44edo

Though commonly neglected, 44edo doubles a very natural tuning, 22edo to which it adds ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's a surprise that extending it in this way has been done rarely or not at all. The most practically useful of these additions is easily the 13th harmonic with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed. In the 13-limit it supplies the optimal patent val for vigin temperament. The 2*44 subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for 88.

Using the 44d val, it is a pretty good tuning for nautilus temperament.