342edo: Difference between revisions
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'''342EDO''' is the [[EDO|equal division of the octave]] into 342 parts of 3.50877 [[cent]]s each (dividing the steps of [[171edo|171EDO]] in half). It is a very strong 11-limit system; not until [[1848edo|1848]] do we reach one with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. It is, as one would expect, distinctly consistent through the 11-limit, but goes no higher; nonetheless, it is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]]. A basis for the 11-limit commas is 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit [[Breedsmic_temperaments#Hemitert|hemitert]] temperament, and supports hemiennealimmal. | '''342EDO''' is the [[EDO|equal division of the octave]] into 342 parts of 3.50877 [[cent]]s each (dividing the steps of [[171edo|171EDO]] in half). It is a very strong 11-limit system; not until [[1848edo|1848]] do we reach one with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. It is, as one would expect, distinctly consistent through the 11-limit, but goes no higher; nonetheless, it is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]]. A basis for the 11-limit commas is 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit [[Breedsmic_temperaments#Hemitert|hemitert]] temperament, and supports hemiennealimmal. | ||
[[Category: | [[Category:Edo]] | ||
Revision as of 10:32, 26 September 2020
342EDO is the equal division of the octave into 342 parts of 3.50877 cents each (dividing the steps of 171EDO in half). It is a very strong 11-limit system; not until 1848 do we reach one with a lower 11-limit relative error. It is, as one would expect, distinctly consistent through the 11-limit, but goes no higher; nonetheless, it is a zeta peak edo. A basis for the 11-limit commas is 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit hemitert temperament, and supports hemiennealimmal.