Graded Response Muscular Contraction

For the piano teacher, the important phase of muscular contraction is that graded reaction actually exists, and that the degree of response varies directly with the intensity of the stimulus. We know that graded response is possible either by gradations in the reaction of a single muscle or by a coordination between muscles.
In the module on Mechanical Principles, a force was shown to depend upon 1) the speed and 2) the mass of the moving body. So long as the number of muscles acting at anyone time remains a constant (these, with the weight of the moving part constitute the mass), variations in force can result only from variations in speed or acceleration, since the force equals the product of the mass and the acceleration.

F=ma
Force=mass X acceleration

Accordingly, if an increase in the force of a movement be desired without changing the extent or spread of the movement, the speed of the moving body must be increased. And conversely, with the same speed, the same muscle can only produce one degree of force.

A second factor in grading muscular response is the 1) form or 2) shape of the muscle itself. The force which a muscle exerts is the result of

1. the size and
2. the number of its fibres.

The distance through which the muscle contracts is the result of the length of the fibres. The force of the muscle is measured by its cross-section.

work = force x distance 

Momentum is traditionally labeled by the letter p, so the definition is:

momentum = p = mv 

for a body having mass m and moving at speed v. Momentum is defined as the mass times velocity.

When the distance through which the muscle acts is a constant, the amount of work done, (that is to say, the force of the contraction) is determined by the thickness of the muscle, thickness being the dimension at right angles to the direction of the tissues and fibres.

When force is constant, the distance through which the muscle can move a body depends upon the length of the muscle. Short thick muscles function best for short, powerful, movements. Long, thin muscles can be used for less powerful, more extended movements.
When both an extended and powerful movement is executed, this demands a coordination of muscular action in which each muscle contributes its efficiency to the efficiency of the whole movement. This is discussed in detail under Coordination.

It follows, if a short, powerful movement be desired, that muscle must be innervated^[1] to augment the thickness sufficiently; otherwise certain other muscles must be used. A movement made slowly and then made rapidly, cannot involve the same muscular response, since greater force is required for the greater speed.
Thus, apart from effects of temporary and permanent physiological condition, the strength of a muscle depends upon the size of its cross-section. A thick muscle is more powerful than a thin one, other things equal. The extent or range through which a muscle acts depends upon the length of the muscle. A muscle of greater length naturally permitting more extensive contraction. A powerful muscle thus has a wider range of gradation than a weak muscle, because it may continue to function when the weaker muscle has already used all its force. The question now suggests itself:
Question: To what extent are powerful muscles desirable in piano-playing?
Any increase in dynamic range of action is desirable because it gives the player command over a greater variety of technical response. Not only does the muscle itself permit this increase, but the possible combinations with other muscles are likewise increased.
Experiment has shown, that a muscle does its best work with relatively light loads, although some investigators have found maximum efficiency at half the maximum load. Accordingly, if a work of eight units is to be done, a muscle capable of twenty units, will do the required work with greater ease and less fatigue than a muscle whose maximum power is ten units. An increase in power is not, in itself, accompanied by loss of sensitivity to fine adjustments.
The fact that the latter frequently accompanies the former results from the increase in tension which heavy work necessarily requires and from the added flesh resistance which accompanies muscular growth.
The more powerfully we play, the greater must be the articular ^[2] tension in order to meet the increased resistance.
But tension, as we shall see precludes accurate judgment of resistance, and, upon such judgment, all tonal effects on the piano depend. A mere increase in muscular strength, therefore, has undesirable as well as desirable results, so far as its application to piano-playing is concerned. Only when the increase in strength reaches a point at which, for the reasons given, it interferes with flexibility and finer adjustment, does it become undesirable. The normal pupil seldom reaches th is point .

A few illust rations will make this clear . A composition such as the Liszt B-minor Sonata, apart from any technical demand of dexterity, requires a considerable output of pure physical force. If the player possesses sufficient strength in the fingers and arms, he can distribute this in any of several economic ways. The player with weak fingers and arms, on the contrary, will have to be satisfied either with less pronounced dynamic effects, or with the utilizat ion of the shoulder and back muscles, a coordination that does not always facilitate the technical demands of the particular passage.
Similar conditions hold for compositions demanding sustained finger-work. If the fingers be sufficiently strong, the required dynamic gradations may be made without calling into play the larger muscle-groups of the arm.
In passages in which held notes against trill figures make arm-movement awkward, if not impossible, sufficient finger-strength is absolutely necessary, particularly if dynamic gradation be desired. In this connection a spread to the arm is often considered poor coordination, something to be avoided. But is not the spread nature's device for reinforcing the fatigued finger muscles with the arm muscles. At least , we never meet this muscular spread in similar short passages, or in strong fingers, where in both cases it would be reasonable to expect it, were mere incorrect coordination the cause.

[1]innervate: vt. [< IN¹- + NERVE + - ATE¹] Med.
1. to supply (a part of the body) with nerves
2. to stimulate (a nerve, muscle, etc.) to movement or action.

[2]articular: adj. [L. articularis} < articulus, a joint: see ARTICLE] of a joint or joints [an articular inflammation].