What I mean by "half-fingered" are where you don't apply enough pressure to actually bring the string into contact with the fingerboard to get what we'd usually call a "true" note.  But it is not the light touch at a node one does when playing a harmonic either.  It is stopping the note with just the finger instead of pressing it against the fingerboard.

The concept came up when were were discussing another instrument the erhu, in another thread here a while ago.  Some might recall that I was thinking that using just the finger as the stop could have some applications as a playing trick/technique.  I think I found one.  I'm just going to call a note played that way a "half fingered" note because it is shorter.

When playing an open string, one of the problems is that you usually can't do vibrato.  No finger on the string, no vibrato.  Also open strings can sound a bit more harsh or bright than fingered notes.  A trick I had heard for taming the harshness when it is being a problem for the feel you are trying to get is to touch the string very lightly right next to the nut to dampen the brightness a little and make it sound more like a fingered note.

Obviously, for most notes you can use a fingered note on a lower string to get the same pitch and be able to use vibrato, but when you get down to your low G on violin, that isn't an option anymore.

So what I stumbled across is that you can put your finger down on the nut when playing an open string, press down just a little lighter than you would when doing a normal vibrato and do whatever vibrato move you normally do.  When the finger rolls to the part of the string that is not resting on the nut, the "half fingered" pitch can go smoothly a little above the pitch of the open string and you can get a sort of vibrato. 

I don't do it well (just thought of this last night), but here's a quick sound sample, first without and then with the "half fingered half vibrato"..

I would only call it a "half vibrato", because you can't go below the target pitch.  Any "wobble" you apply is only up from the pitch.  So far as I was ever taught, a true vibrato goes both above and below so it will average at the target pitch.  But what the heck, I'm a guitarist and guitarists have been stuck with only bending up for vibrato (unless they use a whammy bar) for years.

But it is at least a "sorta" vibrato that can be used on the open G string or other open strings if they are more convenient in your transitions. 

Another thing is you have to hold the instrument a little tighter with the chin when trying this trick, since doing a vibrato move on the nut will shake the instrument more if you don't. 

And yes, my vibrato sucks anyway.  LOL  I'm a 6 month noob, and my vibrato is narrow and fast, i don't have good control yet because I haven't put time into working on it yet.  But someone actually good at vibrato could possibly use this trick to get a better sound with it than I can. 

I'm just putting it up as a trick I stumbled across while playing when I wanted a little vibrato on a low G note for "feel".