Keeping the fingers constantly on the keys reduces the distance each finger must travel, hence increasing the speed.
er ... no, it doesn't. Keeping the fingers always on the keys actually
increases the "distance" that "each finger" travels because a preparatory motion is necessary in order to make a sound.
Even though I used to teach like this (fingers glued to keys), it's actually an absurd concept. Approaching the act of playing the piano as though you will play with your "fingers" is not going to cut it in general (it's like approaching the acting of walking as though *only* your toes are going to propel you along (hee hee ... that's a funny image

)), but also, approaching the *act* of playing as though your "fingers must be glued to the keys" is like approaching the act of walking as though your feet must be glued to the ground. That's just
not the point and it's missing the point entirely !
The point is
motion and utilizing which motion will provide us with the greatest facility for a given circumstance. If, for example, you lived where there were constantly ice on the ground, you may develop a shuffle in your walk. Why ? Because there is ice on the ground and you don't want to slip and crack open your head ! The motion serves a direct purpose and is therefore the most efficient for that particular circumstance. However, using an icey-ground-shuffle when you are being chased by a lion is not going to get you what you need (it will get you dead and with chunks of you stuck inside of lion's teeths and eventually coming out the other end of the lion ! And maybe even several other lion's ends since they live in prides. Who wants that ? Do
you ?! I dont' think so !). When the lion chases you, you need bigger motions and the last thing you are thinking is how close your feet are to the ground !
Different passages will require different uses of the apparatus and one can simply not approach every piece (and the entire concept of playing in general) with the greatest facility as though the key to piano playing is all in keeping one's fingers glued to the piano ! Sure, maybe some "great" pianists appear to be doing this, but if they are truly great, they are doing it only because they
need to be doing it for whatever they are
doing !

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