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There are various historically important or well-known piano training methods or schools (“schools of thought” as opposed to institutions, which are not the focus here):

• The Leschetizky method
• The Russian school
• The Suzuki method

Perhaps others...?

What are the principal distinguishing characteristics of these methods?

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I'm not sure these are really the methods you're after, but they seem to be really important for piano:

According to the introduction to the Bach Essay it was called by Haydn "the school of all schools."

The Cortot was recommended to me a long time ago by someone I knew who was a concert pianist.

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  • Although not quite what I'm after, I do think it's useful, especially a few comments on the nature and significance of those "methods".
    – Aaron
    Dec 30 '20 at 22:05
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There is a wonderful book called FAMOUS PIANISTS AND THEIR TECHNIQUES by by Reginald R. Gerig.

But be warned that you should not work on anything your read in this book without the assistance of a knowledgeable teacher for some of the movements without other movements can hurt you.

For example, Bach taught his students a "scratching" technique because that is what he felt when he played. In reality what was happening was as he was moving in, out, up and down, his fingers were caressing the keys as he lifted up and out in order to move back in and down (because our fingers are different lengths). Some of his students harmed themselves scratching the keys rather than allowing the caressing to be a symptom of the other movements. The problem with most techniques is that they have been developed, defined and delineated but what people felt or saw rather than what was actually happening invisibly within the arm. You don't learn technique by watching someone's fingers, you learn by watching their arm.

Otherwise this book is an excellent resource and historical analysis of how techniques evolved. BUT BE WARNED AGAIN THAT THIS IS NOT A TECHNIQUE BOOK, only a reference to what others tried, for better or worse. Virtuosos make the worse teachers because effortless playing comes naturally to them and they don't know how or why they play the way they play, they can only tell you what they feel which is not always what they are doing.

It is like, if you have cramps playing tremolos, a stupid teacher will say you have to relax. A knowledgeable teacher will say "relax these muscles and rotate from the pronator and supinator." You can't just relax, you must replace it with something. In order to play the piano, something must be moving but . . . what? It is not always what you think you see or feel.

An analogy would be someone who can drive a car but has no idea how any of it works. I took lessons from a great pianist named Stanley Hummel who in hindsight I realize he had no idea what he was doing. He was a terrible teacher whose goto answer was practice more or "watch me." Practice WHAT? Many of his students played with a lot of tension, mediocrity and many incurred injuries. To this day students from his studio are plagued with pain, fatigue and sloppy playing and it is too late for many of them because improper movement is now hardwired into their brains. Beware this book and beware virtuoso teachers. I see there is a new edition. Hmmmmm . . . . Check your local inter-library loan system.

https://www.amazon.com/Famous-Pianists-Their-Technique-New/dp/0253348552

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