494edo: Difference between revisions

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The ''494 equal division'' is a very strong [[13-limit|13]] and [[17-limit]] equal temperament. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]] and uniquely [[consistent]] through the 17-limit. It [[tempering_out|tempers out]] the enneadeca, |-14 -19 19>, the [[Tricot|tricot comma]], |39 -29 3>, and the [[kwazy_comma|kwazy comma]], |-53 10 16>, in the [[5-limit]]. In the [[7-limit]], it tempers out 4375/4374 and 703125/702464; in the [[11-limit]] 3025/3024 and 9801/9800; in the [[13-limit]] 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until [[1506edo|1506]] do we reach a division with a lower 13- or 17-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], and it is the first past [[72edo|72]] with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.

The ''494 equal division'' is a very strong [[13-limit|13]] and [[17-limit]] equal temperament. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the 17-limit. It [[tempering_out|tempers out]] the enneadeca, |-14 -19 19>, the [[Tricot|tricot comma]], |39 -29 3>, and the [[kwazy_comma|kwazy comma]], |-53 10 16>, in the [[5-limit]]. In the [[7-limit]], it tempers out 4375/4374 and 703125/702464; in the [[11-limit]] 3025/3024 and 9801/9800; in the [[13-limit]] 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until [[1506edo|1506]] do we reach a division with a lower 13- or 17-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], and it is the first past [[72edo|72]] with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.

see also <span style="">[[Table_of_494edo_intervals|Table of 494edo intervals]]</span> [[Category:17-limit]]

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	The ''494 equal division'' is a very strong [[13-limit\|13]] and [[17-limit]] equal temperament. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] and uniquely [[consistent]] through the 17-limit. It [[tempering_out\|tempers out]] the enneadeca, \|-14 -19 19>, the [[Tricot\|tricot comma]], \|39 -29 3>, and the [[kwazy_comma\|kwazy comma]], \|-53 10 16>, in the [[5-limit]]. In the [[7-limit]], it tempers out 4375/4374 and 703125/702464; in the [[11-limit]] 3025/3024 and 9801/9800; in the [[13-limit]] 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until [[1506edo\|1506]] do we reach a division with a lower 13- or 17-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and it is the first past [[72edo\|72]] with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.		The ''494 equal division'' is a very strong [[13-limit\|13]] and [[17-limit]] equal temperament. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the 17-limit. It [[tempering_out\|tempers out]] the enneadeca, \|-14 -19 19>, the [[Tricot\|tricot comma]], \|39 -29 3>, and the [[kwazy_comma\|kwazy comma]], \|-53 10 16>, in the [[5-limit]]. In the [[7-limit]], it tempers out 4375/4374 and 703125/702464; in the [[11-limit]] 3025/3024 and 9801/9800; in the [[13-limit]] 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until [[1506edo\|1506]] do we reach a division with a lower 13- or 17-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]], and it is the first past [[72edo\|72]] with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.

	see also <span style="">[[Table_of_494edo_intervals\|Table of 494edo intervals]]</span> [[Category:17-limit]]		see also <span style="">[[Table_of_494edo_intervals\|Table of 494edo intervals]]</span> [[Category:17-limit]]