One effective way to practice a difficult fast passage is to play it slowly and correctly. But sometimes, after all that slow practice, it doesn't seem to fit back into the music. Why is that?
One common problem with slow practice is the universal temptation to practice only the difficult part slowly, then practice everything else up-to-speed. Here's a suggestion: choose a section larger than just the difficult part, and practice it all at one tempo, keeping all rhythms proportional to the slow beat. That means practicing the easy parts slowly, as well as the difficult ones. Only when the whole section is going smoothly at the slow speed, should you start upping the tempo.
At first, this may seem boring, time-consuming and unnecessary. However, in reality, this is one of the most efficient tricks you can use in your practice. Why? Because you are working out how that passage fits into the whole, and this is essential work. If you practice something many times with a sudden shift of tempo, that shift becomes part of the learned whole, and it does not disappear with ease.
This kind of practice works in all levels of study, and it works just as well for learning pieces as it does for etudes and orchestra parts. To demonstrate, I've made a little video, using a section from"Gavotte" by Gossec (last tune in Suzuki Book 1) as an example. I hope you find it useful in your own practice!
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