Here is a factual presentation of how the sound is produced inside the piano:

(1) In order to produce sound, we need energy to deliver to a metal string so that the string can vibrate. Inside the piano, each string is tuned to a primary pitch which is the fundamental tone for that string. But when the string vibrates along its entire length, it also vibrates in segments, producing a series of overtones or harmonics.

(2) Depressing a key in the keyboard causes a series of actions inside the piano that eventually throw the felt covered hammer towards the string, thus causes the string to vibrate producing sound (primary pitch and overtones) . After the sound is produced, the hammer rebounds immediately and a damper will move forward to shut down the vibration if we don't hold it off.

(3) Everyone from high school knows that there are two kind of energies: potential energy and kinetic energy. The main source of energy that the hammer carries is the kinetic energy when it is being thrown or activated. (the potential energy can be ignored here because the hammer can not move vertically anyway.)

The physics formula for kinetic energy is:

                KE =   1/2 mv*v

                where:   KE - Kinetic Energy

                               m - mass (in this case, the mass of the activated hammer)

                               v - velocity (in this case, the speed of the activated hammer)

(If you do not have a scientific background, don't be discouraged. Just get the result and move on. For those with a scientific background, you are welcome to discuss this matter with me.)

(4) Since the m (the mass of the activated hammer) is a constant here, we are not interested. We are only interest in the v, which is the speed of the hammer hitting the string. Notice that the kinetic energy changes with the square of the v. That means, a slight change in the v will result in a larger change in the volume of the sound thus the tone quality. For example, 10% change in the v will cause approximately 20% change in the volume (1.1*1.1= 1.21), 40% change in the v will cause the volume almost double! (1.4*1.4= 1.96) It is good to know when you play the piano.

(5) Furthermore, the sound is produced before the key reaches the key bed. You can experiment it on the piano by depressing the key slowly. You will hear the sound before the key reach the key bed.. Once the sound is produced, the hammer rebounds immediately and the sound diminishes gradually. Nothing in the earth can change the piano sound after it is produced. (manipulate the damper can affect the tone quality, but it is beyond the scope of this article*). It is not like the violin in which the player can use the bow to improve the tone or the singer can use their breath to change the volume. Pressing against the key bed after the sound is produced is most stupid, it is a bad habit, a waste of energy and it causes fatigue. We need to relax our muscle immediately after the sound is produced.

(6) There are only two cases that we need to hold the key down after the sound is produced. (but please be relaxed, holding the key down does not require any muscular effort, just use the weight of your arm.)

1. In the case that we need to hold the key down to keep the damper off the string, thus prolong the sound.( but it diminish gradually anyway.)

2. In the case that we need to use the key bed as the floor for another finger to reach the next key.

The facts presented here may puzzle some piano players, because traditional thinking is that the more force you use, the bigger the sound. Some piano players habitually press the key after the sound is produced. Some used to forcefully strike the key causing too big the v, thus generates unwanted overtone resulting in unpleasant, harsh sound.

Conclusions:

Based on the above factual analysis of the actions of the piano, we come to the following conclusions:

1) Nothing can change the piano sound after it is produced. Pressing against the key bed after the sound is produced is a waste of energy and causes fatigue. We should relax our muscle immediately.

2) The volume of the sound produced is proportional to the square of the v, the speed that the hammer hitting the string. Too big the v will result in harsh sound which we should always avoid.