1848edo: Difference between revisions
→Rank-2 temperaments: +Major arcana |
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It provides the [[optimal patent val]] for 11-limit atomic. | It provides the [[optimal patent val]] for 11-limit atomic. | ||
1848edo is unique in that it consistently tunes both [[81/80]] and [[64/63]] to an integer fraction of the octave, 1/56th and 1/44th respectively. As a corollary, it supports barium and ruthenium temperaments, which have periods 56 and 44 respectively. While every edo that is a multiple of 616 shares the property of directly mapping 81/80 and 64/63 to fractions of the octave, 1848edo is unique due to its strength in simple harmonics and it actually shows how 81/80 and 64/63 are produced. | |||
=== Subsets and supersets === | |||
1848 factors as 2<sup>3</sup> × 3 × 7 × 11. It is a superabundant number in the no-fives subgroup, that is, if only numbers not divisible by 5 are counted. Its divisors are {{EDOs| 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 231, 264, 308, 462, 616, 924 }}. | 1848 factors as 2<sup>3</sup> × 3 × 7 × 11. It is a superabundant number in the no-fives subgroup, that is, if only numbers not divisible by 5 are counted. Its divisors are {{EDOs| 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 231, 264, 308, 462, 616, 924 }}. | ||
[[5544edo]], which divides the edostep into three, provides a good correction for 13- and the 17-limit. | |||
=== Prime harmonics === | === Prime harmonics === | ||