I'm a lapsed violist/pianist and have always also played guitar, first folk/rock and then for 20 yrs or so classical and Brasilian. I have, for decades, noticed that it is almost impossible to tune the B string such that it is properly in tune both open and fretted, in different keys. I often have to take pains to find the compromise between its intonation as open and its intonation as fretted, and that it changes according to the key of the piece. This through many different instruments; however, some sets of strings seem a bit better than others in ability to sound in tune, particularly with major thirds. My sense of pitch is acute in a relative sense, and the beats or heterodyning from the root note and harmonics drive me a bit nuts. Why is this generally true of the B and not e.g. the G or high E?