Towards A Scientific Explanation Of "cramped" Tone

Hi everyone interested in scientific study of music production: As a previous participant in Mathematical research work at the University, I've an interest of understanding theories behind things. One of them, as an music enthusiaist, is why there is a different in the sound played various ways, while in theory the speed at which the hammers strike the strings is the only variable in piano playing. (Ignoring staccato, pedalling, phrasing, etc, and most importantly the micro-pauses in front of notes which subtly changes the overall quality, but don't do anything to a single note.) For instance, a cramped sound could be heard from a cramped coordination (which unfortunately include myself), and the freely vibrating sound characteristic of pianists like Kemal Gekic. Currently descriptions that I've read, by well-known pianists, focus mainly on mass (arm weight), or force, but are not scientific. At best they could only describe a subjective feeling. Speed at which the hammer strike, which is what makes a piano sounds, is related to but not the same as mass or force (both relates to velocity, which I'll explain below). Haven't thought about that since high school, but suddenly the answer appears just as I try to play piano again,and here is some analysis, with a little holes since I don't currently have a real piano to test my idea, but enough to explain a lot. Think it would be great to post the initial thoughts here, for Alan is a rare rationalist among musicians. An important part of the analysis depends on the knowledge of Elastic and inelastic collision. When two free masses collide, say a moving one clashes into a stationary one, the total momentum always conserve, but the kinetic energy may not. Some of the kinetic energy will convert to other forms of energy, depending on what's happening on the impacting surface. Now, one particular way of producing cramped tone is to lock our hand and play only with finger muscles; while a freely vibrating sound is a result of a good hand structure: skeletal playing. I'm going to argue that, at least to a certain extent, cramped tone is a result of inelastic impact on 2 levels, while a freely vibrating sound means elastic (only relatively since kinetic energy is bounded to lose) impact. The freely vibrating voice? As I've said, it's usually a result of good alignment of the hand. By "good'', it's not just a subjective or vague artistic description, When using the and or even the entire hand, the sound is louder partly because of the large mass: it won't be slowed down as much by the key as the finger, thus making it effective to produce useful tone from the impact. A few corrollary, though not very rigorous: 2. I suspect that finger work brilliance has to do with the suppleness of the finger tip fresh. On days where the fingers feel damp and fat, it tends to be good days of playing, with tone richer and of course, less slippy. (the later is totally unrelated to our discussion) That's because such finger tips act more like a spring than a dry finger tip, which tends to give a loud sound and loses energy upon the contact. 3. point 2 may also be individual specific, which may not be encouraging for some pianists. 4. staying close to the key may make give less space for the acceleration of the finger tip, but the bone structure frees the finger muscles from having to work against the friction of the key, it at least saves the energy lost in the impact. The rich sound is a result of initial key speed being LOWER than the hammer striking speed. Anyone any idea? .......To be continued......very tired now......

I've wondered about the physics of piano tone also, and I've found some discussion on the topic you might find interesting: Here, the author theorizes that lateral vibration of the hammer gets transmitted to the string if the attack is too sudden, which causes unpleasing discordant frequences, and that accelerating the keydrop as it progresses will minimize these. In this chapter of his book "The fundamentals of piano practice", Chuan C. Chang explains how he believes that a better piano tone is caused by accelerating keydrop since it will cause the hammer shank to flex backward, and increase the effective mass once it reaches the strings. So far, then, it seems to align with your ideas. However it may not be the whole story!

The first article is quite inspiring. That, if proven, provide the missing link. I'm not that ambitious, and is content with knowing why an uncoordiated hand manifested in the sound, in terms of the changes of the speed of the key after first contact. The rate of acceleration of the hammer is another way of saying it, though I restrain myself from saying so, because in the extreme cases where you strike hard with finger muscles and yet don't enough press "to the bottom'', the hammer will actually be accelerated suddenly (right after you touch the key), but since the key has transfered its energy to the hammer and now is now slowing down due to gravity, it loses contact (only slightly) with the hammer earlier than it should!!! The hammer itself will then also be slowing down. So the acceleration-time curve will be a very sudden, positive one, followed by a slight deceleration as it moves towards the string.