The most widely encountered system for classifying musical instruments started out as an introductory essay to a catalog of the instrument collections of the Royal Conservatory in Brussels, prepared by their curator Victor-Charles Mahillon and published in 1888. His work was expanded by Erich von Hornbostel and Curt Sachs in 1914 and remains in widespread use as the “Hornbostel-Sachs Classification.” A specialist group publishes occasional revisions to it. Here is the segment of the current hierarchy where zithers appear.

3 CHORDOPHONES One or more strings are stretched between fixed points
31 Simple chordophones or zithers The instrument consists solely of a string bearer, or of a string bearer with a resonator which is not integral and can be detached without destroying the sound-producing apparatus
314 Board zithers The string bearer is a board; the ground too, is to be counted as such
314.1 True board zithers The plane of the strings is parallel with that of the string bearer
314.12 With resonator
314.122 With resonator box (box zither) The resonator is made from slats. NB This is true of the early piano only; modern pianos have no bottom and are board zithers. Harpsichords and some clavichords are box zithers Qin, koto, zither, Hackbrett, pianoforte

Numerous authors have extended this informally, following their own conceptual and terminological preferences. Qualifiers such as “chord” and “fretless” are commonly employed, branching further into individually named mechanized forms. The autoharp fits neatly into this framework but its physical attributes don’t always provide a sufficient basis for differentiating subtypes. Such things as alternate placements of damping pads on otherwise identical instruments may also need consideration. A hypothetical addendum to Hornbostel-Sachs might be headed “Box zithers with variable damping mechanisms” with specific types of autoharps placed below it.