Septischismic clan - Revision history

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
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	{{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 ==
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	==== 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 ===
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	: ''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.
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	== 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''.
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	: ''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
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	== 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
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	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]]

FloraC: Recategorize

2026-08-15T07:35:41Z

Recategorize

← Older revision		Revision as of 07:35, 15 August 2026
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	Badness (Sintel): 1.22		Badness (Sintel): 1.22

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

FloraC: /* Newt / don't need neonewt*

2026-08-08T09:08:15Z

Newt: don't need *neonewt*

← Older revision		Revision as of 09:08, 8 August 2026
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	Like [[#Cotoneum\|cotoneum]], newt can be notated in the same way as [[cassaschismic]], but with half-sharps and half-flats and the extra equivalence that two comma steps and an aberschisma step make a half-apotome step. In other words, C–^↑↑E = C–v↓↓E = C–Ed.		Like [[#Cotoneum\|cotoneum]], newt can be notated in the same way as [[cassaschismic]], but with half-sharps and half-flats and the extra equivalence that two comma steps and an aberschisma step make a half-apotome step. In other words, C–^↑↑E = C–v↓↓E = C–Ed.

	Newt continues to be significant as an [[11-limit]] temperament, where it tempers out the lehmerisma ([[3025/3024]]). This extends into a very strong [[13-limit]] temperament and eventually a very strong no-17 [[19-limit]] temperament~~, a.k.a. ''neonewt''~~. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] are more accurate.		Newt continues to be significant as an [[11-limit]] temperament, where it tempers out the lehmerisma ([[3025/3024]]). This extends into a very strong [[13-limit]] temperament and eventually a very strong no-17 [[19-limit]] temperament. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] are more accurate.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Badness (Sintel): 0.571		Badness (Sintel): 0.571

	=== 2.3.5.7.11.13.19 subgroup ~~(neonewt)~~ ===		=== 2.3.5.7.11.13.19 subgroup ===
	Subgroup: 2.3.5.7.11.13.19		Subgroup: 2.3.5.7.11.13.19

FloraC: - "gary comma" (temp name + comma conventionally refers to the comma tempered out in the temp). Stop semantic inflation (good means good). Fix typos

2026-07-28T04:59:28Z

- "gary comma" (temp name + comma conventionally refers to the comma tempered out in the temp). Stop semantic inflation (good means good). Fix typos

← Older revision		Revision as of 04:59, 28 July 2026
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	== Gary ==		== Gary ==
	Gary, the head of this clan, may be viewed as the [[2.3.7 subgroup\|2.3.7-subgroup]] counterpart of [[schismic]]. It is generated by a [[3/2\|perfect fifth]], and 7/4 is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step ~~(sometimes called ''gary comma'')~~ which stands in for both the Pythagorean comma and the septimal comma. Gary can therefore use [[chain-of-fifths notation]] with an additional set of accidentals such as arrows to represent the comma step.		Gary, the head of this clan, may be viewed as the [[2.3.7 subgroup\|2.3.7-subgroup]] counterpart of [[schismic]]. It is generated by a [[3/2\|perfect fifth]], and 7/4 is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma. Gary can therefore use [[chain-of-fifths notation]] with an additional set of accidentals such as arrows to represent the comma step.

	Just as there is the 1/8-schisma tuning for schismic, there is the 1/14-schisma tuning for gary, which tunes 7/4 pure by sharpening the perfect fifth by about 0.272 cents. Similarly, the 1/15-schisma tuning tunes [[7/6]] pure, and the 2/29-schisma tuning splits their difference, tuning the septimal diesis of [[49/48]] pure. [[135edo]] is close to the 1/14-schisma tuning, whereas [[634edo]] gives a tuning practically identical to 1/15-schisma. Other notable tunings not appearing in the optimal ET sequence include [[311edo]] and [[323edo]].		Just as there is the 1/8-schisma tuning for schismic, there is the 1/14-schisma tuning for gary, which tunes 7/4 pure by sharpening the perfect fifth by about 0.272 cents. Similarly, the 1/15-schisma tuning tunes [[7/6]] pure, and the 2/29-schisma tuning splits their difference, tuning the septimal diesis of [[49/48]] pure. [[135edo]] is close to the 1/14-schisma tuning, whereas [[634edo]] gives a tuning practically identical to 1/15-schisma. Other notable tunings not appearing in the optimal ET sequence include [[311edo]] and [[323edo]].
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	==== Subgroup extensions ====		==== Subgroup extensions ====
	Gary can be naturally extended into the no-5's 11-limit with ~~incredible~~ 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 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 ===
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}~~Subgroup [[~~error map]]: {{val\|-0.037, 0.216, -0.139, -0.173}}		* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}~~Subgroup [[~~error map]]: {{val\|-0.000, 0.274, -0.032, -0.051}}		: error map: {{val\| -0.037 0.216 -0.139 -0.173 }}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}
			: error map: {{val\| -0.000 0.274 -0.032 -0.051 }}

	{{Optimal ET sequence\|legend=0\| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}		{{Optimal ET sequence\|legend=0\| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}

Eufalesio: Polished some info about gary, and sold it better!

