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Ultimately, what is the best way to practice a new song??

Right now I'm working on a few different Beethoven sonatas right now, in particular his sonata No. 8 "Pathetique". If you had students just starting this song, how would you go about tackling that song?

I'm just curious to the different ways people would approach this......

I'd start by making sure you had the technical problems solved, primarily the left hand tremolo in the first movement. Be sure you can play a tremolo for a minute or so without becoming tense. If you can't, work on it by doing short stints (maybe four notes, starting both on the top and bottom note) staying relaxed, and gradually lengthen it, always stopping at the first sign of tension.

Spend a bit of time doing staccato scales if you haven't already, you'll need it for the third movement.

Read though and identify the difficult sections, then dig into those, making sure you are comfortable with all hand positions and can move in and out of them quickly and easily.

Fill in the easy parts and start polishing the phrasing and interpretation.

Some time in this process it would probably be helpful to memorize the piece. I usually start by memorizing the technically difficult sections, since it makes them easier to play, and sections where there are a lot of jumps so I can watch my hands for more accuracy. This would encompass a good chunk of the first movement.

Oh, and being familiar with the piece from recordings always significantly speeds the process for me. Reading through the score with a recording can be helpful and informative at any time in the learning process, even after you have the piece at or near performance level.

1. Become familiar with the key but playing the associated scale in both hands.
2. Look over the whole form. Where are the section endings? How is the music being manipulated by the composer? Is it theme and variations, sonata form, rondo?
3. Identify the predominant harmonies and get them into your hands since reading vertically is often the tripping point.
3. Practice the first section painfully slowly but perfectly. Pay as much attention to the rhythm as the pitches usually get. It's counter0intuitive but practicing slowly is the fastest way to learn a piece. If you skip this step, you will take twice as long to learn the piece.

Hope this helps!