The Zither is a stringed instrument where a set of metal strings are stretched flat over a shallow resonance box. The general idea goes back to the BC era. Zithers [in the form still in use] became popular in central and eastern Europe, and then were brought to North America in the 1800’s, using the German term Zither.
The company Menzenhauers sold zithers in the US and Europe, although these stamps are in German. ‘Guitarr-zither’ here seems to be a brand name for a what was more often called a chorded zither; there are no frets as with a guitar, and some strings are grouped to more easily strum chords.
The stamps all have some variation of the phrase “everyone plays immediately.” In the set above, we see three sailors, two African-american [?] performers, a couple dressed as house servants, an elderly couple, and a Pierrot clown. These stamps very probably date circa 1910-14.
Most Americans are more familiar with the term “Autoharp”, which was actually a brand name for a zither with keys that dampen strings so as to simplify playing chords. –T.M.