190edo - 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"

2026-03-13T13:32:07Z

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
Line 186:		Line 186:
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	\|}		\|}
	<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 ==

Francium: changed EDO intro to ED intro

2025-02-19T17:55:15Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:55, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|190~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Regular temperament properties */ cleanup and update

2025-02-19T14:35:06Z

Regular temperament properties: cleanup and update

← Older revision		Revision as of 14:35, 19 February 2025
Line 21:		Line 21:
	! rowspan="2" \| [[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
	\|-		\|-
Line 28:		Line 28:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| -301 190 }}		\| {{Monzo\| -301 190 }}
	\| {{~~mapping~~\| 190 301 }}		\| {{Mapping\| 190 301 }}
	\| +0.285		\| +0.285
	\| 0.285		\| 0.285
Line 36:		Line 36:
	\| 2.3.5		\| 2.3.5
	\| 2109375/2097152, {{monzo\| -7 22 -12 }}		\| 2109375/2097152, {{monzo\| -7 22 -12 }}
	\| {{~~mapping~~\| 190 301 441 }}		\| {{Mapping\| 190 301 441 }}
	\| +0.341		\| +0.341
	\| 0.246		\| 0.246
Line 43:		Line 43:
	\| 2.3.5.7		\| 2.3.5.7
	\| 1029/1024, 4375/4374, 235298/234375		\| 1029/1024, 4375/4374, 235298/234375
	\| {{~~mapping~~\| 190 301 441 533 }}		\| {{Mapping\| 190 301 441 533 }}
	\| +0.479		\| +0.479
	\| 0.321		\| 0.321
Line 50:		Line 50:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 441/440, 4375/4374, 234375/234256		\| 385/384, 441/440, 4375/4374, 234375/234256
	\| {{~~mapping~~\| 190 301 441 533 657 }}		\| {{Mapping\| 190 301 441 533 657 }}
	\| +0.490		\| +0.490
	\| 0.288		\| 0.288
Line 57:		Line 57:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 385/384, 441/440, 625/624, 729/728, 847/845		\| 385/384, 441/440, 625/624, 729/728, 847/845
	\| {{~~mapping~~\| 190 301 441 533 657 703 }}		\| {{Mapping\| 190 301 441 533 657 703 }}
	\| +0.432		\| +0.432
	\| 0.293		\| 0.293
Line 64:		Line 64:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 289/288, 385/384, 441/440, 561/560, 625/624, 847/845		\| 289/288, 385/384, 441/440, 561/560, 625/624, 847/845
	\| {{~~mapping~~\| 190 301 441 533 657 703 776 }} (190g)		\| {{Mapping\| 190 301 441 533 657 703 776 }} (190g)
	\| +0.507		\| +0.507
	\| 0.327		\| 0.327
Line 71:		Line 71:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 289/288, 343/342, 385/384, 441/440, 476/475, 495/494, 847/845		\| 289/288, 343/342, 385/384, 441/440, 476/475, 495/494, 847/845
	\| {{~~mapping~~\| 190 301 441 533 657 703 776 807 }} (190g)		\| {{Mapping\| 190 301 441 533 657 703 776 807 }} (190g)
	\| +0.463		\| +0.463
	\| 0.327		\| 0.327
Line 78:		Line 78:
	\| 2.3.5.7.11.13.17.19.23		\| 2.3.5.7.11.13.17.19.23
	\| 289/288, 343/342, 385/384, 391/390, 441/440, 476/475, 495/494, 529/528		\| 289/288, 343/342, 385/384, 391/390, 441/440, 476/475, 495/494, 529/528
	\| {{~~mapping~~\| 190 301 441 533 657 703 776 807 859 }} (190g)		\| {{Mapping\| 190 301 441 533 657 703 776 807 859 }} (190g)
	\| +0.486		\| +0.486
	\| 0.315		\| 0.315
Line 90:		Line 90:
	\|+ style="font-size: 105%;" \| 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*
	! Temperament		! Temperament
	\|-		\|-
Line 139:		Line 139:
	\|-		\|-
	\| 2		\| 2
	\| 59\190<br />(36\190)		\| 59\190<br>(36\190)
	\| 372.63<br />(227.37)		\| 372.63<br>(227.37)
	\| 26/21<br />(297/260)		\| 26/21<br>(297/260)
	\| [[Essence]]		\| [[Essence]]
	\|-		\|-
	\| 2		\| 2
	\| 71\190<br />(24\190)		\| 71\190<br>(24\190)
	\| 448.42<br />(151.58)		\| 448.42<br>(151.58)
	\| 35/27<br />(12/11)		\| 35/27<br>(12/11)
	\| [[Neusec]]		\| [[Neusec]]
	\|-		\|-
	\| 5		\| 5
	\| 79\190<br />(3\190)		\| 79\190<br>(3\190)
	\| 498.95<br />(18.95)		\| 498.95<br>(18.95)
	\| 4/3<br />(81/80)		\| 4/3<br>(81/80)
	\| [[~~Pental (temperament)\|Pental~~]]		\| [[Quintile]]
	\|-		\|-
	\| 10		\| 10
	\| 50\190<br />(7\190)		\| 50\190<br>(7\190)
	\| 315.79<br />(45.79)		\| 315.79<br>(45.79)
	\| 6/5<br />(40/39)		\| 6/5<br>(40/39)
	\| [[Deca]]		\| [[Deca]]
	\|-		\|-
	\| 10		\| 10
	\| 79\190<br />(3\190)		\| 79\190<br>(3\190)
	\| 498.95<br />(18.95)		\| 498.95<br>(18.95)
	\| 4/3<br />(81/80)		\| 4/3<br>(81/80)
	\| [[~~Decal~~]]		\| [[Decile]]
	\|-		\|-
	\| 19		\| 19
	\| 79\190<br />(1\190)		\| 79\190<br>(1\190)
	\| 498.95<br />(6.32)		\| 498.95<br>(6.32)
	\| 4/3<br />(225/224)		\| 4/3<br>(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|-		\|-
	\| 38		\| 38
	\| 79\190<br />(1\190)		\| 79\190<br>(1\190)
	\| 265.26<br />(6.32)		\| 265.26<br>(6.32)
	\| 4/3<br />(225/224)		\| 4/3<br>(225/224)
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|-		\|-
	\| 38		\| 38
	\| 42\190<br />(2\190)		\| 42\190<br>(2\190)
	\| 265.26<br />(12.63)		\| 265.26<br>(12.63)
	\| 500/429<br />(144/143)		\| 500/429<br>(144/143)
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294 at 15:20, 16 January 2025

