169edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-19T18:05:52Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:05, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|169~~}}		{{ED intro}}

	169edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 169 268 392 }} ([[patent val]]) and {{val\| 169 268 393 }} (169c).		169edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 169 268 392 }} ([[patent val]]) and {{val\| 169 268 393 }} (169c).

FloraC: Note the subset is unique

2024-05-29T08:43:33Z

Note the subset is unique

← Older revision		Revision as of 08:43, 29 May 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 169 factors into {{factorization\|169}}, 169edo contains [[13edo]] as its subset. [[338edo]], which doubles it, provides good correction for the approximations of harmonics [[5/1\|5]] and [[7/1\|7]].		Since 169 factors into {{factorization\|169}}, 169edo contains [[13edo]] as its only nontrivial subset. [[338edo]], which doubles it, provides good correction for the approximations of harmonics [[5/1\|5]] and [[7/1\|7]].

FloraC: +subsets and supersets

2024-04-26T08:16:11Z

+subsets and supersets

← Older revision		Revision as of 08:16, 26 April 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|169}}		{{Harmonics in equal\|169}}

			=== Subsets and supersets ===
			Since 169 factors into {{factorization\|169}}, 169edo contains [[13edo]] as its subset. [[338edo]], which doubles it, provides good correction for the approximations of harmonics [[5/1\|5]] and [[7/1\|7]].

FloraC: Cleanup

2024-04-26T08:14:36Z

Cleanup

← Older revision		Revision as of 08:14, 26 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|169}}		{{EDO intro\|169}}
	~~==Theory==~~
	It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (patent val) and <169 268 393\| (169c). Using the patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the [[Hemifamity temperaments\|buzzard temperament]]. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.

	=== ~~Harmonics~~ ===		169edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 169 268 392 }} ([[patent val]]) and {{val\| 169 268 393 }} (169c).

			Using the patent val, it tempers out the [[sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; [[245/243]], [[1029/1024]], and 9765625/9633792 in the 7-limit; [[385/384]], [[441/440]], [[896/891]], and 312500/307461 in the 11-limit; [[676/675]], 975/968, and 1625/1617 in the 13-limit. Using the 169d val, it tempers out [[225/224]], 51200/50421, and 1071875/1062882 in the 7-limit; [[2200/2187]], 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], and 676/675 in the 13-limit.

			Using the 169cdf val, it tempers out the [[valentine comma]], 1990656/1953125 and the [[vulture comma]], 10485760000/10460353203 in the 5-limit; [[1728/1715]], [[5120/5103]], and 235298/234375 in the 7-limit; [[176/175]], [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit; [[351/350]], [[352/351]], 640/637, and 676/675 in the 13-limit, [[support]]ing the [[buzzard]] temperament.

			=== Prime harmonics ===
	{{Harmonics in equal\|169}}		{{Harmonics in equal\|169}}

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

Aura at 19:11, 4 October 2022

2022-10-04T19:11:47Z

← Older revision		Revision as of 19:11, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|169}}		{{EDO intro\|169}}
	==Theory==		==Theory==

Fredg999 category edits: Sort key

2022-07-02T21:17:31Z

Sort key

← Older revision		Revision as of 21:17, 2 July 2022
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	{{Harmonics in equal\|169}}		{{Harmonics in equal\|169}}

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

Eliora: fixed because wtf

2022-05-17T19:59:53Z

fixed because wtf

← Older revision		Revision as of 19:59, 17 May 2022
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	=~~<span style~~=~~"color: #76653a; font-family: 'Times New Roman',Times,serif; font-size: 113%;">169 equal divisions per octave</span>~~=		{{EDO intro\|169}}
	~~'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each.~~ It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (patent val) and <169 268 393\| (169c). Using the patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the [[Hemifamity temperaments\|buzzard temperament]]. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.		==Theory==
			It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (patent val) and <169 268 393\| (169c). Using the patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the [[Hemifamity temperaments\|buzzard temperament]]. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.

			=== Harmonics ===
			{{Harmonics in equal\|169}}

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

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

2020-12-04T23:13:12Z

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
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	'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (patent val) and <169 268 393\| (169c). Using the patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the [[Hemifamity temperaments\|buzzard temperament]]. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.		'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (patent val) and <169 268 393\| (169c). Using the patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the [[Hemifamity temperaments\|buzzard temperament]]. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.

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

Xenllium: /* 169 equal divisions per octave */

2018-12-17T00:08:36Z

169 equal divisions per octave

← Older revision		Revision as of 00:08, 17 December 2018
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	=<span style="color: #76653a; font-family: 'Times New Roman',Times,serif; font-size: 113%;">169 equal divisions per octave</span>=		=<span style="color: #76653a; font-family: 'Times New Roman',Times,serif; font-size: 113%;">169 equal divisions per octave</span>=
	'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (~~optimal~~ patent val) and <169 268 393\| (169c). Using the ~~optimal~~ patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit. Using the ~~169c~~ val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; ~~126~~/~~125~~, ~~1029~~/~~1024~~, and / in the 7-limit; ~~896~~/~~891~~, ~~2401~~/~~2376~~, 8019/8000, and ~~14700~~/~~14641~~ in the 11-limit. Using the ~~alternative 169cd~~ val, it tempers out ~~1728~~/~~1715~~, ~~5120~~/~~5103~~, and ~~235298~~/~~234375~~ in the 7-limit; ~~176~~/~~175~~, ~~540~~/~~539~~, ~~8019~~/~~8000~~, and ~~43923~~/~~43904~~ in the 11-limit.		'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (patent val) and <169 268 393\| (169c). Using the patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the [[Hemifamity temperaments\|buzzard temperament]]. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.

	[[Category:Edo]]		[[Category:Edo]]

Xenllium: /* 169 equal divisions per octave */

2018-12-03T06:38:15Z

169 equal divisions per octave

← Older revision		Revision as of 06:38, 3 December 2018
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	=<span style="color: #~~b6a140~~; font-family: 'Times New Roman',Times,serif; font-size: 113%;">169 equal divisions per octave</span>=		=<span style="color: #76653a; font-family: 'Times New Roman',Times,serif; font-size: 113%;">169 equal divisions per octave</span>=
	'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (optimal patent val) and <169 268 393\| (169c). Using the optimal patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit. Using the 169c val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit ~~using~~ the ~~alternative 169cd val~~.		'''169edo''' is the [[EDO\|equal division of the octave]] into 169 parts of 7.1006 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392\| (optimal patent val) and <169 268 393\| (169c). Using the optimal patent val, it tempers out the [[Sycamore family\|sycamore comma]], 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit. Using the 169c val, it tempers out the valentine comma, 1990656/1953125 and the [[Vulture family\|vulture comma]], 10485760000/10460353203 in the 5-limit; 126/125, 1029/1024, and / in the 7-limit; 896/891, 2401/2376, 8019/8000, and 14700/14641 in the 11-limit. Using the alternative 169cd val, it tempers out 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit.

	[[Category:Edo]]		[[Category:Edo]]