Mystery
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Mystery is a regular temperament which takes 1\29 period and adds a single generator to correct the harmonics 5, 7, 11, and 13 to almost just qualities. It tempers out the 29-comma in the 5-limit, 5120/5103 in the 7-limit, 441/440, 896/891, 3388/3375, and 4000/3993 in the 11-limit, 196/195, 352/351, 364/363, 676/675, and 847/845 in the 13-limit.
See Hemifamity temperaments #Mystery for technical details.
Interval chain
In the following table, odd harmonics 1–21 are in bold.
| Period | Generator 0 | Generator 1 | ||
|---|---|---|---|---|
| Cents | Approx. ratios | Cents | Approx. ratios | |
| 0 | 0.00 | 1/1 | 15.49 | 91/90, 100/99, 105/104, 121/120 |
| 1 | 41.38 | 40/39, 45/44, 50/49 | 56.87 | 28/27, 33/32 |
| 2 | 82.76 | 21/20, 22/21 | 98.25 | 35/33 |
| 3 | 124.14 | 14/13, 15/14 | 139.63 | 13/12 |
| 4 | 165.52 | 11/10 | 181.01 | 10/9 |
| 5 | 206.90 | 9/8 | 222.38 | 25/22 |
| 6 | 248.28 | 15/13 | 263.76 | 7/6 |
| 7 | 289.66 | 13/11, 32/27, 33/28 | 305.14 | 25/21 |
| 8 | 331.03 | 40/33 | 346.52 | 11/9, 39/32 |
| 9 | 372.41 | 26/21 | 387.90 | 5/4 |
| 10 | 413.79 | 14/11, 33/26, 80/63 | 429.28 | 77/60 |
| 11 | 455.17 | 13/10 | 470.66 | 21/16 |
| 12 | 496.55 | 4/3 | 512.04 | 35/26, 75/56 |
| 13 | 537.93 | 15/11 | 553.42 | 11/8 |
| 14 | 579.31 | 7/5 | 594.80 | 45/32 |
| 15 | 620.69 | 10/7 | 636.18 | 13/9 |
| 16 | 662.07 | 22/15 | 677.56 | 40/27 |
| 17 | 703.45 | 3/2 | 718.94 | 50/33 |
| 18 | 744.83 | 20/13 | 760.32 | 14/9 |
| 19 | 786.21 | 11/7, 52/33, 63/40 | 801.69 | 35/22 |
| 20 | 827.59 | 21/13 | 843.07 | 13/8, 44/27 |
| 21 | 868.97 | 33/20 | 884.45 | 5/3 |
| 22 | 910.34 | 22/13, 27/16, 56/33 | 925.83 | 77/45 |
| 23 | 951.72 | 26/15 | 967.21 | 7/4 |
| 24 | 993.10 | 16/9 | 1008.59 | 25/14, 70/39 |
| 25 | 1034.48 | 20/11 | 1049.97 | 11/6 |
| 26 | 1075.86 | 13/7, 28/15 | 1091.35 | 15/8 |
| 27 | 1117.24 | 21/11, 40/21 | 1133.73 | 25/13, 52/27 |
| 28 | 1158.62 | 39/20, 49/25, 88/45 | 1174.11 | 63/32, 65/33, 77/39, 160/81 |
| 29 | 1200.00 | 2/1 | ||
* in 13-limit CWE tuning
Tunings
Tuning spectrum
| Edo generator |
Eigenmonzo (unchanged-interval)* |
Generator (¢) | Comments |
|---|---|---|---|
| 9\29 | 372.414 | Lower bound of 7- to 15-odd-limit, and 13-limit 21-odd-limit diamond monotone | |
| 15/8 | 384.820 | ||
| 13/8 | 385.355 | ||
| 11/8 | 385.801 | ||
| 28\87 | 386.207 | ||
| 5/4 | 386.314 | ||
| 13/12 | 386.849 | ||
| 11/6 | 387.294 | ||
| 5/3 | 387.807 | ||
| 13/9 | 388.342 | ||
| 21/16 | 388.022 | ||
| 11/9 | 388.787 | ||
| 47\145 | 388.966 | ||
| 9/5 | 389.300 | ||
| 7/4 | 389.516 | ||
| 7/6 | 391.009 | ||
| 9/7 | 392.502 | ||
| 19\58 | 393.103 | Upper bound of 13- and 15-odd-limit, and 13-limit 21-odd-limit diamond monotone | |
| 10\29 | 413.793 | 29cdef val, upper bound of 7- to 11-odd-limit diamond monotone |
* Besides the octave