Parakleismic - Revision history

Xenllium at 22:12, 12 May 2026

2026-05-12T22:12:31Z

← Older revision		Revision as of 22:12, 12 May 2026
Line 2:		Line 2:
	\| Title = Parakleismic		\| Title = Parakleismic
	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
	\| Comma basis = [[1224440064/1220703125]] (5-limit); <br>[[3136/3125]], [[4375/4374]] (7-limit)		\| Comma basis = [[Parakleisma\|1224440064/1220703125]] (5-limit); <br>[[3136/3125]], [[4375/4374]] (7-limit)
	\| Edo join 1 = 19 \| Edo join 2 = 99		\| Edo join 1 = 19 \| Edo join 2 = 99
	\| Mapping = 1; 13 14 35		\| Mapping = 1; 13 14 35

FloraC: /* Tuning spectrum */ general improvements

2026-03-14T12:00:55Z

Tuning spectrum: general improvements

← Older revision		Revision as of 12:00, 14 March 2026
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	<nowiki>*</nowiki> In 7-limit CWE tuning, octave reduced		<nowiki>*</nowiki> In 7-limit CWE tuning, octave reduced

	== Tuning spectrum ==		== Tunings ==
			=== Tuning spectrum ===
	{\| 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~~<br>(¢)		! Generator<br>(¢)
	! ~~comments~~		! Comments
	\|-		\|-
	\| 16\61		\| 16\61
	\|		\|
	\| 314.754		\| 314.754
	\| ~~Lower~~ bound of 9-odd-limit diamond monotone		\| 61d val, lower bound of 9-odd-limit diamond monotone
	\|-		\|-
	\|		\|
	\| 15/14		\| 15/14
	\| 314.930		\| 314.930
	\|		\|
	\|-		\|-
	\| 21\80		\| 21\80
	\|		\|
	\| 315.000		\| 315.000
	\|		\|
	\|-		\|-
	\|		\|
	\| 9/7		\| 9/7
	\| 315.009		\| 315.009
	\|		\|
	\|-		\|-
	\|		\|
	\| 7/5		\| 7/5
	\| 315.118		\| 315.118
	\|		\|
	\|-		\|-
	\|		\|
	\| 7/6		\| 7/6
	\| 315.142		\| 315.142
	\|		\|
	\|-		\|-
	\| 26\99		\| 26\99
	\|		\|
	\| 315.152		\| 315.152
	\|		\|
	\|-		\|-
	\|		\|
	\| 21/20		\| 21/20
	\| 315.163		\| 315.163
	\|		\|
	\|-		\|-
	\|		\|
	\| 49/48		\| 49/48
	\| 315.163		\| 315.163
	\|		\|
	\|-		\|-
	\|		\|
	\| 36/35		\| 36/35
	\| 315.164		\| 315.164
	\|		\|
	\|-		\|-
	\|		\|
	\| 8/7		\| 8/7
	\| 315.176		\| 315.176
	\| 7-odd-limit minimax (error = 1.~~217¢~~)		\| 7-odd-limit minimax (error = 1.217 ¢)
	\|-		\|-
	\|		\|
	\| 80/63		\| 80/63
	\| 315.183		\| 315.183
	\| 9-odd-limit minimax (error = 1.~~345¢~~)		\| 9-odd-limit minimax (error = 1.345 ¢)
	\|-		\|-
	\|		\|
	\| 10/9		\| 10/9
	\| 315.200		\| 315.200
	\|		\|
			\|-
			\| 57\217
			\|
			\| 315.207
			\|
	\|-		\|-
	\|		\|
	\| 4/3		\| 4/3
	\| 315.234		\| 315.234
	\|		\|
	\|-		\|-
	\|		\|
	\| 16/15		\| 16/15
	\| 315.249		\| 315.249
	\| 5-odd-limit minimax (error = 0.~~196¢~~)		\| 5-odd-limit minimax (error = 0.196 ¢)
	\|-		\|-
	\| 31\118		\| 31\118
	\|		\|
	\| 315.254		\| 315.254
	\|		\|
	\|-		\|-
	\|		\|
	\| 5/4		\| 5/4
	\| 315.263		\| 315.263
	\|		\|
	\|-		\|-
	\|		\|
	\| 25/24		\| 25/24
	\| 315.289		\| 315.289
	\|		\|
	\|-		\|-
	\|		\|
	\| 6/5		\| 6/5
	\| 315.641		\| 315.641
	\|		\|
	\|-		\|-
	\|		\|
	\| 28/27		\| 28/27
	\| 315.740		\| 315.740
	\|		\|
	\|-		\|-
	\| 5\19		\| 5\19
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	\| Upper bound of 9-odd-limit diamond monotone		\| Upper bound of 9-odd-limit diamond monotone
	\|}		\|}
			<nowiki>*</nowiki> Besides the octave

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

FloraC: Expand on intro

2026-03-14T11:50:36Z

Expand on intro

← Older revision		Revision as of 11:50, 14 March 2026
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	\| Odd limit 1 = 9 \| Mistuning 1 = 1.34 \| Complexity 1 = 42		\| Odd limit 1 = 9 \| Mistuning 1 = 1.34 \| Complexity 1 = 42
	}}		}}
	'''Parakleismic''' is ~~the~~ microtemperament ~~tempering out~~ the [[~~parakleisma~~]] in the ~~5-limit~~. ~~This article also assumes~~ the ~~canonical mapping for 7, which means tempering out~~ [[~~3136~~/~~3125~~]] and [[~~4375~~/~~4374~~]] in the ~~7-limit~~.		'''Parakleismic''' is a [[microtemperament]] generated by a [[~]][[6/5]] minor third, much like [[catakleismic]] but a good tuning has the generator flat, instead of sharp, than just. The sixth generator step is half a [[syntonic comma]] flat of the [[3/1\|3rd]] [[harmonic]]. Consequently, the 12th generator step after [[octave reduction]] represents [[10/9]] instead of [[9/8]], and the 13th generator step after octave reduction represents [[4/3]]. This results in the [[parakleisma]] being [[tempering out\|tempered out]].

