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]] 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.

Revision as of 12:10, 27 September 2022 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,048 edits It's a zeta peak ← Older edit		Revision as of 22:05, 4 October 2022 view source Plumtree (talk \| contribs) autopatrolled, emailconfirmed 1,976 edits m Infobox ET added Newer edit →
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			{{Infobox ET}}
	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 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.		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 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.