Orgonia - Revision history

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:45:44Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:45, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].		'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T05:34:11Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 05:34, 13 April 2025
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			{{Technical data page}}<br><br>
	'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].		'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].

Lériendil: added links to chromatic pairs

2024-12-12T11:05:04Z

added links to chromatic pairs

← Older revision		Revision as of 11:05, 12 December 2024
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	=== Orgone ===		=== Orgone ===
	{{Main\|Orgone}}		{{Main\|Orgone}}
			{{See also\| Chromatic pairs #Orgone }}

	[[File:orgone_heptatonic.jpg\|thumb\|alt=orgone_heptatonic.jpg\|Orgone heptatonic]]		[[File:orgone_heptatonic.jpg\|thumb\|alt=orgone_heptatonic.jpg\|Orgone heptatonic]]

			Orgone, the 4 & 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].

	[[Subgroup]]: 2.7.11		[[Subgroup]]: 2.7.11

	[[Comma list]]: 65536/65219		[[Comma list]]: [[65536/65219]]

	~~[[Sval]] [[mapping]]: [~~{{~~val~~\| 1 2 4 ~~}}, {{val~~\| 0 3 -2 }}]		{{Mapping\|legend=2\| 1 2 4 \| 0 3 -2 }}

	~~[[POTE generator]]: ~77/64~~ = ~~323.372~~		{{Mapping\|legend=3\| 1 0 0 2 4 \| 0 0 0 3 -2 }}

	{{Optimal ET sequence\|legend=1\| 7, 11, 15, 26~~, 37, 63~~, 89, 115, 141, 167, 308, ~~475bc~~, ~~783bc~~ }}		: [[gencom]]: [2 77/64; 65536/65219]

			[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372

			{{Optimal ET sequence\|legend=1\| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783 }}

			[[Tp tuning #T2 tuning\|RMS error]]: 0.1888 cents

	==== Oregon ====		==== Oregon ====
			{{See also\| Chromatic pairs #Oregon }}

	The subgroup 2.9.15.7.11 is the [[11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[porcupine]] restricted to this subgroup.		The subgroup 2.9.15.7.11 is the [[11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[porcupine]] restricted to this subgroup.

	Subgroup: 2.9.15.7.11		[[Subgroup]]: 2.9.15.7.11

			[[Comma list]]: 55/54, 64/63, 100/99

			{{Mapping\|legend=2\| 1 1 1 5 2 \| 0 3 4 -3 2 }}

			{{Mapping\|legend=3\| 1 2 3 2 4 \| 0 -3/2 -5/2 3 -2 }}

	~~Comma list~~: 55/54, 64/63, 100/99		: [[gencom]]: [2 6/5; 55/54 64/63 100/99]

	~~Sval mapping:~~ [~~{{val~~\| 1 1 1 5 2 }}, ~~{{val\|0 3 4 -3 2 }}]~~		[[Optimal tuning]] ([[Tp tuning\|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
			[[Optimal tuning]] (inharmonic [[POTE]]): ~2 = 1\1, ~6/5 = 326.139

	~~POTE generator: ~6/5~~ = ~~326.139~~		{{Optimal ET sequence\|legend=1\| 7, 11, 37b, 48b, 59b }}

	~~{{Optimal ET sequence~~\|~~legend=1\| 7, 11, 59b, 70bc, 81bcd, 92bcd }}~~		[[Tp tuning #T2 tuning\|RMS error]]: 2.550 cents

	===== Orca =====		===== Orca =====

CompactStar at 01:37, 22 April 2024

2024-04-22T01:37:07Z

← Older revision		Revision as of 01:37, 22 April 2024
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	'''~~The~~ Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].		'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].

	== Orgonismic ==		== Orgonismic ==

CompactStar: Check "Orgonisma"

2024-03-04T04:15:50Z

Check "Orgonisma"

← Older revision		Revision as of 04:15, 4 March 2024
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	~~Welcome to~~ Orgonia, ~~the commatic realm of~~ the [[orgonisma]]~~, the [[11-limit]] [[comma]] 65536/65219!~~		'''The Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].

