A parure is a complete matching suite of jewelry, a term taken from French and used in the trade from the eighteenth century onward. At its fullest it might include a necklace, earrings, a brooch, a bracelet and a tiara.
A demi-parure was the partial version, usually a necklace or a pendant with matching earrings, and it was the form most households actually owned and the one that was worn with any regularity.
The modern half set descends directly from the demi-parure, and the descent is straightforward. The vocabulary moved from French into English; the arrangement of two matching components stayed exactly where it was.