764edo: Difference between revisions

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~~The '''~~764 ~~equal division''' divides the octave into 764 equal parts of 1.571 cents each. It~~ is a very strong 17-limit system distinctly consistent to the 17-limit, and is the fourteenth [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta integral ~~division~~]]. 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 [[~~Ragismic_microtemperaments#Abigail|~~abigail ~~temperament~~]] in the 11-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 ===

[[Category:Equal divisions of the octave|###]]

[[Category:Zeta]]

[[Category:~~Todo:expand~~]]

[[Category:Abigail]]

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 {{Infobox ET}}
-The '''764 equal division''' divides the octave into 764 equal parts of 1.571 cents each. It is a very strong 17-limit system distinctly consistent to the 17-limit, and is the fourteenth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral division]]. 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 [[Ragismic_microtemperaments#Abigail|abigail temperament]] in the 11-limit.
+{{EDO intro|764}}
+edo 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.
-{{Primes in edo|764}}
+=== Prime harmonics ===
+{{Harmonics in equal|764|columns=11}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Zeta]]
-[[Category:Todo:expand]]
+[[Category:Abigail]]