34ed7

Division of the 7th harmonic into 34 equal parts (34ed7) is related to 12 edo, but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 99.0831 cents. It is consistent to the 11-integer-limit, but not to the 12-integer-limit. In comparison, 12edo is only consistent up to the 10-integer-limit.

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	99.0831	18/17
2	198.1662	28/25
3	297.2493	19/16
4	396.3325	49/39, 34/27	pseudo-5/4
5	495.4156	4/3
6	594.4987	24/17
7	693.5818		pseudo-3/2
8	792.6649	30/19, 128/81
9	891.7480	77/46	pseudo-5/3
10	990.8311	85/48, 39/22
11	1089.9143	15/8
12	1188.9974	143/72, 175/88	pseudo-octave
13	1288.0805	21/10, 40/19
14	1387.1636	49/22
15	1486.2467	33/14
16	1585.3298	5/2
17	1684.4130	119/45	pseudo-8/3
18	1783.4961	14/5
19	1882.5792	95/32, 98/33	pseudo-3/1
20	1981.6623	22/7
21	2080.7454	133/40, 10/3
22	2179.8285	88/25
23	2278.9116	56/15
24	2377.9948	154/39, 320/81, 336/85	pseudo-4/1
25	2477.0779	46/11
26	2576.1610	133/30
27	2675.2441
28	2774.3272	119/24	pseudo-5/1
29	2873.4103	21/4	pseudo-16/3
30	2972.4934	39/7
31	3071.5766	112/19	pseudo-6/1
32	3170.6597	25/4
33	3269.7428	119/18
34	3368.8259	exact 7/1	harmonic seventh plus two octaves

34ed7 can also be thought of as a generator of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a cluster temperament with 12 clusters of notes in an octave. This temperament is supported by 12edo, 109edo, and 121edo among others.