Cassaschismic - Revision history

FloraC: Fix reduced mapping

2026-06-08T08:50:38Z

Fix reduced mapping

← Older revision		Revision as of 08:50, 8 June 2026
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	\| Comma basis = [[19712/19683]], [[41503/41472]] (11-limit); <br>[[2080/2079]], [[4096/4095]], [[19712/19683]] (13-limit); <br>[[1216/1215]], [[1540/1539]], [[1729/1728]], <br>[[2080/2079]] (2.3.5.7.11.13.19)		\| Comma basis = [[19712/19683]], [[41503/41472]] (11-limit); <br>[[2080/2079]], [[4096/4095]], [[19712/19683]] (13-limit); <br>[[1216/1215]], [[1540/1539]], [[1729/1728]], <br>[[2080/2079]] (2.3.5.7.11.13.19)
	\| Edo join 1 = 41 \| Edo join 2 = 53 \| Edo join 3 = 270		\| Edo join 1 = 41 \| Edo join 2 = 53 \| Edo join 3 = 270
	\| Mapping = 1; 0 1 0 -14 23 12 5; 0 0 1 0 0 -1 1		\| Mapping = 1; 1 0 -14 23 12 5; 0 1 0 0 -1 1
	\| Generators = 3/2; 5/4 \| Generators tuning = 702.2307; 386.3245		\| Generators = 3/2; 5/4 \| Generators tuning = 702.2307; 386.3245
	\| Optimization method = CWE		\| Optimization method = CWE

FloraC: Text replacement - "rank-3 temperament" to "rank-3 temperament"

2026-06-08T08:36:24Z

Text replacement - "rank-3 temperament" to "rank-3 temperament"

← Older revision		Revision as of 08:36, 8 June 2026
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	\| Odd limit 1 = 11 \| Mistuning 1 = 0.588 \| Complexity 1 = ?		\| Odd limit 1 = 11 \| Mistuning 1 = 0.588 \| Complexity 1 = ?
	}}		}}
	'''Cassaschismic''' is a [[rank-3 ~~temperament\|rank-3]] [[regular temperament\|~~temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[11-limit]] by adding an independent [[generator]] for the [[5/1\|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].		'''Cassaschismic''' is a [[rank-3 temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[11-limit]] by adding an independent [[generator]] for the [[5/1\|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].

	The generator for 5 can be used for [[13/1\|13]] and [[19/1\|19]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351\|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19.		The generator for 5 can be used for [[13/1\|13]] and [[19/1\|19]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351\|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19.

FloraC: What is the italic style even supposed to convey? Lol

2026-06-02T08:04:14Z

What is the italic style even supposed to convey? Lol

← Older revision		Revision as of 08:04, 2 June 2026
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	== Notation ==		== Notation ==
	Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to ~~extremely~~ accurate (217, 270, 311, ~~''581, 851…''~~).		Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to highly accurate (217, 270, 311, …).

	As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step.		As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step.

FloraC: What on earth are "p5" "p13" "p19"? Plz don't invent language here

2026-06-02T08:02:16Z

What on earth are "p5" "p13" "p19"? Plz don't invent language here

← Older revision		Revision as of 08:02, 2 June 2026
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	\| Odd limit 1 = 11 \| Mistuning 1 = 0.588 \| Complexity 1 = ?		\| Odd limit 1 = 11 \| Mistuning 1 = 0.588 \| Complexity 1 = ?
	}}		}}
	'''Cassaschismic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[11-limit]] by adding an independent [[generator]] for [[5/1\|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].		'''Cassaschismic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[11-limit]] by adding an independent [[generator]] for the [[5/1\|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].

	The generator for [[5~~/1\|p5]]~~ can be used for [[13/1\|~~p13~~]] and [[19/1\|~~p19~~]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351\|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach p5, ~~p13~~, ~~p19~~.		The generator for 5 can be used for [[13/1\|13]] and [[19/1\|19]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351\|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19.

	Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], [[vulture]], [[~~heptacot~~]] and [[~~paramity~~]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], [[vulture]], [[paramity]] and [[heptacot]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

	{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) ~~finds it at~~ -41 hemififths~~.<br>~~Cotoneum (41 & 217) ~~finds it at~~ -41 fifths, equating it with the 41-comma~~.<br>~~Gariwizmic (94 & 270) ~~finds it at~~ +53 fifths (mercator comma) - 1/2~~-pythcomma.<br>~~Vulture (53 & 217) ~~finds it at~~ -41 1/4-fifths~~.<br>~~Satin (94 & 217) ~~finds it at~~ -94 1/3-fourths~~.<br>Heptacot~~ (~~12e~~ & 311) ~~finds it at 12~~ 1/7-~~fifths. <br>Paramity~~ (53 & 311) ~~finds it at -53~~ 1/5-~~elevenths~~.}}		{{Databox\|Generators needed to reach the aberschisma\|
			* Newt (41 & 270): -41 hemififths;
			* Cotoneum (41 & 217): -41 fifths, equating it with the 41-comma;
			* Gariwizmic (94 & 270): +53 fifths (mercator comma) - 1/2 pythagorean comma;
			* Vulture (53 & 217): -41 1/4-fifths;
			* Satin (94 & 217): -94 1/3-fourths;
			* Paramity (53 & 311): -53 1/5-elevenths;
			* Heptacot (12e & 311): 12 1/7-fifths.
			}}

	Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]]. [[12edo]] supports it trivially through the 12e [[val]], where both the comma step and the aberschisma step are tempered out.		Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]]. [[12edo]] supports it trivially through the 12e [[val]], where both the comma step and the aberschisma step are tempered out. It can be used in any of those forms.

