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).

        Ithaca I couldn't tell my fingers to play at dynamic level 60, 62, 65, 69, 74, 80 and so on, but I coud feel how I wanted the crescendo to go, and my fingers would do it.

        I remember learning that we humans are very good at hearing slight differences of intensity in sounds when we hear them one after the other, but we are not capable of saying if a sound we hear today is slightly louder or softer than a similar sound we heard yesterday. "Absolute pitch" (long term memory of exact pitch level) exists, but not "absolute volume" (long term memory of exact sound intensity).

        With muscular control it's much the same. Even a first-rate pianist will not be able today to reproduce for the first note or chord of a piece exactly the same intensity that they produced yesterday (even though they'll probably be very close), but, having played that first note, they will be capable of dosing the intensity of subsequent notes very precisely in relation to each other. They won't be consciously deciding that the next note should be 3% louder, or whatever; they'll have a very clear image of the shape of the whole phrase in their head, and their technique will translate this into a series of intensities.

          iternabe There is of course a theoretically infinite number of dynamic levels between 2 any given values. Practically if you are using MIDI you can tweak levels digitally. But acoustically it is much more limited. In fact the main issues remain to be able to consciously decide and be able to execute a given level. Also bear in mind that most pianists do not perform on the same piano they practice on and the acoustics of the room also plays a role (in fact the amount of people in the room affects the volume for each frequency by damping more or less some of them). The regulation and specifics of the piano thus impact heavily the result. Most concert pianists have only a few hours to practice on the actual piano, sometimes only a couple of hours before the concert. So practically they dont have the time to reset. The reason it works is simply because the range of dynamics they use is wide enough that a plus or minus something is good enough to remain within the chosen interpretation. If you could measure precisely the volume level of a given note in a set piece in different concerts of the same pianist, the result would certainly be different. They surely dont control their piano with 127 levels. When I said about 10 levels it also does not mean they always play say a p level at the exact same level but that they play the note with the intention of playing it p; then how the piano reacts to their physical mouvement will vary. You can also make the test by yourself; playing the same piece exactly the same way, you will from day to day get a slightly different result but similar enough that it really sounds the same.

            I like this topic.

            I think the notion of a pianist having control on quality of tone is a myth. People confuse tone quality with other things such as quality of phrasing and dynamic control. The latter two, along with many other things, create the illusion of a different tone. But take each note in isolation and I'd say the tone will be the same if the speed of the hammer hitting the strings is the same. (This is not taking pedals into consideration, because pedals do have an effect on the tone of course.)
            It's not a coincidence that the pianists most famous for the quality of their tones were/are also very finicky about the quality of their instruments and of sound engineering, because the latter two are much more determinant in quality of tone than whatever illusions they can create with their playing. Blasphemy not intended.