Wurschmidt: Difference between revisions
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'''Würschmidt''', '''Wurschmidt''', 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). | '''Würschmidt''', '''Wurschmidt''', 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). | ||
'''Squares''', 17 & 31, is an index-2 subtemperament, most accurately interpreted in 2.3.11.23.25; however, the generator is often interpreted as 14/11~9/7 with the attendant damage. | '''Squares''', 17 & 31, is an index-2 subtemperament, most accurately interpreted in 2.3.11.23.25 (and with generator 23/18 ~ 32/25); however, the generator is often interpreted as 14/11~9/7 with the attendant damage. | ||
== Interval chain == | == Interval chain == | ||
* 1 gen = '''5/4''' | * 1 gen = '''5/4''' | ||
Revision as of 06:00, 22 March 2026
Würschmidt, Wurschmidt, or Wuerschmidt, 31 & 34, is a temperament that splits 6/1 into 8 slightly sharp 5/4's. It is notable for 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).
Squares, 17 & 31, is an index-2 subtemperament, most accurately interpreted in 2.3.11.23.25 (and with generator 23/18 ~ 32/25); however, the generator is often interpreted as 14/11~9/7 with the attendant damage.
Interval chain
- 1 gen = 5/4
- 2 gens = 25/16 ~ 36/23
- 3 gens = 2/1 complement of 46/45 ~ 47/46 ~ 48/47 ~ 49/48 ~ 50/49
- 4 gens = 11/9
- 5 gens = 49/32
- 6 gens = 48/25 ~ 23/12 ~ 44/23
- 7 gens = 6/5
- 8 gens = 3/2
- 9 gens = 15/8
- 10 gens = 27/23
- 11 gens = 47/32
- 12 gens = 11/6 ~ 46/25
- 13 gens = 23/20
- 14 gens = 23/16
- 15 gens = 9/5
- 16 gens = 9/8
- 17 gens = 45/32
- 18 gens = 225/128 ~ 81/46
- 19 gens = 11/10
- 20 gens = 11/8
