This is connected to the question of using nine-nominal notation for EJI.

My choice remains 612, which is a great utility et for notation anyway.

Here is the 3500 row of the Farey sequence, pruned by requiring that the

lcm of the denominator with 18 be less than 3500:

11/270 < ... < 2/49 < 133/3258 < 97/2376 < 61/1494 < 43/1053 < 37/906 <

68/1665 < 25/612 <

139/3402 < 19/465 < 89/2178 < 32/783 < 103/2520 < 71/1737 < 13/318 < ...

< 7/171

Here are the corresponding ets for Ennealimmal:

270 ... 441, 3258, 2376, 1494, 1053, 2718, 1665, 612, 3402, 1395, 2178,

783, 2520, 1737, 954 ... 171

And for Hemiennealimmal:

270 ... 882, 3258, 2376, 1494, 2106, 2718, 3330, 612, 3402, 2790, 2178,

1566, 2520, 3474, 954 ... 342

We have 68/1665, hardly distinguishable from 25/612, as poptimal in the

5-limit. In the 7-limit,

43/1053 and 61/1494, in the range between 441 and 612, are poptimal,

whereas in the 11-limit we go over to the other side, with 23/1566 (1566

= 2*783) a Hemiennealimmal poptimal generator. The 612 et is a good

all-around choice, and it has a nice list of divisors, including 12: [2,

3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612]. We

might compare this to 270: [2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54,

90, 135, 270] which has a 6 but no 12, or

342: [2, 3, 6, 9, 18, 19, 38, 57, 114, 171] for fans of 19, or

882: [2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441]