209edo - 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"

2026-03-13T13:31:48Z

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 13:31, 13 March 2026
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	\| [[Enneadecal]] (209d)		\| [[Enneadecal]] (209d)
	\|}		\|}
	<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

	[[Category:Marvo]]		[[Category:Marvo]]

ArrowHead294 at 22:35, 20 February 2025

2025-02-20T22:35:31Z

← Older revision		Revision as of 22:35, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|209~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:55, 15 January 2025

2025-01-15T16:55:47Z

← Older revision		Revision as of 16:55, 15 January 2025
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	\| [[Enneadecal]] (209d)		\| [[Enneadecal]] (209d)
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Marvo]]		[[Category:Marvo]]

ArrowHead294: Partial undo

2024-11-16T13:11:06Z

Partial undo

← Older revision		Revision as of 13:11, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 27:		Line 36:
	\| 0.3962		\| 0.3962
	\| 6.90		\| 6.90
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 3/2<br>(225/224)		\| 3/2<br>(225/224)
	\| [[Enneadecal]] (209d)		\| [[Enneadecal]] (209d)
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Marvo]]		[[Category:Marvo]]

ArrowHead294 at 02:03, 16 November 2024

2024-11-16T02:03:03Z

← Older revision		Revision as of 02:03, 16 November 2024
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 209 factors into 11 × 19, 209edo contains [[11edo]] and [[19edo]] as its subsets. [[627edo]], which triples it, gives a good correction to the harmonic 7.		Since 209 factors into {{nowrap\|11 × 19}}, 209edo contains [[11edo]] and [[19edo]] as its subsets. [[627edo]], which triples it, gives a good correction to the harmonic 7.

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| -331 209 }}		\| {{monzo\| -331 209 }}
	\| {{mapping\| 209 331 }}		\| {{mapping\| 209 331 }}
	\| 0.4658		\| +0.4658
	\| 0.4660		\| 0.4660
	\| 8.12		\| 8.12
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	\| {{monzo\| -13 17 -6 }}, {{monzo\| -27 -2 13 }}		\| {{monzo\| -13 17 -6 }}, {{monzo\| -27 -2 13 }}
	\| {{mapping\| 209 331 485 }}		\| {{mapping\| 209 331 485 }}
	\| 0.5439		\| +0.5439
	\| 0.3962		\| 0.3962
	\| 6.90		\| 6.90
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 3/2<br>(225/224)		\| 3/2<br>(225/224)
	\| [[Enneadecal]] (209d)		\| [[Enneadecal]] (209d)
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	[[Category:Marvo]]		[[Category:Marvo]]

FloraC: Review +1

2024-04-13T10:14:27Z

Review +1

← Older revision		Revision as of 10:14, 13 April 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	209edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 129140163/128000000 ([[graviton]]) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], 2125764/2100875, and 2500000/2470629 in the 7-limit; [[243/242]], [[3025/3024]], [[4000/3993]], and 16896/16807 in the 11-limit; [[351/350]], [[625/624]], [[1573/1568]], 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 13-limit [[marvo]] temperament ~~and~~ the 13-limit [[spectacle]] temperament.		209edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 129140163/128000000 ([[graviton]]) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], 2125764/2100875, and 2500000/2470629 in the 7-limit; [[243/242]], [[3025/3024]], [[4000/3993]], and 16896/16807 in the 11-limit; [[351/350]], [[625/624]], [[1573/1568]], 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 13-limit [[marvo]] temperament. It also [[support]]s the 13-limit [[spectacle]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
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	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			[[Category:Marvo]]

FloraC: Review

2024-04-13T10:11:53Z

Review

← Older revision		Revision as of 10:11, 13 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|209}}		{{EDO intro\|209}}
	==Theory==
	~~509et~~ tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 11-limit [[~~Marvel temperaments\|~~marvo ~~temperament~~]] and the 13-limit [[~~Marvel family\|~~spectacle ~~temperament~~]].		== Theory ==
	===Odd harmonics===		209edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 129140163/128000000 ([[graviton]]) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], 2125764/2100875, and 2500000/2470629 in the 7-limit; [[243/242]], [[3025/3024]], [[4000/3993]], and 16896/16807 in the 11-limit; [[351/350]], [[625/624]], [[1573/1568]], 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 13-limit [[marvo]] temperament and the 13-limit [[spectacle]] temperament.

