Aberschismic - Revision history

Inthar: /* Names */

2026-06-06T16:56:18Z

Names

← Older revision		Revision as of 16:56, 6 June 2026
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	Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].		Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].
	== Names ==		== Names ==
	The ~~older~~ name ''~~Hemifamity'' is a portmanteau of~~ ''[[~~Hemififths~~]]'' and ~~''[[Amity]]'',~~ both ~~rank-2 temperaments which support this rank-3 temperament~~.		The name ''Aberschismic'', coined by Tristan Bay, comes from the fact that tempering out 5120/5103 manifests in [[aberrismic theory]] where the 7-limit interpretations for chromedye (5L2m5s) and whitedye (5L2m7s) interpret the aberrisma (the s step) as both 81/80 and 64/63.

	The ~~newer~~ and ~~now official name~~ ''~~Aberschismic~~''~~, coined by Tristan Bay, comes~~ from the ~~fact that tempering out 5120/5103 manifests in [[aberrismic theory]] where~~ the ~~7-limit interpretations for chromedye (5L2m5s)~~ and ~~whitedye (5L2m7s) interpret~~ the ~~aberrisma~~ (~~the s step~~) ~~as both 81/80 and 64/63~~.		The names ''Argent'' and ''Argentic'' come from the relationship to the silver ratio and the associated (slightly hard of just) [[Golden_generator#Argent_tuning\|argent tuning]] of MOS diatonic.

	The ~~names~~ ''~~Argent~~'' ~~and~~ ''~~Argentic~~'' ~~come from the relationship to the silver ratio~~ and ~~the associated (slightly hard of just)~~ [[~~Golden_generator#Argent_tuning\|argent tuning~~]] ~~of MOS diatonic~~.		The older name ''Hemifamity'' is a portmanteau of ''[[Hemififths]]'' and ''[[Amity]]'', both rank-2 temperaments which support this rank-3 temperament.

	== Structural theory ==		== Structural theory ==

Inthar at 13:23, 6 June 2026

2026-06-06T13:23:01Z

← Older revision		Revision as of 13:23, 6 June 2026
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	'''Aberschismic''', [[41edo\|41]] & [[46edo\|46]] & [[53edo\|53]], is a [[7-limit]] rank-3 temperament that tempers out '''5120/5103''' (known as the '''aberschisma'''), which manifests in several different ways:		'''Aberschismic''' (formerly known as '''Hemifamity'''), [[41edo\|41]] & [[46edo\|46]] & [[53edo\|53]], is a [[7-limit]] rank-3 temperament that tempers out '''5120/5103''' (known as the '''aberschisma'''), which manifests in several different ways:
	# equates the 3-spine prime commas for 5 and 7, 81/80 and 64/63		# equates the 3-spine prime commas for 5 and 7, 81/80 and 64/63
	# equates the Pythagorean minor second with 21/20		# equates the Pythagorean minor second with 21/20

Inthar: /* Supporting rank-2 temperaments */

2026-06-06T13:22:16Z

Supporting rank-2 temperaments

← Older revision		Revision as of 13:22, 6 June 2026
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	* 53 & 58, [[Buzzard]] (Aberschismic + 2.3.7 Buzzard)		* 53 & 58, [[Buzzard]] (Aberschismic + 2.3.7 Buzzard)
	* 87 & 99, [[Misty]] (Aberschismic + [[Didacus]])		* 87 & 99, [[Misty]] (Aberschismic + [[Didacus]])
	* 7 & 29, Aberschismic + ~~2.3.5~~ [[Porcupine]]		* 7 & 29, Aberschismic + [[Porcupine]]

