Plausibly "Just" Triads and the critical band

Andrew>"Concerning what sounds decent and what doesn't, keep in mind that some chords that don't sound great in the "meat range" of the middle of the piano sound better if placed in higher octaves. To that extent, how much you want to restrict your prime and odd limits depends on how you want to use the resulting pitches."

     This brings to light another point about register...the critical band (on an exponential/not-linear scale) becomes smaller at higher octaves thus allowing more clustered chord at higher octaves with a similar sense of resolve. 

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   Actually, (an extra point for Igs's list), critical band, I've found, plays a major role in chords.  Stacking 16/15 or smaller intervals, for example, is often a sure-fire way to produce a level of dissonance beyond the scope of most listeners.
  If you have a 16/15 or small semitone, you usually have to space the intervals around it pretty widely to make it sound balanced (usually somewhere in between 9/8 and 6/5 distance between any other dyad in the chord).

  And I've found you can have stacked 12/11's in a tetrad...but the third small dyadic gap must be more like 6/5 or over to compensate.  So 12/11 gives you a bit more slack...but not that much.  For example 10:11:12:14 and 9:10:11:12.

  It really seems to level out when you stack 8/7 and 7/6-like intervals into a chord so far as critical band IE 1/1 * 8/7 * 7/6 * 8/7 or 1 4/3 14/9 16/9 AKA 9:12:14:16...that's the one case where you can stack "wide" semi-tones ad-nauseam and still get balanced chords.