User:Godtone/zeta
Below is a list of equal temperaments (that is, edos with octave-tempering) that the zeta function considers to be tuned well relative to their size, up to 311et.
We can be confident in their notability because they appear in a wide range of odd-limits (19 thru 123) according to the optimal_edo_sequences for those odd-limits. (You can calculate them yourself by using my copyleft Python 3 code (which needs no dependencies).)
Specifically, an equal temperament is included if it does better than the 9th-best-scoring equal temperament so far*, and the below details both what is added to the sequence and the top 9 at any given point. These can mostly be thought of as corresponding to edos with the exception of 39 equal temperament, because 39edo is close to a zeta valley so that it isn't meaningfully considered in-tune by zeta without the 3.8 ¢ flat octave that zeta recommends.
* For this reason, we start the list at 10et (corresponding to 10edo) because all previous equal temperaments' inclusion is unsurprising. (The first to be excluded is 18et, corresponding to 18edo being close to a zeta valley.)
10 [10, 7, 9, 5, 8, 4, 6, 3, 2]
11 [10, 7, 9, 5, 8, 4, 11, 6, 3]
12 [12, 10, 7, 9, 5, 8, 4, 11, 6]
13 [12, 10, 7, 9, 5, 8, 13, 4, 11]
14 [12, 14, 10, 7, 9, 5, 8, 13, 4]
15 [12, 15, 14, 10, 7, 9, 5, 8, 13]
16 [12, 15, 14, 10, 16, 7, 9, 5, 8]
17 [12, 17, 15, 14, 10, 16, 7, 9, 5]
19 [19, 12, 17, 15, 14, 10, 16, 7, 9]
21 [19, 12, 17, 15, 14, 10, 16, 7, 21]
22 [22, 19, 12, 17, 15, 14, 10, 16, 7]
24 [22, 19, 24, 12, 17, 15, 14, 10, 16]
26 [22, 19, 24, 26, 12, 17, 15, 14, 10]
27 [27, 22, 19, 24, 26, 12, 17, 15, 14]
29 [27, 22, 19, 24, 29, 26, 12, 17, 15]
31 [31, 27, 22, 19, 24, 29, 26, 12, 17]
34 [31, 34, 27, 22, 19, 24, 29, 26, 12]
36 [31, 34, 27, 22, 36, 19, 24, 29, 26]
38 [31, 34, 27, 22, 36, 19, 38, 24, 29]
39 [31, 34, 27, 22, 36, 19, 38, 24, 39]
41 [41, 31, 34, 27, 22, 36, 19, 38, 24]
43 [41, 31, 34, 43, 27, 22, 36, 19, 38]
46 [41, 46, 31, 34, 43, 27, 22, 36, 19]
50 [41, 46, 31, 34, 50, 43, 27, 22, 36]
53 [53, 41, 46, 31, 34, 50, 43, 27, 22]
58 [53, 58, 41, 46, 31, 34, 50, 43, 27]
60 [53, 58, 41, 46, 60, 31, 34, 50, 43]
62 [53, 58, 41, 46, 60, 31, 34, 50, 62]
63 [53, 58, 41, 46, 60, 31, 63, 34, 50]
65 [53, 58, 65, 41, 46, 60, 31, 63, 34]
68 [53, 58, 65, 68, 41, 46, 60, 31, 63]
72 [72, 53, 58, 65, 68, 41, 46, 60, 31]
77 [72, 53, 77, 58, 65, 68, 41, 46, 60]
80 [72, 53, 77, 80, 58, 65, 68, 41, 46]
84 [72, 53, 77, 84, 80, 58, 65, 68, 41]
87 [72, 87, 53, 77, 84, 80, 58, 65, 68]
94 [72, 87, 94, 53, 77, 84, 80, 58, 65]
99 [99, 72, 87, 94, 53, 77, 84, 80, 58]
103 [99, 72, 87, 94, 103, 53, 77, 84, 80]
106 [99, 72, 87, 94, 103, 53, 77, 106, 84]
111 [99, 72, 111, 87, 94, 103, 53, 77, 106]
113 [99, 72, 111, 87, 94, 103, 113, 53, 77]
118 [118, 99, 72, 111, 87, 94, 103, 113, 53]
121 [118, 99, 72, 111, 87, 94, 121, 103, 113]
125 [118, 99, 72, 111, 87, 94, 121, 125, 103]
130 [130, 118, 99, 72, 111, 87, 94, 121, 125]
140 [130, 140, 118, 99, 72, 111, 87, 94, 121]
149 [130, 140, 118, 99, 72, 149, 111, 87, 94]
152 [152, 130, 140, 118, 99, 72, 149, 111, 87]
159 [152, 130, 140, 118, 159, 99, 72, 149, 111]
171 [171, 152, 130, 140, 118, 159, 99, 72, 149]
183 [171, 183, 152, 130, 140, 118, 159, 99, 72]
190 [171, 183, 152, 190, 130, 140, 118, 159, 99]
193 [171, 183, 152, 190, 130, 193, 140, 118, 159]
198 [171, 183, 152, 190, 130, 198, 193, 140, 118]
217 [217, 171, 183, 152, 190, 130, 198, 193, 140]
224 [224, 217, 171, 183, 152, 190, 130, 198, 193]
239 [224, 217, 171, 183, 152, 190, 130, 198, 239]
243 [224, 243, 217, 171, 183, 152, 190, 130, 198]
255 [224, 243, 217, 171, 183, 152, 190, 130, 255]
270 [270, 224, 243, 217, 171, 183, 152, 190, 130]
282 [270, 224, 243, 217, 171, 282, 183, 152, 190]
289 [270, 224, 243, 217, 171, 282, 183, 289, 152]
301 [270, 224, 301, 243, 217, 171, 282, 183, 289]
311 [270, 311, 224, 301, 243, 217, 171, 282, 183]
The resulting sequence is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 24, 26, 27, 29, 31, 34, 36, 38, 39, 41, 43, 46, 50, 53, 58, 60, 62, 63, 65, 68, 72, 77, 80, 84, 87, 94, 99, 103, 106, 111, 113, 118, 121, 125, 130, 140, 149, 152, 159, 171, 183, 190, 193, 198, 217, 224, 239, 243, 255, 270, 282, 289, 301, 311.