	== Extensions ==		== Extensions ==

Inthar: /* Supporting rank-2 temperaments */

2026-06-06T13:20:30Z

Supporting rank-2 temperaments

← Older revision		Revision as of 13:20, 6 June 2026
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	Given any rank-2 temperament on a rank-3 subgroup of the 7-limit that is not 2.3.7/5 (e.g. 2.3.5, 2.3.7, 2.5.7), Aberschismic tempering may be added to extend the temperament to the full 7-limit. Examples:		Given any rank-2 temperament on a rank-3 subgroup of the 7-limit that is not 2.3.7/5 (e.g. 2.3.5, 2.3.7, 2.5.7), Aberschismic tempering may be added to extend the temperament to the full 7-limit. Examples:
	* 41 & 46, [[Rodan]] (Aberschismic + [[Slendric]], Aberschismic + [[Sensamagic]])		* 41 & 46, [[Rodan]] (Aberschismic + [[Slendric]], Aberschismic + [[Sensamagic]])
	* 7 & 29, Aberschismic + 2.3.5 [[Porcupine]]
	* 41 & 48, [[Tetracot (temperament)#Extensions\|Monkey]] (Aberschismic + [[Tetracot (temperament)\|Tetracot]])		* 41 & 48, [[Tetracot (temperament)#Extensions\|Monkey]] (Aberschismic + [[Tetracot (temperament)\|Tetracot]])
	* 41 & 53, [[Garibaldi]] (Aberschismic + Schismic, Aberschismic + [[Marvel]])		* 41 & 53, [[Garibaldi]] (Aberschismic + Schismic, Aberschismic + [[Marvel]])
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	* 53 & 58, [[Buzzard]] (Aberschismic + 2.3.7 Buzzard)		* 53 & 58, [[Buzzard]] (Aberschismic + 2.3.7 Buzzard)
	* 87 & 99, [[Misty]] (Aberschismic + [[Didacus]])		* 87 & 99, [[Misty]] (Aberschismic + [[Didacus]])
			* 7 & 29, Aberschismic + 2.3.5 [[Porcupine]]

	== Extensions ==		== Extensions ==

Inthar: /* Supporting rank-2 temperaments */

2026-06-06T13:19:38Z

Supporting rank-2 temperaments

← Older revision		Revision as of 13:19, 6 June 2026
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	== Supporting rank-2 temperaments ==		== Supporting rank-2 temperaments ==
			Given any rank-2 temperament on a rank-3 subgroup of the 7-limit that is not 2.3.7/5 (e.g. 2.3.5, 2.3.7, 2.5.7), Aberschismic tempering may be added to extend the temperament to the full 7-limit. Examples:
	* 41 & 46, [[Rodan]] (Aberschismic + [[Slendric]], Aberschismic + [[Sensamagic]])		* 41 & 46, [[Rodan]] (Aberschismic + [[Slendric]], Aberschismic + [[Sensamagic]])
			* 7 & 29, Aberschismic + 2.3.5 [[Porcupine]]
	* 41 & 48, [[Tetracot (temperament)#Extensions\|Monkey]] (Aberschismic + [[Tetracot (temperament)\|Tetracot]])		* 41 & 48, [[Tetracot (temperament)#Extensions\|Monkey]] (Aberschismic + [[Tetracot (temperament)\|Tetracot]])
	* 41 & 53, [[Garibaldi]] (Aberschismic + Schismic, Aberschismic + [[Marvel]])		* 41 & 53, [[Garibaldi]] (Aberschismic + Schismic, Aberschismic + [[Marvel]])

Inthar at 13:08, 6 June 2026

2026-06-06T13:08:08Z

← Older revision		Revision as of 13:08, 6 June 2026
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	~~'''Hemifamity''' or~~ '''Aberschismic''', [[41edo\|41]] & [[46edo\|46]] & [[53edo\|53]], is a [[7-limit]] rank-3 temperament that tempers out '''5120/5103''' (known as ~~the '''hemifamiton''' or~~ the '''aberschisma'''), which manifests in several different ways:		'''Aberschismic''', [[41edo\|41]] & [[46edo\|46]] & [[53edo\|53]], is a [[7-limit]] rank-3 temperament that tempers out '''5120/5103''' (known as the '''aberschisma'''), which manifests in several different ways:
	# equates the 3-spine prime commas for 5 and 7, 81/80 and 64/63		# equates the 3-spine prime commas for 5 and 7, 81/80 and 64/63
	# equates the Pythagorean minor second with 21/20		# equates the Pythagorean minor second with 21/20
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	Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].		Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].
	== Names ==		== Names ==
	~~As of early 2026, the temperament has no single agreed-upon name.~~

	The older name ''Hemifamity'' is a portmanteau of ''[[Hemififths]]'' and ''[[Amity]]'', both rank-2 temperaments which support this rank-3 temperament.		The older name ''Hemifamity'' is a portmanteau of ''[[Hemififths]]'' and ''[[Amity]]'', both rank-2 temperaments which support this rank-3 temperament.

