Jacques said
.....

Here re is a question to ponder. Is there a tone between G# and Ab?

Yes, indeed - it may not have a "name" as such in Western Music terminology - but the "tone" ( or note, or frequency - however you wish to describe it ) - surely exists.

   Very often, if you don't check the tuning on your violin, it may well have drifted slightly - and - if you are "lucky" all the strings "drifted" but ( within what we can recognise ) stayed in tune with each other at 5ths apart - so - what do you do - you wanna PLAY fiddle - yeahhh - pick up the instrument and play G-D, D-A, A-E open and listen - it sounds OK?   Yes?   But that doesn't mean anything.  Your "A" may be a semi-tone-down from 440 Hz - but all the strings sound fine inn relationship to each other.

 So, you just play.   But although the relationship between both the strings and the notes you are fingering are "perfect" and what you play sounds 100% fine to the ear when soloing - it could well be "a sufficient number of cents out" of normal tuning to not be able to play against accompaniment ( unless you are very skilled )

  Although I say that - you should also take into account what Galamian says - these few words are actually very significant.. LOL