197edt - Revision history

Lériendil at 08:38, 31 December 2024

2024-12-31T08:38:43Z

← Older revision		Revision as of 08:38, 31 December 2024
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	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 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 supports [[mebsuta]] temperament, as well as various extensions thereof which slice the generator in thirds. Remarkably, it tempers 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, 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 ==

Lériendil: added more details

2024-12-31T08:38:15Z

added more details

← Older revision		Revision as of 08:38, 31 December 2024
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	{{ED intro}}		{{ED intro}}

	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 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 ==

BudjarnLambeth: /* Harmonics */ copied format from 209edt

2024-10-05T12:10:30Z

Harmonics: copied format from 209edt

← Older revision		Revision as of 12:10, 5 October 2024
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	== Harmonics ==		== 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}}		{{Stub}}

Lériendil at 11:37, 5 October 2024

2024-10-05T11:37:04Z

← Older revision		Revision as of 11:37, 5 October 2024
Line 4:		Line 4:
	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 7 steps of [[870edo]].

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

	== Harmonics ==		== Harmonics ==

Lériendil: more useful to show primes

2024-10-05T11:35:43Z

more useful to show primes

← Older revision		Revision as of 11:35, 5 October 2024
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	== Harmonics ==		== Harmonics ==
	{{Harmonics in equal		{{Harmonics in equal\|197\|3\|1}}
	\| ~~steps =~~ 197		{{Harmonics in equal\|197\|3\|1\|intervals=prime}}
	\| ~~num =~~ 3
	\| ~~denom =~~ 1
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 197
	\| ~~num =~~ 3
	\| ~~denom =~~ 1
	\| ~~start~~ = 12
	~~\| collapsed = 1~~
	}}

	{{~~stub~~}}		{{Stub}}

BudjarnLambeth at 09:55, 5 October 2024

2024-10-05T09:55:33Z

← Older revision		Revision as of 09:55, 5 October 2024
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	It is a very strong no-twos, no-fives 19-limit system.		It is a very strong no-twos, no-fives 19-limit system.

	~~== Intervals ==~~
	~~{{Interval table}}~~

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Intro inter harm

2024-10-05T09:33:50Z

Intro inter harm

@@ Line 6: / Line 6: @@
 It is a very strong no-twos, no-fives 19-limit system.
-==Harmonics==
+== Intervals ==
-{{Harmonics in equal|197|3|1|intervals=prime}}
+{{Interval table}}
-{{Stub}}
+== Harmonics ==

Lériendil at 04:31, 6 August 2024

2024-08-06T04:31:40Z

← Older revision		Revision as of 04:31, 6 August 2024
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	197edt can be described as approximately 124.293[[edo]]. This implies that each step of ~~39edt~~ 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 7 steps of [[870edo]].

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

Fredg999: Use ED intro

2024-07-12T12:47:05Z

Use ED intro

← Older revision		Revision as of 12:47, 12 July 2024
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	{{Infobox ET}}		{{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.

	197edt can be described as approximately 124.293[[edo]]. This implies that each step of 39edt can be approximated by 7 steps of [[870edo]].		197edt can be described as approximately 124.293[[edo]]. This implies that each step of 39edt can be approximated by 7 steps of [[870edo]].

Lériendil at 12:43, 12 July 2024

2024-07-12T12:43:40Z

← Older revision		Revision as of 12:43, 12 July 2024
Line 5:		Line 5:
	197edt can be described as approximately 124.293[[edo]]. This implies that each step of 39edt can be approximated by 7 steps of [[870edo]].		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 17-limit system.		It is a very strong no-twos, no-fives 19-limit system.

	==Harmonics==		==Harmonics==