225edo: Difference between revisions
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== Theory == | == Theory == | ||
225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]]. It has three mappings possible for the 7-limit: | 225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]]. | ||
In fact, 225edo sets the sequential record for being worst for integer harmonics as a whole, when evaluated using how close are its harmonic errors to <math>1 - \phi</math> = 38.1966%, the golden ratio, the number most difficult to approximate with rationals. While other edos with poor approximation usually end up approximating the square of that harmonic well, 225edo performs worst due to it setting a record of how close its harmonic errors are to 38.1966%. | |||
It has three mappings possible for the 7-limit: | |||
* {{val| 225 357 522 632 }} ([[patent val]]), | * {{val| 225 357 522 632 }} ([[patent val]]), | ||
* {{val| 225 '''356''' 522 '''631''' }} (225bd), | * {{val| 225 '''356''' 522 '''631''' }} (225bd), | ||