2026-07-27T21:51:47Z

Polished some info about gary, and sold it better!

← Older revision		Revision as of 21:51, 27 July 2026
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	== Gary ==		== Gary ==
	Gary, the head of this clan, may be viewed as the [[2.3.7 subgroup\|2.3.7-subgroup]] counterpart of [[schismic]]. It is generated by a [[3/2\|perfect fifth]], and 7/4 is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma. Gary can therefore use [[chain-of-fifths notation]] with an additional set of accidentals such as arrows to represent the comma step.		Gary, the head of this clan, may be viewed as the [[2.3.7 subgroup\|2.3.7-subgroup]] counterpart of [[schismic]]. It is generated by a [[3/2\|perfect fifth]], and 7/4 is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step (sometimes called ''gary comma'') which stands in for both the Pythagorean comma and the septimal comma. Gary can therefore use [[chain-of-fifths notation]] with an additional set of accidentals such as arrows to represent the comma step.

	Just as there is the 1/8-schisma tuning for schismic, there is the 1/14-schisma tuning for gary, which tunes 7/4 pure by sharpening the perfect fifth by about 0.272 cents. Similarly, the 1/15-schisma tuning tunes [[7/6]] pure, and the 2/29-schisma tuning splits their difference, tuning the septimal diesis of [[49/48]] pure. [[135edo]] is close to the 1/14-schisma tuning, whereas [[634edo]] gives a tuning practically identical to 1/15-schisma. Other notable tunings not appearing in the optimal ET sequence include [[311edo]] and [[323edo]].		Just as there is the 1/8-schisma tuning for schismic, there is the 1/14-schisma tuning for gary, which tunes 7/4 pure by sharpening the perfect fifth by about 0.272 cents. Similarly, the 1/15-schisma tuning tunes [[7/6]] pure, and the 2/29-schisma tuning splits their difference, tuning the septimal diesis of [[49/48]] pure. [[135edo]] is close to the 1/14-schisma tuning, whereas [[634edo]] gives a tuning practically identical to 1/15-schisma. Other notable tunings not appearing in the optimal ET sequence include [[311edo]] and [[323edo]].
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	==== 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.		Gary can be naturally extended into the no-5's 11-limit with incredible 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.

	=== 2.3.7.11 subgroup ===		=== 2.3.7.11 subgroup ===
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}		* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}Subgroup [[error map]]: {{val\|-0.037, 0.216, -0.139, -0.173}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}Subgroup [[error map]]: {{val\|-0.000, 0.274, -0.032, -0.051}}

	{{Optimal ET sequence\|legend=0\| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}		{{Optimal ET sequence\|legend=0\| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}

Hkm: /* 2.3.5.7.11.13.19 subgroup */

2026-06-08T17:59:58Z

2.3.5.7.11.13.19 subgroup

← Older revision		Revision as of 17:59, 8 June 2026
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	=== 2.3.5.7.11.13.19 subgroup ===		=== 2.3.5.7.11.13.19 subgroup ===
	Subgroup: 2.3.5.7.11.13~~.17~~.19		Subgroup: 2.3.5.7.11.13.19

	Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625		Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625

