# Sometimes Geometry Helps

How to get from one place to another on the keyboard.

First of two entries:

The line “subtended” by a small angle can be very long.

The two-dimensionality of the keyboard discourages us from thinking in three dimensions instead of two.  Getting from one location to another on the keyboard requires a motion that is as much up and down as it is side to side.

First, a geometrical digression.

An isosceles triangle is one in which two of the sides are equal in length.  There is no limit to how long or short the two equal sides can be.

Imagine an isosceles triangle in which the angle at the top is  where the two equal sides meet.  Imagine that the top angle being very small.  No matter how small this angle is, if you make the two equal sides long enough, the distance between those two sides will grow larger and larger.  And if the two equal sides are long enough, the horizontal base at the bottom of the triangle can be as wide as you want. For instance, several octaves on a piano keyboard.

If I need to displace my hand from where it is on the keyboard to a position on the keyboard remote from it, I try to be conscious less on a left to right motion and more of an up and down motion in the ‘third’ dimension.

My hand travels upwards first, rather than right or left, until it reaches the imaginary vertex at the top of an imaginary isosceles triangle.  Once at the vertex, I start to come back down, but on the other of the two equal sides.  At the vertex I make a very small and subtle change of angle.  It almost seems as if I am coming down the way I came up, but as I get closer and closer to the keyboard (the horizontal base of the triangle), I find that I am going to land in place on the keyboard a sizable distance from where I started.   This has been accomplished without almost any conscious sense of sideways displacement.

In a previous blog I spoke of imaginary motion versus actual motion.  Mirror neurons allow us to feel as if we are making a motion even when to the outside world we seem to remain motionless or nearly motionless.  The motion upwards to the vertex angle in the isosceles triangle can feel as if you have traveled upwards quite high with your arms before starting to descend – only the outside observer will not see much motion.  Your muscles however will be engaging as if doing the larger motion.

Sometimes it is necessary to escape into a third dimension, so that when you return just to the two-dimensional horizontal plane of the keyboard, it is “pregnant” with the mobility of having been in three dimensions.

This motion is an example of a more general heading of motions that help break out of the two dimensional confines of the keyboard.

Item Two:

The principle of the lighthouse.

Think of the beam from a lighthouse sweeping the horizon as the light rotates on a vertical axis.  While the part of the physical light itself that happens to be furthest from its axis describes a circle around the axis which is measurable in feet, maybe yards, the result of this limited motion allows the beam to travel across miles of distance along the horizon line.

Now, substitute the torso of the body for the light in the lighthouse, and the extremities of the arm as a horizon.  Rotational motion of the torso, measurable in inches, can cause the arms to travel along the keyboard a distance measurable in feet.

For any motion while playing, it is always best to find the point in the body that moves the least, but causes a motion of the hands that moves the most.  I learned this from my second teacher, Edwine Behre, who in turn learned it from Abby Whiteside.

# Practice Procedures: Part 17:  External Versus Internal Forces

When a movement of a part of the body comes as a result of the muscles in and around that part, I call the force generated ‘internal’.  Alternatively if the left hand takes hold of the right hand and causes the latter to move in some way, the force applied to the right hand is ‘external’ to the point on the right hand where the force is applied.

The motion in the right hand now has a very different physically sensed quality than a force coming from the right side of the body.

The advantage of one hand moving the other is that the hand being moved feels stronger, more agile in its motion, than it would using only its own muscular initiative.

Any point on the playing mechanism can be the point of application for an external force that imparts motion to the point.

The objection might be made that, in performance, one hand cannot take hold of the other when both hands are on the keyboard.   The objection is overcome through the existence of “mirror neurons”.   Here is a definition that shows up on google.com when I search for “mirror neuron”.

“A mirror neuron is a neuron that fires both when an animal acts and when the animal observes the same action performed by another. Thus, the neuron “mirrors” the behavior of the other, as though the observer were itself acting.”   Thank you, to Google.

As a corollary to this definition, even if the model for the movement is not visual but tactile,  in other words,  even without the actual intervention of the left hand to cause the motion in the right hand, we can ‘recreate” the sensation that occurred in the right hand when it was physically being moved by the left hand.

