Thankyou for taking the time to respond in a way that sticks to topical points in a civil tone. Can I politely request in advance that, as I'm about detail points which are logically raised by your own, you appreciate that this is how two-sided discussion functions (rather than some outrageous cheek to your person)?
The whole idea about tapping is the sequence between "idle" relaxation->very short and precise attack->immediate return into stand-by "idle" position. It is very important to take time between those to get the feeling of each state of the hand. What you do instead is just repeatedly slap your finger with your LH. What you want to accomplish with that?--I have no idea.
Well, the first clue should probably come from your words "immediate return". What better way to check for immediacy than actually tapping fast? How would a slow tap then nothing check whether the finger is finding a position in which it is properly in stand-by? And if by "idle" you mean a position in which it's not readied, what relevance would it have to fast repeated notes- in which you need the finger ready for another motion in the instant it has finished sounding a note? That requires a proper link to the key. The point is to check that the stand-by is not "idle" but "ready" against the key, still. I do conventional tapping of each finger through pieces plenty, by the way. The point there was to test something that a single tap simply does not actually test. If a finger is not poised well, it droops and gives a flaccid energy transfer during a tap. Repeating taps quickly help the finger to fine-tune itself properly, so as to become an extension of the key, rather than be limply disconnected and thus incapable of passing on fast motions. The point is to find the state where movement is not wasted on drooping, but goes straight to the key. For that, there's no better test than faster repetition.
I also use a non-tapping exercise in which every finger plays twice. It was said to have been used by numerous great pianists of the past (and comes via Ronald Stevenson, who personally knew many of the greats, including Paderewski and Grainger). If a finger starts in a truly idle position (without joining itself to the resistance of the key) it functions so poorly under the pressure of two instantaneous attacks, that you quickly learn where holes are. I'm not going to write off any individual variants as "wrong", but if you wish to do so regarding faster repetition, it would be worth first asking how a series of very slow attacks are going to do anything to check whether the finger has found a suitable state from which to perform both efficiently and quickly. I'd still very much like to know the specific reasons for your blanket dismissal.
I have no dispute with any of your points about the rhapsody and that is indeed what I'm aiming for. However, you didn't detail any specifics about how to achieve these things and, above all, you didn't give any reason why checking that a finger can transmit energy to the key at a rapid rate would somehow be a "wrong" (your word) way to prepare for the requirement to do just that, within those octaves.
As I said, the film wasn't claiming virtuosity. It was to show how tapping improved the alignment of the 5th finger to the key. The results were certainly imperfect, but compare to this:
I'm not going to claim it demonstrates virtuosity, but in terms of the sound, this what I can do with a properly regulated instrument (as opposed to an antique upright with very sluggish repetition). However, note the even worse wrist position of the right hand and note frequency of a flaccid, drooped 5th finger (notably at 5.10). That's what come of being truly "idle" rather than properly connected to the key. I have a physical issue that makes it physically very difficult to achieve length down the fifth finger side of the wrist and to stop the knuckle sagging. I have all manner of grinding, clicking and popping sounds when trying to open out my hand. There is a great deal of internal resistance to finding what is simply the "normal" place for my left hand to align. What I was showing on the other video is how much better the wrist can go on to align after using tapping on the 5th, to show it how to be more ready. The hand learns to realign itself, so both wrist and 5th finger are better poised to pass movement to the key. You can see in the tapping film that the hand actually managed to find length down the 5th side (at least some of the time) rather than be trapped into a permanently bunched position.
It's simply a fact that if your biggest problem is a limp and underactive finger, trying to be more passive is not the way to prepare. Passivity is the problem, and it requires a more active connection to the key- so it doesn't feel like trying to play through a piece of sponge. Any follow-up thoughts are more than welcome, but I'll politely repeat the request to keep it civil and on-topic.
Topic: Tapping explanation