219edo: Difference between revisions

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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|###]]

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	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 -->