Septischismic - Revision history

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

2026-08-15T18:36:01Z

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

← Older revision	Revision as of 18:36, 15 August 2026
(No difference)

FloraC: Re-implement the latest changes

2026-08-15T18:35:33Z

Re-implement the latest changes

← Older revision		Revision as of 18:35, 15 August 2026
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	{{Infobox regtemp		{{Infobox regtemp
	\| Title = ~~Cassaschismic~~		\| Title = Septischismic
	\| Subgroups = 2.3.5.7.11, 2.3.5.7.11.13, 2.3.5.7.11.13.19		\| Subgroups = 2.3.5.7.11, 2.3.5.7.11.13, 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)		\| 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)
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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]] 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]].		'''Septischismic''' 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\|major 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\|major minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so septischismic 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]], [[newt]], [[gariwizmic]], [[satin]], [[vulture]], [[paramity]] and [[heptacot]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of septischismic include [[cotoneum]], [[newt]], [[gariwizmic]], [[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\|		{{Databox\|Generators needed to reach the aberschisma\|
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	}}		}}

	~~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.		Septischismic 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 [[Septischismic family #Septischismic]] for technical data.

	== Interval lattice ==		== Interval lattice ==
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	An image is provided instead showing copies of a [[Standard Lumatone mapping for Pythagorean]]-like arrangement of the chain of fifths, copied thrice to access most of the no-17 27-odd-limit and then some.		An image is provided instead showing copies of a [[Standard Lumatone mapping for Pythagorean]]-like arrangement of the chain of fifths, copied thrice to access most of the no-17 27-odd-limit and then some.
	[[File:UltimateMapGraphOrtho.png\|thumb\|750x750px\|A visualization of ~~Ultimate (cassaschismic temperament)~~, with 3 copies of a chain of fifths laid out in a Lumatone-like fashion.]]		[[File:UltimateMapGraphOrtho.png\|thumb\|750x750px\|A visualization of septischismic, with 3 copies of a chain of fifths laid out in a Lumatone-like fashion. You see and download the Blender file used to make this picture [[:File:UltimateMapGraph.blend.zip\|here]].]]
	{\| class="wikitable center-1 right-2 right-4"		{\| class="wikitable center-1 right-2 right-4"
	! rowspan="2" \| #		! rowspan="2" \| #
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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 highly accurate (217, 270, 311, …).		Septischismic 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.
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	== See also ==		== See also ==
	* [[User:Eufalesio/Ultimate]] – An opinion-based derivation of ~~cassaschismic~~		* [[User:Eufalesio/Ultimate]] – An opinion-based derivation of septischismic

	== External links ==		== External links ==
	* [https://www.desmos.com/calculator/pbyqpjgrrn Ultimate mapgraph] – A [https://www.desmos.com/calculator Desmos] graph by [[Eufalesio]] showing ~~cassaschismic~~ edos up to 311, [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is the [[patent val]] prime 11, 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 line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.		* [https://www.desmos.com/calculator/pbyqpjgrrn Ultimate mapgraph] – A [https://www.desmos.com/calculator Desmos] graph by [[Eufalesio]] showing Septischismic edos up to 311, [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is the [[patent val]] prime 11, which is not used in Septischismic. 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 line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.

	[[Category:~~Cassaschismic~~\| ]] <!-- main article -->		[[Category:Septischismic\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]
	[[Category:Microtemperaments]]		[[Category:Microtemperaments]]
	[[Category:Septischismic family]]		[[Category:Septischismic family]]
	[[Category:Olympic clan]]		[[Category:Olympic clan]]

FloraC: Undo to keep edit history

2026-08-15T18:34:19Z

Undo to keep edit history

Show changes

Eufalesio: Made septischismic the canon name

2026-08-15T16:49:46Z

Made septischismic the canon name

Show changes

FloraC: Text replacement - "Category:Garischismic family" to "Category:Septischismic family"

2026-08-15T14:21:01Z

Text replacement - "Category:Garischismic family" to "Category:Septischismic family"

← Older revision		Revision as of 14:21, 15 August 2026
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	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]
	[[Category:Microtemperaments]]		[[Category:Microtemperaments]]
	[[Category:~~Garischismic~~ family]]		[[Category:Septischismic family]]
	[[Category:Olympic clan]]		[[Category:Olympic clan]]

Eufalesio: Added visualization, too bad I can't upload blender file

2026-08-02T08:54:48Z

Added visualization, too bad I can't upload blender file

← Older revision		Revision as of 08:54, 2 August 2026
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	Here is a quick compressed cheat sheet of octave-reduced intervals. This is a simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to 8 fifths - 1 aberschisma step, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 aberschisma step. There are no octave reduced primes or prime inverses with positive fifth step and aberschisma step.		Here is a quick compressed cheat sheet of octave-reduced intervals. This is a simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to 8 fifths - 1 aberschisma step, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 aberschisma step. There are no octave reduced primes or prime inverses with positive fifth step and aberschisma step.

