Category: vectors

vectors; counter vectors; and brilliance in playing

practicing notes 9/22/21

If an object is experiencing two equal and oppositely directly forces the net result is an absence of movement on the part of the object. But this is not a static state for the object, for in at any moment in time if one of the two vectors varies in strength, there will be a sudden motion in the object, in the direction of the force that is now relatively the stronger.

I’ve used this principle everywhere in my playing. It is a way of applying two opposite intents to a single situation, to control the balance in any sort of blend of factors whether they are physical, emotional or temporal. It is a way of building up tension until, at the moment of release, there is a sudden overpowering burst of energy*, that will accomplish feats of speed or distance, for instance, that could not otherwise be achieved through a one
directional intent towards being faster or travelling farther.

It is like watching, from a viewpoint on the side, the motion of the rope in a tug of war. Pick a point along the rope, somewhere between the two teams, and you will see it almost quiver with motion that seems, like racers just before the starting pistol fires, both about to happen and restrained.

Or like the escapement of a watch, rocking back and forth, and in so doing parcels out the energy of an unwinding spring in short gradual stages, that suddenly breaks down, allowing all the remaining energy to release in a brief moment. “Things fall apart; the centre cannot hold” (Yeats: the Second Coming). In my practicing today I am trying to enact the  vector/counter-vector principle in a very fast, and very specific way, that  effects the micro movements of the fingers.

First I try to rotate my hand and forearm, ever so slightly clockwise.  But as  soon as I do that I create a strong counter force arising in a    counterclockwise direction, thus limiting the former clockwise motion to a few degrees. If the counterclockwise force has complete stopped the clockwise rotation in the hand, I generate a counter-counter-force in the  clockwise direction, as a way of trying not to loose the albeit tiny gain already achieved in that direction. This effectively halts the counterclockwise motion so that the motion in that direction is kept to just a few degrees. Sort of like being “between a rock and a hard place”. The forearm is trying to rotate in either direction but has barely any wiggle room. I try first one ay then the other and gain minimal ground in either direction.

This contest goes on at a sufficiently fast rate that the hand seems to vibrate or quiver back and forth, irrespective what the fingers are doing to  enunciate the notes of the piece being played. The result is that the fingers are themselves, as an extension of the hand and arm, are never quite striking the keys downwards, vertically, but at a slight rotational bias one way or the other. It is that combination of motion and resistance that then affects, on an instant to instant basis, every move I make, not only with the hand but with the actual five fingers themselves.

* in this regard it dovetails with the principle of a “spring” which, along with vector/counter-vector, is a basic feature of my technique. In a ‘spring’ something is rotated or moved a distance that is beyond its normal fetch.

I am using ‘fetch’ in the sense of the distance a wind blows unobstructed  over water, esp. as a factor affecting the buildup of waves. As the wave hit the shore its store of energy is released suddenly and dramatically.

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Externally applied forces (arpeggios)

J.M.’s lesson: an arpeggio going upwards in the left hand.

I sit to her left. Not very close. I don’t have to be on the piano bench, I can be on a nearby chair. As long as it is close enough to her body to be able to  reach out with my arms and make contact with her left arm. My purpose is to use my arms to lead and guide her playing arm as it moves rightwards through the arpeggio.

Joe to J.M.: I am pushing your arm to the right, but my arm stays ahead of where your left hand is. It is actually trying to push your arm so that your hand is ahead (to the right) of where it needs to be situated to play the current note of the arpeggio. I’m pushing your arm ‘ahead’ of the progress of the arpeggio, giving your hand the feeling of having to constantly catch up with your arm.

I am really trying to create a vector- counter vector situation. For, while at the same time I am trying to have your hand experience how far to the right of its currently located position it is being asked to be, on the other side your job is to have your fingers nonetheless adhere to the surface of the keys that they are playing in such a way that is strong enough to resist the motion I am trying to apply.

However, the stronger your finger sticks to the note, the stronger I’ll push, until eventually the contest isn’t equal any more, and your hand unintentionally shifts / jumps to the right, faster than it could do so if you were using just internal muscles in your arm and body.

Were it not for your adhering to the current notes I might fling your arm helplessly off the keyboard, but because of your counter-vector, when your arm does move, it moves in a controlled manner but at a faster speed than at which it can normally travel. It is this extra momentum that allows the  fingers to make all the difficult connections from one key of the arpeggio to the next, just beyond the limit of their pliability (such as the pliability of the thumb trying to pass under the rest of the hand).

If both forces remained absolutely equal, then we’ll never get to the next note of the arpeggio. You have to know just how long to hold onto the  current before suddenly acceding to the force I’m applying.  This ‘drama’ is re-enacted quite a number of times over the course of the full arpeggio.

For a moment your fingers and hand will fly ‘helplessly’ to the right until your fingers can reestablish contact with the keys. Like a mountain climber who lurches upwards or falls back lower until they can find a place to  reestablish their grip.

The part of this procedure which has to do with staying on the key surface is also the part within you that wants each note to be sonorous. The part of the procedure which has to do with being moved off the key by the external force is the part of the procedure that creates the flow and dynamic sense of shape and motion of the arpeggio.

Ultimately you have to create both of these contesting forces by yourself  from within your body alone. By my doing it to you first, your body ‘learns’ what it feels like when subjected to both pressures. After the learning period it can recreate that (combined) sensation on its own.

Whatever is done to you externally, it produces an inward sensation on the muscles within the body. When there is such an inward sensation, with a little effort of imagination we can recreate the exact same feeling, even without the physical cause from outside. And we can do this without without knowing just which muscles to try to move or by how much.

It is just a conscious (but complex), unified body state. It’s hard to form a static concept or visual image of how both of these parts act within you. On the one hand it may include the self same muscle enacting a synthesis of  both forces. Or the other hand it may be the result of ‘tuning’ two different muscles together.

I do it to you first, so that your body can learn to “remember” and reproduce the sensations it felt when being pushed from the outside.  At the same time your body must plant each finger on its note as if it would permanently stay there. You will create a dynamic equilibrium which then cedes to another dynamic equilibrium.

If we liken the process of playing the piano to that of acting in a play, then one part of this state will be enacting the character saying “come on already, it’s time move to the next note” while another part is enacting the role of the actor who says: “hold on, I’m not ready to come off the note yet, I’m enjoying the sound too much”. The result is a brilliant, smooth, and accurately executed arpeggio.

By having the teacher change their position relative to the student, including from which side of the student’s body the teacher locates their body, this procedure can be repeated just as easily for a downward arpeggio of the left hand (teacher is on the right side of the student’s body), an upwards arpeggio in the right hand (teacher is on the left again), and a downwards arpeggio in the right hand (teacher is back on the right). The distance from the torso of the student has to adjusted in response to whether one is pushing the student’s arm nearest the side from which the teacher is pushing, or pushing the student’s arm that is on the other side of their body from the side from which the pushing is occurring.

In most cases that involve difficult technical situations on the piano, it’s all about vectors and counter vectors*: forces in one direction, countered by forces in other or opposite directions.

* A vector is a combination of a measurable direction and a measurable quantity .  “I am walking northwards at 3 miles per hour”.


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