496edo - Revision history

Eliora: That "compound scale" is not really a temperament so moving accordingly

2026-05-10T21:30:02Z

That "compound scale" is not really a temperament so moving accordingly

← Older revision		Revision as of 21:30, 10 May 2026
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	{{ED intro}}		{{ED intro}}

	496edo is [[enfactoring\|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13~~. As such, in the 11-limit it [[support]]s a compound of two chains of 11-limit [[bischismic]] temperaments~~. In the 13-limit patent val, it tempers out [[4225/4224]].		== Theory ==
			496edo is [[enfactoring\|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. In the 13-limit patent val, it tempers out [[4225/4224]].

	496edo is good with the 2.3.11.19 [[subgroup]]. For higher limits, it has good approximations of [[31/1\|31]], [[37/1\|37]], and [[47/1\|47]]. In the 2.3.11.19 subgroup, it tempers out 131072/131043.		496edo is good with the 2.3.11.19 [[subgroup]]. For higher limits, it has good approximations of [[31/1\|31]], [[37/1\|37]], and [[47/1\|47]]. In the 2.3.11.19 subgroup, it tempers out 131072/131043.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	496 is the 3rd {{w\|perfect number}}, factoring into {{factorization\|496}}. Its nontrivial divisors are {{EDOs\| 2, 4, 8, 16, 31, 62, 124, 248 }}, the most notable being 31.		496 is the 3rd {{w\|perfect number}}, factoring into {{factorization\|496}}. Its nontrivial divisors are {{EDOs\| 2, 4, 8, 16, 31, 62, 124, 248 }}, the most notable being 31.

			== Scales ==
			Since 496edo is enfactored 248edo, in the 11-limit it can represent a [[compound scale\|compound]] of two chains of 11-limit [[bischismic]] temperaments, interlaced.

ArrowHead294 at 22:58, 20 February 2025

2025-02-20T22:58:48Z

← Older revision		Revision as of 22:58, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|496~~}}		{{ED intro}}

	496edo is [[enfactoring\|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. As such, in the 11-limit it [[support]]s a compound of two chains of 11-limit [[bischismic]] temperaments. In the 13-limit patent val, it tempers out [[4225/4224]].		496edo is [[enfactoring\|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. As such, in the 11-limit it [[support]]s a compound of two chains of 11-limit [[bischismic]] temperaments. In the 13-limit patent val, it tempers out [[4225/4224]].

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T13:57:09Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 13:57, 2 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|496}}		{{EDO intro\|496}}
	~~==Theory==~~
	496edo is strongly related to the [[248edo]], but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.

	496edo is ~~good~~ with the ~~2.3~~.11~~.19 subgroup, for low~~-~~complexity just intonation. Higher limits that~~ it ~~appreciates are 31, 37, and 47~~. In the ~~2.3.11.19 subgroup~~, ~~496edo~~ tempers out ~~131072~~/~~131043~~.		496edo is [[enfactoring\|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. As such, in the 11-limit it [[support]]s a compound of two chains of 11-limit [[bischismic]] temperaments. In the 13-limit patent val, it tempers out [[4225/4224]].

	~~496~~ is the ~~3rd perfect number~~, ~~and its divisors are {{EDOs~~\|1, 2, ~~4, 8, 16, 31, 62, 124, 248}}, the most notable being 31~~.		496edo is good with the 2.3.11.19 [[subgroup]]. For higher limits, it has good approximations of [[31/1\|31]], [[37/1\|37]], and [[47/1\|47]]. In the 2.3.11.19 subgroup, it tempers out 131072/131043.
	~~===Odd harmonics===~~
	~~{{harmonics in equal\|496}}~~

	~~[[Category:Equal divisions of~~ the ~~octave~~\|~~###]] <!-- 3-digit~~ number ~~-->~~		=== Odd harmonics ===
			{{Harmonics in equal\|496}}

			=== Subsets and supersets ===
			496 is the 3rd {{w\|perfect number}}, factoring into {{factorization\|496}}. Its nontrivial divisors are {{EDOs\| 2, 4, 8, 16, 31, 62, 124, 248 }}, the most notable being 31.

