1178edo: Difference between revisions
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The 1178 equal tuning divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak, integral and gap edo]]. It is also distinctly consistent through to the 21 odd limit, and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. It is also notable for being divisible by both 19 and 31. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984. | The '''1178 equal tuning''' divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak, integral and gap edo]]. It is also distinctly consistent through to the 21 odd limit, and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. It is also notable for being divisible by both 19 and 31. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984. | ||
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Revision as of 01:14, 4 July 2022
The 1178 equal tuning divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a zeta peak, integral and gap edo. It is also distinctly consistent through to the 21 odd limit, and is the first edo past 742 with a lower 19-limit relative error. It is also notable for being divisible by both 19 and 31. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984.