Misty
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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 parts of 512/405 each. 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
Tunings
- 7-limit POTE tuning: ~3/2 = 703.0212
- 7-limit CTE tuning: ~3/2 = 703.1448
Tuning spectrum
| Edo Generator |
Eigenmonzo (Unchanged-interval) |
Generator (¢) |
Comments |
|---|---|---|---|
| 7\12 | 700.000 | Lower bound of 9-odd-limit diamond monotone | |
| 3/2 | 701.955 | ||
| 81/80 | 702.688 | ||
| 65\111 | 702.703 | ||
| 15/14 | 702.778 | ||
| 7/5 | 702.915 | ||
| 9/7 | 702.924 | ||
| 9/5 | 702.933 | 9-odd-limit minimax (error = 1.955¢) | |
| 7/6 | 703.012 | ||
| 58\99 | 703.030 | ||
| 35/18 | 703.048 | ||
| 49/48 | 703.062 | ||
| 21/20 | 703.107 | ||
| 7/4 | 703.117 | 7-odd-limit minimax (error = 1.217¢) | |
| 5/3 | 703.128 | 5-odd-limit minimax (error = 1.173¢) | |
| 21/16 | 703.247 | ||
| 25/24 | 703.259 | ||
| 63/32 | 703.408 | ||
| 5/4 | 703.422 | ||
| 51\87 | 703.448 | ||
| 15/8 | 703.910 | ||
| 44\75 | 704.000 | ||
| 37\63 | 704.762 | Upper bound of 9-odd-limit diamond monotone |