219edo - Revision history

ArrowHead294 at 22:45, 20 February 2025

2025-02-20T22:45:54Z

← Older revision		Revision as of 22:45, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==
	219edo is in[[consistent]] in the [[5-odd-limit]] as well as higher odd limits. Its approximations to lower [[harmonic]]s are ''exceptionally bad'': [[5/1\|5]], [[11/1\|11]], and [[13/1\|13]] are about halfway between its steps, and [[19/1\|19]] and [[23/1\|23]] are off by about a third step. If anything, it can be considered as a 2.3.7.17.29.31 [[subgroup]] tuning. One can see that there are much better alternatives to 219edo if the goal is to mimick just intonation, for example [[212edo]] (being a superset of [[53edo]]) or [[217edo]] (being a superset of [[31edo]]).		219edo is in[[consistent]] in the [[5-odd-limit]] as well as higher odd limits. Its approximations to lower [[harmonic]]s are ''exceptionally bad'': [[5/1\|5]], [[11/1\|11]], and [[13/1\|13]] are about halfway between its steps, and [[19/1\|19]] and [[23/1\|23]] are off by about a third step. If anything, it can be considered as a 2.3.7.17.29.31 [[subgroup]] tuning. One can see that there are much better alternatives to 219edo if the goal is to mimick just intonation, for example [[212edo]] (being a superset of [[53edo]]) or [[217edo]] (being a superset of [[31edo]]).

	The [[patent val]] for 219edo is {{val\| 214 347 509 615 758 810 }}, which [[tempering out\|tempers out]] the following [[comma]]s up to the 13-limit: [[32805/32768]] in the 5-limit; [[243/242]], [[441/440]] and [[65536/65219]] in the 11-limit; [[364/363]] in the 13-limit.		The [[patent val]] for 219edo is {{val\| 214 347 509 615 758 810 }}, which [[tempering out\|tempers out]] the following [[comma]]s up to the 13-limit: [[32805/32768]] in the 5-limit; [[243/242]], [[441/440]] and [[65536/65219]] in the 11-limit; [[364/363]] in the 13-limit.

Lériendil: /* Theory */

2024-12-26T05:10:31Z

Theory

← Older revision		Revision as of 05:10, 26 December 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 219edo factors into {{factorization\|219}}, 219edo contains [[3edo]] and [[73edo]] as its subsets.		Since 219edo factors into {{factorization\|219}}, 219edo contains [[3edo]] and [[73edo]] as its subsets. [[438edo]], which doubles it, provides a strong correction to the 5th harmonic and improves on the 11th and 13th.

FloraC at 07:21, 2 April 2024

2024-04-02T07:21:32Z

← Older revision		Revision as of 07:21, 2 April 2024
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	219edo is in[[consistent]] in the [[5-odd-limit]] as well as higher odd limits. Its approximations to lower [[harmonic]]s are ''exceptionally bad'': [[5/1\|5]], [[11/1\|11]], and [[13/1\|13]] are about halfway between its steps, and [[19/1\|19]] and [[23/1\|23]] are off by about a third step. If anything, it can be considered as a 2.3.7.17.29.31 [[subgroup]] tuning. One can see that there are much better alternatives to 219edo if the goal is to mimick just intonation, for example [[212edo]] (being a superset of [[53edo]]) or [[217edo]] (being a superset of [[31edo]]).		219edo is in[[consistent]] in the [[5-odd-limit]] as well as higher odd limits. Its approximations to lower [[harmonic]]s are ''exceptionally bad'': [[5/1\|5]], [[11/1\|11]], and [[13/1\|13]] are about halfway between its steps, and [[19/1\|19]] and [[23/1\|23]] are off by about a third step. If anything, it can be considered as a 2.3.7.17.29.31 [[subgroup]] tuning. One can see that there are much better alternatives to 219edo if the goal is to mimick just intonation, for example [[212edo]] (being a superset of [[53edo]]) or [[217edo]] (being a superset of [[31edo]]).

	The [[patent val]] for 219edo is {{val\| 214 347 509 615 758 810 }}, which [[tempering out\|tempers out]] the following [[comma]]s up to the 13-limit: [[32805/32768]] in the 5-limit; [[243/242]], [[441/440]] and [[65536/65219]] in the 11-limit; [[364/363]] in the 13-limit~~. with at least a 10% relative error up to the [[29/1\|29th harmonic]] and just below 5% for the [[31/1\|31st harmonic]]~~.		The [[patent val]] for 219edo is {{val\| 214 347 509 615 758 810 }}, which [[tempering out\|tempers out]] the following [[comma]]s up to the 13-limit: [[32805/32768]] in the 5-limit; [[243/242]], [[441/440]] and [[65536/65219]] in the 11-limit; [[364/363]] in the 13-limit.

