The history of these so-called "numerical instruments" is yet to be written. They're called numerical because they were sold with paper sheets you could put under the strings so that, according to the manufacturers, you didn't need to read music in order to play at sight.

They were all more or less variations on zithers, the common denominator being that nearly all had sets of four strings tuned to each of three or more chords, so that you could strum them to accompany your melody playing. To play melody, each instrument was different: the ukelin (a variation on the bowed psaltery) could be bowed like a violin, accompanied by chord strings. The Marxolin was a one-string slide instrument. The Marxophone had spring-steel hammers that could be played for a harpsichord effect. The Mandolin-Guitar-Harp was held upright in the lap like a harp, and so on. The Practice Zither had (if I remember right) 8 sets of chord strings but was very limited in melody strings.

Perhaps the most basic of all was the "American Zither," just picked with chord strings, and apparently a very good seller—you still find them from time to time. They were not sold in shops so far as I know, but through door-to-door sales during the 1930s, 40s and maybe 50s. Youngsters worked their way through school demonstrating and selling them. They were fairly cheap, of cheap manufacture, yet surprisingly many still hold up after all these years.

The major manufacturer and innovator was the Marxochime Colony; they made the best instruments and came up with the best designs. The American Zither Company made cheaper knockoffs but was very popular.

The survivor in the crowd was the Oscar Schmidt Autoharp, which proved a durable favorite and has established itself as one of the major American folk instruments.

The zither itself is hard to learn and has never caught on in America, except in the novelty recordings of Ruth Welcome, and in the brief popularity of Anton Karas' "Third Man Theme." But its cheap "numerical" imitations are classic Americana.

Bob