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.

[[Category:~~ennealimmal~~]]

[[Category:~~hemiennealimmal~~]]

[[Category:~~semihemiennealimmal~~]]

954edo is a very strong 17-limit system, [[consistency|distinctly consistent]] in the 17-limit, and is a [[zeta edo|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out|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|start=14|columns=17|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}

{{Harmonics in equal|954|start=31|columns=18|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}

=== Subsets and supersets ===

Since 954 = {{factorization|954}}, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.

[[Category:Ennealimmal]]

[[Category:Hemiennealimmal]]

[[Category:Semihemiennealimmal]]

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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&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.
+{{Infobox ET}}
-[[Category:ennealimmal]]
+{{ED intro}}
-[[Category:hemiennealimmal]]
-[[Category:semihemiennealimmal]]
+edo is a very strong 17-limit system, [[consistency|distinctly consistent]] in the 17-limit, and is a [[zeta edo|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out|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=13}}
+{{Harmonics in equal|954|start=14|columns=17|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}
+{{Harmonics in equal|954|start=31|columns=18|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}
+=== Subsets and supersets ===
+Since 954 = {{factorization|954}}, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.
+[[Category:Ennealimmal]]
+[[Category:Hemiennealimmal]]
+[[Category:Semihemiennealimmal]]