"Minor, Blues and Pentatonic" Jew's Harp Scales
Minor scale can be played on the second octave of jew's harp (this way was reccomed me by Bernhard Folkestad - thanks!):
Another way to play minor tunes on jew's harp (not bast IMHO). Jew's harp overtones can create a tone row quite close to the minor row. It starting from 13th overtone and is shown in the picture.
Similarly, "Blues" jew's harp scale starts from the thirteenth harmonic.
One more popular scale in modern music is Pentatonic.
* In fact, you can use other notes, such as third or one-fifth scale degrees, but it's more complicated options that provide a strong additional coloring the overall sound, and here we consider only the simplest case with the tonic.