954edo: Difference between revisions

Line 1:

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]], {{monzo| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[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 the semihemiennealimmal temperament.

=== Prime harmonics ===

[[Category:Equal divisions of the octave|###]]

@@ Line 1: / Line 1: @@
-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&gt;, 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]], {{monzo| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[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 the semihemiennealimmal temperament.
+=== Prime harmonics ===
+{{Harmonics in equal|954|columns=11}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->