The "dulcijo" is a unique 3-string banjo-like instrument that features diatonically spaced frets, a short re-entrantly tuned third string, and a small drum resonator. It was originally developed in the late 1980s by Michael Fox of Hickory, North Carolina - and you can still buy them from him thru this link. As the story goes, he once saw and played with a strum-stick (aka stick dulcimer) and he decided he liked the concept of a diatonic scale, but he preferred a re-entrantly tuned instrument so he could play claw-hammer style, as how he normally played his banjo. With the banjo and strum-stick in mind, he developed the dulcijo - a cross of the strum-stick (a derivation of the mountain dulcimer) and the banjo.
The original dulcijo (as build by Michael Fox and company) has a 25.5" scale length. But my advice is to find a scale length that you are happy playing with and then build the instrument around that spec. This is especially true for chord players as some of the frets are spaced widely apart. With my rather average sized hands, I prefer a scale length of 50cm (about 20 inches), and so that's why I designed my ducijo to have a short 50 cm scale.
Besides the diatonically spaced frets and the small drum resonator, the really unique thing about the dulcijo is the short third string. This string is about 3/4 the scale length of the other two strings, and terminates at fret number 4. The three strings are tuned A'AD as follows:
String 1: D (a whole step above middle C)
String 2: A (below middle C)
String 3: A' (an octave higher than String 2)
Here's how the tuning relates to the notes on the grand staff:
And here is a close up of the fingerboard of a dulcijo with the frets numbers and the notes produced.
The dulcijo also uses three identically sized strings, usually gauge 0.009. The D-string (string 1) is usually used to play the melody of the song while frailing (claw hammer style) during the "dit" part of the "bum-ditty". For more information on frailing the dulcijo, check out this link. For information about melody and chords, check out this link. And here is the link to the dulcijo pages on ezfolk.com.
Besides clawhammer (aka 'frailing'), another style of playing you can use on the Dulcijo is to play your tune on the second string, and use the first and third strings as drone strings. This style of playing make some songs sound great, and others, not so great. Try it with 'Old Joe Clark', which sounds pretty good played this way.
Note: The 'Dulcijo' name is sometimes also applied to the "banjo dulcimer", which is a kind of mountain (or Appalachian) dulcimer modified by adding a vibrating membrane to the body of the instrument and operates in the same manner as a banjo. Some builders market these instruments using the same name: "dulcijo". Here's a photo of one. Perhaps we should be calling our kind a "stick-dulcijo" to prevent miscommunication and this one (picture right) could be called "lap-dulcijo " (in the same way mountain dulcimers are sometimes called "lap dulcimers").
To hear the Dulcijo played, check out these videos on Youtube (videos arranged in no special order).
A reader asked "What scale length is used in the original Dulcijo?", which I didn't know the answer to. So, I did a search and came across a reply that Michael Fox (the Dulcijo inventer) made on a forum discussing the Dulcijo, and in it he said his instruments use a 25.5" scale length, similar to many other dulcimers. My only caution is that the diatonic fretboard has wide fret spacings, so if you are a chord player, you hopefully have a long (and easy) reach with the fingers on your fretting hand. My fingers are rather averaged size, and so I build a shorter instrument, usualy with a 500mm (about 20") scale length. I'd recommend finding a diatonic scale length you are happy playing with, and then build your instrument to that spec.