2022edo: Difference between revisions
Cleanup |
Rework theory; +subsets and supersets |
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== Theory == | == Theory == | ||
2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice. | 2022edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Nonetheless, it offers good appoximations of the 2.3.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice. | ||
In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo| -90 -15 49 }} comma. | In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo| -90 -15 49 }} comma. | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2022|columns=11}} | {{Harmonics in equal|2022|columns=11}} | ||
=== Subsets and supersets === | |||
Since 2022 factors into {{factorization|2022}}, 2022edo has subset edos 2, 3, 6, 337, 674, and 1011. | |||
== Regular temperament properties == | == Regular temperament properties == | ||