.		In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system, but also a [[metatemperament]] to [[yarman]].

	{{Harmonics in equal\|4191814\|columns=12}}		{{Harmonics in equal\|4191814\|columns=12}}

	[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->		[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->

Aura at 12:03, 23 December 2022

2022-12-23T12:03:00Z

← Older revision		Revision as of 12:03, 23 December 2022
Line 7:		Line 7:
	In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system.		In this system, the [[perfect fifth]] at 2452054\4191814 is divisible by the prime factors of 2, 11, 227 and 491. However, the [[perfect fourth]], at 1739760\4191814, has more prime divisors, namely the prime factors of 2^4, 3, 5, 11 and 659. The latter means that just as in [[159edo]], the perfect fourth is divisible by 33, and thus, this system can offer not only a more accurate version of [[Ozan Yarman]]'s original 79-tone system.

	{{Harmonics in equal\|4191814}}		{{Harmonics in equal\|4191814\|columns=12}}

	[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->		[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->