The Biosphere - Revision history

Overthink: replaced "full 13-limit" with 2.3.5.7.11.13

2025-12-13T01:19:33Z

replaced "full 13-limit" with 2.3.5.7.11.13

← Older revision		Revision as of 01:19, 13 December 2025
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	Extends 11-limit superpyth as 22&49.		Extends 11-limit superpyth as 22&49.

	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 64/63, 78/77, 91/90, 100/99		[[Comma list]]: 64/63, 78/77, 91/90, 100/99
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	{{see also\| Archytas clan #Quasisuper }}		{{see also\| Archytas clan #Quasisuper }}

	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 64/63, 78/77, 91/90, 121/120		[[Comma list]]: 64/63, 78/77, 91/90, 121/120
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	===== Full 13-limit ultrapyth =====		===== Full 13-limit ultrapyth =====
	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568		[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568
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	===== Ultramarine =====		===== Ultramarine =====
	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 64/63, 91/90, 100/99, 847/845		[[Comma list]]: 64/63, 91/90, 100/99, 847/845
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	Porcupinefish is the 13-limit extension of [[Porcupine\|porcupine]] that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments.		Porcupinefish is the 13-limit extension of [[Porcupine\|porcupine]] that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments.

	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 55/54, 64/63, 91/90, 100/99		[[Comma list]]: 55/54, 64/63, 91/90, 100/99
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	===== Full 13-limit godzilla =====		===== Full 13-limit godzilla =====
	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 45/44, 49/48, 78/77, 81/80		[[Comma list]]: 45/44, 49/48, 78/77, 81/80
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	===== Varan =====		===== Varan =====
	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 49/48, 66/65, 77/75, 81/80		[[Comma list]]: 49/48, 66/65, 77/75, 81/80
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	===== Baragon =====		===== Baragon =====
	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 49/48, 56/55, 81/80, 91/90		[[Comma list]]: 49/48, 56/55, 81/80, 91/90
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	{{see also\| Diaschismic family #Anguirus }}		{{see also\| Diaschismic family #Anguirus }}

	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 49/48, 56/55, 91/90, 352/351		[[Comma list]]: 49/48, 56/55, 91/90, 352/351
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	13-limit echidnic temperament, the 10&46 temperament, is about as accurate as a biosphere temperament can get.		13-limit echidnic temperament, the 10&46 temperament, is about as accurate as a biosphere temperament can get.

	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 91/90, 169/168, 385/384, 441/440		[[Comma list]]: 91/90, 169/168, 385/384, 441/440

Overthink: /* Biosphere */ more formal notation

2025-12-13T01:00:40Z

Biosphere: more formal notation

← Older revision		Revision as of 01:00, 13 December 2025
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	=== Biosphere ===		=== Biosphere ===
	Subgroup: ~~full~~ 13~~-limit~~		Subgroup: 2.3.5.7.11.13

	Comma list: 91/90		Comma list: 91/90

BudjarnLambeth: /* Oceanfront */

2025-06-10T00:00:53Z

Oceanfront

← Older revision		Revision as of 00:00, 10 June 2025
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	{{Optimal ET sequence\|legend=1\| 27, 32 }}		{{Optimal ET sequence\|legend=1\| 27, 32 }}

			Scales: [[Oceanfront scales]]

	==== Superpyth ====		==== Superpyth ====

FloraC: Undo revision 189182 by Dogwithabome (talk). Not an error, but an underspecific use of language

2025-04-01T11:37:33Z

Undo revision 189182 by Dogwithabome (talk). Not an error, but an underspecific use of language

← Older revision		Revision as of 11:37, 1 April 2025
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	The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate."		The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate."

	The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to 7-limit harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15.		The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to [[9-odd-limit]] harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15.

	The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI.		The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI.

Dogwithabome: i assume that "9-limit" was an error so i corrected it to 7-limit

2025-03-31T17:14:03Z

i assume that "9-limit" was an error so i corrected it to 7-limit

← Older revision		Revision as of 17:14, 31 March 2025
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	The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate."		The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate."

