It's pretty simple, but it only works properly with very clean modal melodies.

Basically, if a scale degree is the higher version, you present the lower version and vice-versa. The fifth is the exception for reasons I will explain should it come to that.

2nd, 3rd, 6th,7th degrees: major and minor are reversed.

4th degree; perfect and augmented are reversed.

Phrygian and Lydian will invert to each other, which is not very interesting.

The interesting things happen with Dorian, Mixolydian, Aeolean and somewhat with Ionian/the major scale, but less so because such melodies tend to depend on shapes that lose a lot and don't gain much when distorted in the manner I have suggested.

Melodies strictly using the Harmonic Minor scale will also (somewhat counterintuitively) be rendered appreciably more 'exotic' when this device is applied to them. In fact, the result is a scale I had derived by entirely different means so as to produce a maximally irregular scale under quasi-Greco-Chinese-Nort- Indian theory (look at it a while as a series of fifhs branching out from 1 and 5 as a starting point).

When you get used to the scale substitutions a bit, you can usually sight-read clean modal melodies (assuming you can to begin with) in the new mode by imagining a mixed key signature of sharps and flats.

I'm using these for imitative counterpoint because the gross unevenness of scale intervals under step sequence allows me to do literal per-line-per-space transpositions to imitative figures without getting the same consonance/dissonance relationships from one point of imitation to the next; graphically literal canons come out sounding rather non-literal and the emergent harmonic progressions are more than merely a reiteration of the points of imitation.

I've also noted that with these kinds of 'false' modes, the best accidentals to add (if it comes to that) will be tones that don't cause the th pitch collection to approach the diatonic; if you have an augmented 2nd in the scale, don't use for an 'extra' pitch either of the ones in the gap. Look, instead, where the major 2nds are and use the tone wedged in there as your 'extra' pitch.

For example...

If you're abusing an Aeolean melody with a scale A-B-C-D-E-F-G-A by rendering it, instead, with A-Bb-C#-D#-E-F#-G#-A, the pitches D, F and G may remind you of the original scale, but if they're used only at special moments they won't have any such effect to the ear. The pitches B and C, though, blunt the basic shape of the new scale, and are probably better avoided.

Try it and get back to me, eh?