a) Dancing of jigs gets on my nerves.
means
It gets on my nerves when people dance gigs.
Yes, it does.
but could
b) Dancing on tables gets on my nerves.
c) Dancing gets on my nerves.
mean
It gets on my nerves when people dance/dance on tables.
Yes, those can have that meaning, too. And they can also have the meaning according to which it is the speaker's dancing on tables that gets on his or her nerves. Suppose the speaker is a cocktail waitress who is sometimes forced to dance on the bar counter in front of inebriated customers. That activity, with the reactions she receives, might get on her nerves.
Grammatically, that second interpretation requires that we parse (consciously or subconsciously)
Dancing as a verb rather than as a noun. When we have a verb, we have an implied subject, and it can either be impersonal (people in general) or specific (deriving from
my). If we had
her, the implied subject of
dancing could be the referent of
her:
d) Dancing (on tables) gets on her nerves.
That sentence could either that it gets on her nerves when people dance on tables or that it gets on her nerves when she dances on tables, perhaps because of the lewd responses she receives from inebriated, raucous audience members. Let's consider a different example set, one with overt subjects:
e) Sally's graceful dancing of waltzes impresses me. (NOT: *
Sally's gracefully dancing of waltzes impresses me.)
f) Sally's gracefully dancing waltzes impresses me. (NOT: *
Sally's graceful dancing waltzes impresses me.)
Those obviate the possibility of having either a noun parse or a verb parse for
dancing. When
dancing is a noun, it needs
of before the name of what is danced, which, when
dancing is a verb, is the direct object. Also, when
dancing is a noun, it can be modified by an adjective, not an adverb. It's just the reverse when
dancing's a verb. Now, what about these?
g) Dancing of waltzes impresses me.
h) ?? Dancing waltzes impresses me.
Sentence (g) is clearly fine. It has the meaning "It impresses me when people dance waltzes." But can (h) have that meaning? If I'm right about the semantic interpretation of these constructions,
dancing can't be interpreted as referring to Sally's dancing or to anyone-else-in-particular's doing so or even to a specific group's doing so.
I don't think (h) works at all, semantically, and I don't deny that the predicate is the culprit. It wants to be interpreted as meaning that the speaker impresses him- or herself by and through dancing, and yet that meaning is fairly absurd. In contrast, the following would, of course, be perfectly fine:
i) Dancing waltzes exhausts me.
j) Dancing waltzes isn't easy.
In (i), the speaker is the implied subject of the verb Dancing. In (j), the implied subject is people in general, the meaning being that, in general, it isn't easy for people to dance waltzes. Presumably, such a sentence doesn't rule out the possibility that for some specialized subset of people (highly trained dancers) it has become easy to do so. 