I tried C tuning on one of my guitars and loved it for a week or so until it hurt my brain too much to remember where the notes are. But is has an amazing sound. I tried the same tuning (relative) on my six string DVI, it would be a form of open F tuning, and there is something about the open C note and how it sounds which is not happening for me in the open F notes on the shorter scale length. So I don't bother with the popular guitar open tunings on the DVI anymore.
Just using the C guitar tuning as an example, and having no concrete proof I am right, it seems that a player has wanted to get a low C and more of an open C sound on a guitar, so they have looked at the notes on each string and just moved it one or two steps to make a C chord without changing tension radically and needing different strings. In some ear tuning methods I have read, the first step involves getting the guitar to EADGBE tuning, and then there is a second step to move to the open tuning. So effectively, when the guitarist tuned by ear he or she did not just go straight to the open tuning, they first set up standard tuning and then used the standard tuning as a reference to work from by ear.
On a short scale ADGCEA instrument you could apply the same concept. Say for an open C chord, lower the A to G, raise the D to E, keep the G and C and E, lower the A to G, to get GEGCEG tuning. Open C tuning on a guitar is CGCGCE, if you move that to fret five on a guitar you get a open F tuning not an open C tuning, you also get different intervals between the strings. So with your guitarlele, instead of just transposing the guitar tunings, look at the ADGCEA set up and work out how to make an open chord without having to adjust the strings a lot. So in addition to the C tuning proposed, maybe a D tuning could be ADF#DF#A. Both of these tunings proposed, but not tried yet by me, have the fifth note as the low note, so that is going to give a different sound to the D tuning and C tuning on a guitar where the root note is the low note. Maybe an open A tuning could be a thing to try with AEAC#EA or AC#AC#EA. An open G could be GDGBDG. I have no idea if this is reinventing a wheel, but if you are looking at open tunings on your ADGCEA instrument, you don't need to blindly follow the EADGBE open tunings made popular by guitarists. Once you work out a tuning, make a fretboard map and you will find the scales and the chord shapes which fit on the map.
More on that soon(ish)
