954edo: Difference between revisions

(11 intermediate revisions by 7 users not shown)

Line 1:

~~{{novelty}}{{stub}}~~{{Infobox ET}}

954edo is a very strong 17-limit system, ~~uniquely~~ [[consistent]] in the 17-limit, and is a [[~~The Riemann~~ zeta ~~function and tuning #Zeta EDO lists~~|zeta peak, integral and 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.

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 a lower [[relative error]] than any previous equal temperaments in the [[29-limit|29-]] and [[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 [[wart]]s.

=== Prime harmonics ===

{{Harmonics in equal|954|start=12|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}

=== ~~Divisors~~ ===

=== Subsets and supersets ===

Since 954 = 2 × 3<sup>2</sup> × 53, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.

Since 954 factors into primes as {{nowrap| 2 × 3<sup>2</sup> × 53 }}, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.

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

[[Category:Ennealimmal]]

[[Category:Hemiennealimmal]]

[[Category:Semihemiennealimmal]]

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|954}}
+{{ED intro}}
-edo is a very strong 17-limit system, uniquely [[consistent]] in the 17-limit, and is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and 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.
+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 a lower [[relative error]] than any previous equal temperaments in the [[29-limit|29-]] and [[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 [[wart]]s.
 === Prime harmonics ===
-{{Harmonics in equal|954|columns=11}}
+{{Harmonics in equal|954}}
+{{Harmonics in equal|954|start=12|collapsed=1|title=Approximation of prime harmonics in 954edo (continued)}}
-=== Divisors ===
+=== Subsets and supersets ===
-Since 954 = 2 × 3<sup>2</sup> × 53, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.
+Since 954 factors into primes as {{nowrap| 2 × 3<sup>2</sup> × 53 }}, 954edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Ennealimmal]]
 [[Category:Hemiennealimmal]]
 [[Category:Semihemiennealimmal]]