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, | '''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.) | ||
== Interval chain == | == Interval chain == | ||
* 1 gen = '''5/4''' | * 1 gen = '''5/4''' | ||
Revision as of 06:53, 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, 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.)
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
| View • Talk • EditRegular temperaments | |
|---|---|
| Rank-2 | |
| Acot | Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave) |
| Monocot | Meantone • Schismic • Leapday • Archy |
| Complexity 2 | Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot) |
| Complexity 3 | Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot) |
| Complexity 4 | Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot) |
| Complexity 5-6 | Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot) |
| Higher complexity | Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot) |
| Straddle-3 | A-Team (alter-tricot) • Machine (alter-monocot) |
| No-3 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperament | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
