Phenomenology of Scales

I want to start work on a phenomenology of scales.

Some attributes that I think might be useful are as follows:
1. "Limit": this is the highest partial involved in the scales. For example, Partch's 43-tone scale is one flavour of an 11-limit scale. Western music is largely an approximation of 5-limit. Organum is 3-limit.
2. Symmetry: what happens beneath the tonic? Is a scale mirrored (complementary) or rotationally symmetrical or non-symmetrical? The Dorian and Ionian modes are unique in being rotationally symmetrical about the tonic (rather than the logarithmic mid-point). Partch's 43-tone scale is mirrored due to an error in understanding the nature of utonality. Organum is both mirrored and rotationally symmetrical. Most western modes and western "minor" are non-symmetrical (I think this is a result of being 5-limit; 3-limit and 7-limit reflect more easily. In general, if the limit is one less than a power of 2 the scale may be easily designed to exhibit good symmetry. Is this related to methods for searching for prime numbers?).
3. Utonal limit: which partials are considered suitable for transposing tones into the home octave? In Pythagorean tuning, only the Octave and Fifth are suitable (it has a Utonal 3-limit). In Partch's 43-tone scale it is an 11-limit. Organum is also a 3-limit. (In these latter two examples the Utonal limit is the same as the Otonal limit.) When I started this, it was because I wanted to create scales with a Utonality of exactly 19. I now see that this is nonsense, but scales could be constructed using this method. Scales with a high Otonal limit and a low Utonal limit will be close to the Harmonic series (the Harmonic series is a scale with an infinite Otonal limit and a Utonal limit of 1).
4. Dissonance-limited: rather than limiting scales by partials, they could be limited less crudely by measuring the dissonance of their intervals.
5. Respect for the Octave: does a scale repeat every 2/1? A pentave, repeating on the 3/2 could be used instead, or even other intervals.

I am sure there are more things that would be useful that will present themselves as time goes on.