Strings Modern strings are a miracle of technology. They are created to exacting specifications, including precise diameters. A brand new string of good quality should have uniform diameter, winding and plating thickness along its length. Change any of these factors and nasty overtones will, not surprisingly, creep in. This makes it more difficult to tune the string and provide good intonation all the way up the fretboard.
Old strings can be virtually impossible to tune.
The surface becomes pitted with corrosion, covered with grease deposits and worn flat through contact with the frets. While you have the cloth under the strings, you should also pass it over the fretboard to remove sweat and grease which would otherwise cause fret corrosion or soak into the fingerboard. Occasionally you may change a pair of strings and find it impossible to get the new ones to fret in unison. This is because of an imperfection in one of the strings which has somehow got past the manufacturer's quality control system. Maybe there is a variation in diameter or some plating is not quite uniform.