FloraC: + devitredecimal extensions for heptacot and garitritonic

2026-05-20T12:37:08Z

+ devitredecimal extensions for heptacot and garitritonic

@@ Line 173: / Line 173: @@
 Like [[#Cotoneum|cotoneum]], newt can be notated in the same way as [[cassaschismic]], but with half-sharps and half-flats and the extra equivalence that two comma steps and an aberschisma step make a half-apotome step. In other words, C–^↑↑E = C–v↓↓E = C–Ed.
-Newt continues to be significant as an [[11-limit]] temperament, where it tempers out the [[lehmerisma]] (3025/3024). This extends into a very strong [[13-limit]] temperament and eventually a very strong no-17 [[19-limit]] temperament, a.k.a. ''neonewt''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] are even better.
+Newt continues to be significant as an [[11-limit]] temperament, where it tempers out the lehmerisma ([[3025/3024]]). This extends into a very strong [[13-limit]] temperament and eventually a very strong no-17 [[19-limit]] temperament, a.k.a. ''neonewt''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] are more accurate.
 [[Subgroup]]: 2.3.5.7
@@ Line 527: / Line 527: @@
 : ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Heptacot (5-limit)]].''
-Heptacot tempers out the [[meter]] and may be described as the {{nowrap| 12 & 311 }} temperament.
+Heptacot tempers out the [[meter]] and may be described as the {{nowrap| 12 & 311 }} temperament, splitting the perfect fifth into seven semitones. It is the natural 7-limit extension of the 5-limit temperament named by [[Tristan Bay]] in 2024. [[311edo]] and [[323edo]] are obvious tuning choices, as well as anything in between such as [[634edo]].
 [[Subgroup]]: 2.3.5.7
@@ Line 545: / Line 547: @@
 [[Badness]] (Sintel): 3.06
 == Garitritonic ==
 : ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Countritonic]].''
-Garitritonic may be described as the {{nowrap| 53 & 581 }} temperament, splitting the [[24/1|24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[634edo]] makes for a strong tuning.
+Garitritonic may be described as the {{nowrap| 53 & 581 }} temperament, splitting the [[24/1|24th harmonic]] into nine tritone generators; its [[ploidacot]] is thus delta-enneacot. [[634edo]] makes for a strong 7-limit tuning, though in the higher limits one may prefer sticking to [[581edo]].
 Garitritonic was named by [[Flora Canou]] in 2026 as a contraction of ''gary'' and ''tritonic''.
@@ Line 569: / Line 619: @@
 [[Badness]] (Sintel): 6.12
 [[Category:Temperament clans]]
 [[Category:Garischismic clan| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: + heptacot, + garitritonic

2026-05-20T11:00:34Z

+ heptacot, + garitritonic

@@ Line 28: / Line 28: @@
 The second comma of the comma list determines which full 7-limit or 11-limit family member we are looking at. Garibaldi adds the [[schisma]], or equivalently [[225/224]] and finds 5/4 at the diminished fourth. Cotoneum adds [[10976/10935]] and finds 5/4 at the septuple-diminished octave. These are generated by the fifth as is gary.
-Newt adds [[2401/2400]], halving the fifth. Gariwizmic adds the [[wizma]] with a 1/2-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. Sextile adds [[250047/250000]] with a 1/6-octave period. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a halved fifth. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five.
+Newt adds [[2401/2400]], halving the fifth. Gariwizmic adds the [[wizma]] with a 1/2-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. Sextile adds [[250047/250000]] with a 1/6-octave period. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a halved fifth. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five. Heptacot adds [[703125/702464]], slicing the fifth in seven. Finally, garitritonic adds 95703125/95551488 ({{monzo| -17 -6 9 2 }}), slicing the 24th harmonic in nine.
 Temperaments discussed elsewhere are:
@@ Line 523: / Line 523: @@
 Badness (Sintel): 1.82
 [[Category:Temperament clans]]
 [[Category:Garischismic clan| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: Expand

2026-05-20T10:25:18Z

Expand

← Older revision		Revision as of 10:25, 20 May 2026
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	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 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.

	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 ~~where~~ the generic aberschisma is identical to the [[41-comma]].		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.

	It can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.		It can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.
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	: ''For the 5-limit version, see [[Schismic–countercommatic equivalence continuum #Newt (5-limit)]].''		: ''For the 5-limit version, see [[Schismic–countercommatic equivalence continuum #Newt (5-limit)]].''

	Newt tempers out the [[breedsma]] and may be described as the {{nowrap\| 41 & 270 }} temperament. It has a generator of a neutral third (0.2 cents flat of [[49/40]]) with a [[ploidacot]] signature of dicot. 41 generator steps fall short of 12 octaves by a [[schisma]]~[[aberschisma]]. From there the intervals of 5 and 7 can be derived.		Newt tempers out the [[breedsma]] and may be described as the {{nowrap\| 41 & 270 }} temperament. It has a generator of a neutral third (0.2 cents flat of [[49/40]]) with a [[ploidacot]] signature of dicot. 41 generator steps fall short of 12 octaves by a generic aberschisma step of a [[schisma]]~[[aberschisma]]. From there the intervals of 5 and 7 can be derived.

	Newt continues to be significant as an [[11-limit]] temperament, where it tempers out the [[lehmerisma]] (3025/3024). This extends into a strong [[13-limit]] temperament and eventually a strong no-17 [[19-limit]] temperament, a.k.a. '''neonewt'''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] are even better.		Like [[#Cotoneum\|cotoneum]], newt can be notated in the same way as [[cassaschismic]], but with half-sharps and half-flats and the extra equivalence that two comma steps and an aberschisma step make a half-apotome step. In other words, C–^↑↑E = C–v↓↓E = C–Ed.

			Newt continues to be significant as an [[11-limit]] temperament, where it tempers out the [[lehmerisma]] (3025/3024). This extends into a very strong [[13-limit]] temperament and eventually a very strong no-17 [[19-limit]] temperament, a.k.a. ''neonewt''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] are even better.

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