Ithaca Randomly pulling stuff out of my hat (sorry, I'm tired - 3 nights of very short sleep) - think about two mechanisms which can make contact at a single point, each of which has a squishy balloon-like or somewhat elastic section somewhere inside. (Say, the finger pad and compressible joints in one mechanism, and a soft hammer + leather accoutrements in the other.) Those soft/elastic sections absorb and then dissipate energy over time, and probably in a non-linear way. So if you whack the first mechanism at the far end in one way, the way that force over time gets transmitted through the first mechanism and then through the second mechanism to produce a hammer taking vertical flight isn't so obvious. If you've modeled systems with multiple springs with different K constants, that might give you a better sense of what you're looking at. But even then, typically when people look at these systems, they're not looking at the time factor, unless they're studying something with a constant-period oscillation, so again, in steady state.

It's certainly interesting to look at the mechanics of your hand and finger but that's not what the contention is about.

There is a cut off point where the escapement mechanism throws the hammer free like a projectile. It doesn't matter how the key action was moved before the escapement point. After this point the hammer is in free fall not touching anything until it hits the string. The only thing that can physically affect the sound at this point is the momentum of the hammer. Unless you can show that it's possible for the action (and all that comes before the escapement) to impart some angular momentum such that the hammer hits the string at a different angle that is controllable by the player then there isn't any physical way to produce a sound that has a different quality at the same volume. If the piano had a mechanism where there is a physical connection between the player and the strings at the point of sound production, like in the harpsichord or clavichord, then I would believe you. But the piano has this air gap which disconects the cause from the effect.

    Ithaca I propose that what the musician hears as control over timbre is effected by careful control over
    timing. For a particular tone, the pianist is indeed able to select only two parameters beyond pitch:
    the hammer strike speed and the hammer strike time (although the time of tone damping is also
    important). I propose that by selecting these two parameters, a pianist can produce a percept in
    his or her listener of timbre being controlled independently of intensity

    That doesn't make sense. How does the player control the strike time? The travel distance of the hammer is constant so the time it takes for the hammer to travel depends on the initial speed. How do you get two independent variables?

        BartK my understanding is authors’s proposal is not about controlling the timing during the hammer free travel, but just the absolute timing of hammer strikes the string. And this control is performed by the pianist’s chosen gesture.

        Since the author did not elaborate further, my own thoughts is the pianist is choosing a gesture not necessarily with the goal to affect timing - rather the choice is aimed to affect timber (independent of loudness). However, variations in gestures started at the same time may inadvertently reach the letoff point at different time, the result is variation in timing. Then, if variation in timing can be psychoacousticly perceived as variation in timber, then both pianist and audience can be lead to believe that timber and loudness was independently controlled.

          Ithaca Although the author did not specifically say, I do believe it is variation of timing in relation to other notes (before, after, or simultaneous).

          I still do not believe a note played in isolation can have its timber controlled independent of its loudness. The other paper I posted today provides experimental proof.

            Ithaca I'm saying that (1) I think finger velocity alone (measured at the relevant location/point in time) is insufficient to completely determine the final hammer velocity

            Yes, I can agree with that. I'm just saying in the end the result is control over the individual note volume and that is linked to timbre not independent of it.

            Ithaca (2) varying finger "gestures" on a key that seem similar in volume/force can affect the timbre of the note, because the gesture can affect how long the note is allowed to sound before it's damped. In my own piano, with the wonky D note, it's very clear: the extra metallic/nasal/brassy/blaring resonance has a much faster decay than the primary resonance of the note at certain volumes, so at those volumes, when you sound the D, the timbre of the note changes over time, if you allow it to ring for long enough. At the worst (seemingly) constant volume, letting the note sound for about a full second makes most of that annoying higher-order resonance go away, whereas a maybe 250 ms press will give you maximum obnoxiousness. For this one note, it's like you've combined a piano with an out-of-breath kazoo player, but for the little bit when the kazoo is going full force, the timbre is decidedly unpleasant.