Rather than another part of the pianist’s body, sometimes the teacher will create the external force to move the student’s right hand.  The only advantage of the teacher making the motion rather than another part of the student’s body, is that the teacher may have a more experienced and refined sense of when, where and how, to apply the force.  But the student can still repeat the action, in all its details, because they have just experienced in their bodies what this combination of motions feels like.

# Practice Procedures – part 5:  ‘Blob’ And Deflect

A strong force initially applied in one direction can be deflected into another direction.   For instance the downward force which benefits from the force of gravity can be deflected, without loosing momentum to a force to the right.  To initiate a rightwards force from an initial location on the keyboard will inherently be weaker and less productive than a rightwards motion that comes as a prolongation of a stronger downward force.

In the case just given, a strong motion downwards takes place towards the keyboard by the arms.  When the hand is about to make contact with the keys, or when the hand has just barely made contact with the keys, the motion can be deflected to the right.  This way the original momentum and impetus of the force is not broken or diminished in any way and continues unabated into the lateral motion.

# PLAYING WITHOUT ANY PAIN OR DISCOMFORT: part six

Second Experiment continued:

2E.

Once you can play two adjacent notes, using one of the two second fingers on each note, with the feeling of one melded hand, you can experiment with separating the second fingers further and further apart, without losing the sense that the fingers are still superimposed, the hands still linked, and no difference in sensation in one arm versus the other.

One can do c-d for a while then experiment with c-e for a while, c-f, etc..  Later one can try doing fewer and fewer iterations of each pair of notes before enlarging their mutual distance.  Eventually you can do only one iteration of each: c-c c-d c-e c-f . . . . as far as you can go and retain the original sensation of oneness.  Once you can do it in an organized pattern, one can experiment with a more random sequence of notes, wherein any change of horizontal distance is rendered unconscious and the inertial sense of  conjoint hands persists without even slight moments of alteration.

Whatever the objective distance is between the two second fingers, subjectively one still feels a tangible connection between them: a shunt, a cross piece, connecting rung if a ladder, that holds together the two vertical sides of the ladder.  So that activity is  never felt as happening in one hand or the other.  That even if you tried to notice a difference you could not ‘find’ it in your inner sensations of the muscles (a little self  hypnosis is useful here).* Even the ‘location’ of the sensation of playing, is in the  imaginary cross piece.  This cross piece always completes the circumference of the circle which originally without interruption and unbroken at any point along the circumference, and which should still be felt so.

*To help with the feeling of the connecting rod, place a pencil or other thing and long object over the two hands, and create the feeling the sounds are being made by the single vertical action of the pencil and not by the separate parts of the anatomy.

# TRANSLATION OF AXES

Originally posted on Facebook on 2/4/16

Sometimes, when we have technical difficulty doing a particular series of notes in the horizontal plane of the keyboard, we can remove some of the difficulty by changing this horizontal axis into a vertical axis that goes up and down from the keyboard rather than side to side.

We need only to repeat the same series of muscular gestures that we would have made in order to play the passage on the horizontal keyboard, but now executing them in a vertical plane. The sensations in the muscles will change in character.

These changes are due to the reorientation of the hand muscle movements relative to the pull of gravity. They are also due to the fact that the measured distance of the hands from torso, instead of varying when moving left and right on the keyboard, now remains fairly constant.

Just wiggle the fingers in the air, first with the palms down, and then with the palms sideways. Attentive introspection will show that the sensations are different. And not only in the fingers but throughout the arm lever.

The key here is not that the gestures are easier or harder in one orientation versus the other, although that too is probably true. It is simply that the sensations are different, and our hand and fingers feel them afresh, in a new light.

We can then go through the same series of motions that we would on the keyboard, the same series that we would enact on the keyboard horizontally, but do it in the air with the motions, now ranged up and down from each other than side to side.

Once we do this, if we then return to the horizontal plane of the keyboard, we will find that we have more facility doing the passage. Things feel fresh, new and different, and the feeling lingers through the return to horizontality.

There are many applications to this spatial reorientation which we will describe in more detail in later blog entries. Among these are arpeggios, repetitive triads played as a sequence of three melodic notes, trills, and broken octaves.