342edo: Difference between revisions

Line 1:

~~The~~ '''~~342~~''' equal division ~~divides~~ the steps of [[171edo|~~171~~]] in half~~, dividing the octave into 342 intervals of 3.509 cents each~~. 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]]

Revision as of 00:00, 17 July 2018 view source Wikispaces>FREEZE No edit summary ← Older edit		Revision as of 06:17, 21 April 2019 view source Xenllium (talk \| contribs) autopatrolled, emailconfirmed 5,024 edits No edit summary Tags: Mobile edit Mobile web edit Newer edit →
Line 1:		Line 1:
	~~The~~ '''~~342~~''' equal division ~~divides~~ the steps of [[171edo\|~~171~~]] in half~~, dividing the octave into 342 intervals of 3.509 cents each~~. 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]]