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 ==