197edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:20Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
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	\| [[Seniority]]		\| [[Seniority]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

Overthink: /* Theory */ note 197ef

2026-02-11T23:08:35Z

Theory: note 197ef

← Older revision		Revision as of 23:08, 11 February 2026
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	197edo gives excellent results for tuning both [[marvel]], the planar temperament [[tempering out]] [[225/224]], and [[catakleismic]], the temperament tempering out both 225/224 and [[4375/4374]]. Among [[patent val]]s, it gives the best results for both. In fact, the [[11-limit]] patent val {{val\| 197 312 457 553 682 }} has a [[comma basis]] {225/224, 441/440, 4375/4374, 65536/65219}, so taking 225/224 and [[441/440]] together ([[prodigy]] temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.		197edo gives excellent results for tuning both [[marvel]], the planar temperament [[tempering out]] [[225/224]], and [[catakleismic]], the temperament tempering out both 225/224 and [[4375/4374]]. Among [[patent val]]s, it gives the best results for both. In fact, the [[11-limit]] patent val {{val\| 197 312 457 553 682 }} has a [[comma basis]] {225/224, 441/440, 4375/4374, 65536/65219}, so taking 225/224 and [[441/440]] together ([[prodigy]] temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

	If we use 197e, the {{val\| 197 312 457 553 681 }} val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out [[385/384]] as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.		If we use 197e, the {{val\| 197 312 457 553 681 }} val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out [[385/384]] as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that. The 197ef val, {{val\| 197 312 457 553 681 728}}, is an excellent tuning for the 13-limit version of catakleismic.

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 14:12, 20 February 2025

2025-02-20T14:12:31Z

← Older revision		Revision as of 14:12, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|197~~}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 15:		Line 15:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
Line 27:		Line 28:
	\| {{monzo\| -312 197 }}		\| {{monzo\| -312 197 }}
	\| {{mapping\| 197 312 }}		\| {{mapping\| 197 312 }}
	\| 0.4566		\| +0.4566
	\| 0.4568		\| 0.4568
	\| 7.50		\| 7.50
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	\| 15625/15552, {{monzo\| -53 32 1 }}		\| 15625/15552, {{monzo\| -53 32 1 }}
	\| {{mapping\| 197 312 457 }}		\| {{mapping\| 197 312 457 }}
	\| 0.6717		\| +0.6717
	\| 0.4813		\| 0.4813
	\| 7.90		\| 7.90
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	\| 225/224, 4375/4374, {{monzo\| -25 6 -3 8 }}		\| 225/224, 4375/4374, {{monzo\| -25 6 -3 8 }}
	\| {{mapping\| 197 312 457 553 }}		\| {{mapping\| 197 312 457 553 }}
	\| 0.5302		\| +0.5302
	\| 0.4834		\| 0.4834
	\| 7.94		\| 7.94
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Seniority]]		\| [[Seniority]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

Francium: /* Music */ +music

2024-07-30T13:15:09Z

Music: +music

← Older revision		Revision as of 13:15, 30 July 2024
Line 81:		Line 81:

	== Music ==		== Music ==
			; [[Francium]]
			* "Have You Ever Eaten A Square Cutlet?" from ''Questions'' (2024) – [https://open.spotify.com/track/7cA0T79hEkzEoMGvufGZ5R Spotify] \| [https://francium223.bandcamp.com/track/have-you-ever-eaten-a-square-cutlet Bandcamp] \| [https://www.youtube.com/watch?v=_LkriwwqbIY YouTube]

	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]
	* [http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 ''Pump1''] – in pump12 1		* [http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 ''Pump1''] – in pump12 1

FloraC: Review

2024-04-15T13:30:52Z

Review

← Older revision		Revision as of 13:30, 15 April 2024
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	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 225/224, 4375/4374, ~~15625/15552~~		\| 225/224, 4375/4374, {{monzo\| -25 6 -3 8 }}
	\| {{mapping\| 197 312 457 553 }}		\| {{mapping\| 197 312 457 553 }}
	\| 0.5302		\| 0.5302
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	\| 316.75		\| 316.75
	\| 6/5		\| 6/5
	\| [[~~Hanson]] / [[catakleismic~~]]		\| [[Catakleismic]]
	\|-		\|-
	\| 1		\| 1

FloraC: Cleanup

2024-04-15T13:24:00Z

Cleanup

← Older revision		Revision as of 13:24, 15 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|197}}		{{EDO intro\|197}}
	~~==Theory==~~
	197edo gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

	If we use 197e, the ~~<~~197 312 457 553 681\| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit ~~[[Marvel family\|~~marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.		== Theory ==
	===Odd harmonics===		197edo gives excellent results for tuning both [[marvel]], the planar temperament [[tempering out]] [[225/224]], and [[catakleismic]], the temperament tempering out both 225/224 and [[4375/4374]]. Among [[patent val]]s, it gives the best results for both. In fact, the [[11-limit]] patent val {{val\| 197 312 457 553 682 }} has a [[comma basis]] {225/224, 441/440, 4375/4374, 65536/65219}, so taking 225/224 and [[441/440]] together ([[prodigy]] temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

			If we use 197e, the {{val\| 197 312 457 553 681 }} val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out [[385/384]] as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.

			=== Odd harmonics ===
	{{Harmonics in equal\|197}}		{{Harmonics in equal\|197}}
	~~===Subsets and supersets===~~
	~~197edo is the 45th [[prime_numbers\|prime]] edo.~~

	==Regular temperament properties==		=== Subsets and supersets ===
			197edo is the 45th [[prime edo]].

			== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-312 197}}		\| {{monzo\| -312 197 }}
	\|{{~~val~~\|197 312}}		\| {{mapping\| 197 312 }}
	\| 0.4566		\| 0.4566
	\| 0.4568		\| 0.4568
	\| 7.50		\| 7.50
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|15625/15552, {{monzo\|-53 32 1}}		\| 15625/15552, {{monzo\| -53 32 1 }}
	\|{{~~val~~\|197 312 457}}		\| {{mapping\| 197 312 457 }}
	\| 0.6717		\| 0.6717
	\| 0.4813		\| 0.4813
	\| 7.90		\| 7.90
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|225/224, 4375/4374, 15625/15552		\| 225/224, 4375/4374, 15625/15552
	\|{{~~val~~\|197 312 457 553}}		\| {{mapping\| 197 312 457 553 }}
	\| 0.5302		\| 0.5302
	\| 0.4834		\| 0.4834
	\| 7.94		\| 7.94
	\|}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|52\197		\| 52\197
	\|316.75		\| 316.75
	\|6/5		\| 6/5
	\|[[Hanson]] / [[catakleismic]]		\| [[Hanson]] / [[catakleismic]]
	\|-		\|-
	\|1		\| 1
	\|53\197		\| 53\197
	\|322.84		\| 322.84
	\|3087/2560		\| 3087/2560
	\|[[Seniority]]		\| [[Seniority]]
	\|}		\|}

	==Scales==		== Scales ==
	* [[Prismarv]]		* [[Prismarv]]
	* [[Marveldene]]		* [[Marveldene]]
	* [[~~Pump12_1~~]~~]<br>[http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 Pump1 by Chris Vaisvil~~]		* [[Pump12 1]]
	* [[~~Pump12_2~~]]		* [[Pump12 2]]
	* [[Pump13]]		* [[Pump13]]
	* [[Pump14]]		* [[Pump14]]
Line 76:		Line 80:
	* [[Pump18]]		* [[Pump18]]

	[[~~Category:197edo\|~~ ]] ~~<!-- main article -->~~		== Music ==
	[~~[Category~~:~~Equal divisions of the octave\|###]] <!~~-- 3-~~digit number~~ -->		; [[Chris Vaisvil]]
			* [http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 ''Pump1''] – in pump12 1

	[[Category:Catakleismic]]		[[Category:Catakleismic]]
	[[Category:Marvel]]		[[Category:Marvel]]
	~~[[Category:Prime EDO]]~~

Francium: +regular temperament properties

2023-11-03T20:25:16Z

+regular temperament properties

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''197edo''' is the [[EDO|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family|catakleismic]], the temperament [[tempering_out|tempering out]] both 225/224 and 4375/4374, which has wedgie &lt;&lt;6 5 22 -6 18 37||. Among [[Patent_val|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val &lt;197 312 457 553 682| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.
+{{EDO intro|197}}
 If we use 197e, the &lt;197 312 457 553 681| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit [[Marvel family|marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.
-edo is the 45th [[prime_numbers|prime]] edo.
+==Regular temperament properties==
 ==Scales==

Plumtree: Infobox ET added

2022-10-04T21:18:48Z

Infobox ET added

← Older revision		Revision as of 21:18, 4 October 2022
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			{{Infobox ET}}
	'''197edo''' is the [[EDO\|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.		'''197edo''' is the [[EDO\|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

Fredg999 category edits: Sort key

2022-07-02T21:25:56Z

Sort key

← Older revision		Revision as of 21:25, 2 July 2022
Line 6:		Line 6:

	==Scales==		==Scales==
	~~<ul><li>~~[[Prismarv]]~~</li><li>~~[[Marveldene]]~~</li><li>~~[[~~Pump12_1\|~~Pump12_1]]<br>[http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 Pump1 by Chris Vaisvil]~~</li></ul>~~		* [[Prismarv]]
			* [[Marveldene]]
	~~<ul><li>~~[[~~Pump12_2\|~~Pump12_2]]~~</li><li>~~[[Pump13]]~~</li><li>~~[[Pump14]]~~</li><li>~~[[Pump15]]~~</li><li>~~[[Pump16]]~~</li><li>~~[[Pump17]]~~</li><li>~~[[Pump18]]~~</li></ul>~~		* [[Pump12_1]]<br>[http://micro.soonlabel.com/pump_tunings/pump1/daily20111029-a-pump1-woodwinds-no-verb.mp3 Pump1 by Chris Vaisvil]
			* [[Pump12_2]]
			* [[Pump13]]
			* [[Pump14]]
			* [[Pump15]]
			* [[Pump16]]
			* [[Pump17]]
			* [[Pump18]]

	[[Category:197edo\| ]] <!-- main article -->		[[Category:197edo\| ]] <!-- main article -->
			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Catakleismic]]		[[Category:Catakleismic]]
	~~[[Category:Equal divisions of the octave]]~~
	[[Category:Marvel]]		[[Category:Marvel]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Cmloegcmluin: unhyphenate "comma basis"

2021-11-12T20:19:28Z

unhyphenate "comma basis"

← Older revision		Revision as of 20:19, 12 November 2021
Line 1:		Line 1:
	'''197edo''' is the [[EDO\|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma-basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.		'''197edo''' is the [[EDO\|equal division of the octave]] into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and [[Kleismic_family\|catakleismic]], the temperament [[tempering_out\|tempering out]] both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37\|\|. Among [[Patent_val\|patent vals]], in fact, it gives the best results for both. In fact, the [[11-limit]] patent val <197 312 457 553 682\| has a [[comma basis]] [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together ([[Marvel family\|prodigy temperament]]) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.

	If we use 197e, the <197 312 457 553 681\| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit [[Marvel family\|marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.		If we use 197e, the <197 312 457 553 681\| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit [[Marvel family\|marvel]], we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.