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This article is from the Piano Playing from Memory FAQ, by Isako Hoshino rmmpfaq@yahoo.com with numerous contributions by
others.
3.6) Working backwards (Piano Playing from Memory)
The famous 19th Century teacher Leschetizky taught memorization by
having his students learn pieces a part at a time starting at the
end. They would first memorize, e.g., the last measure, then the
next to last, then play them together (in order), etc.
Learning in reverse probably increases your ability to begin
somewhere in the middle of a piece if you need to do so. The time
you need to do this is when you have had a memory lapse while
performing and you must recover and carry on.
Another advantage of learning in reverse is that, since many
pieces are more difficult toward the end, you spend more time
practicing the more difficult parts. Always starting over from
the beginning while integrating all the parts you have learned up
to now results in devoting the most time to practicing the easiest
parts!
An alternate approach is taken by Charles Cooke in his book
"Playing the Piano for Pleasure." Cooke advocates learning the
most difficult passages first, even spending so much time on them
that they become the easiest parts to play.
 
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