Decatonic harmony - help needed!

Hello!

I'm currently digging deeper into Paul Erlich's pentachordal
decatonic scales.

I'm making slow progress but I need help with chord progressions.

What kinds of chord progressions can be considered cadential in these
scales?

I have a hunch that they involve charasteristic dissonances and/or
progressions of three consonant tetrads covering the entire scale.
Finding such three chords was left as an exercise for the reader in
Paul's paper. If I did it right there are two such triples of chords
and neither of them include tonic chords. So I suppose cadences
involving these chords need at least four chords, those three chords
in some order and then the tonic as the final chord.

Kalle