Myhill’s Property

I am trying to get my head around this idea in the context of the diatonic scale (diatonic collection).   First, I hope I am beginning to understand the definition, in terms of c- and d-distances (just stating that there are two possible intervals for each “generic” interval does not really explain it for me.)  Next, what is its importance? Coming from a jazz perspective, I feel it somehow exemplifies the importance/interaction of the diatonic collection and “melodic minor collection” in jazz and perhaps other music forms.