Modifying Entire Clauses

Sometimes an adverb modifies not just a specific word but an entire clause or sentence:

Oddly, no one had thought of that solution.

Fortunately, the check was in the mail.

Interestingly, in Erwin Schrödinger’s thought experiment the cat is simultaneously alive and dead.

As you can see from these examples, the adverb is not specific enough to modify one word, but provides a comment on the entire sentence.