342edo: Difference between revisions

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'''342EDO''' is the [[EDO|equal division of the octave]] into 342 parts of 3.50877 [[cent]]s each (dividing the steps of [[171edo|171EDO]] in half). It is a very strong 11-limit system; not until [[1848edo|1848]] do we reach one with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]]. It is, as one would expect, distinctly consistent through the 11-limit, but goes no higher; nonetheless, it is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]]. A basis for the 11-limit commas is 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit [[Breedsmic_temperaments#Hemitert|hemitert]] temperament, and supports hemiennealimmal.

[[Category:~~Edo~~]]

[[Category:Equal divisions of the octave]]

Revision as of 10:32, 26 September 2020 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,878 edits m Fix category ← Older edit		Revision as of 23:13, 4 December 2020 view source Keenan Pepper category edits (talk \| contribs) Bots 555 edits m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot Newer edit →
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	'''342EDO''' is the [[EDO\|equal division of the octave]] into 342 parts of 3.50877 [[cent]]s each (dividing the steps of [[171edo\|171EDO]] in half). It is a very strong 11-limit system; not until [[1848edo\|1848]] do we reach one with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]]. It is, as one would expect, distinctly consistent through the 11-limit, but goes no higher; nonetheless, it is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]]. A basis for the 11-limit commas is 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit [[Breedsmic_temperaments#Hemitert\|hemitert]] temperament, and supports hemiennealimmal.		'''342EDO''' is the [[EDO\|equal division of the octave]] into 342 parts of 3.50877 [[cent]]s each (dividing the steps of [[171edo\|171EDO]] in half). It is a very strong 11-limit system; not until [[1848edo\|1848]] do we reach one with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]]. It is, as one would expect, distinctly consistent through the 11-limit, but goes no higher; nonetheless, it is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]]. A basis for the 11-limit commas is 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit [[Breedsmic_temperaments#Hemitert\|hemitert]] temperament, and supports hemiennealimmal.

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]