5L 3s/Temperaments - Revision history

VectorGraphics: Phase out wedgies

2025-06-12T04:16:04Z

Phase out wedgies

← Older revision		Revision as of 04:16, 12 June 2025
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	Mapping generators: ~2, ~21/16		Mapping generators: ~2, ~21/16

	~~Wedgie: <<4 21 -3 24 -16 -66\|\|~~

	{{Optimal ET sequence\|legend=1\| 48, 53, 111, 164d, 275d}}		{{Optimal ET sequence\|legend=1\| 48, 53, 111, 164d, 275d}}

ArrowHead294 at 17:21, 23 December 2024

2024-12-23T17:21:32Z

← Older revision		Revision as of 17:21, 23 December 2024
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	{{breadcrumb}}		{{breadcrumb}}
	[[Oneirotonic]] temperaments have a sort of analogy to diatonic temperaments superpyth and meantone in how they treat the large step. In diatonic the large step approximates 9/8 (a very good 9/8 in 12edo), but superpyth has 9/8 ~ 8/7, and meantone has 9/8 ~ 10/9. In oneirotonic the large step tends to approximate 10/9 (and is a very good 10/9 in 13edo which is the oneirotonic analogue to 12edo), but different oneiro temperaments do different things with it. In A-Team (13&18), 10/9 is equated with 9/8, making the major oneirothird a 5/4 (thus is "meantone" in that sense). In both Petrtri (13&21) and Tridec (21&29), 10/9 is equated with 11/10, making the major oneirothird a 11/9; and the perfect oneirofourth is equated to 13/10. So the compressed major triad add2 (~~R-M2-M3-M5~~, M5 = major oneirofifth = minor fifth in 13edo) is interpreted as 9:10:11:13 in petrtri, analogous to meantone's 8:9:10:12. Thus Petrtri and Tridec are the same temperament when you only care about the 9:10:11:13, or equivalently the 2.9/5.11/5.13/5 subgroup. This is one reason why Tridec can be viewed as the oneirotonic analogue of [[flattone]]~~: it~~'s a flatter variant of the flat-of-13edo oneiro temperament on the 2.9/5.11/5.13/5 subgroup.		[[Oneirotonic]] temperaments have a sort of analogy to diatonic temperaments superpyth and meantone in how they treat the large step. In diatonic the large step approximates 9/8 (a very good 9/8 in 12edo), but [[superpyth]] has {{nowrap\|9/8 ~ 8/7}}, and meantone has {{nowrap\|9/8 ~ 10/9}}. In oneirotonic the large step tends to approximate 10/9 (and is a very good 10/9 in 13edo which is the oneirotonic analogue to 12edo), but different oneiro temperaments do different things with it. In A-Team ({{nowrap\|13 & 18}}), 10/9 is equated with 9/8, making the major oneirothird a 5/4 (thus is "meantone" in that sense). In both Petrtri ({{nowrap\|13 & 21}}) and Tridec ({{nowrap\|21 & 29}}), 10/9 is equated with 11/10, making the major oneirothird a 11/9; and the perfect oneirofourth is equated to 13/10. So the compressed major triad add2 (R–M2–M3–M5, {{nowrap\|M5 {{=}} major oneirofifth}} {{nowrap\|{{=}} minor fifth in 13edo}}) is interpreted as 9:10:11:13 in petrtri, analogous to meantone's 8:9:10:12. Thus Petrtri and Tridec are the same temperament when you only care about the 9:10:11:13, or equivalently the 2.9/5.11/5.13/5 subgroup. This is one reason why Tridec can be viewed as the oneirotonic analogue of [[flattone]]—it's a flatter variant of the flat-of-13edo oneiro temperament on the 2.9/5.11/5.13/5 subgroup.

	Vulture/[[~~Hemifamity_temperaments~~\|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only [[harmonic entropy]] minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.		Vulture/[[Hemifamity temperaments\|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only [[harmonic entropy]] minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.