	The newer name ''Aberschismic'', coined by Tristan Bay, comes from the fact that tempering out 5120/5103 manifests in [[aberrismic theory]] where the 7-limit interpretations for chromedye (5L2m5s) and whitedye (5L2m7s) interpret the aberrisma (the s step) as both 81/80 and 64/63.		The newer and now official name ''Aberschismic'', coined by Tristan Bay, comes from the fact that tempering out 5120/5103 manifests in [[aberrismic theory]] where the 7-limit interpretations for chromedye (5L2m5s) and whitedye (5L2m7s) interpret the aberrisma (the s step) as both 81/80 and 64/63.

	The names ''Argent'' and ''Argentic'' come from the relationship to the silver ratio and the associated (slightly hard of just) [[Golden_generator#Argent_tuning\|argent tuning]] of MOS diatonic.		The names ''Argent'' and ''Argentic'' come from the relationship to the silver ratio and the associated (slightly hard of just) [[Golden_generator#Argent_tuning\|argent tuning]] of MOS diatonic.
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	== List of patent vals ==		== List of patent vals ==
	:''Main article: [[~~Hemifamity~~/Patent vals]]''		:''Main article: [[Aberschismic/Patent vals]]''
	{{navbox regtemp}}		{{navbox regtemp}}
	{{Cat\|Temperaments}}		{{Cat\|Temperaments}}

Inthar: Inthar moved page Hemifamity to Aberschismic over a redirect without leaving a redirect: "Aberschismic" is now official on Xen Wiki

2026-06-06T13:07:30Z

Inthar moved page Hemifamity to Aberschismic over a redirect without leaving a redirect: "Aberschismic" is now official on Xen Wiki

← Older revision	Revision as of 13:07, 6 June 2026
(No difference)

Vector at 23:41, 14 May 2026

2026-05-14T23:41:59Z

← Older revision		Revision as of 23:41, 14 May 2026
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	# equates the Pythagorean chroma with 15/14		# equates the Pythagorean chroma with 15/14
	# equates the Pythagorean augmented fourth with 10/7		# equates the Pythagorean augmented fourth with 10/7
	# splits 36/35 into two equal parts each representing the "common comma" 81/80 ~ 64/63		# splits 36/35 into two equal parts each representing the "common comma" 81/80 ~ 64/63 (hence 36/35 might humorously be referred to as the "famity")
	# splits 7/5 into two equal parts each representing 32/27		# splits 7/5 into two equal parts each representing 32/27
	# makes 28/27 - 21/20 - 16/15 - 27/25 equidistant and 35/32 - 10/9 - 9/8 - 8/7 equidistant		# makes 28/27 - 21/20 - 16/15 - 27/25 equidistant and 35/32 - 10/9 - 9/8 - 8/7 equidistant

Inthar at 21:37, 18 April 2026

2026-04-18T21:37:45Z

← Older revision		Revision as of 21:37, 18 April 2026
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	# splits 36/35 into two equal parts each representing the "common comma" 81/80 ~ 64/63		# splits 36/35 into two equal parts each representing the "common comma" 81/80 ~ 64/63
	# splits 7/5 into two equal parts each representing 32/27		# splits 7/5 into two equal parts each representing 32/27
	# makes 28/27 - 21/20 - 16/15 - 27/25 equidistant		# makes 28/27 - 21/20 - 16/15 - 27/25 equidistant and 35/32 - 10/9 - 9/8 - 8/7 equidistant

	Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].		Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].

Inthar at 20:50, 18 April 2026

2026-04-18T20:50:13Z

← Older revision		Revision as of 20:50, 18 April 2026
Line 6:		Line 6:
	# splits 36/35 into two equal parts each representing the "common comma" 81/80 ~ 64/63		# splits 36/35 into two equal parts each representing the "common comma" 81/80 ~ 64/63
	# splits 7/5 into two equal parts each representing 32/27		# splits 7/5 into two equal parts each representing 32/27
	# ~~equates 16/15 * 28/27 to (21/20)^2, making~~ 28/27 - 21/20 - 16/15 - 27/25 equidistant		# makes 28/27 - 21/20 - 16/15 - 27/25 equidistant

	Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].		Restricted to the subgroup 2.3.7/5, it becomes the fifth-generated rank-2 temperament '''Argent''' or '''Argentic''', 2.3.7/5[5120/5103] = 2.3.7/5[12 & 29].