I was just curious about this particular topic. Looking at the most advanced violin repertoire (Paganini, various cadenzas), I noticed that there are some passages where extremely fast playing is required (i.e. a three octave scale in 32nd notes at 120 bpm). I'm almost advanced enough to start learning that kind of repertoire, but the fastest I can play three octave scales/arpeggios with good intonation and accurate shifting is 16th notes at about 160 bpm. Now, as I practice to get to higher speeds, it seems that the amount I have to practice to achieve even a small improvement in speed is approaching infinity. That leads me to this question: is it that there is a secret to achieving such speeds? By the way, I do not take private lessons, so the problem might be a subtle one in my technique or something like that.
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