1059edo: Difference between revisions

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1059edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, lending itself to a 2.9.5.7 [[subgroup]] interpretation.

1059edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, lending itself to a 2.9.5.7.13 [[subgroup]] interpretation.

103 steps of 1059edo represent a continued fraction approximation for the [[secor]] generator interval in the form of [[46/43]]. In the 2.3.5.7.11.23.43 subgroup this results in a 329 & 1059 temperament. The comma basis for such (assuming both patent vals) is 1376/1375, 2646/2645, 172032/171875, 16401231/16384000, 51759729/51536320.

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=== Subsets and supersets ===

[[2118edo]], which divides the edostep in two, provides a good correction for 3rd and 11th harmonics.

Since 1059 factors into {{factorization|1059}}, 1059edo contains [[3edo]] and [[353edo]] as subsets. [[2118edo]], which divides the edostep in two, provides a good correction for 3rd and 11th harmonics.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1059}}
+{{ED intro}}
-edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, lending itself to a 2.9.5.7 [[subgroup]] interpretation.
+edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, lending itself to a 2.9.5.7.13 [[subgroup]] interpretation.
 steps of 1059edo represent a continued fraction approximation for the [[secor]] generator interval in the form of [[46/43]]. In the 2.3.5.7.11.23.43 subgroup this results in a 329 & 1059 temperament. The comma basis for such (assuming both patent vals) is 1376/1375, 2646/2645, 172032/171875, 16401231/16384000, 51759729/51536320.
@@ Line 10: / Line 10: @@
 === Subsets and supersets ===
-[[2118edo]], which divides the edostep in two, provides a good correction for 3rd and 11th harmonics.
+Since 1059 factors into {{factorization|1059}}, 1059edo contains [[3edo]] and [[353edo]] as subsets. [[2118edo]], which divides the edostep in two, provides a good correction for 3rd and 11th harmonics.