Septischismic clan - Revision history

FloraC: Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

2026-09-30T17:44:26Z

Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

← Older revision		Revision as of 17:44, 30 September 2026
Line 48:		Line 48:
	Comma list: 19712/19683, 41503/41472		Comma list: 19712/19683, 41503/41472

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 25 -33 \| 0 1 -14 23 }}		{{Mapping\|legend=2\| 1 0 25 -33 \| 0 1 -14 23 }}

	Optimal tunings:		Optimal tunings:
Line 501:		Line 501:
	Comma list: 2025/2023, 24576/24565, 390625/388962		Comma list: 2025/2023, 24576/24565, 390625/388962

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 4 1 -44 86 3 \| 0 2 -13 -28 5 }}		{{Mapping\|legend=2\| 4 1 -44 86 3 \| 0 2 -13 -28 5 }}

	Optimal tunings:		Optimal tunings:
Line 516:		Line 516:
	Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000		Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 4 1 -44 86 3 25 \| 0 2 -13 -28 5 -3 }}		{{Mapping\|legend=2\| 4 1 -44 86 3 25 \| 0 2 -13 -28 5 -3 }}

	Optimal tunings:		Optimal tunings:

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:18Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:38, 30 September 2026
Line 11:		Line 11:
	[[Comma list]]: 33554432/33480783		[[Comma list]]: 33554432/33480783

	{{Mapping\|legend=2\| 1 0 25 \| 0 1 -14 }}		{{Mapping\|legend=3\| 1 0 25 \| 0 1 -14 }}
	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:19Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

Show changes

Overthink: /* World calendar */ seems easier to read (revert or change if you want)

2026-09-16T15:50:56Z

World calendar: seems easier to read (revert or change if you want)

← Older revision		Revision as of 15:50, 16 September 2026
Line 477:		Line 477:

	== World calendar ==		== World calendar ==
	World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name ― because a possible scale is 31 30 30 31 30 30 31 30 30 31 30 30 in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.		World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name ― because a possible scale is [31 30 30 31 30 30 31 30 30 31 30 30] in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.

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

FloraC: /* Gary */ update

2026-09-16T06:36:18Z

Gary: update

← Older revision		Revision as of 06:36, 16 September 2026
Line 38:		Line 38:
	* ''[[Garistearn]]'' (+118098/117649) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]		* ''[[Garistearn]]'' (+118098/117649) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]

	Considered below are cotoneum, newt, gariwizmic, satin, sextile, ~~and~~ world calendar.		Considered below are [[#Cotoneum\|cotoneum]], [[#Newt\|newt]], [[#Gariwizmic\|gariwizmic]], [[#Satin\|satin]], [[#Sextile\|sextile]], [[#World calendar\|world calendar]], [[#Heptacot\|heptacot]], and [[#Garitritonic\|garitritonic]].

	==== Subgroup extensions ====		==== Subgroup extensions ====

FloraC: /* Gary */ update

2026-09-16T06:33:48Z

Gary: update

← Older revision		Revision as of 06:33, 16 September 2026
Line 36:		Line 36:
	* ''[[Quintagar]]'' (+3136/3125) → [[Quindromeda family #Quintagar\|Quindromeda family]]		* ''[[Quintagar]]'' (+3136/3125) → [[Quindromeda family #Quintagar\|Quindromeda family]]
	* ''[[Paramity]]'' (+65625/65536) → [[Amity family #Paramity\|Amity family]]		* ''[[Paramity]]'' (+65625/65536) → [[Amity family #Paramity\|Amity family]]
	* ''[[Garistearn]]'' (+118098/117649) → [[~~Stearnsmic clan~~ #Garistearn\|~~Stearnsmic clan~~]]		* ''[[Garistearn]]'' (+118098/117649) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]

	Considered below are cotoneum, newt, gariwizmic, satin, sextile, and world calendar.		Considered below are cotoneum, newt, gariwizmic, satin, sextile, and world calendar.

Eliora: /* World calendar */

2026-09-01T18:31:55Z

World calendar

← Older revision		Revision as of 18:31, 1 September 2026
Line 477:		Line 477:

	== World calendar ==		== World calendar ==
	World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name ― because a possible scale is 31 30 30 31 30 30 31 30 30 31 30 30 in 364edo, which is the proposed layout for month lengths in the namesake calendar.		World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name ― because a possible scale is 31 30 30 31 30 30 31 30 30 31 30 30 in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.

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

Eliora: /* World calendar */ explain why exactly its named world calendar

2026-09-01T18:31:37Z

World calendar: explain why exactly its named world calendar

← Older revision		Revision as of 18:31, 1 September 2026
Line 477:		Line 477:

	== World calendar ==		== World calendar ==
	World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name.		World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name ― because a possible scale is 31 30 30 31 30 30 31 30 30 31 30 30 in 364edo, which is the proposed layout for month lengths in the namesake calendar.

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

FloraC: FloraC moved page Garischismic clan to Septischismic clan: Rename (see talk at Septischismic family)

2026-08-15T14:17:38Z

FloraC moved page Garischismic clan to Septischismic clan: Rename (see talk at Septischismic family)

← Older revision	Revision as of 14:17, 15 August 2026
(No difference)

FloraC: Initiate temp & comma rename

2026-08-15T13:59:58Z

Initiate temp & comma rename

← Older revision		Revision as of 13:59, 15 August 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	The '''~~garischismic~~ clan''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[~~garischisma~~]] ({{monzo\|legend=1\| 25 -14 0 -1 }}, [[ratio]]: ~~33554432~~/~~33480783~~), the amount by which the [[Pythagorean comma]] falls short of the [[septimal comma]], thus equating the two.		The '''septischismic clan''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[septischisma]] ({{monzo\|legend=1\| 25 -14 0 -1 }}, [[ratio]]: 33 554 432 / 33 480 783), the amount by which the [[Pythagorean comma]] falls short of the [[septimal comma]], thus equating the two.