	~~Parakleismic is much like~~ [[~~catakleismic~~]] ~~but a good tuning has~~ the generator ([[6/5]]) ~~flat, instead of sharp, than the just version~~. ~~The sixth generator step is half a~~ [[~~syntonic comma~~]] ~~flat of the harmonic 3. Consequently,~~ the ~~12th generator step is mapped to~~ [[~~10/9~~]] ~~instead of~~ [[~~9/8~~]]~~, and the 13th generator step is mapped to~~ [[4/3]] ~~instead of~~ [[27/20]].		Note that [[5/4]] is found at the 14th generator step (as the [[octave complement]] of [[8/5]]) and is already split in halves. Letting each part represent [[28/25]] gives rise to the canonical [[7-limit]] [[extension]] where it tempers out [[3136/3125]] and [[4375/4374]].

	Extensions for harmonic 11 ~~includes~~ ''undecimal parakleismic'', mapping it to +36 steps, ''paralytic'', to -82 steps, ''parkleismic'', to -63 steps, and ''paradigmic'', to +17 steps.		Extensions for harmonic 11 include ''undecimal parakleismic'', mapping it to +36 steps, ''paralytic'', to -82 steps, ''parkleismic'', to -63 steps, and ''paradigmic'', to +17 steps.

	See [[Ragismic microtemperaments #Parakleismic]] for technical data.		See [[Ragismic microtemperaments #Parakleismic]] for technical data. See [[Parakleismic extensions]] for a discussion on [[11-limit\|11-]] and [[13-limit]] extensions.

	== Interval chain ==		== Interval chain ==

FloraC: + infobox

2026-03-14T11:03:37Z

+ infobox

← Older revision		Revision as of 11:03, 14 March 2026
Line 1:		Line 1:
			{{Infobox regtemp
			\| Title = Parakleismic
			\| Subgroups = 2.3.5, 2.3.5.7
			\| Comma basis = [[1224440064/1220703125]] (5-limit); <br>[[3136/3125]], [[4375/4374]] (7-limit)
			\| Edo join 1 = 19 \| Edo join 2 = 99
			\| Mapping = 1; 13 14 35
			\| Generators = 5/3
			\| Generators tuning = 884.81
			\| Optimization method = CWE
			\| MOS scales = [[4L 15s]], [[19L 4s]], [[19L 23s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = 1.34 \| Complexity 1 = 42
			}}
	'''Parakleismic''' is the microtemperament tempering out the [[parakleisma]] in the 5-limit. This article also assumes the canonical mapping for 7, which means tempering out [[3136/3125]] and [[4375/4374]] in the 7-limit.		'''Parakleismic''' is the microtemperament tempering out the [[parakleisma]] in the 5-limit. This article also assumes the canonical mapping for 7, which means tempering out [[3136/3125]] and [[4375/4374]] in the 7-limit.

FloraC: /* Interval chain */ extend

2026-03-14T10:50:41Z

Interval chain: extend

Show changes

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

2025-06-21T06:59:24Z

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

← Older revision		Revision as of 06:59, 21 June 2025
Line 114:		Line 114:
	{\| 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<br>(¢)		! generator<br>(¢)
	! comments		! comments

FloraC: - parent category

2025-04-28T14:31:43Z

- parent category

← Older revision		Revision as of 14:31, 28 April 2025
Line 224:		Line 224:
	\|}		\|}

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

Lériendil at 23:35, 19 April 2025

2025-04-19T23:35:20Z

← Older revision		Revision as of 23:35, 19 April 2025
Line 226:		Line 226:
	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Parakleismic\| ]] <!-- main article -->		[[Category:Parakleismic\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Hemimean clan]]		[[Category:Hemimean clan]]
	[[Category:Ragismic microtemperaments]]		[[Category:Ragismic microtemperaments]]
	[[Category:Hemimage temperaments]]		[[Category:Hemimage temperaments]]
	[[Category:Canousmic temperaments]]		[[Category:Canousmic temperaments]]

Cmloegcmluin: unchanged interval → unchanged-interval

2023-05-05T23:42:00Z

unchanged interval → unchanged-interval

← Older revision		Revision as of 23:42, 5 May 2023
Line 113:		Line 113:
	== Tuning spectrum ==		== Tuning spectrum ==
	{\| 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~~<br>(¢)		! generator<br>(¢)
	! ~~Comments~~		! comments
	\|-		\|-
	\| 16\61		\| 16\61

FloraC: /* Tuning spectrum */ style

2022-10-01T03:49:00Z

Tuning spectrum: style

← Older revision		Revision as of 03:49, 1 October 2022
Line 112:		Line 112:

	== Tuning spectrum ==		== Tuning spectrum ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all left-4"
	! Edo<br>Generator		! Edo<br>Generator
	! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]		! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]