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]]). | 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 --> | ||
Revision as of 21:23, 4 October 2022
| ← 218edo | 219edo | 220edo → |
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 exceptionally bad 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).