After much philosophy, I've identified 16 prime emotions, not counting the negatives separately. Note that I'm not done with this - I'm sure this isn't entirely right, but it's close, and someday I'll understand it all. Also note that I had to fudge the English language a bit, even to the point of outright reusing names, because English was not invented by philosophers.
(Note that the "future-minded" emotions like fear and excitement are actually reducible to these; they're just the partial-certainty forms: if you think there's a 50% chance that something upsetting will happen, you'll experience half the upset.)
|Gladness, Self-Pity||Own percieved fortune|
|Companionship, Loneliness||Sharing one's thoughts and interests with others / being unable to do so (footnote below)|
|Epiphany, Frustration||Understanding gained/lost|
|Pride, Humbling||Skill gained/lost|
|Empowerment, Disempowerment||Using power / Having no outlet for such (footnote below)|
|Engagement, Boredom||Applying one's skills and effort / Not having a need for them (footnote below)|
|Novelty Fun, Boredom||Change/progression, stagnation (footnote below)|
|Exhilaration, Restlessness||Being involved in big things / being irrelevant (footnote below)|
|Appreciation, Disdain||Experiencing good/bad works of art|
|Amusement, Disamusement||Humor, failed humor|
|Self-Esteem, Self-Hatred||Assessment of one's alignment with one's ideals|
|Satisfaction, Regret||Assessment of the result of one's actions|
|Admiration, Disgust||Other wills in accord/discord with own ideals (footnote below)|
|Validation, Embarrassment||Being seen by others whose opinion we care about as being the way we do/don't aspire to be (footnote below)|
|Empathy, Sympathy||Wanted prosperity of other / unwanted suffering of other|
|Schadenfreude, Anger||Wanted suffering of other / unwanted prosperity of other (footnote below)|
Footnote on Empowerment/Disempowerment: This encompasses the pleasure of physical exercise, but also things like the powerful feeling of the weapons in Halo 1 and the way a lot of CCG cards seem to play off their "awesome factor". It's also part of the enjoyment of winning at games in general (the other part being pride), and even the enjoyment of customization.
Footnote on Engagement/Boredom: This can be understood as the "fun of trying", whereas Empowerment is "the fun of winning".
Footnote on Novelty Fun/Boredom: This "feeling of progress" notion is the reason why game players seem to universally enjoy mechanics like having levels be locked until they've beaten the previous level, even though from a logical perspective it seems like this is strictly worse for the player.
Footnote on Companionship/Loneliness: This also explains why playing games with other people is almost universally much more fun than single-player.
Footnote on Exhilaration/Restlessness: This shows itself in a lot of ways, including getting to the climax of a good game or story, being on a large team and/or playing with stakes in a competition, and I think the enjoyment of spectating a prestigious tournament or similar is also a form. It can also show itself in more meaningful ways, such as playing an important role in one's real-world cause (although most people have little to no experience with that, myself included).
Footnote on Admiration/Disgust: The concept of "ideals" is one that took me a long time to pin down. I think it's "what you'd will if you didn't have a personal stake in it". So by this token you can admire someone for being closer to your ideals than you, whereas back when I just called it "other wills in accord with self", I couldn't understand how that was possible.
Footnote on Validation/Embarrassment: A lot of things about human behavior and psychology are explained by this.
It's embarrassing to receive a compliment, condolescence or similar social idiom and not know how to respond. This is because we're worried that we'll be seen as rude or ungrateful. This is supported by my experience that the effect is less pronounced or gone entirely when the onlookers are people whose opinion you don't care much about, or who you know will understand that you're just having trouble finding a tactful response.
It's embarrassing to be seen as acting one-sidedly hostile, such as being ungrateful for a significant favor, or physically or verbally attacking someone who isn't retaliating.
The general concepts of "dignity" or "formality" are often a form of this. For example, slouching while receiving grim news shows disrespect. The principle of purity is behind this; such things have moral value through the feelings they project, affecting everyone present. Everyone understands reverence on a conscientious level and so it affects their emotions even if they consciously deny that it has moral value. Similarly, if a heated argument takes place while eating, ceasing to eat while making your point is dignified.
Of course, losing an argument or being the last one to solve a puzzle is often embarrassing, because it makes you appear less intelligent, and everyone wishes they were intelligent.
Footnote on Schadenfreude/Anger: Sometimes, when you're having a really hard time with something (programming triggers me like this all the time), self-pity would be the "natural" response, but you might feel something you'd rather label as "frustration" instead. I believe this is actually the feeling I'm labeling "anger", and it comes from implicitly personifying fortune as victimizing you. The reason for doing this is that it can be more comfortable due to the shifting of the blame off yourself and thereby elevating your self-opinion. It can even lead to some synthesized schadenfreude when you finally get it working (I experienced this a lot when I was younger). One should avoid this though; it's worse for your productivity in my experience, and also you're likely to end up taking your anger out with other people and making their day worse as well.
A few notes about things that aren't on the list and what they're composed of:
Gaming "salt" is self-pity turned into a more anger-like annoyance (through the means described above) + embarrassment, because we feel it when we feel we 'should' have won the match, but didn't because of something that we see as 'bullshit', so we try hard to convince everyone of the same so that it won't damage their opinion of our skill.
Gaming "tilt" (at least as I used to feel it) is frustration, combined with zero or more of a couple others: humbling (finding out I'm not as good as I thought), embarrassment (losing to a much weaker player), and losing rating is a trigger of both (since it's both how I measure my own skill and how other people measure my skill).
I think "grief" is actually mostly a form of self-pity (from how much worse your life will be without the person) and loneliness, coupled with some amount of sympathy.
I think the feeling of agitation from being around someone you don't like is actually just instinct - you associate negative emotions with being around those people, so just being around them can make you feel unhappy even if nothing's happening. Their presence is a reminder. Likewise the feeling that it's pleasant to be with someone you like even if you're not interacting with them.