			=== Odd harmonics ===
	{{Harmonics in equal\|209}}		{{Harmonics in equal\|209}}
	===Subsets and supersets===
	209 factors into 11 × 19, ~~with subset edos {{EDOs\|11,~~ and ~~19}}~~. [[627edo]], which triples it, gives a good correction to the harmonic 7.		=== Subsets and supersets ===
	==Regular temperament properties==		Since 209 factors into 11 × 19, 209edo contains [[11edo]] and [[19edo]] as its subsets. [[627edo]], which triples it, gives a good correction to the harmonic 7.

			== 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\|-331 209}}		\| {{monzo\| -331 209 }}
	\|{{~~val~~\|209 331}}		\| {{mapping\| 209 331 }}
	\| 0.4658		\| 0.4658
	\| 0.4660		\| 0.4660
	\| 8.12		\| 8.12
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-13 17 -6}}, {{monzo\|-27 -2 13}}		\| {{monzo\| -13 17 -6 }}, {{monzo\| -27 -2 13 }}
	\|{{~~val~~\|209 331 485}}		\| {{mapping\| 209 331 485 }}
	\| 0.5439		\| 0.5439
	\| 0.3962		\| 0.3962
	\| 6.90		\| 6.90
	\|}		\|}

	=== 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
	\|71\209		\| 71\209
	\|407.66		\| 407.66
	\|15625/12288		\| 15625/12288
	\|[[Ditonic]]		\| [[Ditonic]]
	\|-		\|-
	\|1		\| 1
	\|90\209		\| 90\209
	\|516.75		\| 516.75
	\|27/20		\| 27/20
	\|[[~~Gravity~~]] / [[~~Zarvo~~]] (209d)		\| [[Larry]] / [[marvo]] (209) / [[zarvo]] (209d)
	\|-		\|-
	\|19		\| 19
	\|122\209<br>(1\209)		\| 122\209<br>(1\209)
	\|700.48<br>(5.74)		\| 700.48<br>(5.74)
	\|3/2<br>(225/224)		\| 3/2<br>(225/224)
	\|[[Enneadecal]] (209d)		\| [[Enneadecal]] (209d)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct
	[[~~Category:Equal divisions of~~ the octave\|~~###~~]] ~~<!-- 3-digit number -->~~

Francium at 04:45, 19 October 2023

2023-10-19T04:45:27Z

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''209edo''' is the [[EDO|equal division of the octave]] into 209 parts of 5.7416 [[cent]]s each. It tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 11-limit [[Marvel temperaments|marvo temperament]] and the 13-limit [[Marvel family|spectacle temperament]].
+{{EDO intro|209}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:21:57Z

Infobox ET added

← Older revision		Revision as of 21:21, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''209edo''' is the [[EDO\|equal division of the octave]] into 209 parts of 5.7416 [[cent]]s each. It tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 11-limit [[Marvel temperaments\|marvo temperament]] and the 13-limit [[Marvel family\|spectacle temperament]].		'''209edo''' is the [[EDO\|equal division of the octave]] into 209 parts of 5.7416 [[cent]]s each. It tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 11-limit [[Marvel temperaments\|marvo temperament]] and the 13-limit [[Marvel family\|spectacle temperament]].

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Fredg999 category edits: Sort key

2022-07-03T18:33:04Z

Sort key

← Older revision		Revision as of 18:33, 3 July 2022
Line 1:		Line 1:
	'''209edo''' is the [[EDO\|equal division of the octave]] into 209 parts of 5.7416 [[cent]]s each. It tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 11-limit [[Marvel temperaments\|marvo temperament]] and the 13-limit [[Marvel family\|spectacle temperament]].		'''209edo''' is the [[EDO\|equal division of the octave]] into 209 parts of 5.7416 [[cent]]s each. It tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the [[optimal patent val]] for the 11-limit [[Marvel temperaments\|marvo temperament]] and the 13-limit [[Marvel family\|spectacle temperament]].

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->