I have built several 3 strings and find the EBe tuning good for my voice.I just finished a 4 string and want to tune it EBe and wonder what the 4th string would be. EBe? any ideas would help and what gauge string should I use.
I'm just building my first 4-string now - a short-scale (470 mm scale, or about 18.5 inches), which I will mostly tune GBDg, sometimes G Bb D g. This is like taking an open D tuning and capoing at the 5th fret. I play my 6-string that way a lot, and I find it really versatile, though others might disagree.
I love the chord voicings you can get by using this tuning, it's great for finger-style playing, and allows you to play fast scales across all 4 strings without having to do the stretch that having the longer interval between the 1st and second string that you have with your root - 5th - octave tuning you use on your 3-string.
The drawback is that the range is limited to the same range you currently have on your 3-string, since the interval between the 1st and 4th string is still just one octave. Another approach would be to tune it like a tenor guitar or a mandolin, i.e. in 5ths, so maybe D A e b, (or some shift of that). A lot of people love this, but I find it kind of annoying except on really short scale instruments. YMMV. And there could be E B e b. The list goes on just about endlessly...
BTW, in your case, my tuning would correspond to E G# B e, which would fit your voice, and would be appropriate since, (I assume), you're using a longer scale length.