197edt: Difference between revisions

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197edt can be described as approximately 124.293[[edo]]. This implies that each step of 197edt can be approximated by 7 steps of [[870edo]].

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.

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 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]].

== Harmonics ==

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

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 {{ED intro}}
-edt can be described as approximately 124.293[[edo]]. This implies that each step of 197edt can be approximated by 7 steps of [[870edo]].
+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.
-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 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]].
 == Harmonics ==
-{{Harmonics in equal|197|3|1}}
+{{Harmonics in equal|197|3|1|intervals = prime|columns = 9}}
-{{Harmonics in equal|197|3|1|intervals=prime}}
+{{Harmonics in equal|197|3|1|start = 12|collapsed = 1|intervals = odd}}
 {{Stub}}