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.)

Emotion Name Trigger
Intrinsic, self-based
Gladness, Self-Pity Own percieved fortune
Companionship, Loneliness Sharing one's thoughts and interests with others / being unable to do so (footnote below)
Intrinsic, power-based
Epiphany, Frustration Understanding gained/lost
Pride, Humbling Skill gained/lost
Intrinsic, activity-based
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)
Intrinsic, existential
Novelty Fun, Boredom Change/progression, stagnation (footnote below)
Exhilaration, Restlessness Being involved in big things / being irrelevant (footnote below)
Intrinsic, analytic
Appreciation, Disdain Experiencing good/bad works of art
Amusement, Disamusement Humor, failed humor
Ideal-dependent, self-based
Self-Esteem, Self-Hatred Assessment of one's alignment with one's ideals
Satisfaction, Regret Assessment of the result of one's actions
Ideal-dependent, interpersonal-based
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)
Ideal-dependent, other-based
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 accounts for 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 appeal to an "awesome factor". It's also part of the enjoyment of winning at games in general (the other part being pride), and the enjoyment of customization.

Disempowerment is the frustration we often feel "at nature"; hence why empowerment (manifested in outlets like punching bags) relieves it.

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 accounts for playing games with other people being 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 that's why 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 are accounted for by this.

A few notes about things that aren't on the list and what they're composed of:

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