	The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to 9-limit harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15.		The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to 7-limit harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15.

	The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI.		The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI.

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

2023-05-07T18:43:34Z

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

← Older revision		Revision as of 18:43, 7 May 2023
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	{{val\| 0 0 1 -1 }}		{{val\| 0 0 1 -1 }}

	{{~~Val list~~\|legend=1\| 5, 9, 14, 17, 22, 27, 32, 46 }}		{{Optimal ET sequence\|legend=1\| 5, 9, 14, 17, 22, 27, 32, 46 }}

	=== Biosphere ===		=== Biosphere ===
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	{{val\| 0 0 0 0 1 0 }}		{{val\| 0 0 0 0 1 0 }}

	{{~~Val list~~\|legend=1\| 8d, 9, 10, 14cf, 15, 17c, 19, 22, 27e, 29, 31f, 37, 38df, 46 }}		{{Optimal ET sequence\|legend=1\| 8d, 9, 10, 14cf, 15, 17c, 19, 22, 27e, 29, 31f, 37, 38df, 46 }}

	== Rank two temperaments ==		== Rank two temperaments ==
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	[[POTE generator]]: ~4/3 = 486.090		[[POTE generator]]: ~4/3 = 486.090

	{{~~Val list~~\|legend=1\| 27, 32 }}		{{Optimal ET sequence\|legend=1\| 27, 32 }}

	==== Superpyth ====		==== Superpyth ====
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	[[POTE generator]]: ~4/3 = 489.521		[[POTE generator]]: ~4/3 = 489.521

	{{~~Val list~~\|legend=1\| 22, 27e, 49, 76bcde }}		{{Optimal ET sequence\|legend=1\| 22, 27e, 49, 76bcde }}

	[[Badness]]: 0.024673		[[Badness]]: 0.024673
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	[[POTE generator]]: ~4/3 = 491.996		[[POTE generator]]: ~4/3 = 491.996

	{{~~Val list~~\|legend=1\| 17c, 22, 39d, 61df, 100bcdf }}		{{Optimal ET sequence\|legend=1\| 17c, 22, 39d, 61df, 100bcdf }}

	[[Badness]]: 0.030219		[[Badness]]: 0.030219
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	[[POTE generator]]: ~4/3 = 486.255		[[POTE generator]]: ~4/3 = 486.255

	{{~~Val list~~\|legend=1\| 5, 32, 37 }}		{{Optimal ET sequence\|legend=1\| 5, 32, 37 }}

	===== Full 13-limit ultrapyth =====		===== Full 13-limit ultrapyth =====
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	[[POTE generator]]: ~4/3 = 486.500		[[POTE generator]]: ~4/3 = 486.500

	{{~~Val list~~\|legend=1\| 5, 32, 37 }}		{{Optimal ET sequence\|legend=1\| 5, 32, 37 }}

	[[Badness]]: 0.049172		[[Badness]]: 0.049172
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	[[POTE generator]]: ~4/3 = 486.189		[[POTE generator]]: ~4/3 = 486.189

	{{~~Val list~~\|legend=1\| 5e, 32e, 37, 79bcef, 116bbcef }}		{{Optimal ET sequence\|legend=1\| 5e, 32e, 37, 79bcef, 116bbcef }}

	[[Badness]]: 0.045653		[[Badness]]: 0.045653
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	[[POTE generator]]: ~10/9 = 162.277		[[POTE generator]]: ~10/9 = 162.277

	{{~~Val list~~\|legend=1\| 15, 22, 37, 59 }}		{{Optimal ET sequence\|legend=1\| 15, 22, 37, 59 }}

	[[Badness]]: 0.025314		[[Badness]]: 0.025314
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	[[POTE generator]]: ~7/6 = 251.507		[[POTE generator]]: ~7/6 = 251.507

	{{~~Val list~~\|legend=1\| 19, 24 }}		{{Optimal ET sequence\|legend=1\| 19, 24 }}

	==== Godzilla ====		==== Godzilla ====
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	[[POTE generator]]: ~7/6 = 252.429		[[POTE generator]]: ~7/6 = 252.429

