4004edo: Difference between revisions
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{{ | {{ED intro}} | ||
4004edo has an extremely accurate [[5/4]], as it is a [[convergent]] to the approximation of log<sub>2</sub>5. Unfortunately it is consistent only this far, in the [[5-odd-limit]]. | 4004edo has an extremely accurate [[5/4]], as it is a [[convergent]] to the approximation of log<sub>2</sub>5. Unfortunately it is consistent only this far, in the [[5-odd-limit]]. | ||
In higher limits, there is a number of representations to be considered. The 2.5.13/11 subgroup is very precise, where 4004edo tempers out 2.5.13/11 {{monzo|17 -4 -32}}. Alternately, 2.7.11.13.19 can be considered as an all-sharp system, and 2.3.17.19.23 as an all-flat system. In the 2.3.17, it tempers out {{monzo|0 49 -19}}, and in 2.3.5.17, 531441/531250. | In higher limits, there is a number of representations to be considered. The 2.5.13/11 subgroup is very precise, where 4004edo tempers out 2.5.13/11 {{monzo|17 -4 -32}}. Alternately, 2.7.11.13.19 can be considered as an all-sharp system, and 2.3.17.19.23 as an all-flat system. In the 2.3.17, it tempers out {{monzo|0 49 -19}}, and in 2.3.5.17, 531441/531250. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|4004}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 4004edo factors as {{Factorization|4004}}, it has subset edos {{EDOs|1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002}}. | Since 4004edo factors as {{Factorization|4004}}, it has subset edos {{EDOs|1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002}}. | ||