What is tone? Tone is the natural sound of the instrument - the primary pitch plus the overtones (harmonic series), combined with the performer's particular technique of playing.

The tone of a piano is affected by a number of different factors. Firstly, there is the piano itself - different makes, different model or sizes of piano have different tones. Secondly, a piano, like any instrument, can sound like a different instrument in the hands of different players. The better the pianist the better the tone. This is because tone is more than something determined by fixed acoustical properties of the instrument itself, it is also determined by the touch habits of the piano player.

Why the tone is determined by the touch habits of the player? As we have discussed in The Piano, the overtones that a metal string generates depending on the speed of the activated hammer. The kinetic energy of the hammer is transmitted from the energy that the piano player delivered to the key. Depressing the same key from different height, with different speed or weight produces the same primary pitch but also produces different overtones resulting in different tonality.

To present a theoretical analysis of the tone, we start with the energies that produce the tone. For those who don't understand the formula, skip it and just grasp the results and apply them to your piano playing.

The Energies Generated by the Key Descent:

There are two kinds of energies: Potential Energy and Kinetic Energy, the first is the energy due to the position of the object; the latter due to the movement of the object. Their familiar physics formulas are the following:

Potential Energy: PE = mgh

where:   m mass ( in this case: the upper arm, forearm, hand, finger, etc)

             g gravitational acceleration (it is a constant!)

             h high (in this case: the distance between the hand and the key surface)

Kinetic Energy: KE = 2 mv*v

where:   m mass (in our case: the upper arm, forearm, hand or finger)

              v  velocity or speed ( in our case: the speed of key descend)

As we know, g is the gravitational acceleration. since it is a constant, we are not interest in it. We are only interested in the variables : m, v and h. By changing them , we can produce a wide arrange of sound and tones out of the piano, raging from pianissimo to fortissimo; from the softest, warmest to the loudest, hardest.

The h, m and v are briefly mentioned in the "Art of piano playing"by the famous Russian piano pedagogue Heinrich Neuhaus, but it is not clearly defined there. With my physics background, I try to define and discuss them here:

The v and h are somehow related.

In Slow to Moderate Tempo:

We can utilize the potential energy, let the weight of different parts of our arm freely fall from a certain h (not too high!) only by the force of gravity alone without any muscular effort. The potential energy is the main source of energy in this case. The higher the h, the greater the v, thus the greater the sound. Because the energy generated by this v is transferred to the hammer's kinetic energy resulting in the greater speed of the hammer hitting the string. However, this higher h only applied to a slow to moderate tempo.

In Fast Tempo:

The v not only can be generated by the h but also can be generated by the muscular effort which is the main source of energy in a fast tempo. When we play fast and loud , there is no time to waste on the higher h. We need to play close to the key. In order to generate the v, we throw our hand into play position with the help of our upper arm, forearm and the wrist, just like a whip (see The Pianist and The Technique). The shoulder joint is the handle of the whip, the fingers - the tip of the whip. The kinetic energy of this v is generated by the contraction of the strong shoulder and chest muscles and is transferred to the hammer's kinetic energy.

Sometimes the h would become zero. Especially in playing big chords, we place our hand on the surface of the key and suddenly contract some of the strongest body and arm muscles- A press (push) against the key bed (just for a split second, please!) This can cause the great speed in key descent thus the great speed of the hamper hitting the string.

Extreme h and v will cause the string to generate unpleasant overtones, thus resulting in a harsh sound and poor tone quality. Some piano players habitually strike the key. The sound produced by this habit is harsh and not agreeable. We should always avoid.

The m:

The m could be the weight of our upper arm, forearm, hand, fingers or any combined, blended muscular activities. Smaller m generates softer sound, bigger m generates louder sound. There could be different combination of our four components (see The Pianist ). Sometimes we feel that our arm is heavy and the fingers are firm and passive; Sometimes we feel our arm is light and passive, like floating in the air and the fingers are active. etc.

CONCLUSIONS:

Based on the above theoretical analysis of tone, we come to the following conclusions:

1) When the m is big and the v and h is small, you produce a rich, deep, sonorous sound like the sound from the big church bell; When the m is small and the v and h are moderate, you produce a vivid, pearly sound like the sound of the little bell; when the m is big and the v and the h are high, you produce a loud, harsh sound like a bang.

2) By varying the m, v and h, We can literally produce a wide range of volumes and sonorities, create nuances and dynamics in music. Of course, we need to practice, experiment it on the piano consciously and distinctly.