814edo: Difference between revisions
+RTT table and rank-2 temperaments |
Rework |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
814edo is | 814edo is distinctly [[consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. The equal temperament is [[enfactoring|enfactored]] in the 5-limit, tempering out the [[schisma]] as does 407et. In the 7-limit it tempers out [[2401/2400]] so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171 & 643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|814|columns=11}} | {{Harmonics in equal|814|columns=11}} | ||
=== | === Subsets and supersets === | ||
Since 814 | Since 814 factors into 2 × 11 × 37, 814edo has subset edos {{EDOs| 2, 11, 22, 37, 74, and 407 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 50: | Line 50: | ||
| 3.50 | | 3.50 | ||
|} | |} | ||
* 814et is notable in the 17- and 23-limit | * 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo|764]] in the 17-limit and [[742edo|742i]] in the 23-limit, and is only bettered by [[935edo|935]] in either subgroup. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
| Line 70: | Line 70: | ||
|} | |} | ||
[[Category:Sesquiquartififths]] | [[Category:Sesquiquartififths]] | ||