2025-01-16T15:20:41Z

← Older revision		Revision as of 15:20, 16 January 2025
Line 5:		Line 5:
	190edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with a flat tendency, as [[harmonic]]s 3 through 13 are all tuned flat.		190edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with a flat tendency, as [[harmonic]]s 3 through 13 are all tuned flat.

	~~The equal temperament~~ is interesting because of the utility of its approximations; it [[tempering out\|tempers out]] [[1029/1024]], [[4375/4374]], [[385/384]], [[441/440]], [[3025/3024]] and [[9801/9800]]. It provides the [[optimal patent val]] for both the 7- and 11-limit versions of [[unidec]], the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament [[portent]], which tempers out 385/384 and 441/440, and [[gamelan]], the rank-3 7-limit temperament which tempers out 1029/1024, as well as [[slendric]], the 2.3.7 subgroup temperament featured in the [[#Music]] section. In the 13-limit, 190et tempers out [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.		190edo is interesting because of the utility of its approximations; it [[tempering out\|tempers out]] [[1029/1024]], [[4375/4374]], [[385/384]], [[441/440]], [[3025/3024]], and [[9801/9800]]. It provides the [[optimal patent val]] for both the 7- and 11-limit versions of [[unidec]], the {{nowrap\|72 & 118}} temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament [[portent]], which tempers out 385/384 and 441/440, and [[gamelan]], the rank-3 7-limit temperament which tempers out 1029/1024, as well as [[slendric]], the 2.3.7 subgroup temperament featured in the [[#Music]] section. In the 13-limit, 190et tempers out [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.

