K*N subgroups: Difference between revisions
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For example, to find the 7-limit 2*6 subgroup we first find {{nowrap|''m'' {{=}} 3 × 5 × 7 {{=}} 105}}. The subgroup of Eu(105) consisting of those intervals mapped to an even number by {{vector|12 19 28 34}} is 2.5.7. The subgroup of Eu(105<sup>2</sup>) is 2.9.5.7, not the same. However, the subgroup of Eu(105<sup>3</sup>) is again 2.9.5.7. If to this we add 81/80, we still obtain 2.9.5.7. It is clear this is maximal, as 3 is mapped by 12et to an odd number (19), and the rest of the values are prime. | For example, to find the 7-limit 2*6 subgroup we first find {{nowrap|''m'' {{=}} 3 × 5 × 7 {{=}} 105}}. The subgroup of Eu(105) consisting of those intervals mapped to an even number by {{vector|12 19 28 34}} is 2.5.7. The subgroup of Eu(105<sup>2</sup>) is 2.9.5.7, not the same. However, the subgroup of Eu(105<sup>3</sup>) is again 2.9.5.7. If to this we add 81/80, we still obtain 2.9.5.7. It is clear this is maximal, as 3 is mapped by 12et to an odd number (19), and the rest of the values are prime. | ||
[[Category: | [[Category:Algorithms]] | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category: | [[Category:Regular temperament theory]] | ||