            I see what you're getting at but I don't think this gives you as much control as you might think. The time until releasing the note is basically what pianists call articulation and depending on how fast the music is going you don't have that much choice in when to release a note. Maybe you have a bit more leeway in slow music.

                In this discussion it may sound as though I don't believe you can control piano timbre at all and that I'm against any notions of doing extra motions to affect it but that is not true.

                The evocative descriptions that pianists use to describe music such as "shimmering like the wind" or "horn call" are useful to help you imagine the sound you want, which with enough experience a pianist can express by making the appropriate movements. The process is mostly a psychological one where the inner ear and imagination combine to control the playing aparatus in a subconscious manner. At a more basic level using specific movements like flatter fingers or arm dampening gives you more control over the nuances and makes it easier to achieve the sound. I'm not against descriptions like that if they help achieve the sound you want.

                What I object to is the "play it loud but not harsh" kind of descriptions, as if the two could be separated. A more realistic description is "play it as loud as it needs to be but not louder".

                I think the reason some pianists think like that is psycho-accoustic. From their training they are used to moving a certain way to produce loud chords because it gives more control and is more natural. When they play in unnatural ways, such as rigid fingers and no arm dampening, the sound comes out much louder (and thus harsher) than it would using the same force, so they have the impression of playing equally loud but with a harsher tone. But I think that if you recorded the spectrum of the sound and the speed of the hammers you would in fact find that the volume is different. It's all an illusion as with everything on the piano.

                  BartK In this discussion it may sound as though I don't believe you can control piano timbre at all and that I'm against any notions of doing extra motions to affect it but that is not true.

                  Ditto. In fact, this whole discussion, together with the scientific research articles, makes me believe even more in the pianists' ability to create the perception of varying timber while maintaining the loudness. I also see more clearly the importance of find the gesture(s) that allow one to create the tone quality desired.

                  BartK What I object to is the "play it loud but not harsh" kind of descriptions, as if the two could be separated. A more realistic description is "play it as loud as it needs to be but not louder".

                  I really like this example. But even here, my new understanding is that direction of "play it loud but not harsh" is in fact referring to what the player and ultimately the audience should perceive. Therefore a student may actually benefit by understanding such description is not to be taken as a strict and simplistic direction in the magnitude of physical execution.

                      I looked a bit more into Brent Gillespie. He is a professor of mechanical engineering. The chapter on piano was part of his PhD thesis on how to create a digital synthesizer (or digital piano) that is truly faithful to acoustic piano not only in the capability to produce whole palette of sound but also give the pianist the exact same control and feedback. His analysis of how pianist make the sounds from the instrument is a mechanical engineer's view. To me, that is not only interesting but also rigorous, probably even more so than you can get from many of the YT pop scientists.

                      One of his concepts is to reduce the mechanism of playing the piano to "mapping". In beginner piano learner's term, I understand this as "if I do this move, I will get that sound". He further breaks down the mapping to two stages: the mapping from hammer's escape velocity and timing to the final sound (this is one-to-one); and the mapping from the player's gesture (movement of all involved body parts over a short time and distance) to the hammer's escape velocity and timing (this is many-to-one).

                      This model of thinking excites me with some new insights:

                      First, if many gestures can map to one hammer escape velocity & timing (thus the same tone), then one can claim a gesture makes this particular tone but cannot claim that particular gesture is the only way. It may very well be that certain gesture works better for the anatomy of the majority. But when it doesn't work for a few, there exists other gestures to be explored for the same effect. Furthermore, for one desired tone, with a number of gestures to choose from, the decision can be made on other criteria, such as which will give the player more control, more consistency, and less stress.

                      Second, how we learn to manipulate the piano is in fact how we learn the mapping. It can be done empirically, by trying and listening as many variations as we can. This is why it takes time and there is no shortcut. Then, a good teacher is the shortcut by leading the student to try first the gestures that's most effective, and not wasting time on those gestures that's not (or even harmful). But then, can a pianist help themselves by having a better ability or sense on what new variation in gesture to try that has a better chance to work? Here, I think having the correct understanding of underlying mechanical and physical model can give one the edge.

