Are there any initial consonants/syllables in modern Chinese dialects which are incompatible with some tones? Are there any initial consonants/syllables in modern Chinese dialects which are incompatible with some tones? 

Can certain tones occur only in certain syllables (that is, within open or close ones)?

I am referring mainly to 普通话 (or 華語), but any other dialect will do
Here's an example of this sort of phenomenon:


  Syllables that begin with unaspirated stops b, d, g, or affricates j, zh, z, and end in a nasal n or ng, as a rule don’t have second-tone forms.


Here's a more extensive explanation of how this came about