	== Petrtri ==		== Petrtri ==

ArrowHead294 at 20:40, 25 November 2024

2024-11-25T20:40:04Z

← Older revision		Revision as of 20:40, 25 November 2024
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			{{breadcrumb}}
	[[Oneirotonic]] temperaments have a sort of analogy to diatonic temperaments superpyth and meantone in how they treat the large step. In diatonic the large step approximates 9/8 (a very good 9/8 in 12edo), but superpyth has 9/8 ~ 8/7, and meantone has 9/8 ~ 10/9. In oneirotonic the large step tends to approximate 10/9 (and is a very good 10/9 in 13edo which is the oneirotonic analogue to 12edo), but different oneiro temperaments do different things with it. In A-Team (13&18), 10/9 is equated with 9/8, making the major oneirothird a 5/4 (thus is "meantone" in that sense). In both Petrtri (13&21) and Tridec (21&29), 10/9 is equated with 11/10, making the major oneirothird a 11/9; and the perfect oneirofourth is equated to 13/10. So the compressed major triad add2 (R-M2-M3-M5, M5 = major oneirofifth = minor fifth in 13edo) is interpreted as 9:10:11:13 in petrtri, analogous to meantone's 8:9:10:12. Thus Petrtri and Tridec are the same temperament when you only care about the 9:10:11:13, or equivalently the 2.9/5.11/5.13/5 subgroup. This is one reason why Tridec can be viewed as the oneirotonic analogue of [[flattone]]: it's a flatter variant of the flat-of-13edo oneiro temperament on the 2.9/5.11/5.13/5 subgroup.		[[Oneirotonic]] temperaments have a sort of analogy to diatonic temperaments superpyth and meantone in how they treat the large step. In diatonic the large step approximates 9/8 (a very good 9/8 in 12edo), but superpyth has 9/8 ~ 8/7, and meantone has 9/8 ~ 10/9. In oneirotonic the large step tends to approximate 10/9 (and is a very good 10/9 in 13edo which is the oneirotonic analogue to 12edo), but different oneiro temperaments do different things with it. In A-Team (13&18), 10/9 is equated with 9/8, making the major oneirothird a 5/4 (thus is "meantone" in that sense). In both Petrtri (13&21) and Tridec (21&29), 10/9 is equated with 11/10, making the major oneirothird a 11/9; and the perfect oneirofourth is equated to 13/10. So the compressed major triad add2 (R-M2-M3-M5, M5 = major oneirofifth = minor fifth in 13edo) is interpreted as 9:10:11:13 in petrtri, analogous to meantone's 8:9:10:12. Thus Petrtri and Tridec are the same temperament when you only care about the 9:10:11:13, or equivalently the 2.9/5.11/5.13/5 subgroup. This is one reason why Tridec can be viewed as the oneirotonic analogue of [[flattone]]: it's a flatter variant of the flat-of-13edo oneiro temperament on the 2.9/5.11/5.13/5 subgroup.

	Vulture/[[Hemifamity_temperaments\|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only [[harmonic entropy]] minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.		Vulture/[[Hemifamity_temperaments\|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only [[harmonic entropy]] minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.

	== Petrtri ==		== Petrtri ==
	Subgroup: 2.11/5.13/5		Subgroup: 2.11/5.13/5
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	! Size in POTE tuning		! Size in POTE tuning
	! Note name on Q		! Note name on Q
	! class="unsortable"\| Approximate ratios		! class="unsortable" \| Approximate ratios
	! #Gens up		! #Gens up
	\|-		\|-
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	! Size in POTE tuning		! Size in POTE tuning
	! Note name on Q		! Note name on Q
	! class="unsortable"\| Approximate ratios		! class="unsortable" \| Approximate ratios
	! #Gens up		! #Gens up
	\|-		\|-
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	! Size in 31edo		! Size in 31edo
	! Note name on Q		! Note name on Q
	! class="unsortable"\| Approximate ratios~~<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>~~		! class="unsortable" \| Approximate ratios*
	! #Gens up		! #Gens up
	\|-		\|-
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	\| +5		\| +5
	\|}		\|}
	<~~references~~/>		<nowiki />* The ratio interpretations that are not valid for 18edo are italicized.