	The 190g [[val]] shows us a smooth path to the even higher limits. This extension tempers out [[289/288]], [[561/560]], [[595/594]] in the 17-limit; [[343/342]], [[476/475]], [[495/494]] in the 19-limit; and [[391/390]], [[529/528]] in the 23-limit.		The 190g [[val]] shows us a smooth path to the even higher limits. This extension tempers out [[289/288]], [[561/560]], [[595/594]] in the 17-limit; [[343/342]], [[476/475]], [[495/494]] in the 19-limit; and [[391/390]], [[529/528]] in the 23-limit.
Line 186:		Line 186:
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T11:45:53Z

Partial undo

← Older revision		Revision as of 11:45, 16 November 2024
Line 16:		Line 16:

	== 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 73:		Line 82:
	\| 0.315		\| 0.315
	\| 4.98		\| 4.98
	~~{{comma basis end}~~}		\|}
	* 190et (190g val) has a lower relative error in the 23-limit than any previous equal temperaments, being the first to beat [[94edo\|94]]. However, [[193edo\|193]], only slightly larger, beats it.		* 190et (190g val) has a lower relative error in the 23-limit than any previous equal temperaments, being the first to beat [[94edo\|94]]. However, [[193edo\|193]], only slightly larger, beats it.
	* It is also prominent in the 13- and 19-limit, with lower absolute errors than any previous equal temperaments. It beats [[183edo\|183]] in either subgroup and is bettered by [[198edo\|198]] in the 13-limit, and by 193 in the 19-limit.		* It is also prominent in the 13- and 19-limit, with lower absolute errors than any previous equal temperaments. It beats [[183edo\|183]] in either subgroup and is bettered by [[198edo\|198]] in the 13-limit, and by 193 in the 19-limit.

	=== 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*
			! Temperament
	\|-		\|-
	\| 1		\| 1
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	\| 500/429<br />(144/143)		\| 500/429<br />(144/143)
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	~~{{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

	== Scales ==		== Scales ==

ArrowHead294 at 05:56, 16 November 2024

2024-11-16T05:56:37Z

← Older revision		Revision as of 05:56, 16 November 2024
Line 16:		Line 16:

	== 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
Line 81:		Line 73:
	\| 0.315		\| 0.315
	\| 4.98		\| 4.98
	\|}		{{comma basis end}}
	* 190et (190g val) has a lower relative error in the 23-limit than any previous equal temperaments, being the first to beat [[94edo\|94]]. However, [[193edo\|193]], only slightly larger, beats it.		* 190et (190g val) has a lower relative error in the 23-limit than any previous equal temperaments, being the first to beat [[94edo\|94]]. However, [[193edo\|193]], only slightly larger, beats it.
	* It is also prominent in the 13- and 19-limit, with lower absolute errors than any previous equal temperaments. It beats [[183edo\|183]] in either subgroup and is bettered by [[198edo\|198]] in the 13-limit, and by 193 in the 19-limit.		* It is also prominent in the 13- and 19-limit, with lower absolute errors than any previous equal temperaments. It beats [[183edo\|183]] in either subgroup and is bettered by [[198edo\|198]] in the 13-limit, and by 193 in the 19-limit.