	{{~~Val list~~\|legend=1\| 5, 14cf, 19 }}		{{Optimal ET sequence\|legend=1\| 5, 14cf, 19 }}

	===== Full 13-limit godzilla =====		===== Full 13-limit godzilla =====
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	[[POTE generator]]: ~7/6 = 253.603		[[POTE generator]]: ~7/6 = 253.603

	{{~~Val list~~\|legend=1\| 5e, 14cf, 19, 33cdff, 52cdff }}		{{Optimal ET sequence\|legend=1\| 5e, 14cf, 19, 33cdff, 52cdff }}

	[[Badness]]: 0.022503		[[Badness]]: 0.022503
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	[[POTE generator]]: ~7/6 = 251.165		[[POTE generator]]: ~7/6 = 251.165

	{{~~Val list~~\|legend=1\| 19e, 24, 43de }}		{{Optimal ET sequence\|legend=1\| 19e, 24, 43de }}

	[[Badness]]: 0.025676		[[Badness]]: 0.025676
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	[[POTE generator]]: ~7/6 = 251.198		[[POTE generator]]: ~7/6 = 251.198

	{{~~Val list~~\|legend=1\| 5, 14cef, 19, 24, 43d }}		{{Optimal ET sequence\|legend=1\| 5, 14cef, 19, 24, 43d }}

	[[Badness]]: 0.026703		[[Badness]]: 0.026703
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	[[POTE generator]]: ~8/7 = 247.691		[[POTE generator]]: ~8/7 = 247.691

	{{~~Val list~~\|legend=1\| 10, 24, 34, 58d, 92def }}		{{Optimal ET sequence\|legend=1\| 10, 24, 34, 58d, 92def }}

	[[Badness]]: 0.030829		[[Badness]]: 0.030829
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	[[POTE generator]]: ~8/7 = 235.088		[[POTE generator]]: ~8/7 = 235.088

	{{~~Val list~~\|legend=1\| 10, 46, 102, 148f, 194bcdf }}		{{Optimal ET sequence\|legend=1\| 10, 46, 102, 148f, 194bcdf }}

	[[Badness]]: 0.028874		[[Badness]]: 0.028874

FloraC: Categories

2022-03-02T22:58:58Z

Fredg999 category edits: Moving from Category:Temperament collection to Category:Temperament collections using Cat-a-lot

2022-02-28T17:08:54Z

Moving from Category:Temperament collection to Category:Temperament collections using Cat-a-lot

← Older revision		Revision as of 17:08, 28 February 2022
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	[[Category:Theory]]		[[Category:Theory]]
	[[Category:Temperament ~~collection~~]]		[[Category:Temperament collections]]
	[[Category:Biome]]		[[Category:Biome]]
	[[Category:Biosphere]]		[[Category:Biosphere]]

Xenllium at 02:41, 8 January 2022

2022-01-08T02:41:30Z

@@ Line 110: / Line 110: @@
 [[Badness]]: 0.049172
-===== Counterultrapyth =====
+===== Ultramarine =====
 Subgroup: full 13-limit
@@ Line 152: / Line 152: @@
 {{Val list|legend=1| 19, 24 }}
 ==== Anguirus ====

KingHyperio at 00:41, 26 November 2021

2021-11-26T00:41:23Z

← Older revision		Revision as of 00:41, 26 November 2021
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	=== Biosphere ===		=== Biosphere ===
	Subgroup: ~~2.3.5.7.11.~~13		Subgroup: full 13-limit

	Comma list: 91/90		Comma list: 91/90

← Older revision		Revision as of 22:58, 2 March 2022
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	[[Badness]]: 0.028874		[[Badness]]: 0.028874

	[[Category:~~Theory~~]]		[[Category:Regular temperament theory]]
	[[Category:~~Temperament collections~~]]		[[Category:Commatic realms]]
	[[Category:Biome]]		[[Category:Biome]]
	[[Category:Biosphere]]		[[Category:Biosphere]]