A contrary negative is a type of interruption that clarifies what we are talking about by stating what it is not. Here are some examples:
Contrary negative interruptions always have a comma before and after. Make sure not to confuse them with the correlative conjunction not only, but also. This structure does not require any commas:
In a contrary negative, you are cutting out a possibility; with a correlative conjunction, you are adding a possibility. A possible memory aid is when you are cutting out a possibility, you also cut out that part of the sentence with commas.
So go ahead and interrupt yourself for clarity, but be sure to use the commas correctly.