	== Buzzard ==		== Buzzard ==
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	! Size in POTE tuning		! Size in POTE tuning
	! Note name on Q		! Note name on Q
	! class="unsortable"\| Approximate ratios		! class="unsortable" \| Approximate ratios
	! #Gens up		! #Gens up
	\|-		\|-

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

2023-05-07T18:06:14Z

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

← Older revision		Revision as of 18:06, 7 May 2023
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	Mapping generators: ~2, ~13/10		Mapping generators: ~2, ~13/10

	{{~~Vals~~\|legend=1\| 21, 29, 37 }}		{{Optimal ET sequence\|legend=1\| 21, 29, 37 }}

	==== Intervals ====		==== Intervals ====
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	Mapping generators: ~2, ~13/10		Mapping generators: ~2, ~13/10

	{{~~Vals~~\|legend=1\| 13, 21, 34 }}		{{Optimal ET sequence\|legend=1\| 13, 21, 34 }}

	==== Intervals ====		==== Intervals ====
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	Mapping generators: ~2, ~21/16		Mapping generators: ~2, ~21/16

	{{~~Vals~~\|legend=1\| 13, 18, 31, 44 }}		{{Optimal ET sequence\|legend=1\| 13, 18, 31, 44 }}

	=== Intervals ===		=== Intervals ===
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	Wedgie: <<4 21 -3 24 -16 -66\|\|		Wedgie: <<4 21 -3 24 -16 -66\|\|

	~~[[Val]]s:~~ {{~~Vals~~\| 48, 53, 111, 164d, 275d}}		{{Optimal ET sequence\|legend=1\| 48, 53, 111, 164d, 275d}}

	Badness: 0.0480		Badness: 0.0480

Francium: /* Petrtri */

2023-04-14T05:54:24Z

Petrtri

← Older revision		Revision as of 05:54, 14 April 2023
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	Mapping: [<1 0 1\|, <0 3 1\|]		Mapping: [<1 0 1\|, <0 3 1\|]

	EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c		EDOs: {{EDOs\|21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c}}

	=== Tridec ===		=== Tridec ===

Fredg999 category edits: Moving from Category:Temperament to Category:Lists of temperaments using Cat-a-lot

2022-02-28T17:23:12Z

Moving from Category:Temperament to Category:Lists of temperaments using Cat-a-lot

← Older revision		Revision as of 17:23, 28 February 2022
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	\|}		\|}

	[[Category:~~Temperament~~]]		[[Category:Lists of temperaments]]
	[[Category:Oneirotonic\|T]]		[[Category:Oneirotonic\|T]]

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2022-02-26T16:48:53Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 16:48, 26 February 2022
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	\|}		\|}

	~~[[Category:Theory]]~~
	[[Category:Temperament]]		[[Category:Temperament]]
	[[Category:Oneirotonic\|T]]		[[Category:Oneirotonic\|T]]

Cmloegcmluin: map → mapping

2021-11-05T20:21:41Z

map → mapping

← Older revision		Revision as of 20:21, 5 November 2021
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	[[Gencom\|Gencom]]: [2 13/10; 2200/2197]		[[Gencom\|Gencom]]: [2 13/10; 2200/2197]

	Gencom ~~map~~: [<1 0 -1/3 0 -1/3 2/3\|, <0 0 -4/3 0 5/3 -1/3\|]		Gencom mapping: [<1 0 -1/3 0 -1/3 2/3\|, <0 0 -4/3 0 5/3 -1/3\|]

	~~Map~~: [<1 0 1\|, <0 3 1\|]		Mapping: [<1 0 1\|, <0 3 1\|]

	EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c		EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c
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	Commas: 1728/1715, 5120/5103		Commas: 1728/1715, 5120/5103

	~~Map~~: [<1 0 -6 4\|, <0 4 21 -3\|]		Mapping: [<1 0 -6 4\|, <0 4 21 -3\|]

	Mapping generators: ~2, ~21/16		Mapping generators: ~2, ~21/16

Inthar: /* Petrtri */

2021-04-17T23:59:26Z

Petrtri

← Older revision		Revision as of 23:59, 17 April 2021
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	Vulture/[[Hemifamity_temperaments\|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only [[harmonic entropy]] minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.		Vulture/[[Hemifamity_temperaments\|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only [[harmonic entropy]] minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.
	== Petrtri ==		== Petrtri ==
	Subgroup: 2~~.9/5~~.11/5.13/5		Subgroup: 2.11/5.13/5