	See [[Garischismic family #Cassaschismic]] for technical data.		See [[Garischismic family #Cassaschismic]] for technical data.
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	<nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced		<nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced

	[https://www.desmos.com/calculator/pbyqpjgrrn Here] is a Desmos graph showing how cassaschismic edos up to 311 [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is patent val p11, which ~~isn't~~ used in cassaschismic. The blue dots indicate going up and down by pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in the line of cassandra; since halving it results in 270edo, it is used instead, also to showcase the use of aberschismas to reach p5, ~~p13~~, ~~p19~~.		[https://www.desmos.com/calculator/pbyqpjgrrn Here] is a Desmos graph showing how cassaschismic edos up to 311 [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is patent val p11, which is not used in cassaschismic. The blue dots indicate going up and down by pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in the line of cassandra; since halving it results in 270edo, it is used instead, also to showcase the use of aberschismas to reach primes 5, 13, and 19.

	== Notation ==		== Notation ==
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	As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step.		As an example, we can use up and down arrows with shafts (↑/↓) for the comma step, and arrows without shafts (^/v) for the aberschisma step.
	{\| class="wikitable~~" style="text-align:~~center~~; vertical~~-~~align:middle;~~"
			{\| class="wikitable center-all"
	\|+Nomenclature of selected intervals		\|+Nomenclature of selected intervals
	!Ratio		! Ratio
	!Example on C		! Example on C
	\|-		\|-
	\|3/2		\| 3/2
	\|C–G (perfect fifth)		\| C–G (perfect fifth)
	\|-		\|-
	\|5/4		\| 5/4
	\|C–^↓E (upsubmajor third)		\| C–^↓E (upsubmajor third)
	\|-		\|-
	\|7/4		\| 7/4
	\|C–↓Bb (subminor seventh)		\| C–↓Bb (subminor seventh)
	\|-		\|-
	\|11/8		\| 11/8
	\|C–↑↑F (hyperfourth)		\| C–↑↑F (hyperfourth)
	\|-		\|-
	\|13/8		\| 13/8
	\|C–v↑↑Ab (downhyperminor sixth)		\| C–v↑↑Ab (downhyperminor sixth)
	\|-		\|-
	\|19/16		\| 19/16
	\|C–^Eb (upminor third)		\| C–^Eb (upminor third)
	\|}		\|}
	[[Category:Cassaschismic\| ]] <!-- main article -->		[[Category:Cassaschismic\| ]] <!-- main article -->

Eufalesio: Added Heptacot and Paramity and reworded some things

2026-06-01T23:23:46Z

Added Heptacot and Paramity and reworded some things

← Older revision		Revision as of 23:23, 1 June 2026
Line 11:		Line 11:
	\| Odd limit 1 = 11 \| Mistuning 1 = 0.588 \| Complexity 1 = ?		\| Odd limit 1 = 11 \| Mistuning 1 = 0.588 \| Complexity 1 = ?
	}}		}}
	'''Cassaschismic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] that expands ~~the~~ [[~~chain of fifths~~]] of [[~~gary~~]] into the full [[11-limit]] by adding an independent [[generator]] for ~~the~~ [[5/1\|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].		'''Cassaschismic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[11-limit]] by adding an independent [[generator]] for [[5/1\|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].

	~~By moving the generators around, the~~ generator for 5 can be used for [[13/1\|13]] and [[19/1\|19]]. It can also be taken to be a ~~3–5~~{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], and many other important commas around that size. [[Tempering out]] this ~~tiny interval~~ results in [[cassandra]], so cassaschismic ~~may be viewed as~~ a rank-3 [[detemperament]] ~~thereof~~, modifying its mapping by ±1 aberschisma ~~step~~ to reach ~~the rest of primes~~.		The generator for [[5/1\|p5]] can be used for [[13/1\|p13]] and [[19/1\|p19]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351\|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach p5, p13, p19.

	Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[~~vulture~~]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], [[vulture]], [[heptacot]] and [[paramity]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

	{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths, equating it with the 41-comma.<br>Gariwizmic (94 & 270) finds it at +53 fifths (mercator comma) ~~minus a half pythagorean comma~~.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}		{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths, equating it with the 41-comma.<br>Gariwizmic (94 & 270) finds it at +53 fifths (mercator comma) - 1/2-pythcomma.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.<br>Heptacot (12e & 311) finds it at 12 1/7-fifths. <br>Paramity (53 & 311) finds it at -53 1/5-elevenths.}}

	Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]]~~, and of course,~~ [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out~~, so it can be used in any of those forms as well~~.		Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]]. [[12edo]] supports it trivially through the 12e [[val]], where both the comma step and the aberschisma step are tempered out.

