I have recently been trying out some non-octave scales, and I think they contain a lot of potential that is yet untapped.

Some ideas however:

How about having a nonoctave repeat interval, but add all the inverses of all the intervals less wide than an octave - thus, basically, having a limited selection of octaves available.

Take for instance, the 3/2 in 8 scale, with a smallest step of ~87.75 cents.

We get

87.75
175.50
263.25
351.00
438.75
526.50
614.25
702.00

What we need to get an octave is adding these:
498.00
585.75
...
which amounts to having every other step be 27.25 cents and every other be 60.50. Ok, that gets a bit unwieldy, and I have no idea what new intervals pop in except octaves and octave inversions.

This might work better with some other scale - maybe Bohlen-Pierce or somesuch would be well suited.