39edt

From Xenharmonic Wiki
Jump to: navigation, search

The 39 equal division of 3, the tritave, divides it into 39 equal parts of 48.678 cents each, a nonoctave tuning corresponding to 24.606 edo. It is a strong no-twos 13-limit system, a fact first noted by Paul Erlich, and like 26edt and 52edt it is a multiple of 13edt and so contains the Bohlen-Pierce scale. It is contorted in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&172f temperament tempering out 245/243, 275/273, 847/845 and 1575/1573, which has map [<1 0 0 0 0 0|, <0 39 57 69 85 91|]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth no-twos zeta peak edt.

Intervals of 39EDT

Degrees of 39EDT Cents Value hekts ¢ Octave-Reduced Degrees of BP Comments
0 0 1/1
1 48.768 33.333 39th root of 3
2 97.536 66.667
3 146.304 100 1 13th root of 3
4 195.072 133.333
5 243.840 166.667
6 292.608 200 2
7 341.377 233.333
8 390.145 266.667
9 438.913 300 3
10 487.681 333.333
11 536.449 366.667
12 585.217 400 4
13 633.985 433.333 cube root of 3
14 682.753 466.667
15 731.521 500 5
16 780.289 533.333
17 829.057 566.667
18 877.825 600 6
19 926.593 633.333
20 975.362 666.667
21 1024.13 700 7
22 1072.898 733.333
23 1121.666 766.667
24 1170.434 800 8
25 1219.202 833.333 19.202
26 1267.97 866.667 67.97
27 1316.738 900 116.738 9
28 1365.506 933.333 165.506
29 1414.274 966.667 214.274
30 1463.042 1000 263.042 10
31 1511.81 1033.333 311.81
32 1560.578 1066.667 360.578
33 1609.347 1100 409.347 11
34 1658.115 1133.333 458.115
35 1706.883 1166.667 506.883
36 1755.651 1200 555.651 12
37 1804.419 1233.333 604.419
38 1853.187 1266.667 653.187
39 1901.955 1300 701.955 13 3/1 (tritave)
40 1950.723 1333.333 750.723
41 1999.491 1366.667 799.491
42 2048.259 1400 848.259 14
43 2097.027 1433.333 897.027
44 2145.795 1466.667 945.795
45 2194.563 1500 994.563 15
46 2243.332 1533.333 1043.332
47 2292.100 1566.667 1092.100
48 2340.868 1600 1140.868 16
49 2389.636 1633.333 1189.636
50 2438.404 1666.667 38.404
51 2487.172 1700 87.172 17
52 2535.940 1733.333 135.940
53 2584.708 1766.667 184.708
54 2633.476 1800 233.476 18
55 2682.244 1833.333 282.244
56 2731.012 1866.667 331.012
57 2779.78 1900 379.78 19
58 2828.548 1933.333 428.548
59 2877.317 1966.667 477.317
60 2926.085 2000 526.085 20
61 2974.853 2033.333 574.853
62 3023.621 2066.667 623.621
63 3072.389 2100 672.389 21
64 3121.157 2133.333 721.157
65 3169.925 2166.667 769.925
66 3218.693 2200 818.693 22
67 3267.461 2233.333 867.461
68 3316.229 2266.667 916.229
69 3364.997 2300 964.997 23
70 3413.765 2333.333 1013.765
71 3462.533 2366.667 1062.533
72 3511.302 2400 1111.302 24
73 3560.07 2433.333 1160.07
74 3608.838 2466.667 8.838
75 3657.606 2500 57.606 25
76 3706.374 2533.333 106.374
77 3755.142 2566.667 155.142
78 3803.91 2600 203.91 26 9/1