219edo: Difference between revisions
Rework (10% relative error isn't sufficient for a comment like "exceptionally bad"; add more specific reasons) |
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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 | 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 === | ||