	== Orgonismic ==		== Orgonismic ==
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	== Subgroup temperaments ==		== Subgroup temperaments ==
	=== Orgone ===		=== Orgone ===
			{{Main\|Orgone}}
	[[File:orgone_heptatonic.jpg\|thumb\|alt=orgone_heptatonic.jpg\|Orgone heptatonic]]		[[File:orgone_heptatonic.jpg\|thumb\|alt=orgone_heptatonic.jpg\|Orgone heptatonic]]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T16:22:00Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 16:22, 7 May 2023
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	* [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.		* [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.

	{{~~Val list~~\|legend=1\| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}		{{Optimal ET sequence\|legend=1\| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}

	[[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11		[[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11
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	[[POTE generator]]: ~77/64 = 323.372		[[POTE generator]]: ~77/64 = 323.372

	{{~~Val list~~\|legend=1\| 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc }}		{{Optimal ET sequence\|legend=1\| 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc }}

	==== Oregon ====		==== Oregon ====
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	POTE generator: ~6/5 = 326.139		POTE generator: ~6/5 = 326.139

	Optimal ~~GPV~~ sequence~~: {{val list~~\| 7, 11, 59b, 70bc, 81bcd, 92bcd }}		{{Optimal ET sequence\|legend=1\| 7, 11, 59b, 70bc, 81bcd, 92bcd }}

	===== Orca =====		===== Orca =====
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	POTE generator: ~6/5 = 326.644		POTE generator: ~6/5 = 326.644

	Optimal ~~GPV~~ sequence~~: {{val list~~\| 7, 11, 92bcd, 103bcd }}		{{Optimal ET sequence\|legend=1\| 7, 11, 92bcd, 103bcd }}

	===== Ork =====		===== Ork =====
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	POTE generator: ~17/14 = 325.714		POTE generator: ~17/14 = 325.714

	Optimal ~~GPV~~ sequence~~: {{val list~~\| 11, 37, 48, 59, 70c }}		{{Optimal ET sequence\|legend=1\| 11, 37, 48, 59, 70c }}

	[[Category:Orgonia]]		[[Category:Orgonia]]
	[[Category:Commatic realms]]		[[Category:Commatic realms]]

Cmloegcmluin: add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group

2023-05-05T23:42:40Z

add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group

← Older revision		Revision as of 23:42, 5 May 2023
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	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[Eigenmonzo basis]]: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.		* [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.

	{{Val list\|legend=1\| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}		{{Val list\|legend=1\| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}

FloraC: Cleanup

2022-08-03T12:57:24Z

Cleanup

← Older revision		Revision as of 12:57, 3 August 2022
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	Welcome to Orgonia, the commatic realm of the [[orgonisma]], the [[~~11-limit\|~~11-limit]] [[~~Comma\|~~comma]] 65536/65219!		Welcome to Orgonia, the commatic realm of the [[orgonisma]], the [[11-limit]] [[comma]] 65536/65219!

	== Orgonismic ~~temperament~~ ==		== Orgonismic ==
	~~Comma~~: ~~65536/65219~~		[[Subgroup]]: 2.3.5.7.11

	[[~~Eigenmonzo_subgroup\|Minimax tuning subgroup~~]]: ~~2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (~~65536/65219~~)^(1/5), which is 1.679 cents, and the [[5-limit\|5-limit]] just.~~		[[Comma list]]: 65536/65219

	Mapping: ~~<<~~1 0 0 2 4]		[[Mapping]]: <br>
			[{{val\| 1 0 0 2 4 }}<br>
			{{val\| 0 1 0 0 0 }}<br>
			{{val\| 0 0 1 0 0 }}<br>
			{{val\| 0 0 0 3 -2 }}]

	[0 1 ~~0 0 0~~]		[[Minimax tuning]]:
			* [[Eigenmonzo basis]]: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.

