Misty
Jump to navigation
Jump to search
Misty is the regular temperament tempering out the misty comma. It equates the Pythagorean comma with the diesis, and splits this interval into three equal parts, one representing the schisma~diaschisma, and two representing the syntonic comma. Consequently, the octave is also split into three. This temperament, supported by 12et, is notably in the schismic-Pythagorean equivalence continuum, with n = 3.
In the 7-limit, the canonical extension tempers out 3136/3125 and 5120/5103. Possible tunings include 87edo, 99edo and 111edo.
See Misty family for more technical data.
Interval chain
| # | Period 0 | Period 1 | Period 2 | |||
|---|---|---|---|---|---|---|
| Cents* | Approximate Ratios | Cents* | Approximate Ratios | Cents* | Approximate Ratios | |
| 0 | 0.0 | 1/1 | 400.0 | 63/50 | 800.0 | 100/63 |
| 1 | 96.9 | 135/128 | 496.9 | 4/3 | 896.9 | 42/25 |
| 2 | 193.7 | 28/25 | 593.7 | 45/32 | 993.7 | 16/9 |
| 3 | 290.6 | 32/27 | 690.6 | 112/75 | 1090.6 | 15/8 |
| 4 | 387.4 | 5/4 | 787.4 | 63/40 | 1187.4 | 125/63, 448/225 |
* in 7-limit CTE tuning
Tuning spectra
- 7-limit POTE tuning: ~3/2 = 703.0212
- 7-limit CTE tuning: ~3/2 = 703.1448
| ET generator |
eigenmonzo (unchanged-interval) |
generator (¢) |
comments |
|---|---|---|---|
| 7\12 | 700.000 | Lower bound of 9-odd-limit diamond monotone | |
| 4/3 | 701.955 | ||
| 65\111 | 702.703 | ||
| 15/14 | 702.778 | ||
| 28/27 | 702.849 | ||
| 7/5 | 702.915 | ||
| 9/7 | 702.924 | ||
| 10/9 | 702.933 | 9-odd-limit minimax (error = 1.955¢) | |
| 7/6 | 703.012 | ||
| 58\99 | 703.030 | ||
| 36/35 | 703.048 | ||
| 49/48 | 703.062 | ||
| 21/20 | 703.107 | ||
| 8/7 | 703.117 | 7-odd-limit minimax (error = 1.217¢) | |
| 6/5 | 703.128 | 5-odd-limit minimax (error = 1.173¢) | |
| 25/24 | 703.259 | ||
| 5/4 | 703.422 | ||
| 51\87 | 703.448 | ||
| 16/15 | 703.910 | ||
| 44\75 | 704.000 | ||
| 37\63 | 704.762 | Upper bound of 9-odd-limit diamond monotone |