BudjarnLambeth at 06:37, 9 July 2023

2023-07-09T06:37:18Z

← Older revision		Revision as of 06:37, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|496}}		{{EDO intro\|496}}
	==Theory==		==Theory==

BudjarnLambeth at 05:44, 9 July 2023

2023-07-09T05:44:02Z

← Older revision		Revision as of 05:44, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|496}}		{{EDO intro\|496}}
	==Theory==		==Theory==

Eliora: /* Theory */ cleanup

2023-01-05T16:32:55Z

Theory: cleanup

← Older revision		Revision as of 16:32, 5 January 2023
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	{{EDO intro\|496}}		{{EDO intro\|496}}
	==Theory==		==Theory==
	496edo is strongly related to the [[248edo]], but the patent vals differ on the mapping for 13~~. contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo~~. As such, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.		496edo is strongly related to the [[248edo]], but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.

	496edo is good with the 2.3.11.19 subgroup, for low-complexity just intonation. Higher limits that it appreciates are 31, 37, and 47. In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.		496edo is good with the 2.3.11.19 subgroup, for low-complexity just intonation. Higher limits that it appreciates are 31, 37, and 47. In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.

	496 is the 3rd perfect number, and its divisors are {{EDOs\|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.		496 is the 3rd perfect number, and its divisors are {{EDOs\|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.
	===~~Harmonics~~===		===Odd harmonics===
	{{harmonics in equal\|496}}		{{harmonics in equal\|496}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Eliora at 22:45, 28 November 2022

2022-11-28T22:45:07Z

← Older revision		Revision as of 22:45, 28 November 2022
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	{{Infobox ET}}		{{Infobox ET}}
	496 ~~EDO divides the octave into steps of 2.42 cents each.~~		{{EDO intro\|496}}

	==Theory==		==Theory==
	~~{{primes in edo\|496\|columns=15}}~~		496edo is strongly related to the [[248edo]], but the patent vals differ on the mapping for 13. contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo. As such, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.
	496edo is ~~good with~~ the 2~~.3.~~11.~~19 subgroup~~, ~~for low~~-~~complexity just intonation~~. ~~Higher limits that it appreciates are 31~~, 37, ~~and 47~~.

	In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.		496edo is good with the 2.3.11.19 subgroup, for low-complexity just intonation. Higher limits that it appreciates are 31, 37, and 47. In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.

	496 is the 3rd perfect number, and its divisors are {{EDOs\|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.		496 is the 3rd perfect number, and its divisors are {{EDOs\|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.
			===Harmonics===
	~~496edo is contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo. As such,~~ in ~~the 11-limit it is a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.~~		{{harmonics in equal\|496}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:58:04Z

Infobox ET added

← Older revision		Revision as of 21:58, 4 October 2022
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			{{Infobox ET}}
	496 EDO divides the octave into steps of 2.42 cents each.		496 EDO divides the octave into steps of 2.42 cents each.

Fredg999 category edits: Categories

2022-07-04T01:00:15Z

Eliora at 17:07, 24 January 2022

2022-01-24T17:07:33Z

← Older revision		Revision as of 17:07, 24 January 2022
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	==Theory==		==Theory==
	{{primes in edo\|496\|columns=15}}		{{primes in edo\|496\|columns=15}}
			496edo is good with the 2.3.11.19 subgroup, for low-complexity just intonation. Higher limits that it appreciates are 31, 37, and 47.

			In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.

			496 is the 3rd perfect number, and its divisors are {{EDOs\|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.

			496edo is contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo. As such, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.

← Older revision		Revision as of 01:00, 4 July 2022
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	496edo is contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo. As such, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.		496edo is contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo. As such, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.

			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->