			An image is provided instead showing copies of a [[Standard Lumatone mapping for Pythagorean]]-like arrangement of the chain of fifths, copied thrice to access most of the no-17 27-odd-limit and then some.
			[[File:UltimateMapGraphOrtho.png\|thumb\|750x750px\|A visualization of Ultimate (cassaschismic temperament), with 3 copies of a chain of fifths laid out in a Lumatone-like fashion.]]
	{\| class="wikitable center-1 right-2 right-4"		{\| class="wikitable center-1 right-2 right-4"
	! rowspan="2" \| #		! rowspan="2" \| #

FloraC: Fix (minor minthma -> major minthma) & sort rank-2 temps by ploidacot

2026-07-24T16:35:51Z

Fix (minor minthma -> major minthma) & sort rank-2 temps by ploidacot

Overthink: /* External links */ link text; name creator

2026-07-06T02:42:21Z

External links: link text; name creator

← Older revision		Revision as of 02:42, 6 July 2026
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	== External links ==		== External links ==
	* [https://www.desmos.com/calculator/pbyqpjgrrn] – A [https://www.desmos.com/calculator Desmos] graph showing cassaschismic edos up to 311, [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is the [[patent val]] prime 11, 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 line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.		* [https://www.desmos.com/calculator/pbyqpjgrrn Ultimate mapgraph] – A [https://www.desmos.com/calculator Desmos] graph by [[Eufalesio]] showing cassaschismic edos up to 311, [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is the [[patent val]] prime 11, 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 line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.

	[[Category:Cassaschismic\| ]] <!-- main article -->		[[Category:Cassaschismic\| ]] <!-- main article -->

Overthink: /* External links */ en dash

2026-06-27T16:25:56Z

External links: en dash

← Older revision		Revision as of 16:25, 27 June 2026
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	== External links ==		== External links ==
	* [https://www.desmos.com/calculator/pbyqpjgrrn] A [https://www.desmos.com/calculator Desmos] graph showing cassaschismic edos up to 311, [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is the [[patent val]] prime 11, 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 line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.		* [https://www.desmos.com/calculator/pbyqpjgrrn] – A [https://www.desmos.com/calculator Desmos] graph showing cassaschismic edos up to 311, [[8afdo\|harmonic mode 8]] (green), and [[5L 7s]] 6\|5 (red). The purple line on 12 is the [[patent val]] prime 11, 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 line for cassandra; since halving it results in 270edo, it is used instead, and also to showcase the use of aberschismas to reach primes 5, 13, and 19.

	[[Category:Cassaschismic\| ]] <!-- main article -->		[[Category:Cassaschismic\| ]] <!-- main article -->

Overthink: see also

2026-06-22T05:05:10Z

← Older revision		Revision as of 05:05, 22 June 2026
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	\| C–^Eb (upminor third)		\| C–^Eb (upminor third)
	\|}		\|}

			== See also ==
			* [[User:Eufalesio/Ultimate]] – An opinion-based derivation of cassaschismic

	== External links ==		== External links ==

← Older revision		Revision as of 16:35, 24 July 2026
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	'''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]].		'''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\|major 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]], [[paramity]] and [[heptacot]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.		Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[newt]], [[gariwizmic]], [[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\|		{{Databox\|Generators needed to reach the aberschisma\|
			* Cotoneum (41 & 217): -41 fifths, equating it with the 41-comma;
	* Newt (41 & 270): -41 hemififths;		* 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;		* Gariwizmic (94 & 270): +53 fifths (mercator comma) - 1/2 pythagorean comma;
			* Satin (94 & 217): -94 1/3-fourths;
	* Vulture (53 & 217): -41 1/4-fifths;		* Vulture (53 & 217): -41 1/4-fifths;
	* Satin (94 & 217): -94 1/3-fourths;
	* Paramity (53 & 311): -53 1/5-elevenths;		* Paramity (53 & 311): -53 1/5-elevenths;
	* Heptacot (12e & 311): 12 1/7-fifths.		* Heptacot (12e & 311): 12 1/7-fifths.