Where does “quartet” come from?

I need to carefully analyze this etymology chain, which appears to have some issues. Looking at the chain provided: - French quartette | Italian quartetto | Italian quarto | Latin quartus | Latin quattuor | Latin caput | Proto-Indo-European kauput- | Proto-Indo-European kauput- This chain doesn't make linguistic sense. "Quartet" comes from Italian "quartetto" (a group of four), which derives from "quarto" (fourth), from Latin "quartus" (fourth), from Latin "quattuor" (four). However, the chain then jumps to "caput" (head) and "kauput-" (head in PIE), which is incorrect—"quattuor" doesn't derive from "caput." The correct chain should be: quartet ← quartette ← quartetto ← quarto ← quartus ← quattuor (four

quartet (English): A music composition in four parts, each performed...