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

FloraC: Rework (10% relative error isn't sufficient for a comment like "exceptionally bad"; add more specific reasons)

2024-04-02T07:20:56Z

Rework (10% relative error isn't sufficient for a comment like "exceptionally bad"; add more specific reasons)

← Older revision		Revision as of 07:20, 2 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~219edo is the equal division of the octave into 214 parts of 5.4795 cents each.~~		{{EDO intro}}

	== Theory ==		== Theory ==
	219edo is ~~incosistent~~ in the [[5-odd-limit]] as well as higher odd-limits ~~and tempers out the following commas up~~ to ~~the 13-limit~~: ~~32805~~/~~32768 in the~~ 5~~-limit; 243~~/~~242~~, ~~441~~/~~440~~ and ~~65536~~/~~65219 in the 11-limit; 364~~/~~363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615~~\|~~. Its approximations to lower harmonics~~ are ~~<i>exceptionally bad</i> with at least~~ a ~~10% error (relative to the~~ step ~~size) up to the 29th harmonic and just below 5% for the 31st harmonic~~. If anything, it can be considered as a 2.17/3.~~23/11~~.31 subgroup tuning. One can see that there are much better alternatives to ~~219EDO~~ if the goal is to mimick just intonation, for example [[212edo]] (being ~~an extension~~ of [[53edo]]) or [[217edo]] (being ~~an extension~~ of [[31edo]]).		219edo is in[[consistent]] in the [[5-odd-limit]] as well as higher odd limits. Its approximations to lower [[harmonic]]s are ''exceptionally bad'': [[5/1\|5]], [[11/1\|11]], and [[13/1\|13]] are about halfway between its steps, and [[19/1\|19]] and [[23/1\|23]] are off by about a third step. If anything, it can be considered as a 2.3.7.17.29.31 [[subgroup]] tuning. One can see that there are much better alternatives to 219edo if the goal is to mimick just intonation, for example [[212edo]] (being a superset of [[53edo]]) or [[217edo]] (being a superset of [[31edo]]).

			The [[patent val]] for 219edo is {{val\| 214 347 509 615 758 810 }}, which [[tempering out\|tempers out]] the following [[comma]]s up to the 13-limit: [[32805/32768]] in the 5-limit; [[243/242]], [[441/440]] and [[65536/65219]] in the 11-limit; [[364/363]] in the 13-limit. with at least a 10% relative error up to the [[29/1\|29th harmonic]] and just below 5% for the [[31/1\|31st harmonic]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|219}}		{{Harmonics in equal\|219}}

	[[~~Category:Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		=== Subsets and supersets ===
			Since 219edo factors into {{factorization\|219}}, 219edo contains [[3edo]] and [[73edo]] as its subsets.

FloraC: Fix unclear pronoun

2022-10-27T07:20:58Z

Fix unclear pronoun

← Older revision		Revision as of 07:20, 27 October 2022
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	== Theory ==		== Theory ==
	It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).		219edo is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|219}}		{{Harmonics in equal\|219}}

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

Eliora at 16:00, 26 October 2022

2022-10-26T16:00:29Z

← Older revision		Revision as of 16:00, 26 October 2022
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).		219edo is the equal division of the octave into 214 parts of 5.4795 cents each.

			== Theory ==
			It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).

			=== Prime harmonics ===
			{{Harmonics in equal\|219}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:23:46Z

Infobox ET added

← Older revision		Revision as of 21:23, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).		219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).

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

Fredg999 category edits: Categories

2022-07-03T18:34:17Z

ThisIsOutrageous at 21:18, 31 August 2019

2019-08-31T21:18:44Z

← Older revision		Revision as of 21:18, 31 August 2019
Line 1:		Line 1:
	219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[3-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).		219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).

ThisIsOutrageous: Created page with "219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the 3-odd-limit as well as higher odd-limits and tempers out the follo..."

2019-08-31T21:18:26Z

Created page with "219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the 3-odd-limit as well as higher odd-limits and tempers out the follo..."

New page

219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[3-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).

← Older revision		Revision as of 18:34, 3 July 2022
Line 1:		Line 1:
	219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).		219edo is the equal division of the octave into 214 parts of 5.4795 cents each. It is incosistent in the [[5-odd-limit]] as well as higher odd-limits and tempers out the following commas up to the 13-limit: 32805/32768 in the 5-limit; 243/242, 441/440 and 65536/65219 in the 11-limit; 364/363 in the 13-limit. The patent val for 219-EDO is <214 347 509 615\|. Its approximations to lower harmonics are <i>exceptionally bad</i> with at least a 10% error (relative to the step size) up to the 29th harmonic and just below 5% for the 31st harmonic. If anything, it can be considered as a 2.17/3.23/11.31 subgroup tuning. One can see that there are much better alternatives to 219EDO if the goal is to mimick just intonation, for example [[212edo]] (being an extension of [[53edo]]) or [[217edo]] (being an extension of [[31edo]]).

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