26edt

The 26 equal division of 3 (the tritave), divides it into 26 equal parts of 73.152 cents each, corresponding to 16.404 edo. It is contorted in the 7-limit, tempering out the same commas, 245/243 and 3125/3087, as 13edt. In the 11-limit it tempers out 125/121 and 3087/3025, in the 13-limit 175/169, 147/143, and 847/845, and in the 17-limit 119/117. It is the seventh zeta peak tritave division. A reason to double 13edt to 26edt is to approximate the 8th, 13th, 17th, 20th, and 22nd harmonics particularly well. Moreover, it has an exaggerated diatonic scale with 11:16:21 supermajor triads, though only the 16:11 is particularly just due to its best 16 still being 28.04 cents sharp, or just about as bad as the 25 of 12edo (which is 27.373 cents sharp, an essentially just 100:63).

Intervals

Steps	Cents	BP nonatonic degree	Diatonic degree	Corresponding JI intervals	Comments	Generator for...
1	73.15	Sa1/sd2	A1/dd2	25/24
2	146.3	A1/m2	AA1/sm2	27/25~49/45
3	219.5	N2	m2	9/8~312/275
4	292.6	M2/d3	M2	25/21~13/11
5	365.8	Sa2/sd3	SM2/dd3	5/4~243/196	False 11/9
6	438.9	A2/P3/d4	AA2/sm3	9/7
7	512.1	Sa3/sd4	m3	27/20	False 21/16
8	585.2	A3/m4/d5	M3	7/5
9	658.4	N4/sd5	SM3/dd4	16/11	False 13/9
10	731.5	M4/m5	AA3/d4	75/49	False 3/2
11	804.7	Sa4/N5	P4	8/5	False 11/7
12	877.8	A4/M5/d6	A4	5/3	False 27/16
13	951.0	Sa5/sd6	AA4/dd5	125/72
14	1024.1	A5/m6/d7	d5	9/5	False 16/9
15	1097.3	N6/sd7	P5	15/8	False 21/11
16	1170.4	M6/m7	A5/dd6	49/25	False 2/1
17	1243.6	Sa6/N7	AA5/sm6	33/16	False 27/13
18	1316.7	A6/M7/d8	m6	15/7
19	1389.9	Sa7/sd8	M6	20/9	False 16/7
20	1463.0	A7/P8/d9	SM6/dd7	7/3
21	1536.2	Sa8/sd9	AA6/sm7	12/5~196/81	False 27/11
22	1609.3	A8/m9	m7	63/25~33/13
23	1682.5	N9	M7	8/3~275/104
24	1755.65	M9/d10	SM7/dd8	25/9~135/49
25	1828.8	Sa9/sd10	A7/d8	72/25
26	1902.0	A9/P10	P8	3/1	Tritave

It is a weird coincidence how 26edt intones any 26edo intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:

26edt	26edo	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 8/5, 11/7, 19/12, 27/17, 30/19, 38/24, 46/29, 57/36. So all this table does is demonstrate that {{#rreplace: 5edo, 7edo, 12edo, 17edo, 19edo, 24edo, 29edo, 36edo|/(\d+)(\D+)?/|\1\2}} are good for 3-limit.

The Eel And Loach To Attack In Lasciviousness Are Insane play by Omega9