[octatonic]

When working on a 3 part harmony don't have each singer/voice spaced equally.

So if you have a melody that is the following notes:

A C E D A

Have the second singer start with a 3rd (or in this case minor 3rd) above and then move to the 5th then to the octave above then back to the 5th then the 3rd (or in this case minor 3rd.)

You have the folowing

1st singer: A C E D A
2nd singer: C G E F C

So the 3rd singer could do a variation on this like maybe:

5th, octave above, octave + minor 3rd, octave, 5th

So the whole harmony is as follows:

1st singer: A C E D A
2nd singer: C G E F C
3rd singer: E C G D E

So basically you have some melodic movement with the chords rather than static block chord movements.

Then you start playing with the timing, gliassando and such so the notes don't start and stop at exactly the same time.

It is all a matter of taste though- I've just pulled that off the top of my head- to illustrate the idea behind it.