Sometimes we need to reframe the problem at hand in order to make real headway.For example, if a passage of double stops is out of tune, it is not sufficient to slowly adjust each isolated double stop in consecutive order. Doing this only makes you an adjustment expert and nothing more.Instead, you need to identify the main melodic line in the double stop passage (or at least the more prominent one) and prioritise that i.e. tuning the less important line to the main one.Also, you need to check that you know exactly what each interval in each double stop is eg. minor 6th, followed by major 3rd, followed by perfect 5th etc.Additionally, it helps to know what harmony each double stop is a part of. This is but one of the many reasons why a solid foundation in music theory (beyond the drudgery of the ABRSM exams) is important.
Unfortunately, many classical musicians, teachers especially, have certain pet interpretations from recordings they love that they have grown accustomed to. Indeed, for any given piece, certain classic recordings have formed the basis for an accepted standard interpretation and any deviation from this interpretative benchmark is not usually tolerated (at least, not unless you’re famous). This leads to many teachers rejecting anything new or surprising to them as wayward and objectionable, often, without real concrete reasons to back up that rejection.
Does this therefore mean that no expressive or interpretative choice can be wrong?
— Of course not.
The key to this lies in what we mean by ‘interpretation’. If we simply mean a vague sort of expressivity (some extra vibrato here and a dash of rubato there), then one can be assured that this is in fact not interpretation at all.
What, then, is interpretation?
Interpretation is rooted in the understanding of the underlying structure of the music — the large sections, the phrases that make up those sections, the lengths of those phrases, and the harmonies that shape each phrase. Once we can convert all of that dry analysis into something that we can feel in an intuitive and visceral way, directing the music in a way that reflects how we understand it both intellectually and emotionally, only THEN do we have an interpretation.
And because different people have different emotional makeups, we can be assured that even very similar theoretical analyses of structure and harmony can yield playing of excitingly different practical interpretations.
If you follow your teacher mindlessly, you are a human photocopy machine, not an artist. If you play whatever you wish, you can be expressive in disconnected bursts but never tell a full story.