Wurschmidt: Difference between revisions

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Created page with "'''Würschmidt''' or '''Wurschmidt''', 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. == 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 *..."
 
Line 17: Line 17:
* 14 gens = 23/16
* 14 gens = 23/16
* 15 gens = 9/5
* 15 gens = 9/5
* 16 gens = 9/8
* 16 gens = '''9/8'''
* 17 gens = 45/32
* 17 gens = 45/32
* 18 gens = 225/128 ~ 81/46
* 18 gens = 225/128 ~ 81/46

Revision as of 05:41, 22 March 2026

Würschmidt or Wurschmidt, 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.

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
  • 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 • Gentle-fifth temperaments • 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 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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