	~~[0 0~~ 1 ~~0 0]~~		{{Val list\|legend=1\| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}

	[~~0 0 0~~ 3 ~~-2]\|\|~~		[[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11

	~~EDOs~~: ~~15, 19, 22, 37, 41, 89, 111, 130, 152, 282~~		== Subgroup temperaments ==
			=== Orgone ===
			[[File:orgone_heptatonic.jpg\|thumb\|alt=orgone_heptatonic.jpg\|Orgone heptatonic]]

	[[~~Spectrum_of_a_temperament\|Spectrum~~]]: ~~4/3, 11/8, 12/11, 5/4, 8/~~7~~, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/~~11		[[Subgroup]]: 2.7.11

	~~== Subgroup temperaments ==~~		[[Comma list]]: 65536/65219
	~~== Orgone ==~~
	~~Commas~~:65536/65219

	~~Subgroup~~: 2~~.7.11~~		[[Sval]] [[mapping]]: [{{val\| 1 2 4 }}, {{val\| 0 3 -2 }}]

	POTE generator: ~77/64 = 323.372		[[POTE generator]]: ~77/64 = 323.372

	~~Sval mapping: [<~~1 ~~2 4~~\|, ~~<0 3 -2\|]~~		{{Val list\|legend=1\| 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc }}

	~~EDOs:~~ 7, 11, ~~15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc~~		==== Oregon ====
			The subgroup 2.9.15.7.11 is the [[11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[porcupine]] restricted to this subgroup.

	~~[[File~~:~~orgone_heptatonic~~.~~jpg\|alt=orgone_heptatonic~~.~~jpg\|orgone_heptatonic~~.~~jpg]]~~		Subgroup: 2.9.15.7.11

	~~=== Oregon ===~~		Comma list: 55/54, 64/63, 100/99
	~~Commas~~: 55/54, 64/63, 100/99

	~~Subgroup~~: 2~~.9.15.7.11~~		Sval mapping: [{{val\| 1 1 1 5 2 }}, {{val\|0 3 4 -3 2 }}]

	POTE generator: ~6/5 = 326.139		POTE generator: ~6/5 = 326.139

	~~Sval mapping~~: ~~[<1 1 1 5 2~~\|, ~~<0 3 4 -3 2\|]~~		Optimal GPV sequence: {{val list\| 7, 11, 59b, 70bc, 81bcd, 92bcd }}

	~~EDOs~~: ~~7, 11, 59b, 70bc, 81bcd, 92bcd~~		===== Orca =====
			Subgroup: 2.9.15.7.11.17
	~~The subgroup~~ 2.9.15.7.11 is the [[11-limit\|11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo\|11edo]] acts like [[22edo\|22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine_family\|porcupine temperament]] restricted to this subgroup.

	~~==== Orca ====~~		Comma list: 55/54, 64/63, 100/99, 85/84
	~~Commas~~: 55/54, 64/63, 100/99, 85/84

	~~Subgroup~~: 2~~.9.15.~~7~~.11.17~~		Sval mapping: [{{val\| 1 1 1 5 2 7 }}, {{val\| 0 3 4 -3 2 -4 }}]

	POTE generator: ~6/5 = 326.644		POTE generator: ~6/5 = 326.644

	~~Sval mapping~~: ~~[<1 1 1 5 2~~ 7\|, ~~<0 3 4 -3 2 -4\|]~~		Optimal GPV sequence: {{val list\| 7, 11, 92bcd, 103bcd }}

	~~EDOs~~: 7, 11~~, 92bcd, 103bcd~~		===== Ork =====
			Subgroup: 2.9.15.7.11.17

	~~==== Ork ====~~		Comma list: 99/98, 121/120, 136/135, 256/255
	~~Commas~~: 99/98, 121/120, 136/135, 256/255

