52edt

The 52 equal division of 3, the tritave, divides it into 52 equal parts of 36.576 cents each, corresponding to 32.808 edo. It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not super-accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 11-limit, so that it tempers out the same commas as 26edt in the 11-limit and 13edt in the 7-limit. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh no-twos zeta peak edt.

Intervals

Steps	Cents	BP nonatonic degree	Diatonic degree	Corresponding JI intervals	Comments	Generator for...
1	36.6	Qa1/3d2	Sa1	50/49~33/32~49/48
2	73.15	Sa1/sd2	A1/dd2	25/24~28/27~22/21~27/26~24/23~21/20~29/28
3	109.7	3A1/qd2	A+1/d-2	15/14~16/15~29/27~121/112
4	146.3	A1/m2	AA1/sm2	27/25~25/23~49/45~13/12~14/13~11/10~169/162
5	182.9	Sm2	sm+2	10/9
6	219.5	N2	m2	9/8~8/7~44/39
7	256.0	sM2	N2	147/128~7/6
8	292.6	M2/d3	M2	32/27~25/21~13/11~27/23
9	329.2	Qa2/3d3	SM-2/d-2	6/5	11/9-
10	365.8	Sa2/sd3	SM2/dd3	5/4~16/13	11/9+
11	402.3	3A3/qd3	SM+2	81/64~63/50~33/26~23/18
12	438.9	A2/P3/d4	AA2/sm3	32/25~9/7~14/11~104/81~13/10
13	475.5	Qa3/3d4	sm+3	21/16~98/75
14	512.1	Sa3/sd4	m3	4/3~27/20~162/121
15	548.6	3A3/qd4	N3	11/8~243/169	18/13-
16	585.2	A3/m4/d5	M3	7/5~25/18~112/81~88/63~32/23~29/21	18/13+
17	621.8	Sm4/3d5	SM-3	10/7~36/25~81/56~63/44~23/16~42/29	13/9-
18	658.4	N4/sd5	SM3/dd4	16/11~338/243	13/9+
19	694.95	sM4/qd5	SM+3/d-4	3/2~40/27~121/81
20	731.5	M4/m5	AA3/d4	32/21~75/49
21	768.1	Qa4/Sm5	d+4	25/16~14/9~11/7~81/52
22	804.7	Sa4/N5	P4	8/5~36/23
23	841.25	3A4/sM5	A-4	13/8
24	877.8	A4/M5/d6	A4	5/3
25	914.4	Qa5/3d6	A+4	27/16~42/25~22/13~46/27
26	951.0	Sa5/sd6	AA4/dd5	125/72
27	987.55	3A5/qd6	d-5	16/9~8/7~39/22~75/46
28	1024.1	A5/m6/d7	d5	9/5
29	1060.7	Sm6/3d7	d+5	50/27~46/25~90/49~24/13~13/7~20/11
30	1097.3	N6/sd7	P5	15/8
31	1133.9	sM6/qd7	A-5	48/25~27/14~21/11~52/27~23/12~40/21~56/29
32	1170.4	M6/m7	A5/dd6	49/25~64/33~96/49
33	1207.0	Qa6/Sm7	A+5	2/1
34	1243.6	Sa6/N7	AA5/sm6	33/16~100/49~49/24~729/338
35	1280.2	3A6/sM7	sm+6	25/12~56/27~44/21~27/13
36	1316.7	A6/M7/d8	m6	15/7~32/15~58/27
37	1353.3	Qa7/3d8	N6	54/25~50/23~98/45~13/6~169/81
38	1389.9	Sa7/sd8	M6	20/9
39	1426.5	3A7/qd8	SM-6	9/4~16/7
40	1463.0	A7/P8/d9	SM6/dd7	147/64~7/3
41	1499.6	Qa8/3d9	SM+6/sm-7	64/27~50/21~26/11~81/23
42	1536.2	Sa8/sd9	AA6/sm7	12/5	22/9-
43	1572.7	3A8/qd9	sm-7	5/2~32/13	22/9+
44	1609.3	A8/m9	m7	81/32~63/25~33/13~23/9
45	1645.9	Sm9	N7	64/45~18/7~28/11~208/81~13/5
46	1682.5	N9	M7	21/8~196/75
47	1719.1	sM9	SM-7	8/3~27/10
48	1755.65	M9/d10	SM7/dd8	69/25~135/49	36/13-
49	1792.2	Qa9/3d10	SM+7/d-8	14/5~25/9~224/81~176/63~64/23~58/21	36/13+
50	1828.8	Sa9/sd10	A7/d8	20/7~72/25~81/28~63/22~23/8~84/29	26/9-
51	1865.4	3A9/qd10	P-8	147/50~32/11~338/81~144/49	26/9+
52	1902.0	A9/P10	P8	3/1	Tritave

It is a weird coincidence how 52edt intones any 52edo intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:

52edt	52edo	Discrepancy
365.761	369.231	-3.47
512.065	507.692	+4.373
877.825	876.923	+0.902
1243.586	1246.154	-2.168
1389.89	1384.615	+5.275
1755.651	1753.846	+1.805
2121.411	2123.077	-1.666
2633.476	2630.769	+2.647

…and so on

It's not actually a coincidence. It is simply a demonstration of rational approximations to log₂(3). In this table are shown 16/10, 22/14, 38/24, 54/34, 60/38, 76/48, 92/58, 114/72.