1776edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
1776edo is [[consistent]] in the 15-odd-limit, and has good representation of it, with errors less than 26%. In the 2.5.7.11.13 subgroup, it is [[Saturation, torsion, and contorsion#Torsion and contorsion|enfactored]] with the same mapping as [[888edo]], and corrects the latter's mapping for harmonic 3. A comma basis for the 13-limit is {4096/4095, 9801/9800, 67392/67375, 250047/250000, 531674/531441}. | 1776edo is [[consistent]] in the 15-odd-limit, and has good representation of it, with errors less than 26%. In the 2.5.7.11.13 subgroup, it is [[Saturation, torsion, and contorsion#Torsion and contorsion|enfactored]] with the same mapping as [[888edo]], and corrects the latter's mapping for harmonic 3. A comma basis for the 13-limit is {4096/4095, 9801/9800, 67392/67375, 250047/250000, 531674/531441}. | ||
In the 5-limit, it supports the [[squarschmidt]] temperament, tempering out the {{monzo|61 4 -29}} comma, and it also tempers out {{monzo|55 -64 -20}}, {{monzo|6, 68, -49}}, {{monzo|116, -60, -9}}. | In the 5-limit, it supports the [[squarschmidt]] temperament, tempering out the {{monzo|61 4 -29}} comma, and it also tempers out {{monzo|55 -64 -20}}, {{monzo|6, 68, -49}}, {{monzo|116, -60, -9}}. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{harmonics in equal|1776}} | {{harmonics in equal|1776}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1776 factors as {{Factorization|1776}}, it has subset edos {{EDOs|1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888}}. | Since 1776 factors as {{Factorization|1776}}, it has subset edos {{EDOs|1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888}}. | ||