                          I think the gesture of pianists is usefull in the sense that it allows them to associate a particular physical mouvement with a given sound result. Indeed the pianists cant determine what the velocity is (that is an internal value not known to the pianist), so the only possibility is to control the physical mouvement one makes. As a consequence, and maybe unconsciously it may lead some people to believe that their mouvement does influence the sound (and it does but only indirectly). So by categorizing the sound result, one may define some typical ways to get to those results. And yes I believe there are better ways because they have been in use for a long time. I dont think that the pianist needs to understand the physics behind it. On the other hand, some knowledge may prevent the "voodoo" approach, for example some people believe that by raising the hand high it gives a particular result (it probably does for them) or that by moving the finger on the key after it has been hit produce a different tone.

                          I believe Steinway has put a ton of money and research into this phenomenon and the result is that their pianos have (arguably) the best tone in the business.

                          That tells me that it's not the velocity of the hammers, though it probably plays a part, it's the tonal qualities of the instrument itself that control whether the sound is pleasing or not. Yet even that has limitations. One need only listen to notes played in the midrange of the keyboard as contrasted to the same notes played in the upper bass to understand that our ears prefer certain tonal ranges over others and will judge the sounds not in that tonal range as "harsh" or "disliked." This is especially true when the sound is louder or emphasized.

                          Singing would be another example of the "it's the instrument's quality" idea. Everyone can "sing." However, not everyone can "sing pleasantly." The difference between those two extremes is based in what is producing the noise, not the noise itself.

                          The unfortunate part is that people are trying to use physics to explain what is essentially an emotional response to sound.

                          Or so I believe.

                          iternabe I looked a bit more into Brent Gillespie. He is a professor of mechanical engineering. The chapter on piano was part of his PhD thesis on how to create a digital synthesizer (or digital piano) .....
                          One of his concepts is to reduce the mechanism of playing the piano to "mapping". In beginner piano learner's term, I understand this as "if I do this move, I will get that sound"

                          I'd first want to know whether he plays the piano, and plays it decently. I would not take advice from this kind of write-up but I would listen to someone who has taught a lot of students, worked with these things, observed, and so on. I was once gifted an old hard cover book written by Matthew who proposed that the actual piano playing actions happen deep inside, and intricately. Two people who externally do the same gesture may get different results because what is happening internally isn't the same. Conversely, two people who look very different may be doing the same thing inside and get the same results. (Something like that.)

                          I once watched a teacher on-line demonstrating certain motions which the students carried out. Later in a recital you could see those motions, but the expected sound from those motions didn't appear. Imagine someone throwing a ball and releasing it; someone else having their arms copy the same trajectory but they are not whipping their arm forward with body follow-through the same way. What is happening inside?

                          Or, stir coffee and then pudding with a spoon. Your hand and its senses interact with the feeling of viscosity of the liquid, and makes umpteen tiny motions and adjustments. Try doing the same thing, first thinking of "necessary hand motions", all the angles, the greater energy needed against the pudding as opposed the coffee. You'll probably be clumsy when you weren't before, and maybe tense up from the effort. What role does the feedback from your senses play? Here we have the weight of the spoon, resistance from the liquid, and even the familiar sound of clinking may guide the action.

                          Just spontaneous thoughts. 🙂

                              keystring Good thoughts. And I agree completely that any and all effect produced by the piano originates from the pianist's mind. I also subscribe to the idea that directing the mind is probably the most effective way to direct the body.

                              On the other hand, there is a part in me that still thinks whatever originated from the mind always manifests in physical executions that is measurable. If two same motion with different thoughts produced two different tones, it should show quantifiable difference in the hammer's motion and interaction with the string. Same if two different motions with same thoughts produced the same tone. To take the physical measurements, one do not need to be a decent piano player, but need to be a decent engineer. To hear the tone difference, one may not even need to have a good ear, because the more objective way is to recruit group of people with good ear and do controlled tests.

                              I really enjoy reading your spontaneous thoughts. At the same time, I just cannot let those interesting observations remain as myth.

