Where does “halftone” come from?

I cannot write this etymology for halftone based on the chain provided. The chain traces back to Proto-Indo-European roots meaning "stretch" and "split/cut," but halftone is a printing/photography term (a technique using dots to create tonal gradations) whose etymology would logically derive from "half" + "tone," not from these ancient roots. The chain you've provided appears to be for the word "tone" alone, not "halftone." To write an accurate one-sentence origin summary, I would need the correct etymological chain for halftone specifically, which should show how the compound term formed in English.

halftone (English): Half the interval between two notes on a scale; A...