69edo

The 69 equal division or 69-EDO, which divides the octave into 69 equal parts of 17.391 cents each, has been called "the love-child of 23edo and quarter-comma meantone". Nice. As a meantone system, it is on the flat side, with a fifth of 695.652 cents. Such a fifth is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.

In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as 126/125 maps to one step. It also supports the 12&69 temperament tempering out 3125/3087 along with 81/80. In the 11-limit it tempers out 99/98, and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in 31EDO but not in 69.

Degree	Name and Abbreviation	Cents	Approximate Ratios*	Error (abs, ¢)
0	Natural Unison, 1	0.000	1/1	0.000
1		17.391
2		34.783
3		52.174	20/19	-1.844
4		69.565
5		86.957
6		104.348	17/16	-0.608
7		121.739	15/14	2.296
8		139.130	13/12	0.558
9		156.522
10		173.913
11		191.304	19/17	-1.253
12		208.696	9/8	4.786
13		226.087	8/7	-5.087
14		243.478	23/20	1.518
15		260.870	7/6, 29/25	-6.001, 3.920
16		278.261	27/23	0.670
17		295.652	32/27	1.517
18		313.043	6/5	-2.598
19		330.435	23/19	-0.327
20		347.826	11/9	0.418
21		365.217	21/17	-0.608
22		382.609	5/4	-3.705
23		400.000
24		417.391	14/11	-0.117
25		434.783	9/7	-0.301
26		452.174	13/10	-2.040
27		469.565	21/16	-1.216
28		486.957
29		504.348	4/3	6.303
30		521.739	23/17	-1.580
31		539.130	15/11	2.180
32		556.522	11/8, 29/21	5.204, -2.275
33		573.913	7/5, 25/18	-8.600, 5.196
34		591.304	31/22	-2.413
35		608.696	10/7, 27/19	-8.792, 0.344
36		626.087	33/23	1.088
37		643.478	29/20	0.215
38		660.870	19/13, 22/15	3.884, -2.180
39		678.261	34/23, 37/25	1.580, -0.456
40		695.652	3/2	-6.303
41		713.043
42		730.435	32/21, 29/19	1.216, -1.630
43		747.826	17/11	-5.811
44		765.217	14/9	0.301
45		782.609	11/7	0.117
46		800.000	27/17
47		817.391	8/5	3.705
48		834.783	34/21
49		852.174
50		869.565
51		886.957	5/3	2.598
52		904.348
53		921.739
54		939.130
55		956.522
56		973.913
57		991.304
58		1008.696
59		1026.087
60		1043.478
61		1060.870
62		1078.261	28/15	-2.296
63		1095.652
64		1113.043
65		1130.435
66		1147.826
67		1165.217
68		1182.609
69	Octave, 8	1200.000	2/1	0.000

*some simpler ratios listed