Catakleismic - Revision history

FloraC: "19 & 34d" is contentious (it might give the impression that the optimum is around 34d or 53)

2026-02-16T09:42:43Z

"19 & 34d" is contentious (it might give the impression that the optimum is around 34d or 53)

← Older revision		Revision as of 09:42, 16 February 2026
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	The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].		The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].

	In addition to the kleisma, catakleismic tempers out the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the [[2.3.5.13 subgroup]] interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found four [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]—or further, between [[19edo]] and [[53edo]], as beyond 53, the [[countercata]] mapping of 7 is more reasonable, with the two meeting at 53edo~~. In fact, catakleismic is the 19 & 34d temperament in the 7-limit~~. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.		In addition to the kleisma, catakleismic tempers out the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the [[2.3.5.13 subgroup\|2.3.5.13-subgroup]] interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found four [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]—or further, between [[19edo]] and [[53edo]], as beyond 53, the [[countercata]] mapping of 7 is more reasonable, with the two meeting at 53edo. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.

	Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to −21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to −2 steps. Undecimal catakleismic is shown in the tables below; additionally, tempering out [[286/285]] gives us an extension to prime 19 at -18 generator steps.		Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to −21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to −2 steps. Undecimal catakleismic is shown in the tables below; additionally, tempering out [[286/285]] gives us an extension to prime 19 at -18 generator steps.
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! Edo<br />generator		! Edo<br>generator
	! [[Eigenmonzo\|Eigenmonzo<br />(unchanged interval)]]*		! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

FloraC: + infobox

2026-02-16T09:31:56Z

+ infobox

← Older revision		Revision as of 09:31, 16 February 2026
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			{{Infobox regtemp
			\| Title = Catakleismic
			\| Subgroups = 2.3.5.7, 2.3.5.7.13, 2.3.5.7.11.13
			\| Comma basis = [[225/224]], [[4375/4374]] (7-limit); <br>[[169/168]], [[225/224]], [[325/324]] (2.3.5.7.13); <br>[[169/168]], [[225/224]], [[325/324]], [[385/384]] <br>(13-limit)
			\| Edo join 1 = 53 \| Edo join 2 = 72
			\| Mapping = 1; 6 5 22 -21 14
			\| Generators = 6/5 \| Generators tuning = 316.7 \| Optimization method = CWE
			\| MOS scales = [[4L 7s]], [[4L 11s]], [[15L 4s]], [[15L 19s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = ??? \| Complexity 1 = 34
			\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = ??? \| Complexity 2 = 53
			}}
	The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].		The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].

FloraC: Move music here. Misc. cleanup and linking

2026-02-16T09:24:24Z

Move music here. Misc. cleanup and linking

← Older revision		Revision as of 09:24, 16 February 2026
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	The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13-[[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].		The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a [[2.3.5.7.13 subgroup\|2.3.5.7.13-]][[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].

	In addition to the kleisma, catakleismic tempers out the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found four [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]~~—or~~ further, between [[19edo]] and [[53edo]], as beyond 53, the [[countercata]] mapping of 7 is more reasonable, with the two meeting at 53edo. In fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.		In addition to the kleisma, catakleismic tempers out the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the [[2.3.5.13 subgroup]] interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found four [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]—or further, between [[19edo]] and [[53edo]], as beyond 53, the [[countercata]] mapping of 7 is more reasonable, with the two meeting at 53edo. In fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.

	Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to ~~−21~~ generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to ~~−2~~ steps. Undecimal catakleismic is shown in the tables below; additionally, tempering out [[286/285]] gives us an extension to prime 19 at -18 generator steps.		Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to −21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to −2 steps. Undecimal catakleismic is shown in the tables below; additionally, tempering out [[286/285]] gives us an extension to prime 19 at -18 generator steps.

	See [[Kleismic family #Catakleismic]] for technical data.		See [[Kleismic family #Catakleismic]] for technical data. See [[Catakleismic extensions]] for a discussion on [[11-limit]] extensions.

	== Interval chain ==		== Interval chain ==
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	Notice also the little interval between the largest of a category and the smallest of the next. This interval spans 53 generator steps, so it vanishes in 53edo, but is tuned to the same size as the syntonic comma in 72edo. 125edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise.		Notice also the little interval between the largest of a category and the smallest of the next. This interval spans 53 generator steps, so it vanishes in 53edo, but is tuned to the same size as the syntonic comma in 72edo. 125edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise.

