764edo: Difference between revisions
→Regular temperament properties: +list of temperaments |
Cleanup |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
764edo is a very strong 17-limit system distinctly [[consistent]] to the 17-odd-limit, and is the fourteenth [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]]. In the 5-limit it tempers out the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit | 764edo is a very strong 17-limit system distinctly [[consistent]] to the 17-odd-limit, and is the fourteenth [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]]. In the 5-limit it tempers out the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit 2431/2430, 2500/2499, 4914/4913 and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 61: | Line 61: | ||
| 3.36 | | 3.36 | ||
|} | |} | ||
764et is the first equal temperament past [[684edo|684]] with a lower 13-limit absolute error, and is only bettered by [[935edo|935]]. It is also the first equal temperament past [[742edo|742]] with a lower 17-limit absolute error, and is only bettered by [[814edo|814]]. | * 764et is the first equal temperament past [[684edo|684]] with a lower 13-limit absolute error, and is only bettered by [[935edo|935]]. It is also the first equal temperament past [[742edo|742]] with a lower 17-limit absolute error, and is only bettered by [[814edo|814]]. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
| Line 97: | Line 97: | ||
|} | |} | ||
[[Category:Abigail]] | [[Category:Abigail]] | ||