742edo: Difference between revisions
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The ''742 equal division'' divides the octave into 742 equal parts of 1.617 cents each. It is a very strong 19-limit system and a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak tuning]], and is uniquely [[consistent|consistent]] in the 21-limit. It has a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit. | The ''742 equal division'' divides the octave into 742 equal parts of 1.617 cents each. It is a very strong 19-limit system and a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak tuning]], and is uniquely [[consistent|consistent]] in the 21-limit. It has a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit. | ||
It is a multiple of [[53edo]] and [[14edo]]. | |||
[[Category:zeta]] | [[Category:zeta]] | ||
Revision as of 16:48, 1 November 2021
The 742 equal division divides the octave into 742 equal parts of 1.617 cents each. It is a very strong 19-limit system and a zeta peak tuning, and is uniquely consistent in the 21-limit. It has a lower 19-limit relative error than any edo until 1178. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.