Thomas -

Your reference to "natural" versus "equal tempered" made it sound like you were refering to the old argument of how best to divide the octave into a "standard western" 12 semitone scale. In that usage, the answer I gave is still applicable (in my opinion).

If, however, you - and others who have commented - are refering to scales in other music traditions, then the choice is not one of harmonic intervals versus equi-tempered intervals. Many other music traditions do not use a 12 semitone division of the octave. In quite a few "eastern" traditions, there seems to be no standard number of notes in the octave - although some academicians resolve this problem by saying there are arbitrarily "many ways" of tuning.

Certainly, if you are looking at music that does not use the twelve-tone scale, then you need to ignore equal-tempered tuning. You also need to ignore what is commonly refered to as "natural" or "harmonic" scale tuning, and simply find and use the "scale(s)" appropriate to the tradition of interest.

One of the difficulties you should keep in mind is that for the most part "non-western/non-twelve-tone" instruments are seldom made to "machine" tolerances (precisely tuned to established standard pitches), so that being (to our western ears) slightly "out of tune" is often part of the tradition. If you are going to play within one of these traditions, you will need to do things largely "by ear," so the argument of tempered vs harmonic/natural is not really applicable.
That argument applies only within the confines of how to tune for "western academic" music.

Try some good native-American flute music. Every flute, and every flutist, sounds somewhat different - and plays a different "scale."

John