Francis Hutcheson, in his An Inquiry into the Original of Our Ideas of Beauty and Virtue and elsewhere, identified a number of internal senses, where sense means a way in which our ideas originate: sense of beauty, sense of harmony, sense of order, sense of the ridiculous, consciousness (which is something like a sense of self), public sense (which gives us pleasure at the happiness of others and pains us when they are miserable), sense of honour (which gives us pleasure at others being approving of or grateful to us), moral sense (which gives us recognition of virtue and vice). He's probably not intending to be exhaustive. Alexander Gerard, in his Essay on Taste, suggested the following senses, which he takes all internal senses, or at least those concerned with aesthetics, to be reducible to: sense of novelty, sense of sublimity, sense of beauty, sense of imitation, sense of harmony, sense of riducule, sense of virtue. So let's take the Gerardian list, with minor modification for perspicacity. Then we have the following aesthetic qualities:
the novel/new
the sublime
the beautiful
the imitative
the harmonious
the humorous
the moral
(That the moral is an aesthetic effect can be seen easily in the portrayal of heroes and villains in literature; the moral sense is what distinguishes the two, and we all recognize that failing actually to convey the heroism of the hero or the villainy of the villain is an artistic flaw.) But it seems reasonable to say that we can combine these in one; some things, for instance, are such that we 'sense' them as new and as beautiful, for instance. Then we get the following combinations of two:
novel sublime
novel beautiful
novel imitative
novel harmonious
novel humorous
novel moral
sublime beautiful
sublime imitative
sublime harmonious
sublime humorous
sublime moral
beautiful imitative
beautiful harmonious
beautiful humorous
beautiful moral
imitative harmonious
imitative humorous
imitative moral
harmonious humorous
harmonious moral
humorous moral
These are different families of artistic effect, deliberately cultivated. Many of the families are quite interesting. For instance [imitative moral] is something you see deliberately developed in hagiography -- indeed, hagiography is specifically focused on the [sublime imitative moral], since saints are supposed to be morally recognized, are supposed to be recognizable as imitations of Christ, and thus to open up on the divine infinite. Some effects are clearly very, very difficult to achieve -- [sublime humorous] is perhaps the most obvious. If we accept the theory of Jean Paul, the humorous is the inverted sublime, which makes the category appear an oxymoron and perhaps a contradiction. But there are other accounts of humor in which this problem might not exist. And, while not easy, there are cases where the difficult union of the humorous (even in its form of the ridiculous) and the sublime seems achieved -- G. K. Chesterton's The Man Who Was Thursday is arguably an example. Another apparent paradox is the [novel imitative] -- but I think it is quite a common aim of acting to achieve it.
The [harmonious] families are also somewhat tricky; harmony is a matter of sound, and thus the conditions for combining with the others have to be just right. We do get them in poetry, where sound can and often does matter, and of course in sung poetry. But we also have other situations in which they can occur without words: [harmonious humorous] is not common in pure music, but, for instance Haydn was famous for his musical jokes: the Surprise Symphony (no. 94), the Clock Symphony (no. 101), the Joke Quartet (Op. 33, no. 2). Beethoven's Eroica Symphony (no. 3) is a famous example of [sublime harmonious]. Interestingly, [beautiful harmonious], [sublime harmonious], and [novel harmonious] are associated with (although not completely definitive of) three major approaches to music, the classical, romantic, and avant-garde respectively.
