Sometime in 16th C. Italy, a second, chromatic, row of strings was added to the harp, thus enabling harpists to play every note, without having to fret any strings (for fretting: see Gothic harp). A third row of strings was added in the early 17th C., in order to make the diatonic strings equally accessible for both hands.
An Arpa doppia ('double harp') can be double or triple strung, the name refers not only to the multiple rows, but also to its size (roughly twice as big as its predecessor, the Gothic harp) and to the fact that is has a bass register, a bit like we now say a 'double bass'.
Unfortunately there are very few surviving instruments, so my arpe doppie are not copies, but reconstructions, based on iconography, surviving instruments, research into other period instruments and creativity from the makers. My little double harp (not on the picture) was made in 1999 by Tim Hobrough in Fordyce, Scotland. Its lime soundboard makes it sound slow-speaking and warm. My triple harps are made by Claus Hüttel and both have a spruce soundboard, which yields a bright crystal ringing treble, with a clear and deep bass. The small one (left on the picture) is loosely based on the 'Kaiser' double harp in the MIM in Brussels, and fits into an airplane seat! The big one (picture middle) is a reconstruction after a painting by Carlo Francesco Nuovolone (Milan, Brera gallery).
These are the harps for the music of Monteverdi and his contemporaries. The harp on the right in the picture is, although double, not an arpa doppia, it is the Davidsharfe.