197edt: Difference between revisions

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~~'''197 equal divisions~~ of ~~the tritave''' ('''~~197edt~~''') is the~~ [[~~nonoctave~~]] [[~~tuning system~~]] ~~derived by dividing the~~ [[~~tritave~~]] (3~~/1) into 197 equal steps of approximately 9~~.~~655~~ [[~~cent~~]]~~s each~~, or the ~~197th root of 3~~.

197edt can be described as approximately 124.293[[edo]]. This implies that each step of 197edt can be approximated by 3 steps of [[373edo]], 7 steps of [[870edo]], or 10 steps of [[1243edo]]. In the 2.3.7.11.13.17.19 [[subgroup]], these are represented by the 373g, 870df, and 1243g warted [[val]]s respectively.

~~197edt can be described as approximately 124~~.~~293~~[[~~edo~~]]. ~~This implies that each step of 39edt~~ can be ~~approximated~~ by 7 ~~steps of~~ [[~~870edo~~]].

It is a very strong no-twos, no-fives 19-limit system, though it additionally represents the interval of [[5/4]] very well, and the 8th harmonic decently. It supports [[mebsuta]] temperament, as well as various extensions thereof which slice the generator in thirds. Remarkably, it tempers out, and can be defined in this subgroup by tempering out, all the [[Don Page comma]]s among the intervals [[9/7]], [[11/9]], [[13/11]], [[17/13]], [[19/17]], and [[21/19]], forming a complete tritave-spanning 7:9:11:13:17:19:21 [[heptad]].

~~It is a very strong no-twos, no-fives 19-limit system.~~

== Harmonics ==

==Harmonics==

{{Harmonics in equal|197|3|1|start = 12|collapsed = 1|intervals = odd}}

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 {{Infobox ET}}
+{{ED intro}}
-'''197 equal divisions of the tritave''' ('''197edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 197 equal steps of approximately 9.655 [[cent]]s each, or the 197th root of 3.
+edt can be described as approximately 124.293[[edo]]. This implies that each step of 197edt can be approximated by 3 steps of [[373edo]], 7 steps of [[870edo]], or 10 steps of [[1243edo]]. In the 2.3.7.11.13.17.19 [[subgroup]], these are represented by the 373g, 870df, and 1243g warted [[val]]s respectively.
-edt can be described as approximately 124.293[[edo]]. This implies that each step of 39edt can be approximated by 7 steps of [[870edo]].
+It is a very strong no-twos, no-fives 19-limit system, though it additionally represents the interval of [[5/4]] very well, and the 8th harmonic decently. It supports [[mebsuta]] temperament, as well as various extensions thereof which slice the generator in thirds. Remarkably, it tempers out, and can be defined in this subgroup by tempering out, all the [[Don Page comma]]s among the intervals [[9/7]], [[11/9]], [[13/11]], [[17/13]], [[19/17]], and [[21/19]], forming a complete tritave-spanning 7:9:11:13:17:19:21 [[heptad]].
-It is a very strong no-twos, no-fives 19-limit system.
+== Harmonics ==
+{{Harmonics in equal|197|3|1|intervals = prime|columns = 9}}
-==Harmonics==
+{{Harmonics in equal|197|3|1|start = 12|collapsed = 1|intervals = odd}}
-{{Harmonics in equal|197|3|1|intervals=prime}}
 {{Stub}}