616edo - Revision history

ArrowHead294 at 22:39, 20 February 2025

2025-02-20T22:39:06Z

← Older revision		Revision as of 22:39, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|616~~}}		{{ED intro}}

	616edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering. Finally, as every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 ~~cents~~.		616edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering. Finally, as every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057{{c}}.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Rework on theory; adopt template: Factorization

2023-11-02T13:17:02Z

Rework on theory; adopt template: Factorization

← Older revision		Revision as of 13:17, 2 November 2023
Line 2:		Line 2:
	{{EDO intro\|616}}		{{EDO intro\|616}}

	The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		616edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering. Finally, as every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 8:		Line 8:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 616 factors into ~~2<sup>3</sup> × 7 × 11~~, 616edo has subset edos {{EDOs\| 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308 }}.		Since 616 factors into {{factorization\|616}}, 616edo has subset edos {{EDOs\| 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308 }}.

FloraC: Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

2023-10-25T08:17:51Z

Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

← Older revision		Revision as of 08:17, 25 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''616edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		{{EDO intro\|616}}

	[[~~Category:Equal divisions~~ of the ~~octave~~\|~~###~~]] <~~!--~~ 3~~-digit number --~~>		The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

			=== Odd harmonics ===
			{{Harmonics in equal\|616}}

			=== Subsets and supersets ===
			Since 616 factors into 2<sup>3</sup> × 7 × 11, 616edo has subset edos {{EDOs\| 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308 }}.

BudjarnLambeth at 06:41, 9 July 2023

2023-07-09T06:41:28Z

← Older revision		Revision as of 06:41, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

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

BudjarnLambeth at 05:38, 9 July 2023

2023-07-09T05:38:14Z

← Older revision		Revision as of 05:38, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

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

Eliora: oops, 3* 616 = 1848, 3 * 1848 would be 5544

2023-05-14T14:04:38Z

oops, 3* 616 = 1848, 3 * 1848 would be 5544

← Older revision		Revision as of 14:04, 14 May 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3~~1848~~]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|3616]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

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

Eliora: relation to 1848edo

2023-03-09T18:36:13Z

relation to 1848edo

← Older revision		Revision as of 18:36, 9 March 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. As every third step of [[1848edo]], it provides an excellent tuning for the [[KN subgroups\|31848]] 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

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

Plumtree: Infobox ET added

2022-10-04T22:00:04Z

Infobox ET added

← Older revision		Revision as of 22:00, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

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

Fredg999 category edits: Sort key

2022-07-04T01:03:28Z

Sort key

← Older revision		Revision as of 01:03, 4 July 2022
Line 1:		Line 1:
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

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

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:56Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
Line 1:		Line 1:
	'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.		'''616edo''' is the [[EDO\|equal division of the octave]] into 616 parts of 1.948052 [[cent]]s each. It tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It provides an excellent tuning for 2.5/3.7/3.11 subgroup, approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057 cents.

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]