Misty: Difference between revisions
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'''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 | ||
== 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
- 128/125 = 126/125 * 64/63 is equated to 126/125 * 81/80 by the aberschisma
- 81/80 itself = 126/125 * 225/224
- Didacus equates 225/224 to 126/125
- So we have 128/125 ~ 126/125 * 81/80 = 126/125 * 126/125 * 225/224 ~ 126/125 * 126/125 * 126/125
- 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 • 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 |
