Mystery

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Mystery is the regular temperament which takes 1\29 period and adds a single generator to correct the harmonic 5, 7, 11, and 13 to almost just versions. 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 also: Hemifamity temperaments #Mystery

Interval chain

Period Generator 0 Generator 1
Cents Approx. Ratios Cents Approx. Ratios
0 0.00 1/1 15.94 91/90, 100/99, 105/104, 121/120
1 41.38 40/39, 45/44, 50/49 57.32 28/27, 33/32
2 82.76 21/20 98.70 35/33
3 124.14 14/13, 15/14 140.08 13/12
4 165.52 11/10 181.46 10/9
5 206.90 9/8 222.84 25/22
6 248.28 15/13 264.22 7/6
7 289.66 13/11, 32/27, 33/28 305.60 25/21
8 331.03 40/33 346.97 11/9, 39/32
9 372.41 26/21 388.35 5/4
10 413.79 14/11, 33/26, 80/63 429.73
11 455.17 13/10 471.11 21/16
12 496.55 4/3 512.49 35/26, 75/56
13 537.93 15/11 553.87 11/8
14 579.31 7/5 595.25 45/32
15 620.69 10/7 636.63 13/9
16 662.07 22/15 678.01 40/27
17 703.45 3/2 719.39 50/33
18 744.83 20/13 760.77 14/9
19 786.21 11/7, 52/33, 63/40 802.15 35/22
20 827.59 33/20 843.53 13/8, 27/22
21 868.97 21/13 884.91 5/3
22 910.34 22/13, 27/16, 56/33 926.29
23 951.72 26/15 967.66 7/4
24 993.10 16/9 1009.04 25/14, 70/39
25 1034.48 20/11 1050.42 11/6
26 1075.86 13/7, 28/15 1090.80 15/8
27 1117.24 40/21 1133.18 25/13, 52/27
28 1158.62 39/20, 49/25, 88/45 1174.56 63/32, 65/33, 77/39, 160/81
29 1200.00 2/1

* in 13-limit POTE tuning