	~~Subgroup~~: 2~~.9.15.7.11.17~~		Sval mapping: [{{val\| 1 1 5 2 4 3 }}, {{val\| 0 8 -4 3 -2 4 }}]

	POTE generator: ~17/14 = 325.714		POTE generator: ~17/14 = 325.714

	~~Sval mapping~~: ~~[<1 1 5 2 4 3~~\|~~, <0 8 -4 3 -2 4\|]~~		Optimal GPV sequence: {{val list\| 11, 37, 48, 59, 70c }}

	~~EDOs:~~ 11, 37, 48, 59, 70c

	[[Category:Orgonia]]		[[Category:Orgonia]]
	[[Category:Commatic realms]]		[[Category:Commatic realms]]

Inthar: /* =Orca = */

2022-03-03T02:15:58Z

=Orca =

← Older revision		Revision as of 02:15, 3 March 2022
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	The subgroup 2.9.15.7.11 is the [[11-limit\|11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo\|11edo]] acts like [[22edo\|22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine_family\|porcupine temperament]] restricted to this subgroup.		The subgroup 2.9.15.7.11 is the [[11-limit\|11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo\|11edo]] acts like [[22edo\|22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine_family\|porcupine temperament]] restricted to this subgroup.

	=== =Orca ====		==== Orca ====
	Commas: 55/54, 64/63, 100/99, 85/84		Commas: 55/54, 64/63, 100/99, 85/84

Fredg999: Misc. edits, categories

2022-03-02T22:26:06Z

Misc. edits, categories

← Older revision		Revision as of 22:26, 2 March 2022
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	~~__FORCETOC__~~
	Welcome to Orgonia, the commatic realm of the [[orgonisma]], the [[11-limit\|11-limit]] [[Comma\|comma]] 65536/65219!		Welcome to Orgonia, the commatic realm of the [[orgonisma]], the [[11-limit\|11-limit]] [[Comma\|comma]] 65536/65219!

	=Orgonismic temperament=		== Orgonismic temperament ==
	Comma: 65536/65219		Comma: 65536/65219

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	[[Spectrum_of_a_temperament\|Spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11		[[Spectrum_of_a_temperament\|Spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11

	=Subgroup temperaments=		== Subgroup temperaments ==
			== Orgone ==
	==Orgone==
	Commas:65536/65219		Commas:65536/65219

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	[[File:orgone_heptatonic.jpg\|alt=orgone_heptatonic.jpg\|orgone_heptatonic.jpg]]		[[File:orgone_heptatonic.jpg\|alt=orgone_heptatonic.jpg\|orgone_heptatonic.jpg]]

	==Oregon==		=== Oregon ===
	Commas: 55/54, 64/63, 100/99		Commas: 55/54, 64/63, 100/99

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	The subgroup 2.9.15.7.11 is the [[11-limit\|11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo\|11edo]] acts like [[22edo\|22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine_family\|porcupine temperament]] restricted to this subgroup.		The subgroup 2.9.15.7.11 is the [[11-limit\|11-limit]] [[kN_subgroups\|211 subgroup]], the largest subgroup of the 11-limit on which [[11edo\|11edo]] acts like [[22edo\|22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine_family\|porcupine temperament]] restricted to this subgroup.

	===Orca===		=== =Orca ====
	Commas: 55/54, 64/63, 100/99, 85/84		Commas: 55/54, 64/63, 100/99, 85/84

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	EDOs: 7, 11, 92bcd, 103bcd		EDOs: 7, 11, 92bcd, 103bcd

	===Ork===		==== Ork ====
	Commas: 99/98, 121/120, 136/135, 256/255		Commas: 99/98, 121/120, 136/135, 256/255

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	[[Category:Orgonia]]		[[Category:Orgonia]]
			[[Category:Commatic realms]]