Misty: Difference between revisions

From XenReference
← Older editNewer edit →

Inthar (talk | contribs)

3 user groups
4,744 edits
VisualWikitext
No edit summary
mNo edit summary
Line 1: Line 1:
'''Misty''', 87 & 99, is a 7-limit temperament with generator 3/2 and period 1/3-octave which represents 63/50. It results from tempering out the following 2 commas:
'''Misty''', 87 & 99, is a 7-limit temperament with generator 3/2 and period 1/3-octave which represents 63/50, the difference between 56/25 and 16/9. It results from tempering out the following 2 commas:
* 5120/5103, the aberschisma, which equates 64/63 and 81/80
* 5120/5103, the aberschisma, which equates 64/63 and 81/80
* 3136/3125, the [[Didacus]] comma
* 3136/3125, the [[Didacus]] comma
[TODO: explain how that leads to a 1/3-octave temperament]{{Navbox regtemp}}
 
== Theory ==
=== Intervals ===
=== Derivation of 1/3-octave period ===
# {{adv|128/125 {{=}} 126/125 * 64/63 is equated to 126/125 * 81/80 by the aberschisma}}
# {{adv|81/80 itself {{=}} 126/125 * 225/224}}
# {{adv|Didacus equates 225/224 to 126/125}}
# {{adv|So we have 128/125 ~ 126/125 * 81/80 {{=}} 126/125 * 126/125 * 225/224 ~ 126/125 * 126/125 * 126/125}}
# {{adv|Hence, 2/1 {{=}} 5/4 * 5/4 * 5/4 * 128/125 ~ (5/4 * 126/125)<sup>3</sup> {{=}} (63/50)<sup>3</sup>}}
 
{{Navbox regtemp}}
{{Cat|Temperaments}}
{{Cat|Temperaments}}

Revision as of 13:25, 2 April 2026

Misty, 87 & 99, is a 7-limit temperament with generator 3/2 and period 1/3-octave which represents 63/50, the difference between 56/25 and 16/9. It results from tempering out the following 2 commas:

  • 5120/5103, the aberschisma, which equates 64/63 and 81/80
  • 3136/3125, the Didacus comma

Theory

Intervals

Derivation of 1/3-octave period

  1. 128/125 = 126/125 * 64/63 is equated to 126/125 * 81/80 by the aberschisma
  2. 81/80 itself = 126/125 * 225/224
  3. Didacus equates 225/224 to 126/125
  4. So we have 128/125 ~ 126/125 * 81/80 = 126/125 * 126/125 * 225/224 ~ 126/125 * 126/125 * 126/125
  5. Hence, 2/1 = 5/4 * 5/4 * 5/4 * 128/125 ~ (5/4 * 126/125)3 = (63/50)3


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) • Miracle (hexacot) • Kleismic (alpha-hexacot) • Hemiseven (gamma-hexacot) • Hedgehog (diploid alpha-tricot)
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) • Paddle (alter-dicot)
No-3 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph) • Sidewalk (epsilon-heptaseph)
No-2 Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Aberschismic • Marvel • Parapyth • Pentagoth • Intergan
Straddle Rank-3 Hibernal • Monarch
Retrieved from "https://xenreference.com/wiki/index.php?title=Misty&oldid=5494"