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If you're going up or down the piano playing octaves you'll need to move your arm, but you should minimize the movement as much as possible. A lot of times beginners will move their arm up much more than they need to in general when moving up or down the piano. Minimizing the movement minimizes the distance you need to move from one octave to another. As ...
Practice longtones with crescendos and decrescendos, practice all your scales, and practice scales with different tongueing patterns like tongue slur, tongue two slur two, etc.
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