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Great article! As a mathematician who used to play the violin I must admit to never enjoying the sound I made, so gave up after getting to grade 7. I would much rather listen to Itzhak Perlman doing it right! The bowing was never a problem to me but the vibrato on the sustained notes makes such a difference to a whether you get a flat sound or a sonorous one. I would be interested to hear more of the mathematics of vibrato. As with bowing it has boundaries. Too much vibrato disrupts the note but none makes for a dead sound.

Confidence has a great deal to do with the sound a violinist makes. A fear of hitting wrong notes with gusto leads to timid bowing and all of the consequences you so eloquently explained in your article.