Tetracot (temperament) - Revision history

Inthar: Explicitly state subgroup

2026-07-01T06:21:26Z

Explicitly state subgroup

← Older revision		Revision as of 06:21, 1 July 2026
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	}}		}}

	'''Tetracot''', [27 & 34] or [34 & 41], is a temperament that splits 3/2 into four flattened 10/9's.		'''Tetracot''', 2.3.5[27 & 34] or 2.3.5[34 & 41], is a temperament that splits 3/2 into four flattened 10/9's.

	== Interval chain ==		== Interval chain ==

Inthar: /* Extensions */

2026-04-13T04:46:08Z

Extensions

← Older revision		Revision as of 04:46, 13 April 2026
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	*** {{adv\|Modus tempers out 64/63.}}		*** {{adv\|Modus tempers out 64/63.}}
	*** {{adv\|Wollemia tempers out 126/125.}}		*** {{adv\|Wollemia tempers out 126/125.}}
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). ~~{{Adv\|The elegance of the extension can also be seen in the fact that it tempers out S49.}}~~ Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

	== List of patent vals ==		== List of patent vals ==

Inthar: /* Extensions */

2026-04-13T04:42:07Z

Extensions

← Older revision		Revision as of 04:42, 13 April 2026
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	*** {{adv\|Modus tempers out 64/63.}}		*** {{adv\|Modus tempers out 64/63.}}
	*** {{adv\|Wollemia tempers out 126/125.}}		*** {{adv\|Wollemia tempers out 126/125.}}
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). {{Adv\|The elegance of the extension can also be seen in the fact that it tempers out S49.}} Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

	== List of patent vals ==		== List of patent vals ==

Inthar: /* Extensions */

2026-04-13T04:40:04Z

Extensions

← Older revision		Revision as of 04:40, 13 April 2026
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	*** {{adv\|Bunya tempers out 225/224, the [[Marvel]] comma.}}		*** {{adv\|Bunya tempers out 225/224, the [[Marvel]] comma.}}
	*** {{adv\|Monkey is the extension tempering out [[5120/5103]], the aberschisma.}}		*** {{adv\|Monkey is the extension tempering out [[5120/5103]], the aberschisma.}}
	*** {{adv\|Modus tempers out 64/63 ~~or equivalently 4375/4374~~.}}		*** {{adv\|Modus tempers out 64/63.}}
	*** {{adv\|Wollemia tempers out 126/125.}}		*** {{adv\|Wollemia tempers out 126/125.}}
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

Inthar: /* Extensions */

2026-04-05T03:04:48Z

Extensions

← Older revision		Revision as of 03:04, 5 April 2026
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	* Prime 11 is often added by equating 10/9 with 11/10 (thus placing 11/8 at +10 generators), but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo). An alternate extension (27p & 34), associated with 7-limit Wollemia, places 11/8 at -24 generators.		* Prime 11 is often added by equating 10/9 with 11/10 (thus placing 11/8 at +10 generators), but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo). An alternate extension (27p & 34), associated with 7-limit Wollemia, places 11/8 at -24 generators.
	* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).		* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).
	** In terms of commas:		** {{adv\|In terms of commas:}}
	*** Bunya tempers out 225/224, the [[Marvel]] comma.		*** {{adv\|Bunya tempers out 225/224, the [[Marvel]] comma.}}
	*** Monkey is the extension tempering out [[5120/5103]], the aberschisma.		*** {{adv\|Monkey is the extension tempering out [[5120/5103]], the aberschisma.}}
	*** Modus tempers out 64/63 or equivalently 4375/4374.		*** {{adv\|Modus tempers out 64/63 or equivalently 4375/4374.}}
	*** Wollemia tempers out 126/125.		*** {{adv\|Wollemia tempers out 126/125.}}
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

Inthar: /* Extensions */

2026-04-05T03:04:01Z

Extensions

← Older revision		Revision as of 03:04, 5 April 2026
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	*** Bunya tempers out 225/224, the [[Marvel]] comma.		*** Bunya tempers out 225/224, the [[Marvel]] comma.
	*** Monkey is the extension tempering out [[5120/5103]], the aberschisma.		*** Monkey is the extension tempering out [[5120/5103]], the aberschisma.
	*** Modus tempers out 64/63.		*** Modus tempers out 64/63 or equivalently 4375/4374.
	*** Wollemia tempers out 126/125.		*** Wollemia tempers out 126/125.
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

Inthar: /* Extensions */

2026-04-05T03:01:23Z

Extensions

← Older revision		Revision as of 03:01, 5 April 2026
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	* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).		* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).
	** In terms of commas:		** In terms of commas:
	*** Bunya tempers out 225/224, the Marvel comma.		*** Bunya tempers out 225/224, the [[Marvel]] comma.
	*** Monkey is the extension tempering out [[5120/5103]], the aberschisma.		*** Monkey is the extension tempering out [[5120/5103]], the aberschisma.
	*** Modus tempers out 64/63.		*** Modus tempers out 64/63.

