What is "Good Tone"?
Tone is the quality of the sound; it is a subjective judgment of whether the sum total of all the properties of the sound is appropriate for the music. There is controversy over whether a pianist can control the "tone" of each note on the piano. If you were to sit at the piano and play one note, it seems nearly impossible to alter the tone except for things like staccato, legato, loud, soft, etc. On the other hand, there is no question that different pianists produce differing tones. Two pianists can play the same composition on the same piano and produce music with very different tonal quality. Most of this apparent contradiction can be resolved by carefully defining what "tone" means. For example, a large part of the tonal differences among famous pianists can be attributed to the particular pianos they use, and the way those pianos are regulated or tuned. Controlling the tone of a single note is probably just one minor aspect of a multi-faceted, complex issue. The most important distinction we must make initially is whether we are talking about a single note or a group of notes. Most of the time, when we hear different tones, we are listening to a group of notes. In that case, tone is easier to explain. It is mostly produced by the control of the notes relative to each other. This almost always comes down to precision, control and musical content. Therefore, tone is mainly a property of a group of notes and depends on the musical sensitivity of the pianist.
However, it is also clear that we can control the tone of a single note in many ways. We can control it by use of the soft and damper pedals. We can also change the harmonic content (the number of overtones) by playing louder or softer. These methods control the timbre and there is no reason why timbre should not be part of tone. The soft pedal changes the timbre by reducing the prompt sound relative to the after sound. When a string is struck with a higher force, more harmonics are generated. Thus when we play softly, we produce sound containing stronger fundamentals. If the piano is played loudly with the soft pedal depressed, we hear an after sound with higher harmonic content. The damper pedal also changes the timbre by adding vibrations from the non-struck strings.
The tone or timbre can be controlled by the tuner, by working on the hammer or by tuning differently. A harder hammer produces a more brilliant tone (larger harmonic content) and a hammer with a flat striking area produces a harsher tone (more high frequency harmonics). The tuner can change the stretch or control the amount of detuning among the unisons. Up to a point, larger stretch tends to produce brighter music and insufficient stretch can produce a piano with unexciting sound. When detuned within the sympathetic vibration frequency range, all strings of a note will be in perfect tune (vibrate at the same frequency), but will interact differently with each other. For example, the note can be made to "sing" which may be an after sound whose volume wavers. Note that the importance of the after sound is often overblown because the prompt sound typically lasts over several seconds and most notes are not held that long. Thus most of the "singing" quality of sound from good pianos must be attributed to sustain, tone, and timbre, and not to the after sound.
Finally, we come to the difficult question: can you vary the tone of a single note by controlling the key drop? Most of the arguments over tone control center on the free flight property of the hammer before it strikes the strings. Opponents (of single note tone control) argue that, because the hammer is in free flight, only its velocity matters and therefore tone is not controllable for a note played at a specified loudness. But the assumption of free flight has never been proven, as we shall now see. One factor affecting tone is the flex of the hammer shaft. For a loud note, the shaft may be significantly flexed as the hammer is launched into free flight. In that case, the hammer can have a larger effective mass than its original mass when it hits the strings. This is because the force, F, of the hammer on the strings, is given by F = Ma where M is the mass of the hammer and a is its deceleration upon impact with the strings. Positive flex adds an extra force because, as the flex recovers after the jack is released, it pushes the hammer forwards; when F increases, it doesn't matter if M or a increases, the effect is the same. However, a is more difficult to measure than M (for example you can easily simulate a larger M by using a heavier hammer) so we usually say, in this case, that the "effective mass" has increased, to make it easier to visualize the effect of the larger F on how the strings respond. In reality, however, positive flex increases a. For a note played staccato, the flex may be negative by the time the hammer strikes the strings, so that the tone difference between "deep" playing and staccato may be considerable. These changes in effective mass will certainly change the distribution of overtones and affect the tone we hear. Since the shaft is not 100% rigid, we know that there is always a finite flex. The only question is whether it is sufficient to affect tone as we hear it. It almost certainly is. If this is true, then the tone of the lower notes, with the heavier hammers, should be more controllable because the heavier hammers will cause a larger flex. Although one might expect the flex to be negligible because the hammer is so light, the knuckle is very close to the hammer flange bushing, creating a tremendous leverage. The argument that the hammer is too light to induce flex is not valid because the hammer is sufficiently massive to hold all of the kinetic energy required to make even the loudest sounds. That is a lot of energy!
Note that the static hammer let-off is only several millimeters and this distance is extremely critical for tone. Such a small let-off suggests that the hammer is designed to be in acceleration when it hits the string. The hammer is not in free flight after the jack releases because for the first few millimeters after release the hammer is being accelerated by the recovery of the shaft flex. The let-off is the smallest controllable distance that can maintain the acceleration without any chance of locking the hammer onto the strings because the jack could not release. The flex explains four otherwise mysterious facts: (i) the tremendous energy that such a light hammer can transfer to the strings, (ii) the decrease in tone quality (or control) when the let-off is too large, (iii) the critical dependence of the sound output and tone control on hammer weight and size, and (iv) the clicking sound that the piano makes when the hammer shank bushing deteriorates. The clicking is the sound of the bushing snapping back when the jack releases and the shank flex takes over -- without the flex unwinding, the bushing will not snap back; therefore, without flex, there will be no click. Since the clicking can be heard even for moderately soft sounds, the shank is flexed for all except the softest sounds.
Can the difference in tone of a single note be heard on the piano by playing just one note? Usually not; most people are not sensitive enough to hear this difference with most pianos. You will need a Steinway B or better piano, and you will start to hear this difference (if you test this with several pianos of progressively higher quality) with the lower notes. Tone is more important for lower notes because the hammers are heavier and the lower notes contain more harmonics than higher notes. When actual music is played, the human ear is amazingly sensitive to how the hammer impacts the strings, and this tone difference can be easily heard, even with lesser pianos than the Steinway B. This is analogous to tuning: most people (including most pianists) will be hard pressed to hear the difference between a super tuning and an ordinary tuning by playing single notes or even testing intervals. However, practically any pianist can hear the difference by playing a piece of their favorite music. You can demonstrate this yourself. Play an easy piece twice, in an identical way except for touch. First, play with arm weight and "pressing deeply" into the piano, making sure that the key drop accelerates all the way down. Then compare this to the music when you press shallowly so that there is complete key drop, but there is no acceleration at the bottom. You may need to practice a little to make sure that the first time is not louder than the second. You should hear an inferior tone quality for the second mode of play. In the hands of great pianists, this difference can be quite large. Of course, we discussed above that tone is controlled most strongly by how you play successive notes, so that playing music to test the effect of single notes is clearly not the best way. However, it is the most sensitive test.
In summary, tone is primarily a result of uniformity and control of playing and depends on the musical sensitivity of the player. Tone control is a very complex issue involving any aspect that changes the nature of the sound and we have seen that there are many ways to change the piano sound. It all starts with how the piano is regulated. Each pianist can control the tone by numerous means, such as by playing loudly or softly, or by varying the speed. For example, by playing louder and at a higher speed, we can produce music consisting mainly of the prompt sound. And there are innumerable ways in which to incorporate the pedal into your playing. We saw that the tone of a single note can be controlled because the hammer shank has flex. It is small wonder that, as far as I know, there has not been any definitive study of tone control, because the subject is so complex.