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So as I've been going through my long and hard process of learning to practice properly and efficiently this semester, it's been almost entirely with pieces I already had the basic feel for under my hands [could play through most of the composition HT slowly]. But now, as the semester comes to the close, jury pieces are prepared, and I look to the future, I am beginning to start my new set of pieces. So I'm starting to enjoy putting my new practice habits into full swing and finding I learn music a lot quicker now, but I definitely still have a ways to go.

So, with that said, I'm curious to see what do YOU do when you pick up a new piece? What are your "steps" and how do you ensure efficient learning of the music?

When it's "business" stuff - that is, some piece I don't want to play, usually a lousy accompaniment part for a low-grade song, I'll talk to the piece and be mean to it, and mock it. For extra-bizarre insight, sometimes I do it in the terribly bad Russian accent John Malkovitch took on for his role as KGB in the movie, "Rounders." Something like, "Oh, doubling here? Yes, you feel very brave and you won't-be-pushed-a-round."

Any piece I decide to work on starts out like this, I play as fast as I can without making a mistake. That translates to playing very slowly without making a mistake. It may not sound very musical at first but the tempo does increase ... eventually.

Also, since this can be tiring for the mind, set a limit as to how much you decide to work through in one session ... eight bars? ... 16 bars? ... one whole page? ... two pages? It helps to set an initial goal.

Slow and sure.

Fingering (it's shocking how many editions--especially the older ones from 19th century--have just god-awful fingering suggestions!!)

More fingering while learning notes; perhaps re-distribute some notes to the other hand, or re-group the notes in big chords.

When I can play the piece through continuously with a metronome, revise the fingering again.

Finally, when I can play it up to tempo, revise the fingering again if necessary.

Analysis, interpretation, and all that important "musical" stuff come later. I want to get the technical stuff out of the way first.

I read through the music first, mentally playing it in my mind (often with my fingers twitching involuntarily) away from the keyboard, and noting the potential trouble spots, where the melody, counter-melody etc is. Usually, if there is fingering given in the score, I'll also have some idea of whether it generally suits my type of hand (which is of course unique ) or whether I'll have to disregard it totally.

Then, I'll sight-read it (though technically not really sight-reading, as I've already looked at the whole piece) through from beginning to end, slowly but not so slowly that the musical flow is lost. And I don't worry about wrong/missed notes at all, though I make mental notes of the places where I go wrong or have to fudge my way through. Then I'll think about whether I need to write some fingering down (in addition to, or in place of what's in the score, if any) or whether it's already obvious. Then I decide how I want to learn it - in sections, or all at once, and whether I want to memorize it (or whether it's worth memorizing).

That's assuming, of course, that I do decide that it's worth learning.....

I usually start with the denser, more difficult bits.

With regards to choosing a fingering, I think it's quite important to try to play things up to speed quite soon after learning them, at least in isolation. I'm convinced a lot of the 'bad' fingerings one finds in scores are the result of their being devised at a slower tempo. It's important to get a feel for what will work at full speed when learning something at a slow speed.

My son and I have completely different approaches. I like to read through the music to see where I feel most comfortable and to pace myself. I like to listen to a variety of recordings by performers I respect. Once I have the big picture, I start with the real work, which begins by memorizing and then filling in details - measure by measure, slow practice, lots of repetition. I love getting new pieces.

My son does not like to listen to recordings. He starts at the beginning and practices a little bit at a time, very slowly, measure by measure then line by line (sometimes beat by beat) - if it is Baroque, he will play hands separately and figure out the voices. He struggles with memory, but he gets the details filled in. He hates the beginning part of learning a piece, but thrives once he has the whole piece down and memorized.

He is the better pianist of the two of us because he learns the details as he goes along, while I fill them in later.

I think my way is more in line with your sons. I practice slow, and it seems like it'll be forever for a piece to start clicking, but once it clicks I bring my pieces to performance level really quick, because I learned all the details while memorizing & practicing notes.
Also your son and I do the EXACT same thing for Baroque music. I finally began serious work on my bach Fugue this last week and I spent forever playing individual voices inbetween hands, then super slow hand separate to really listen for the balance of voices. It's tedious, but I know that in another couple weeks I'll have a nice little figue to play!