764edo: Difference between revisions
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the same prec is now estimated by EDO magnitude; show 8 columns, so also readers can see the consistency limit |
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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. | 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. | ||
{{Primes in edo|764}} | {{Primes in edo|764}} | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Todo:expand]] | [[Category:Todo:expand]] | ||
Revision as of 01:06, 4 July 2022
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 zeta integral division. In the 5-limit it tempers out the hemithirds comma, [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 abigail temperament in the 11-limit.
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