	== Gary ==		== Gary ==
Line 41:		Line 41:

	==== Subgroup extensions ====		==== Subgroup extensions ====
	Gary can be naturally extended into the no-5's 11-limit with good accuracy by equating (64/63)<sup>2</sup> with 33/32 at the cost of doubling the complexity, acting as a temperament of [[olympic clan #Olympian\|olympian]] which accurately represents the entire 2.3.7.11 into the chain of fifths. The major third additionally is extremely close to [[19/15]], and is a natural interpretation in extensions with 5 and 19.		Gary can be naturally extended into the no-5's 11-limit with good accuracy by equating (64/63)<sup>2</sup> with 33/32 at the cost of doubling the complexity, acting as a temperament of [[olympic clan #Olympian\|olympian]] which accurately represents the entire [[2.3.7.11 subgroup]] into the chain of fifths. The major third additionally is extremely close to [[19/15]], and is a natural interpretation in extensions with 5 and 19.

	=== 2.3.7.11 subgroup ===		=== 2.3.7.11 subgroup ===
Line 64:		Line 64:
	: ''For the 5-limit version, see [[Schismic–countercommatic equivalence continuum #Cotoneum (5-limit)]].''		: ''For the 5-limit version, see [[Schismic–countercommatic equivalence continuum #Cotoneum (5-limit)]].''

	Cotoneum tempers out 10976/10935 ([[hemimage comma]]), and 823543/819200 ([[quince comma]]) in addition to the ~~garischisma~~. This temperament can be described as {{nowrap\| 41 & 217 }}, and is supported by [[176edo\|176-]], [[217edo\|217-]], and [[258edo]]. 5/4 is found -49 generators away. In terms of chain-of-fifths notation, this is a sextuple-diminished octave, or a perfect fourth minus four generic commas.		Cotoneum tempers out 10976/10935 ([[hemimage comma]]) and 823543/819200 ([[quince comma]]) in addition to the septischisma. This temperament can be described as {{nowrap\| 41 & 217 }}, and is supported by [[176edo\|176-]], [[217edo\|217-]], and [[258edo]]. 5/4 is found -49 generators away. In terms of chain-of-fifths notation, this is a sextuple-diminished octave, or a perfect fourth minus four generic commas.

	However, cotoneum can be notated like [[cassaschismic]], where 5/4 is conceptualized as an aberschisma-up comma-down major third (C–^↓E), but with the extra equivalence that the generic aberschisma is identical to the [[41-comma]]. In other words, we have C–^↑↑E = C–↓↓E.		However, cotoneum can be notated like [[cassaschismic]], where 5/4 is conceptualized as an aberschisma-up comma-down major third (C–^↓E), but with the extra equivalence that the generic aberschisma is identical to the [[41-comma]]. In other words, we have C–^↑↑E = C–↓↓E.
Line 240:		Line 240:

	== Gariwizmic ==		== Gariwizmic ==
	Gariwizmic tempers out the [[wizma]] and the ~~garischisma~~, and may be described as the {{nowrap\| 94 & 176 }} temperament. It assumes a [[semioctave]] period and a [[3/2\|perfect fifth]] generator that is slightly sharp of just. It finds [[5/4]] 39 fifths away, shifted by a semioctave. It extends extremely well to the 2.3.5.7.11.13.19 subgroup. Notable tunings not appearing in the optimal ET sequence include [[364edo]] and [[634edo]].		Gariwizmic tempers out the [[wizma]] and the septischisma, and may be described as the {{nowrap\| 94 & 176 }} temperament. It assumes a [[semioctave]] period and a [[3/2\|perfect fifth]] generator that is slightly sharp of just. It finds [[5/4]] 39 fifths away, shifted by a semioctave. It extends extremely well to the 2.3.5.7.11.13.19 subgroup. Notable tunings not appearing in the optimal ET sequence include [[364edo]] and [[634edo]].

	Gariwizmic was named by [[Eufalesio]] in 2026 as a concatenation of ''gary'' and ''wizmic''.		Gariwizmic was named by [[Eufalesio]] in 2026 as a concatenation of ''gary'' and ''wizmic''.
Line 315:		Line 315:
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Satin]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Satin]].''

	Satin tempers out the [[rainy comma]] and the [[~~canousma~~]] in addition to the ~~garischisma~~, and may be described as the {{nowrap\| 94 & 217 }} temperament. It uses [[~]][[11/10]] as a generator, three of which gives a [[4/3\|perfect fourth]], tempering out [[4000/3993]] in the 11-limit and onwards. Its [[ploidacot]] is omega-tricot.		Satin tempers out the [[rainy comma]] and the [[cathartic comma]] in addition to the septischisma, and may be described as the {{nowrap\| 94 & 217 }} temperament. It uses [[~]][[11/10]] as a generator, three of which gives a [[4/3\|perfect fourth]], tempering out [[4000/3993]] in the 11-limit and onwards. Its [[ploidacot]] is omega-tricot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 477:		Line 477:

	== World calendar ==		== World calendar ==
	World calendar tempers out the [[dimcomp comma]] and the ~~garischisma~~, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name.		World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap\| 12 & 364 }} temperament. The name derives from a {{w\|World Calendar\|certain calendar layout}} by the same name.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 667:		Line 667:
	Badness (Sintel): 1.22		Badness (Sintel): 1.22

	[[Category:~~Garischismic~~ clan\| ]] <!-- main article -->		[[Category:Septischismic clan\| ]] <!-- main article -->
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Catalogs of rank-2 temperaments]]		[[Category:Catalogs of rank-2 temperaments]]