41&58-hemififths

By this I mean the hemififths which 17deg58 of 58-et supports. Aside
from the 46 and 34 range of tunings we've been discussing, there is
another interesing range, with fifths 1-1.5 cents sharp, into which
29/58/87 and 99 fall.

99-et is a superb 7-limit system, but for higher limits choices must be
made as to the mapping if the plan is to use it consistently. In the 11
limit, you can take the 11/8 flat (patent val) or sharp. Taking it flat
gives the comma basis [121/120, 176/175, 1375/1372, 2200/2187], and
using the first three commas gives the 31&68 version of 11-limit
hemiwuer. But we are interested in low complexity fifths temperaments,
and for that, we want to take the sharp version of 11/8. This gives a
comma basis of [243/242, 441/440, 896/891, 3136/3125], where now taking
the first three commas leads to the 41&58 version of 11-limit
hemififths, and for this, 99 is a poptimal tuning.

In the 13-limit, the sharp tuning version for 99 gives commas
[144/143, 196/195, 243/242, 364/363, 625/624], and the first four
commas again give 41&58 hemififths. Now 58 is poptimal, which starts to
inch the tuning up towards the range which makes George happy.

Hemififths, with its complex 5's, makes for a good no-fives system, and
the 17 and 24 note MOS make for good scales using that system. I'd
suggest George and Margo might like playing with Hemififths[17] and
Hemififths[24] in the 58-et or even 99-et tuning. The fifth isn't quite
as sharp, but the exotic harmony is certainly there. Nothing like a few
8:11:14 chords to liven things up.