39edt

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			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