Intonation 5: Limited Scales

It would appear that a common approach used by "microtonal" musicians (the last thing I want to do is get involved with microtonal music; I just want to tune better) is to take a set of prime numbers and find all the combinations of these as ratios. It's so ingrained that you can say something like "11-limit scale" and it is understood that all the combinations of prime numbers less than eleven are used to make up the ratios which define the scale.

That's all well and good but you end up with the sound of maths rather than something more sophisticated. All that abstract 20th century music seems pretty pointless from where I'm sitting, although I can see that it had merit in context.

Why use prime numbers only? Sure, there's something special about the prime-numbered partials, but that doesn't make the decision for you. Why not use only secondary partials and suggest the primes through harmony? The contrapuntal possibilities of this approach are exciting. You could use two lines harmonious to the fundamental to make a third, purer line ring out. With the right instrument that would sound eerily beautiful like icicles on a crisp winter day.

I think there's a fair case for assessing 12-TET (modern tuning) as an approximation of a selective 19-limit scale (with no 7, 11 or 13) filled in with secondary and ternary tones. That can never be more than opinion, but it's where I'm working from at present. Another valid approach is that 12-TET is an approximation of a 3-limited scale, but with each number used up to 12 times.

So I want to design scales. Here's some approaches that can be used:
1. Traditional microtonal prime-limited sets
2. Secondary-limited sets, ternary sets etc.
3. Sets with more limited denominators than numerators (e.g. Pythagorean tuning is a subset of a scale which is 3-limited in the denominator but not really limited at all in the numerator. My initial interest in this was because I wanted to create a 5-denominator-limited scale, although I did not know that was what it was at the time)
4. Do not use a denominator at all. One way this could work would be to take the partials that exist in the fifth octave above the fundamental.
5. Use a function like the product of the primes as the limit. This would mean that that if you used a low prime in the ratio, you could use a larger number for the other part, but you couldn't have two large numbers.
6. Introduce a lower limit, for example 3-19 limited or somesuch.
7. Sets limited by the number of repetitions of each prime in some way.
8. Pick a set of harmonies that just sound good together. I suspect this will yield the best music. How am I going to find these? By experimenting with the other options I've laid out in 1-7.

A more distant goal would be to aim at rotationally symmetrical just-derived scales. An approximation would be to introduce an extra 3/2 (fifth) to create the mirrored notes, but I think there will be a more perfect way.