Perhaps an example of falsibility may be in order. 

I'm finding it hard to understand what the Rothenberg property is. I gather that the diatonic scale satisfies it, but it is quasiperiodic. Then again, the scale "C, C#, D, D#, E, F, F#" (repeating at all octaves) is also quasiperiodic, but it doesn't satisfy the Rothenberg property. Explaining why the first satisfies it, but the second doesn't, may make things a lot clearer.