I found myself yesterday trying to explain the evolution of equal temperament, off the top of my head, which I never do a particularly good job of...not least because it's not really anything I could call a speciality. Something I find particularly difficult is making the jump from abstract mathematical concepts to how the sounds of earlier tuning systems exploited the character of individual keys which resulted.
I'm gradually putting together playlists of useful recordings for students working at exam pieces. They're a mixture of original versions, interesting performances, and at the later grades some of the actual pieces specified in the syllabus. Hopefully people will find them helpful - please do recommend any other good recordings that would complement them well, especially when they offer contrasting perspectives on a piece. The following are for the violin exams; grade 8 plus viola to follow: