Misty: Difference between revisions
From XenReference
| Line 9: | Line 9: | ||
# {{adv|81/80 itself {{=}} 126/125 * 225/224}} | # {{adv|81/80 itself {{=}} 126/125 * 225/224}} | ||
# {{adv|Didacus equates 225/224 to 126/125}} | # {{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)<sup>3</sup>}} | # {{adv|So we have 128/125 ~{{=}} 126/125 * 81/80 {{=}} 126/125 * 126/125 * 225/224 ~{{=}} (126/125)<sup>3</sup>}} | ||
# {{adv|Hence, 2/1 {{=}} 5/4 * 5/4 * 5/4 * 128/125 ~ (5/4 * 126/125)<sup>3</sup> {{=}} (63/50)<sup>3</sup>}} | # {{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}} | {{Navbox regtemp}} | ||
{{Cat|Temperaments}} | {{Cat|Temperaments}} | ||
Revision as of 14:17, 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)3
- Hence, 2/1 = 5/4 * 5/4 * 5/4 * 128/125 ~= (5/4 * 126/125)3 = (63/50)3
