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WieWaldi Everything is true what you wrote about LH and RH. And I am very aware of it. I was just simplifying it, because most of the time the LH plays the bass clef and the RH plays the treble clef.
The problem with this kind of simplification is that it suggests what you understand and hold to be true. I'm not sure that I agree with the "most of the time".
WieWaldi And suddenly piano players are forced to read the treble clef on the lower staff. Most piano player are not used to do it.
This points to a major flaw in how music is taught. That situation should not exist. Here we're back in the world of teaching. For the last statement, most pianists would be used to it because it happens all over the place. But above all, we're getting at teaching flaws. That is a different topic.
If your system allows for the fact of what actually exists in music, namely that either hand can play anywhere on the keyboard, then all's good.