Wurschmidt - Revision history

Inthar at 13:58, 14 April 2026

2026-04-14T13:58:53Z

← Older revision		Revision as of 13:58, 14 April 2026
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	'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', {{e\|31}} & {{e\|34}}, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 (equivalently, tempering out 243/242) and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)		'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', 2.3.5[{{e\|31}} & {{e\|34}}], is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 (equivalently, tempering out 243/242) and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)

	'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)		'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)

Inthar at 13:57, 14 April 2026

2026-04-14T13:57:28Z

← Older revision		Revision as of 13:57, 14 April 2026
Line 1:		Line 1:
	'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', 31 & 34, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 (equivalently, tempering out 243/242) and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)		'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', {{e\|31}} & {{e\|34}}, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 (equivalently, tempering out 243/242) and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)

	'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)		'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)

Inthar: /* Patent vals */

2026-04-14T13:56:10Z

Patent vals

← Older revision		Revision as of 13:56, 14 April 2026
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	== Patent vals ==		== Patent vals ==
	The following patent vals support Wurschmidt. Vals contorted in 2.3.5 are not included.~~{ class="wikitable sortable"~~		The following patent vals support Wurschmidt. Vals contorted in 2.3.5 are not included.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	!\|Edo!!11 extension!!23 extension!!Generator!!3/2 tuning!!11/8 tuning!!23/16 tuning		!\|Edo!!11 extension!!23 extension!!Generator!!3/2 tuning!!11/8 tuning!!23/16 tuning

Inthar: /* Patent vals */

2026-04-14T13:55:57Z

Patent vals

Show changes

Inthar: /* Patent vals */

2026-04-14T13:49:54Z

Patent vals

← Older revision		Revision as of 13:49, 14 April 2026
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	== Patent vals ==		== Patent vals ==
	The following patent vals support Wurschmidt. Vals contorted in 2.3.5 are not included.		The following patent vals support Wurschmidt. Vals contorted in 2.3.5 are not included.
	{ class="wikitable sortable"		{\| class="wikitable sortable"
	!\|Edo!!11 extension!!Generator!!3/2 tuning!!11/8 tuning		!\|Edo!!11 extension!!Generator!!3/2 tuning!!11/8 tuning
	\|-		\|-

Inthar at 13:49, 14 April 2026

2026-04-14T13:49:44Z

@@ Line 38: / Line 38: @@
 == Extensions ==
 [[Hemiwurschmidt]] is a weak extension that divides the 5/4 into two 28/25's. As such, it provides a high-accuracy extension of Didacus.
 {{Navbox regtemp}}
 {{Cat|temperaments}}

Inthar at 13:45, 14 April 2026

2026-04-14T13:45:28Z

← Older revision		Revision as of 13:45, 14 April 2026
Line 1:		Line 1:
	'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', 31 & 34, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)		'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', 31 & 34, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 (equivalently, tempering out 243/242) and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)

	'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)		'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)

Vector: "resp." is confusing

2026-03-25T01:12:39Z

"resp." is confusing

← Older revision		Revision as of 01:12, 25 March 2026
Line 1:		Line 1:
	'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', 31 & 34, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 ~~resp.~~ S50; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)		'''Wurschmidt''', '''Würschmidt''', or '''Wuerschmidt''', 31 & 34, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for [[Canonical extension\|extending structurally]] into higher-limit subgroups by tempering together a sequence of diesis-sized superparticulars: 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49 (all equated with 128/125). (Primes 11 and 17 can be added by tempering out S45 and S50 respectively; however, adding prime 11 implies less extra damage than prime 17, so we'll treat Wurschmidt as canonically having prime 11 but not 17.)

	'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)		'''Squares''', 17 & 31, is an index-2 subtemperament, which can be considered a 2.3.7.11.23.25 temperament, with a generator of 32/25~23/18~14/11~9/7. However, it is most accurately interpreted as a no-7s temperament. (You can't add 7 to a strong extension of Wurschmidt without high damage.)

Inthar: /* Interval chain */

2026-03-24T22:48:38Z

Interval chain

← Older revision		Revision as of 22:48, 24 March 2026
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	* 1 gen = '''5/4'''		* 1 gen = '''5/4'''
	* 2 gens = '''25/16''' ~ 36/23 (~ 11/7 ~ 14/9)		* 2 gens = '''25/16''' ~ 36/23 (~ 11/7 ~ 14/9)
	* 3 gens = ~~2/1 complement of 46~~/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49		* 3 gens = 44/45 ~ 45/46 ~ 46/47 ~ 47/48 ~ 48/49 ~ 49/50
	* 4 gens = 11/9 ~ 27/22 ~ 49/40		* 4 gens = 11/9 ~ 27/22 ~ 49/40 ~ 60/49
	* 5 gens = 49/32 ~ 72/47		* 5 gens = 49/32 ~ 72/47
	* 6 gens = 48/25 ~ 23/12 ~ 44/23		* 6 gens = 48/25 ~ 23/12 ~ 44/23
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	* 17 gens = 45/32		* 17 gens = 45/32
	* 18 gens = 225/128 ~ 81/46 (~ '''7/4''')		* 18 gens = 225/128 ~ 81/46 (~ '''7/4''')
	* 19 gens = 11/10		* 19 gens = 11/10 ~ 54/49
	* 20 gens = '''11/8'''		* 20 gens = '''11/8'''
	* 21 gens = 55/32		* 21 gens = 55/32
Line 29:		Line 29:
	* 24 gens = '''27/16'''		* 24 gens = '''27/16'''
	* 25 gens = 135/128		* 25 gens = 135/128
	~~...~~		* 26 gens = 33/25
			* 27 gens = 33/20
			* 28 gens = 33/32
			* 29 gens = 165/128
			* 30 gens = 81/50
	* 31 gens = 81/80		* 31 gens = 81/80

Inthar: /* Interval chain */

2026-03-24T22:12:13Z

Interval chain

← Older revision		Revision as of 22:12, 24 March 2026
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	* 3 gens = 2/1 complement of 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49		* 3 gens = 2/1 complement of 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49
	* 4 gens = 11/9 ~ 27/22 ~ 49/40		* 4 gens = 11/9 ~ 27/22 ~ 49/40
	* 5 gens = ~~'''~~49/32~~'''~~		* 5 gens = 49/32 ~ 72/47
	* 6 gens = 48/25 ~ 23/12 ~ 44/23		* 6 gens = 48/25 ~ 23/12 ~ 44/23
	* 7 gens = 6/5		* 7 gens = 6/5