Vengeance - Revision history

Inthar at 18:09, 6 June 2026

2026-06-06T18:09:31Z

← Older revision		Revision as of 18:09, 6 June 2026
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	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue (temperament)\|armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue (temperament)\|armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

	For technical data, see [[~~no-threes subgroup temperaments~~ #Vengeance]].		For technical data, see [[2023/2000#Vengeance]].

	== History ==		== History ==

Inthar: Groundfault has redefined pentagoth as a rank-3 temperament

2026-06-06T17:48:53Z

Groundfault has redefined pentagoth as a rank-3 temperament

← Older revision		Revision as of 17:48, 6 June 2026
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	\| Odd limit 2 = 2.5.7.17 25 \| Mistuning 2 = 8.88 \| Complexity 2 = 16		\| Odd limit 2 = 2.5.7.17 25 \| Mistuning 2 = 8.88 \| Complexity 2 = 16
	}}		}}
	'''Vengeance''' ~~(CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name)~~ is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.		'''Vengeance''' is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.

	Pentagoth was defined by ground and Userminusone as having an extension to the 2.5.13/11.17 subgroup that identifies 20/17 and [[13/11]] by tempering out [[221/220]]. The [[eigenmonzo\|exact]]-13/11 tuning is 672.3¢, near [[25edo\|14\25]] (672.0¢), and the exact-20/17 tuning is 670.3¢, near [[34edo\|19\34]] (670.6¢).

	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue (temperament)\|armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue (temperament)\|armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

	For technical data, see [[no-threes subgroup temperaments #Vengeance]].		For technical data, see [[no-threes subgroup temperaments #Vengeance]].

			== History ==
			Pentagoth was originally defined by ground and Userminusone as having an extension to the 2.5.13/11.17 subgroup that identifies 20/17 and [[13/11]] by tempering out [[221/220]]. The [[eigenmonzo\|exact]]-13/11 tuning is 672.3¢, near [[25edo\|14\25]] (672.0¢), and the exact-20/17 tuning is 670.3¢, near [[34edo\|19\34]] (670.6¢).

			Pentagoth now refers to a rank-3 temperament on 2.5.7.17 tempering out [[2023/2000]].

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

Xenllium at 08:31, 17 February 2026

2026-02-17T08:31:26Z

← Older revision		Revision as of 08:31, 17 February 2026
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			{{Infobox regtemp
			\| Title = Vengeance
			\| Subgroups = 2.5.17, 2.5.7.17
			\| Comma basis = [[78608/78125]] (2.5.17) <br>[[2023/2000]], [[4165/4096]] (2.5.7.17)
			\| Edo join 1 = 16 \| Edo join 2 = 25
			\| Mapping = 1; 3 -5 7
			\| Generators = 34/25 \| Generators tuning = 527.718 \| Optimization method = CWE
			\| MOS scales = [[2L 5s]], [[7L 2s]]
			\| Pergen = (P8, M10<sup>5</sup>/3)
			\| Odd limit 1 = 2.5.7.17 17 \| Mistuning 1 = 8.88 \| Complexity 1 = 16
			\| Odd limit 2 = 2.5.7.17 25 \| Mistuning 2 = 8.88 \| Complexity 2 = 16
			}}
	'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.		'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.

Line 35:		Line 47:
	\| C		\| C
	\|-		\|-
	\|3		\| 3
	\| 383.784		\| 383.784
	\| '''5/4'''		\| '''5/4'''
Line 56:		Line 68:
	\| 767.568		\| 767.568
	\| 25/16		\| 25/16
	\| ~~minor 6th~~		\| augmented 5th
	\| B		\| A#
	\|-		\|-
	\| 7		\| 7

FloraC: Update

2025-09-06T14:18:36Z

Update

← Older revision		Revision as of 14:18, 6 September 2025
Line 3:		Line 3:
	Pentagoth was defined by ground and Userminusone as having an extension to the 2.5.13/11.17 subgroup that identifies 20/17 and [[13/11]] by tempering out [[221/220]]. The [[eigenmonzo\|exact]]-13/11 tuning is 672.3¢, near [[25edo\|14\25]] (672.0¢), and the exact-20/17 tuning is 670.3¢, near [[34edo\|19\34]] (670.6¢).		Pentagoth was defined by ground and Userminusone as having an extension to the 2.5.13/11.17 subgroup that identifies 20/17 and [[13/11]] by tempering out [[221/220]]. The [[eigenmonzo\|exact]]-13/11 tuning is 672.3¢, near [[25edo\|14\25]] (672.0¢), and the exact-20/17 tuning is 670.3¢, near [[34edo\|19\34]] (670.6¢).

	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue (temperament)\|armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

	For technical data, see [[no-threes subgroup temperaments #Vengeance]].		For technical data, see [[no-threes subgroup temperaments #Vengeance]].

