Consider the sentence:
You didn't leave the dog in the car, did you?
In spoken English, this statement may be spoken with a rising intonation or a falling one. If the former, it suggests that leaving the dog in the car is a bad thing, and might even suggest incredulity and consternation on the part of the person asking.
In the latter case, when the sentence ends with a falling intonation, the speaker probably believes that the dog should have been left in the car, and that the person being addressed fell short. It amounts to an accusation.
Now, given that question tags are always questions, it seems they ought to be punctuated with a question mark. But in written form, especially dialogue, it feels to me that question tags meant to be spoken with a falling intonation might get by with just a period:
You didn't leave the dog in the car, did you.
I've tried Web searches but haven't gotten close to a set of search terms that point me toward an appropriate source. Anybody know of a definitive answer to this question?
One of the reasons I ask this is that any declarative statement may be changed into a question by means of a rising intonation at the end.
You left the dog in the car.
becomes a question if your voice modulates upward at the end. In written English, it is customary to show that by means of a question mark:
You left the dog in the car?
I include this information because @FumbleFingers asserts that "punctuation may not be used to differentiate [someone's] two intonations." Yet clearly there are cases in which punctuation is used in precisely that way (though in this case involving the opposite modulation from what I'm suggesting). So I wonder if it might not be possible to move the needle in the other direction.
If not, why not?
Note: I almost accepted my own answer to this question, but retracted it. If someone comes up with a better one I'll certainly consider awarding that one the checkmark. I think this question touches on an important concept, despite the scant attention it has received.