A 105 plays just fine at 30 inches. You can easily find these things out by capo-ing your long-scale bass at whatever fret and then re-tuning it to EADG.
First fret = 32 inches, second fret = 30 inches, etc ... fifth fret = 25.5 inches.
At 25.5 inches, I find a 125 works well, a 105 does not work at all. Heavier strings at such a short scale begin to feel more like solid bars - extremely stiff. Tuning and intonation for a super-short 25.5" bass are very touchy, which is a good reason you don't find them. A standard short-scale has no such issues.
String tensions from D'Addario:
E A D G
scale 0.105 0.085 0.070 0.050 total
34.0 40.3 48.4 60.1 53.4 202.2
32.0 35.7 42.9 53.2 47.3 179.1
30.3 32.0 38.4 47.7 42.4 160.5
Note that a 34" 125 tuned to low-B is E at the fifth fret = 25.5" scale.
Most of the people who don't like short-scales have probably never really tried one. * Leo Fender was wrong when he selected the 34" scale. He was trying to please double-bass players, who were already used to a scale length that does not fit a human hand. There is an acoustic reason for that on an acoustic bass that originally used gut strings, but there is no reason to carry that over to an electric instrument with wire strings.
* If you don't actually own a short-scale bass, then don't even reply - you're one of the people I'm talking about !!!
Very few musical instruments are not made to fit human dimensions, and when they are, it is always for some reason related to acoustics and tuning that probably does not apply to an electric. Another example - the tuba. Or try to imagine a bass trombone - it would probably require two people to operate, one to hold his end and blow, and the other to (literally) run the slide in and out.
I much prefer 32 and 30 inch scales, especially now that my hands are older and less flexible. After a few experiments with different strings, I have built a couple of 25.5" basses that play just fine, and feel great in your hands. I skipped the in-between scales 28.5 & 27, because for a 25.5" I could use an off-the shelf guitar neck rather than have to build it from scratch. I expect with the right strings, either of those scales would work just as well. 30-inch became popular I think because it is the shortest scale that can use standard-weight strings.
How do I know all this?
It is not just theory. All of the Strats are short-scales. The block neck is 25.5", the red JM is 32". Fretless 30" 4th from the left; 30" Bass VI 3rd from left, 21" 'Uke' scale at right. 5th from the left is a "Bass IV" that uses super-lightweight strings ( basically the lower 4 from a Bass VI set ) to balance a Strat tremolo mechanism. The tremolo on the Bass VI is over-tight and doesn't really function. There are a few standard long-scales as well, and an odd 12-string. A 24-fret 30" neck is roughly the same overall length as a 20-fret 34" neck, the difference is the bridge placement. The big advantage of a double-octave 30" neck is that you can bolt it onto a guitar body without having to move the bridge. Many of these use guitar-sized headstocks so as not to unbalance the guitar-sized body.
Scale is similar for guitars. Standard guitar scale is 25" plus or minus 1/2" - that covers everything from Fender to Gibson. People obsess over the difference between a 25.5" Fender and a 24.who-knows-what Gibson, but overall the differences really are minor. Drop to 24 inches, though, and it begins to feel cramped, and by the time you get down to kiddie-scale 22.5", you start wishing for a longer neck. The sweet spot to fit a human hand is clearly around 25 inches.
27 and 28.5 inch baritones feel fine, but to tune them up to standard EADGBE guitar tuning would require strings that would probably feel very strange, and would likely be very fragile as well. Note that at 28.5", the difference between a baritone and a bass vi is just the choice of strings. 28.5" 4-string basses have been made, but I have never played one. Mandolins, ukuleles, and banjos have different scale lengths, but all still fit human hands. Only the 34" bass scale requires such stretches and contortions.
One thing that is funny is putting down one scale length an immediately picking up another, especially if they are far apart. It takes a minute or two for my left hand to re-program itself and the fingers go to the right places. Playing a short-scale should be no different than playing a few frets up the neck of a long-scale, but somehow it is.
One area where I think a super-short scale is a detriment is fretless. The longer the scale of a fretless instrument, the smaller the relative errors in fingering. My 30" fretless plays fine, but I made the 20" uke fretted for this reason - I don't see how you could find the notes. Yes, fretless is a matter of ear, but you still have to find the right spot on the neck, and that spot gets very small on a micro scale. On the other hand, people play violins. That is probably why a bad violin player sounds so awful, while a bad double-bass player can get away with it. But again, acoustic vs electric, bass vs tenor, gut vs wire - all apples and oranges.
