Equal Temperaments

Here is a table showing the simplest equal temperaments with consistent
representations of all just intervals through the m-limit _and_ unique
representations of all just intervals through the n-limit (these are odd
limits):

m- 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
n
|
3 3 3 5 5 22 26 29 58 80 94 94 282 282 282 311 311 311
5 9 9 12 22 26 29 58 80 94 94 282 282 282 311 311 311
7 27 27 31 41 41 58 80 94 94 282 282 282 311 311 311
9 41 41 41 41 58 80 94 94 282 282 282 311 311 311
11 58 58 58 58 80 94 94 282 282 282 311 311 311
13 87 87 94 94 94 94 282 282 282 311 311 311
15 111 111 111 111 282 282 282 282 311 311 311
17 149 217 217 282 282 282 282 311 311 311
19 217 217 282 282 282 282 311 311 311
21 282 282 282 282 282 311 311 311
23 282 282 282 282 311 311 311
25 388 388 388 388 388 388
27 388 388 388 388 388

This table cannot be extended without going beyond 650-tET. Notice that
58 is encountered in any progression from lower to higher limits. 282 is
also, but that's more a curiosity than a musically important result. 7,
19, 46, 53, and 72 are conspicuous by their absence: there are simpler
ETs that can "do" what they "do", just not always as accurately; namely,
3, 12, 41, 41, and 58 respectively. (Of course there can be other
reasons besides accuracy to use 7, 19, 46, 53, or 72.)

Source: ftp://ella.mills.edu/ccm/tuning/papers/consist_limits.txt
(Manuel, can you update my e-mail address on that?)