“Tritet” is not attested. (It’s “not a word”; doesn’t occur in dictionaries, etc.)
The rest of these words have the *-et* diminutive ending, but “trio” doesn’t. All of these words came into English via Italian and French, as with many other words used in music and theater.
A *duo* (two people) sing a *duet* (literally “a little two”).
Why the difference? It could be because some of these forms would collide with other uses. A *quarto* for instance is a size of paper (made from one big sheet folded into four), and a *triolet* (diminutive of “trio”) is a short poem where the first line is repeated twice later in the poem.
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