	=== 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
Line 137:		Line 123:
	\|-		\|-
	\| 2		\| 2
	\| 59\190<br>(36\190)		\| 59\190<br />(36\190)
	\| 372.63<br>(227.37)		\| 372.63<br />(227.37)
	\| 26/21<br>(297/260)		\| 26/21<br />(297/260)
	\| [[Essence]]		\| [[Essence]]
	\|-		\|-
	\| 2		\| 2
	\| 71\190<br>(24\190)		\| 71\190<br />(24\190)
	\| 448.42<br>(151.58)		\| 448.42<br />(151.58)
	\| 35/27<br>(12/11)		\| 35/27<br />(12/11)
	\| [[Neusec]]		\| [[Neusec]]
	\|-		\|-
	\| 5		\| 5
	\| 79\190<br>(3\190)		\| 79\190<br />(3\190)
	\| 498.95<br>(18.95)		\| 498.95<br />(18.95)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]]		\| [[Pental (temperament)\|Pental]]
	\|-		\|-
	\| 10		\| 10
	\| 50\190<br>(7\190)		\| 50\190<br />(7\190)
	\| 315.79<br>(45.79)		\| 315.79<br />(45.79)
	\| 6/5<br>(40/39)		\| 6/5<br />(40/39)
	\| [[Deca]]		\| [[Deca]]
	\|-		\|-
	\| 10		\| 10
	\| 79\190<br>(3\190)		\| 79\190<br />(3\190)
	\| 498.95<br>(18.95)		\| 498.95<br />(18.95)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Decal]]		\| [[Decal]]
	\|-		\|-
	\| 19		\| 19
	\| 79\190<br>(1\190)		\| 79\190<br />(1\190)
	\| 498.95<br>(6.32)		\| 498.95<br />(6.32)
	\| 4/3<br>(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|-		\|-
	\| 38		\| 38
	\| 79\190<br>(1\190)		\| 79\190<br />(1\190)
	\| 265.26<br>(6.32)		\| 265.26<br />(6.32)
	\| 4/3<br>(225/224)		\| 4/3<br />(225/224)
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|-		\|-
	\| 38		\| 38
	\| 42\190<br>(2\190)		\| 42\190<br />(2\190)
	\| 265.26<br>(12.63)		\| 265.26<br />(12.63)
	\| 500/429<br>(144/143)		\| 500/429<br />(144/143)
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	\|}		{{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}}

	== Scales ==		== Scales ==
Line 197:		Line 183:
	* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 ''16 Slendric Virgins'']		* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 ''16 Slendric Virgins'']

	~~[[Category:Unidec]]~~
	[[Category:Ekadash]]		[[Category:Ekadash]]
	[[Category:Gamelismic]]		[[Category:Gamelismic]]
			[[Category:Listen]]
	[[Category:Portent]]		[[Category:Portent]]
	[[Category:Portentous]]		[[Category:Portentous]]
	[[Category:~~Listen~~]]		[[Category:Unidec]]

Fredg999: Skip disambiguation

2024-09-09T01:57:01Z

Skip disambiguation

← Older revision		Revision as of 01:57, 9 September 2024
Line 152:		Line 152:
	\| 498.95<br>(18.95)		\| 498.95<br>(18.95)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]]		\| [[Pental (temperament)\|Pental]]
	\|-		\|-
	\| 10		\| 10

FloraC: /* Theory */ expand

2024-04-19T03:32:19Z

Theory: expand

← Older revision		Revision as of 03:32, 19 April 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	190edo is interesting because of the utility of its approximations; it tempers out [[1029/1024]], [[4375/4374]], [[385/384]], [[441/440]], [[3025/3024]] and [[9801/9800]]. It provides the [[optimal patent val]] for both the 7- and 11-limit versions of [[unidec]], the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament [[portent]], which tempers out 385/384 and 441/440, and [[gamelan]], the rank-3 7-limit temperament which tempers out 1029/1024, as well as [[slendric]], the 2.3.7 subgroup temperament featured in the [[#Music]] section. In the 13-limit, 190et tempers out [[~~847~~/~~845~~]], [[~~625~~/~~624~~]], [[~~729~~/~~728~~]], [[~~1575~~/~~1573~~]] and [[~~1001~~/~~1000~~]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.		190edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with a flat tendency, as [[harmonic]]s 3 through 13 are all tuned flat.