	See [[Garischismic family #Cassaschismic]] for technical data.		See [[Garischismic family #Cassaschismic]] for technical data.
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	<nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced		<nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced

	[https://www.desmos.com/calculator/pbyqpjgrrn Here] is a Desmos graph showing how cassaschismic edos up to 311 [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is patent val p11, which isn't used in cassaschismic. The blue dots indicate going up and down by pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 ~~comes from the fact that~~ 135edo is next in the line of cassandra~~, but~~ halving it results in 270edo, ~~so the latter~~ is used.		[https://www.desmos.com/calculator/pbyqpjgrrn Here] is a Desmos graph showing how cassaschismic edos up to 311 [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is patent val p11, which isn't used in cassaschismic. The blue dots indicate going up and down by pythagorean commas in the 12L 29s scale, and the orange dots indicate the leftover edosteps. The jump from 94 to 270 is due to 135edo being next in the line of cassandra; since halving it results in 270edo, it is used instead, also to showcase the use of aberschismas to reach p5, p13, p19.

	== Notation ==		== Notation ==

Eufalesio: Desmos graph and things to synchronize with Garibaldi article

2026-05-30T21:52:54Z

Desmos graph and things to synchronize with Garibaldi article

@@ Line 186: / Line 186: @@
 | 33/32
 |}
-<nowiki/>* In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced
+<nowiki>*</nowiki> In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced
 == Notation ==
-Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to highly accurate (217, 270, 311, …).
+Cassaschismic is easily notated with [[chain-of-fifths notation]] with two extra pairs of accidentals: one for the comma step, and the other for the aberschisma step. It can therefore be seen as an addition to the cassandra chain of fifths, which itself can be seen as an addition to the 12edo chain of fifths, providing a layered-precision system of notation that ranges from rough (12), to moderately accurate (41, 53, 94), to extremely accurate (217, 270, 311, ''581, 851…'').
 [[Category:Cassaschismic| ]] <!-- main article -->
 [[Category:Rank-3 temperaments]]

Eufalesio: Reversal on rank-2 aberschisma location: I use gariwizmic regularly, trust me on this one... besides, all these temperaments are connected by the chain of fiths, so it's logical that chain-of-fifthy numbers of gens would appear

2026-05-25T07:05:45Z

Reversal on rank-2 aberschisma location: I use gariwizmic regularly, trust me on this one... besides, all these temperaments are connected by the chain of fiths, so it's logical that chain-of-fifthy numbers of gens would appear

← Older revision		Revision as of 07:05, 25 May 2026
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	Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

	{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths.<br>Gariwizmic (94 & 270) finds it at +47 fifths minus a half ~~octave~~.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}		{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths, equating it with the 41-comma.<br>Gariwizmic (94 & 270) finds it at +53 fifths (mercator comma) minus a half pythagorean comma.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}

	Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.		Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.

Overthink: fix (note that gariwizmic was originally also correct, but subtracting the half-octave feels more natural than half a Pythagorean comma)

2026-05-25T02:44:14Z

fix (note that gariwizmic was originally also correct, but subtracting the half-octave feels more natural than half a Pythagorean comma)

← Older revision		Revision as of 02:44, 25 May 2026
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	Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

	{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at +41 fifths.<br>Gariwizmic (94 & 270) finds it at +53 fifths minus a half ~~pythagorean comma~~.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}		{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths.<br>Gariwizmic (94 & 270) finds it at +47 fifths minus a half octave.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}

	Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.		Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.

Overthink: grammar

2026-05-24T18:22:22Z

grammar

← Older revision		Revision as of 18:22, 24 May 2026
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	Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

	{{Databox\|Generators needed to reach the ~~aberschismas~~\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at +41 fifths.<br>Gariwizmic (94 & 270) finds it at +53 fifths minus a half pythagorean comma.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}		{{Databox\|Generators needed to reach the aberschisma\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at +41 fifths.<br>Gariwizmic (94 & 270) finds it at +53 fifths minus a half pythagorean comma.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}

	Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.		Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.

Overthink: ET joins

2026-05-24T17:58:53Z

ET joins

← Older revision		Revision as of 17:58, 24 May 2026
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	Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

	{{Databox\|Generators needed to reach the aberschismas\|Newt finds it at -41 hemififths.<br>Cotoneum finds it at +41 fifths.<br>Gariwizmic finds it at +53 fifths minus a half pythagorean comma.<br>Vulture finds it at -41 1/4-fifths.<br>Satin finds it at -94 1/3-fourths.}}		{{Databox\|Generators needed to reach the aberschismas\|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at +41 fifths.<br>Gariwizmic (94 & 270) finds it at +53 fifths minus a half pythagorean comma.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}}

	Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.		Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs\| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo\|41]], [[53edo\|53]], [[94edo\|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.