                                @iternabe - I am in no way ascribing to an idea of the mind directing everything. Actually with my coffee/pudding stirring imagery, I was putting together various senses and the mind isn't in the equation at all. Do you "think about" how to stir your coffee? What bothers me is the idea of an engineer who has studied the mechanics of the piano then thinking he can propose the physical playing of the piano and the training thereof. Doubly so if he himself doesn't play the piano, or to any kind of calibre. There is a lot more involved, interactive and so on. There is what goes into a "motion" and series of motions on all levels.

                                  keystring I am in no way ascribing to an idea of the mind directing everything. Actually with my coffee/pudding stirring imagery, I was putting together various senses and the mind isn't in the equation at all. Do you "think about" how to stir your coffee?

                                  Would it be more accurate to say only the conscious mind may not always be involved in all body motions?

                                    keystring I'd first want to know whether he plays the piano, and plays it decently.

                                    I found the answer to this question:

                                    R. Brent Gillespie received the B.S. degree in mechanical engineering from the University of California, Davis, in 1986, the M.M. degree in music (piano performance) from the San Francisco Conservatory of Music, San Francisco, CA, in 1989, and the M.S. and Ph.D. degrees in mechanical engineering from Stanford University, Stanford, CA, in 1992 and 1996. He is currently with the Department of Mechanical Engineering, University of Michigan, Ann Arbor. His current research interests include haptic interface and teleoperator control, human motor control, and robot-assisted rehabilitation after neurological injury.

                                        Ithaca Go ahead. You can find his email on his UMich faculty page.

                                          iternabe I found the answer to this question:

                                          Excellent, and thank you! That is very helpful.

                                            All in all for any given key, there is probably no more than about 10 dynamic levels that can be clearly distinguished (and most amateur dont even have the level of control to consciously be able to select one of those 10, I would say most control no more than 5 levels). So there isnt really any need to have an infinite number of mouvements to access those levels. And in many pieces (typically Mozart or Haydn) one is not using more than 5 levels or so.

                                              Sidokar You brought up another interesting aspect that I happened to be pondering over recently as well. It originated from questions in PW about limitations of MIDI 1.0's 127 level of dynamics, and whether apply a velocity curve would the worsen the resolution enough to become a valid concern. The topic interested me enough to go to my digital piano and mapped out MIDI range for each dynamics marking:

                                              Dynamics: MIDI range

                                              • ppp: 1-13 (13 steps)
                                              • pp: 14-32 (19 steps)
                                              • p: 33-52 (20 steps)
                                              • mp: 53-72 (20 steps)
                                              • mf: 73-91 (19 steps)
                                              • f: 92-110 (19 steps)
                                              • ff: 111-122 (12 steps)
                                              • fff: 123-127 (5 steps)

                                              At first, my reactions is just like what you said. There is no way for me to accurately and reliably produce the 20 steps in mezzopiano range! If a maestro can do that, I am in awe! In any case, 20 or so gradations for each dynamics marking seems more than adequate. And I might agree with you even 10 is enough, so applying a velocity curve should be of no concern.

                                              Then, I put more thought into this, and realized it's more complicated than that. Take an example that I personally noticed - it is much harder for me to get the very first note of a piece played at a desired dynamics than any of the subsequent notes. And it makes sense because the first note has no reference, but the notes following have. So even when I have no hope to ensure my first note come out at MIDI value 60, I could imagine with practice one day I can make a crescendo from there within ±2 (e.g. 61-63-64-65-67...) because the ear and the muscle are just better at executing increments than absolutes.

                                              Relate this back to my original revelation that tone quality is affected by context, then the need of precise control of the relative velocity of a cluster of notes would make high resolution of MIDI value of great importance.

                                                  Yes, this. Micro phrasing requires very subtle dynamic changes.

                                                  Also you can make a different sound at the piano by deciding to move your fingers and arm slightly differently, holding slightly more or less weight, the angle of the wrist, etc. This creates a virtually infinite number of variations. If you carefully listen to professional pianists, you can see that they seem to play at the same volume but sound different -- this is usually because they are playing with a slightly different attack which creates a slightly different volume or balance (in the case of multiple notes).