954edo: Difference between revisions
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The ''954 equal division'' divides the octave into 954 equal parts of 1.258 cents each. It is a very strong 17-limit system, uniquely [[consistent|consistent]] in the 17-limit, and is the fifteenth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and is also a zeta gap edo. The tuning of the primes to 17 are all flat, and it tempers out the ennealimma, |1 -27 18>, in the 5-limit and 2401/2400 and 4375/4374 in the 7-limit, so that it [[support]]s [[Ragismic_microtemperaments#Ennealimmal|ennealimmal temperament]]. In the 11-limit it tempers out 3025/3024, 9801/9800, 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out 4225/4224 and 10648/10647 and in the 17-limit 2431/2430 and 2601/2600. It supports and gives the optimal patent val for semihemiennealimmal temperament. | The '''954 equal division''' divides the octave into 954 equal parts of 1.258 cents each. It is a very strong 17-limit system, uniquely [[consistent|consistent]] in the 17-limit, and is the fifteenth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and is also a zeta gap edo. The tuning of the primes to 17 are all flat, and it tempers out the ennealimma, |1 -27 18>, in the 5-limit and 2401/2400 and 4375/4374 in the 7-limit, so that it [[support]]s [[Ragismic_microtemperaments#Ennealimmal|ennealimmal temperament]]. In the 11-limit it tempers out 3025/3024, 9801/9800, 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out 4225/4224 and 10648/10647 and in the 17-limit 2431/2430 and 2601/2600. It supports and gives the optimal patent val for semihemiennealimmal temperament. | ||
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[[Category: | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category: | [[Category:Ennealimmal]] | ||
[[Category:Hemiennealimmal]] | |||
[[Category:Semihemiennealimmal]] | |||
Revision as of 01:08, 4 July 2022
The 954 equal division divides the octave into 954 equal parts of 1.258 cents each. It is a very strong 17-limit system, uniquely consistent in the 17-limit, and is the fifteenth zeta integral edo and is also a zeta gap edo. The tuning of the primes to 17 are all flat, and it tempers out the ennealimma, |1 -27 18>, in the 5-limit and 2401/2400 and 4375/4374 in the 7-limit, so that it supports ennealimmal temperament. In the 11-limit it tempers out 3025/3024, 9801/9800, 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out 4225/4224 and 10648/10647 and in the 17-limit 2431/2430 and 2601/2600. It supports and gives the optimal patent val for semihemiennealimmal temperament.