In his Book Basics, Simon Fischer wrote in a footnote that:
The exact tuning of a sharp or a flat depends on the key, style and character of the music. For example, Bb as the tonic of Bb Major is higher than the Bb as the third of G minor. Tuning also depends on whether it is a single or a double stop, and what notes other instruments are playing
So my first question is, does this imply that accidentals need not be a particular pitch all the time? it is subject to other factors? There is no set frequency for an accidental unlike a normal tone, say for example: A=440? However, this matter is further complicated on another part in the same book; where it is written that:
The exact tuning of major, minor, augmented and diminished intervals depends, to a certain extent, on individual taste and the character of the music. For example, some players prefer wider (brighter) major thirds, or narrower (darker) minor thirds, than others. But perfect intervals- fourths, fifths and octaves- are either in tune or not, and cannot be adjusted according to taste.
So this time in stead of accidentals the focus is on intervals. In this case, if the piece starts with an accidental, i.e. Bb then there cannot be any variation for it. But this also implies that a natural note can be sharpened or flattened. In Bb Major, one might want to slightly sharpen the D note so that it resolves more easily into Eb, that is to say a wider major third.
So, my final question in relation to all of this is that, does this mean no note in music has a particular pitch/frequency that must absolutely be maintained? it is subject to the construction of the piece and other factors?