			The equal temperament is interesting because of the utility of its approximations; it [[tempering out\|tempers out]] [[1029/1024]], [[4375/4374]], [[385/384]], [[441/440]], [[3025/3024]] and [[9801/9800]]. It provides the [[optimal patent val]] for both the 7- and 11-limit versions of [[unidec]], the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament [[portent]], which tempers out 385/384 and 441/440, and [[gamelan]], the rank-3 7-limit temperament which tempers out 1029/1024, as well as [[slendric]], the 2.3.7 subgroup temperament featured in the [[#Music]] section. In the 13-limit, 190et tempers out [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.

			The 190g [[val]] shows us a smooth path to the even higher limits. This extension tempers out [[289/288]], [[561/560]], [[595/594]] in the 17-limit; [[343/342]], [[476/475]], [[495/494]] in the 19-limit; and [[391/390]], [[529/528]] in the 23-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|190}}		{{Harmonics in equal\|190\|intervals=prime}}

			=== Subsets and supersets ===
			Since 190 factors into {{factorization\|190}}, 190edo has subset edos {{EDOs\| 2, 5, 10, 19, 38, and 95 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Notable in the 13-, 19- and 23-limit

2024-04-19T03:16:21Z

Notable in the 13-, 19- and 23-limit

@@ Line 53: / Line 53: @@
 | 0.293
 | 4.63
 |}
 === Rank-2 temperaments ===

FloraC: Cleanup

2024-04-19T02:59:53Z

Cleanup

← Older revision		Revision as of 02:59, 19 April 2024
Line 6:		Line 6:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|190~~\|columns=11~~}}		{{Harmonics in equal\|190}}

	== Regular temperament properties ==		== Regular temperament properties ==
Line 21:		Line 21:
	\| 2.3		\| 2.3
	\| {{monzo\| -301 190 }}		\| {{monzo\| -301 190 }}
	\| [{{~~val~~\| 190 301 }}]		\| {{mapping\| 190 301 }}
	\| +0.285		\| +0.285
	\| 0.285		\| 0.285
Line 28:		Line 28:
	\| 2.3.5		\| 2.3.5
	\| 2109375/2097152, {{monzo\| -7 22 -12 }}		\| 2109375/2097152, {{monzo\| -7 22 -12 }}
	\| [{{~~val~~\| 190 301 441 }}]		\| {{mapping\| 190 301 441 }}
	\| +0.341		\| +0.341
	\| 0.246		\| 0.246
Line 35:		Line 35:
	\| 2.3.5.7		\| 2.3.5.7
	\| 1029/1024, 4375/4374, 235298/234375		\| 1029/1024, 4375/4374, 235298/234375
	\| [{{~~val~~\| 190 301 441 533 }}]		\| {{mapping\| 190 301 441 533 }}
	\| +0.479		\| +0.479
	\| 0.321		\| 0.321
Line 42:		Line 42:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 441/440, 4375/4374, 234375/234256		\| 385/384, 441/440, 4375/4374, 234375/234256
	\| [{{~~val~~\| 190 301 441 533 657 }}]		\| {{mapping\| 190 301 441 533 657 }}
	\| +0.490		\| +0.490
	\| 0.288		\| 0.288
Line 49:		Line 49:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 385/384, 441/440, 625/624, 729/728, 847/845		\| 385/384, 441/440, 625/624, 729/728, 847/845
	\| [{{~~val~~\| 190 301 441 533 657 703 }}]		\| {{mapping\| 190 301 441 533 657 703 }}
	\| +0.432		\| +0.432
	\| 0.293		\| 0.293
Line 59:		Line 59:
	\|+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
	\|-		\|-
Line 74:		Line 74:
	\| 271.58		\| 271.58
	\| 75/64		\| 75/64
	\| [[~~Orson]] / [[sabric~~]]		\| [[Sabric]]
	\|-		\|-
	\| 1		\| 1
Line 154:		Line 154:
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==