From A Study of the Drama (1910), pg 118:
"That is to say, tragedy is applied strictly to only one of the several types of serious drama... whereas comedy is stretched to include every kind of humorous piece. As a result, we have no name for the special type of comedy which corresponds to the special type of tragedy -- the comic play which deals with life sincerely and satirically, without exaggerated caricature in the character-drawing and without extravagant fun-making in the episodes. High-comedy is what one might call the play of this class... In this wise and witty comedy-of-manners, -- to give it another name, more widely used but less exactly descriptive -- the action, however serious it may seem, never stiffens into serious drama; and, on the other hand, however amusing it may be, it never relaxes into the robust and boisterous mirth of mere farce. Rich as is the dramatic literature of the world, the plays worthy to be classified under this head are surprisingly few."
The classification in film is just as spare. And the lack of critical attention is alarming. The comedy-of-manners name has stuck with us, perhaps for the worst, and few people seem to understand it.
As an illustration, read the Wikipedia page on comedy of manners: http://en.wikipedia.org/wiki/Comedy_of_manners:
"The comedy of manners satirizes the manners and affectations of a social class, often represented by stock characters, such as the miles gloriosus in ancient times, the fop and the rake during the Restoration, or an old person pretending to be young. The plot of the comedy, often concerned with an illicit love affair or some other scandal, is generally less important than its witty and often bawdy dialogue."
This is not a description of high comedy; it is much closer to farce. One example of high comedy will serve to refute every single claim in that paragraph -- the film is not a satire of high society (it is entirely about working-class people), it uses no stock characters, the plot is key, it is not about an illicit love affair or a scandal, and it certainly has no bawdy dialogue -- The Shop Around the Corner (1940).
For lovers of high comedy in film, Lubitsch is our master. The Shop Around the Corner is usually categorized as a romantic comedy, but the broadness of that term fails to articulate the film's uniqueness (romantic comedy is itself another name in need of critical saving). The Shop Around the Corner is pure high comedy, and it stands apart even from other high comedy, which often does engage high society in gentle satire.
Of course even with such pure examples, high comedy is not easily defined. That Brander Matthews, of the opening quote, parallels it to tragedy's place in drama is fascinating and perhaps the best placement of high comedy I have yet read. But what qualities exemplify high comedy? Sincerity and restraint, certainly. An emphasis on situational and character humor, perhaps.
But it is today as it was when Matthews wrote; we lack the critical vocabulary and understanding to approach comedy. We lack modern comedy worthy of critical attention (absurdism = "the death of comedy"). Who can match Sturges's "offhand profundity"? When will Renoir's comic legacy finally be recognized? Where is our contemporary Lubitsch?
I want a new Lubitsch. I dream of a new Lubitsch.