	~~Period~~: ~~1\1~~		Comma: 2200/2197

	~~Optimal ([[Lp tuning\|POL2]]) generator~~: ~~458.0950~~		Svalname: 3&5

	~~EDO generators:~~ [[~~13edo~~\|~~5\13~~]]~~, [[21edo\|8\21]], [[34edo\|~~13~~\34]]~~		[[Tp_tuning\|POT2 generator]]: ~13/10 = 455.012

	[[~~Comma~~]] ~~list~~: ~~100~~/~~99, 144~~/~~143~~		[[Gencom\|Gencom]]: [2 13/10; 2200/2197]

	~~[[Mapping]]~~: [~~⟨2:~~ 1~~, 9~~/~~5: 2, 11/5:~~ 0~~, 13/5:~~ 1~~], ⟨2: 0, 9~~/~~5: -~~3~~, 11~~/5: 3, 13/5: 1]]		Gencom map: [<1 0 -1/3 0 -1/3 2/3\|, <0 0 -4/3 0 5/3 -1/3\|]

	~~Mapping generators~~: ~2, ~~~13/10~~		Map: [<1 0 1\|, <0 3 1\|]

	~~{{Vals\|legend=1\| 13~~, 21, ~~34 }}~~		EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c

	=== Tridec ===		=== Tridec ===

Inthar: use new notation for svals

2021-04-12T03:34:51Z

use new notation for svals

← Older revision		Revision as of 03:34, 12 April 2021
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	[[Comma]] list: 100/99, 144/143		[[Comma]] list: 100/99, 144/143

	[[Mapping]] ~~(for 2~~, 9/5, 11/5, 13/5): ~~[⟨1 2 0~~ 1], ⟨0 -3 3 1]]		[[Mapping]]: [⟨2: 1, 9/5: 2, 11/5: 0, 13/5: 1], ⟨2: 0, 9/5: -3, 11/5: 3, 13/5: 1]]

	Mapping generators: ~2, ~13/10		Mapping generators: ~2, ~13/10
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	[[Comma]] list: 196/195, 847/845, 1001/1000		[[Comma]] list: 196/195, 847/845, 1001/1000

	[[Mapping]] ~~(for~~ 2, 3, 7/5, 11/5, 13/5): ~~[{{val\|1 5 2 0~~ 1}}, {{val\|0 -9 -4 3 1}}]		[[Mapping]]: [{{val\|2: 1, 3: 5, 7/5: 2, 11/5: 0, 13/5: 1}}, {{val\|2: 0, 3: -9, 7/5: -4, 11/5: 3, 13/5: 1}}]

	Mapping generators: ~2, ~13/10		Mapping generators: ~2, ~13/10
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	[[Comma]] list: 100/99, 144/143, 170/169, 221/220		[[Comma]] list: 100/99, 144/143, 170/169, 221/220

	[[Mapping]] (for 2, 5, 9, 11, 13, 17): [{{val\|1 5 7 5 6 6}}, {{val\|0 -7 -10 -4 -6 -5}}]		[[Mapping]] (for 2, 5, 9, 11, 13, 17): [{{val\|2: 1, 5: 5, 9: 7, 11: 5, 13: 6, 17: 6}}, {{val\|2: 0, 5: -7, 9: -10, 11: -4, 13: -6, 17: -5}}]

	Mapping generators: ~2, ~13/10		Mapping generators: ~2, ~13/10
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	[[Comma]] list: 81/80, 1029/1024		[[Comma]] list: 81/80, 1029/1024

	[[Mapping]] ~~(for 2, 5, 9, 21)~~: [{{val\|1 0 2 4}}, {{val\|0 6 3 1}}]		[[Mapping]]: [{{val\|2: 1, 5: 0, 9: 2, 21: 4}}, {{val\|2: 0, 5: 6, 9: 3, 21: 1}}]

	Mapping generators: ~2, ~21/16		Mapping generators: ~2, ~21/16