Archytas clan - Revision history

CompactStar: /* Sixix */

2026-11-06T08:24:14Z

Sixix

← Older revision		Revision as of 08:24, 6 November 2026
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	Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of [[5/4]] (the 369-cent one inherited from [[13edo]]). It is also supported by [[57edo\|57b-edo]], which uses the sharper of [[57edo]]'s two diatonic fifths.		Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of [[5/4]] (the 369-cent one inherited from [[13edo]]). It is also supported by [[57edo\|57b-edo]], which uses the sharper of [[57edo]]'s two diatonic fifths.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

CompactStar: /* Sixix */

2026-11-06T08:24:07Z

Sixix

← Older revision		Revision as of 08:24, 6 November 2026
Line 663:		Line 663:
	{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}		{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}

	Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of [[5/4]] (the 369-cent one inherited from [[13edo]]).		Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of [[5/4]] (the 369-cent one inherited from [[13edo]]). It is also supported by [[57edo\|57b-edo]], which uses the sharper of [[57edo]]'s two diatonic fifths.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

CompactStar: /* Sixix */

2026-11-05T21:13:11Z

Sixix

← Older revision		Revision as of 21:13, 5 November 2026
Line 663:		Line 663:
	{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}		{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}

	Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of 5/4 (the 369-cent one inherited from [[13edo]]).		Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of [[5/4]] (the 369-cent one inherited from [[13edo]]).

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

CompactStar: /* Sixix */

2026-11-05T21:12:52Z

Sixix

← Older revision		Revision as of 21:12, 5 November 2026
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	{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}		{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}

	Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is [[~~39c~~-~~edo\|39c~~-~~edo~~]].		Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of 5/4 (the 369-cent one inherited from [[13edo]]).

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

CompactStar: /* Sixix */

2026-11-05T21:12:15Z

Sixix

← Older revision		Revision as of 21:12, 5 November 2026
Line 663:		Line 663:
	{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}		{{See also\| Dual-fifth temperaments #Dual-3 Sixix }}

	Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot.		Sixix tempers out 3125/2916 and may be described as {{nowrap\| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot. An important val not in the [[optimal ET sequence]] is [[39c-edo\|39c-edo]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Wording (canonicalize -> canonize)

2026-10-27T16:53:14Z

Wording (canonicalize -> canonize)

← Older revision		Revision as of 16:53, 27 October 2026
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	Kangaroo splits the [[3/1\|perfect twelfth]] into three [[35/24]][[~]][[40/27]] generators; its [[ploidacot]] is alpha-tricot. The 11-limit extension simply equates the generator to [[16/11]]. This favors a particularly sharp diatonic fifth (around 710–720 cents) because otherwise the ~[[5/4]] will be too flat.		Kangaroo splits the [[3/1\|perfect twelfth]] into three [[35/24]][[~]][[40/27]] generators; its [[ploidacot]] is alpha-tricot. The 11-limit extension simply equates the generator to [[16/11]]. This favors a particularly sharp diatonic fifth (around 710–720 cents) because otherwise the ~[[5/4]] will be too flat.

	Originally the canonical extension of 5-limit kangaroo was [[trienstonic clan #Parakangaroo\|parakangaroo]], but it was ~~decanonicalized~~ in 2024 in favor of this extension because parakangaroo is an [[exotemperament]] that only supports the [[patent val]] of [[15edo]], while this extension is a bit more practical since it is at least low-medium accuracy and supports the [[patent val]]s of 15edo, [[17edo]] and [[32edo]].		Originally the canonical extension of 5-limit kangaroo was [[trienstonic clan #Parakangaroo\|parakangaroo]], but it was decanonized in 2024 in favor of this extension because parakangaroo is an [[exotemperament]] that only supports the [[patent val]] of [[15edo]], while this extension is a bit more practical since it is at least low-medium accuracy and supports the [[patent val]]s of 15edo, [[17edo]] and [[32edo]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: /* Archy */ + link to phlegyas

2026-10-19T12:38:16Z

Archy: + link to phlegyas

← Older revision		Revision as of 12:38, 19 October 2026
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
			* ''[[Phlegyas]]'' (+10/9) → [[Very low accuracy temperaments #Phlegyas\|Very low accuracy temperaments]]
			* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
	* ''[[Mother]]'' (+16/15) → [[Father family #Mother\|Father family]]		* ''[[Mother]]'' (+16/15) → [[Father family #Mother\|Father family]]
	* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]		* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]
	* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
	* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic\|Dicot family]]		* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic\|Dicot family]]
	* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]

CompactStar: /* 11-limit */

2026-10-15T17:56:06Z

11-limit

← Older revision		Revision as of 17:56, 15 October 2026
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	=== 11-limit ===		=== 11-limit ===
	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7.11

	Comma list: 55/54, 64/63, 245/242		Comma list: 55/54, 64/63, 245/242

Lucius Chiaraviglio: /* Fervor */ Found that 9704/9375 is actually a typo for 9604/9375 — fix this

2026-10-15T16:28:53Z

Fervor: Found that 9704/9375 is actually a typo for 9604/9375 — fix this

← Older revision		Revision as of 16:28, 15 October 2026
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''

	Fervor tempers out [[~~9704~~/9375]] and may be described as {{nowrap\| 25 & 27 }}. It splits the [[6/1\|6th harmonic]] into five generators of [[~]][[10/7]]; its ploidacot is beta-pentacot. The 11-limit extension simply equates the generator to [[16/11]]. [[27edo]] is about as accurate as it can be tuned.		Fervor tempers out [[9604/9375]] and may be described as {{nowrap\| 25 & 27 }}. It splits the [[6/1\|6th harmonic]] into five generators of [[~]][[10/7]]; its ploidacot is beta-pentacot. The 11-limit extension simply equates the generator to [[16/11]]. [[27edo]] is about as accurate as it can be tuned.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Lucius Chiaraviglio: /* Fervor */ Add link to 9704/9375, even though the page doesn't exist yet

2026-10-15T15:22:24Z

Fervor: Add link to 9704/9375, even though the page doesn't exist yet

← Older revision		Revision as of 15:22, 15 October 2026
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''

	Fervor tempers out 9704/9375 and may be described as {{nowrap\| 25 & 27 }}. It splits the [[6/1\|6th harmonic]] into five generators of [[~]][[10/7]]; its ploidacot is beta-pentacot. The 11-limit extension simply equates the generator to [[16/11]]. [[27edo]] is about as accurate as it can be tuned.		Fervor tempers out [[9704/9375]] and may be described as {{nowrap\| 25 & 27 }}. It splits the [[6/1\|6th harmonic]] into five generators of [[~]][[10/7]]; its ploidacot is beta-pentacot. The 11-limit extension simply equates the generator to [[16/11]]. [[27edo]] is about as accurate as it can be tuned.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

← Older revision		Revision as of 12:38, 19 October 2026
Line 44:		Line 44:

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
			* ''[[Phlegyas]]'' (+10/9) → [[Very low accuracy temperaments #Phlegyas\|Very low accuracy temperaments]]
			* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
	* ''[[Mother]]'' (+16/15) → [[Father family #Mother\|Father family]]		* ''[[Mother]]'' (+16/15) → [[Father family #Mother\|Father family]]
	* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]		* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]
	* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
	* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic\|Dicot family]]		* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic\|Dicot family]]
	* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]