	== Chords ==		== Chords and harmony ==
	~~: ''Main article: [[~~Chords of catakleismic~~]] and [[~~Chords of tridecimal catakleismic~~]]''~~		{{See also\| Chords of catakleismic \| Chords of tridecimal catakleismic }}

	== Scales ==		== Scales ==
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	\|		\|
	\|}		\|}
	<nowiki />* Besides the octave		<nowiki/>* Besides the octave

			== Music ==
			; [[Budjarn Lambeth]]
			* [https://youtu.be/6Kxq5uxu-c8 ''Improv in CWE Catakleismic11''] (2026)

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

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:06:08Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:06, 12 September 2025
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	== Tunings ==		== Tunings ==
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.5.7.13-subgroup ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.5.7.13-subgroup norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.5.7.11.13.19-subgroup ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.5.7.11.13.19-subgroup norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|

Lériendil: Text replacement - "(unchanged-interval)" to "(unchanged interval)"

2025-06-21T06:59:25Z

Text replacement - "(unchanged-interval)" to "(unchanged interval)"

← Older revision		Revision as of 06:59, 21 June 2025
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	\|-		\|-
	! Edo<br />generator		! Edo<br />generator
	! [[Eigenmonzo\|Eigenmonzo<br />(unchanged-interval)]]*		! [[Eigenmonzo\|Eigenmonzo<br />(unchanged interval)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

FloraC: - parent category

2025-04-28T13:56:25Z

- parent category

← Older revision		Revision as of 13:56, 28 April 2025
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	<nowiki />* Besides the octave		<nowiki />* Besides the octave

	~~[[Category:Temperaments]]~~
	[[Category:Catakleismic\| ]] <!-- main article -->		[[Category:Catakleismic\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

FloraC: We're documenting this temp as a coherent 7-limit structure

2025-04-26T12:29:53Z

We're documenting this temp as a coherent 7-limit structure

← Older revision		Revision as of 12:29, 26 April 2025
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	~~{{breadcrumb\|Hanson and cata}}~~

	The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13-[[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].		The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13-[[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].

Lériendil at 23:01, 19 April 2025

2025-04-19T23:01:38Z

← Older revision		Revision as of 23:01, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Catakleismic\| ]] <!-- main article -->		[[Category:Catakleismic\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Kleismic family]]		[[Category:Kleismic family]]
	[[Category:Marvel temperaments]]		[[Category:Marvel temperaments]]
	[[Category:Ragismic microtemperaments]]		[[Category:Ragismic microtemperaments]]

Lériendil: added breadcrumb here, like didacus < hemithirds

2025-04-12T15:38:57Z

added breadcrumb here, like didacus < hemithirds

← Older revision		Revision as of 15:38, 12 April 2025
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			{{breadcrumb\|Hanson and cata}}

	The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13-[[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].		The '''catakleismic''' [[regular temperament\|temperament]] is one of the best [[7-limit]] [[extension]]s of [[hanson]], the [[5-limit]] temperament [[tempering out]] the [[15625/15552\|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13-[[subgroup]] temperament, first extending hanson to include the [[harmonic]] [[13/1\|13]] (called [[cata]]), and then to include [[7/1\|7]].

Lériendil: mentioned flora's extension to 19

2025-04-12T15:34:42Z

mentioned flora's extension to 19

← Older revision		Revision as of 15:34, 12 April 2025
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	In addition to the kleisma, catakleismic tempers out the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found four [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]—or further, between [[19edo]] and [[53edo]], as beyond 53, the [[countercata]] mapping of 7 is more reasonable, with the two meeting at 53edo. In fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.		In addition to the kleisma, catakleismic tempers out the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found four [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]—or further, between [[19edo]] and [[53edo]], as beyond 53, the [[countercata]] mapping of 7 is more reasonable, with the two meeting at 53edo. In fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.

	Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to −21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to −2 steps.		Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to −21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to −2 steps. Undecimal catakleismic is shown in the tables below; additionally, tempering out [[286/285]] gives us an extension to prime 19 at -18 generator steps.

	See [[Kleismic family #Catakleismic]] for technical data.		See [[Kleismic family #Catakleismic]] for technical data.