954edo: Difference between revisions

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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.

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.

Beyond the 17-limit, the 954hj val is the most accurate, with lower a [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with warts.

=== 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=12|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)}}

{{Harmonics in equal|954|start=23|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}

{{Harmonics in equal|954|start=34|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}

{{Harmonics in equal|954|start=45|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 }}.

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 {{ED intro}}
-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.
+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.
+Beyond the 17-limit, the 954hj val is the most accurate, with lower a [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with warts.
 === Prime harmonics ===
-{{Harmonics in equal|954|columns=13}}
+{{Harmonics in equal|954}}
-{{Harmonics in equal|954|start=14|columns=17|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}
+{{Harmonics in equal|954|start=12|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)}}
+{{Harmonics in equal|954|start=23|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}
+{{Harmonics in equal|954|start=34|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}
+{{Harmonics in equal|954|start=45|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 }}.