Inthar: /* Extensions */

2026-04-05T03:01:03Z

Extensions

← Older revision		Revision as of 03:01, 5 April 2026
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	* Prime 11 is often added by equating 10/9 with 11/10 (thus placing 11/8 at +10 generators), but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo). An alternate extension (27p & 34), associated with 7-limit Wollemia, places 11/8 at -24 generators.		* Prime 11 is often added by equating 10/9 with 11/10 (thus placing 11/8 at +10 generators), but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo). An alternate extension (27p & 34), associated with 7-limit Wollemia, places 11/8 at -24 generators.
	* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).		* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).
	** Monkey is ~~notable because it's~~ the extension tempering out [[5120/5103]], the aberschisma.		** In terms of commas:
			*** Bunya tempers out 225/224, the Marvel comma.
			*** Monkey is the extension tempering out [[5120/5103]], the aberschisma.
			*** Modus tempers out 64/63.
			*** Wollemia tempers out 126/125.
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

Inthar: /* Extensions */

2026-04-04T02:16:07Z

Extensions

← Older revision		Revision as of 02:16, 4 April 2026
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	* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).		* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).
	** Monkey is notable because it's the extension tempering out [[5120/5103]], the aberschisma.		** Monkey is notable because it's the extension tempering out [[5120/5103]], the aberschisma.
	** The weak extension [[Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

	== List of patent vals ==		== List of patent vals ==

Inthar: /* Extensions */

2026-04-04T01:29:20Z

Extensions

← Older revision		Revision as of 01:29, 4 April 2026
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	* Prime 11 is often added by equating 10/9 with 11/10 (thus placing 11/8 at +10 generators), but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo). An alternate extension (27p & 34), associated with 7-limit Wollemia, places 11/8 at -24 generators.		* Prime 11 is often added by equating 10/9 with 11/10 (thus placing 11/8 at +10 generators), but this is questionable because it produces either a very sharp 11/8 (as in 27edo and 34edo) or a flat 5/4 (as in 41edo and 48edo). An alternate extension (27p & 34), associated with 7-limit Wollemia, places 11/8 at -24 generators.
	* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).		* There isn't a canonical way to add prime 7. This is because 27edo and 41edo have good 7 approximations but 34edo does not. There are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41 or 41 & 48), Modus (27 & 34d), and Wollemia (27 & 34).
	** ~~Moneky~~ is notable because it's the extension tempering out [[5120/5103]], the aberschisma.		** Monkey is notable because it's the extension tempering out [[5120/5103]], the aberschisma.
	** The weak extension [[Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).

← Older revision		Revision as of 04:40, 13 April 2026
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	*** {{adv\|Bunya tempers out 225/224, the [[Marvel]] comma.}}		*** {{adv\|Bunya tempers out 225/224, the [[Marvel]] comma.}}
	*** {{adv\|Monkey is the extension tempering out [[5120/5103]], the aberschisma.}}		*** {{adv\|Monkey is the extension tempering out [[5120/5103]], the aberschisma.}}
	*** {{adv\|Modus tempers out 64/63 ~~or equivalently 4375/4374~~.}}		*** {{adv\|Modus tempers out 64/63.}}
	*** {{adv\|Wollemia tempers out 126/125.}}		*** {{adv\|Wollemia tempers out 126/125.}}
	** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).		** The weak extension [[Octacot (temperament)\|Octacot]] (27 & 41) is more elegant; it splits the Tetracot generator into two semitones (about 88.1c) representing 21/20, thus equating three Octacot generators with 7/6 (and 11 of them with 7/4). Octacot can be extended to have prime 19 (at 17 generators) by equating 21/20 to 20/19 (equivalently, 10/9 to 21/19 or 27/20 to 19/14).