FloraC: - parent category

2025-04-28T14:49:30Z

- parent category

← Older revision		Revision as of 14:49, 28 April 2025
Line 5:		Line 5:
	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

	For technical data, see [[no-threes subgroup temperaments#Vengeance]].		For technical data, see [[no-threes subgroup temperaments #Vengeance]].

	== Interval chain ==		== Interval chain ==
	In the following table, prime harmonics are labeled in '''bold'''.		In the following table, prime harmonics are labeled in '''bold'''.
Line 11:		Line 12:
	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	!#		! #
	!Cents*		! Cents*
	!Approximate ratios		! Approximate ratios
	!colspan=2\|Melodic antidiatonic notation		! colspan=2\| Melodic antidiatonic notation
	\|-		\|-
	\|0		\| 0
	\|0.00		\| 0.00
	\|'''1/1'''		\| '''1/1'''
	\|perfect unison		\| perfect unison
	\|D		\| D
	\|-		\|-
	\|1		\| 1
	\|527.928		\| 527.928
	\|34/25		\| 34/25
	\|perfect 4th		\| perfect 4th
	\|G		\| G
	\|-		\|-
	\|2		\| 2
	\|1055.856		\| 1055.856
	\|119/64, 125/68		\| 119/64, 125/68
	\|major 7th		\| major 7th
	\|C		\| C
	\|-		\|-
	\|3		\|3
	\|383.784		\| 383.784
	\|'''5/4'''		\| '''5/4'''
	\|major 3rd		\| major 3rd
	\|F		\| F
	\|-		\|-
	\|4		\| 4
	\|911.712		\| 911.712
	\|17/10		\| 17/10
	\|major 6th		\| major 6th
	\|B#		\| B#
	\|-		\|-
	\|5		\| 5
	\|239.64		\| 239.64
	\|'''8/7'''		\| '''8/7'''
	\|major 2nd		\| major 2nd
	\|E#		\| E#
	\|-		\|-
	\|6		\| 6
	\|767.568		\| 767.568
	\|25/16		\| 25/16
	\|minor 6th		\| minor 6th
	\|B		\| B
	\|-		\|-
	\|7		\| 7
	\|95.496		\| 95.496
	\|'''17/16'''		\| '''17/16'''
	\|augmented unison		\| augmented unison
	\|D#		\| D#
	\|}		\|}
	<nowiki>*</nowiki> in 2.5.7.17 subgroup CTE tuning		<nowiki>*</nowiki> in 2.5.7.17 subgroup CTE tuning

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

Lériendil at 00:08, 20 April 2025

2025-04-20T00:08:41Z

← Older revision		Revision as of 00:08, 20 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Subgroup temperaments]]		[[Category:Subgroup temperaments]]
			[[Category:Rank-2 temperaments]]

Inthar: Added information about the 2.5.13/11.17 extension of Pentagoth.

2024-02-28T01:12:56Z

Added information about the 2.5.13/11.17 extension of Pentagoth.

← Older revision		Revision as of 01:12, 28 February 2024
Line 1:		Line 1:
	'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.		'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.

			Pentagoth was defined by ground and Userminusone as having an extension to the 2.5.13/11.17 subgroup that identifies 20/17 and [[13/11]] by tempering out [[221/220]]. The [[eigenmonzo\|exact]]-13/11 tuning is 672.3¢, near [[25edo\|14\25]] (672.0¢), and the exact-20/17 tuning is 670.3¢, near [[34edo\|19\34]] (670.6¢).

	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

Inthar at 18:24, 27 January 2024

2024-01-27T18:24:00Z

← Older revision		Revision as of 18:24, 27 January 2024
Line 1:		Line 1:
	'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.		'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.

	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

Inthar: Added "Pentagoth" as an alternate name.

2024-01-27T18:23:51Z

Added "Pentagoth" as an alternate name.

← Older revision		Revision as of 18:23, 27 January 2024
Line 1:		Line 1:
	'''Vengeance''' is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. ~~Its~~ name was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.		'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s\|antidiatonic scale]] and [[7L 2s\|superdiatonic scale]] but being comparatively very low in [[error]] and [[badness]], because the flat fifth generator is represented by [[25/17]] rather than [[3/2]] (or equivalently, [[34/25]] rather than [[4/3]]). It is defined by [[tempering out]] the [[comma]] [[78608/78125]]. The name "vengeance' was coined by [[User:CompactStar\|CompactStar]] and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by [[5/4]], but the minor third is represented by [[20/17]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone.

	The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).		The harmonic 7 can be added in a similar way to how mavila is extended to [[armodue]], by having [[7/4]] reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).

CompactStar at 08:52, 17 November 2023

2023-11-17T08:52:09Z

← Older revision		Revision as of 08:52, 17 November 2023
Line 42:		Line 42:
	\|17/10		\|17/10
	\|major 6th		\|major 6th
	\|F		\|B#
	\|-		\|-
	\|5		\|5