Misty
From Xenharmonic Reference
Misty, 87 & 99, is a 7-limit temperament with
- generator 3/2 (period-reduced: 25/21)
- 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
(exact-7/4 tuning)
| +0 periods | +1 periods | +2 periods | ||||||
|---|---|---|---|---|---|---|---|---|
| # gens | Cents | JI | # gens | Cents | JI | # gens | Cents | JI |
| -1 | 1103.1 | 189/100 | -1 | 303.1 | 25/21 | -1 | 703.1 | 3/2 |
| 0 | 0 | 1/1 | 0 | 400 | 63/50 | 0 | 800 | 100/63 |
| 1 | 96.9 | 200/189 | 1 | 496.9 | 4/3 | 1 | 896.9 | 42/25 |
| 2 | 193.8 | 28/25 | 2 | 593.8 | 2 | 993.8 | 16/9 | |
| 3 | 290.6 | 32/27 | 3 | 690.6 | 3 | 1090.6 | 15/8 | |
| 4 | 387.5 | 5/4 | 4 | 787.5 | 63/40, 128/81 | 4 | 1187.5 | 125/126, 224/225 |
| 5 | 484.4 | 5 | 884.4 | 5/3 | 5 | 84.4 | 21/20 | |
| 6 | 581.3 | 7/5 | 6 | 981.3 | 6 | 181.3 | 10/9 | |
| 7 | 678.2 | 7 | 1078.2 | 28/15 | 7 | 278.2 | 75/64 | |
| 8 | 775.1 | 25/16 | 8 | 1175.1 | 63/64, 80/81 | 8 | 375.1 | |
| 9 | 871.9 | 9 | 71.9 | 25/24 | 9 | 471.9 | 21/16 | |
| 10 | 968.8 | 7/4 | 10 | 168.8 | 10 | 568.8 | 50/36 | |
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
| 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 |
