More physical modelling:
Collision: http://createdigitalmusic.com/tag/physical-modeling/

As for techniques, my piano teacher studied at the Royal Academy in London and I remember being taught "portamento" i.e. stroking the key.  Even at age 10, this struck me as nonsense.  Again it comes down to lever efficiency; in this case, your finger.  By stroking the key, you're vectoring the force and transmitting less force to the mechanism, resulting in more *control* of lower volumes.  The hammer certainly isn't "massaging" the strings in the same mode as your finger.

I think, therefore, that we believe we're influencing the tone through changing the "touch" because if we didn't do this, we'd actually be limited, through our biomechanics, in the subtlety of force we can apply.  I hope that makes some kind of sense to someone.

Best//Neil

Correct me if I'm wrong, but since there is an escapement in the action of an acoustic grand, there is a physical limit during a very slow keypress, where the hammer will be loosed and if the key velocity is below a certain threshold, the hammer will fall away (stop accelerating) without striking the string. 
Neil

This is exactly true!  And it's something that is reproduced quite authentically on my RD-700GX.  However I have found that NONE of the software-based pianos work this way without some tweaking to the curves and even then it ends up feeling a little "fake" if it even works at all.

For example, I can't seem to get Ivory to NOT sound a note at all no matter how lightly I press the key.

BTW, I'm also a guitarist.

Always keep in mind (because of the escapement action of pianos) that once the hammer escapes its connection to the key, we have no influence over it at all.

Oddly, many pianists that absolutely rely on this escapement feature, seem to forget what it means - it means that when the hammer flies to the strings, we no longer have any control over it until it returns to be re-activated by the key.  Sadly most piano teachers are not physicists either, and the myth of the control over tone lingers.

This is an interesting discourse (that may or may not convince some with long held beliefs):

http://www.nybooks.com/articles/214

Demolition of this myth is long overdue.  However, I know neither I nor others will ever convince many pianists - beliefs are extremely hard to change.

(Of course if the hammer hits the string at higher velocities, the tone will be harsher, in part due to a louder noise of the hammer hitting an object (if you take a piano hammer out and hit a table it makes a noise), and of course the previously mentioned larger component of dissonant harmonics.)

Glenn

PS - I do envy guitarists and other musicians that interact directly with the strings/reeds/mouthpieces of their instruments - they can do all sorts of shaping and changing of the sound.  Perhaps the unfounded belief of pianists is rooted in envy; I have it.

As an afterthought, my mother was not only an accomplished pianists, she was a registered music teacher.  She also taught me that my touch could affect tone - however, later when I became an engineer (applied physicist), I realized that the reason I couldn't affect the tone was based on a sound understanding of physics, not my lack of touch.

G

If force applied in situation 1 and situation 2 are identical, the sound will be identical in timbre and volume.  If force 1 != force 2 then the timbre and volume will be different, but due to the non-linear nature of hammer hardness, they won't necessarily vary by the same amount, which would explain how the "same" volume could have different tonality.

If it's that simple, then the developers of Pianoteq can simply program a tiny bit of randomness into the algorithms. Something I suggested a long time ago. Besides, I think you got it backwards. Applying the same force with your fingers to the key in case 2 as in case 1 should produce a softer sound due the smaller travel distance of the hammer, no?

You have quite an imagination. LOL

Ergo, Joshua's system is unnecessarily complex and all we're really talking about is trying to impose more control at lower velocities.  By depressing the key part way and then starting to actually key the note, the player is simply decreasing the efficiency of the lever system, as in some "soft pedal" actions which bring the hammer closer to the strings.

1) Key depressed from top of keystroke to keybed in one continuous movement:  Potential energy stored, transferred to the lever, converted to kinetic energy when hammer is thrown.

2) Key depressed part way, held, then depressed again:  LESS potential energy stored, transferred to the lever, coverted to less kinetic energy and hammer thrown less forcefully.

If force applied in situation 1 and situation 2 are identical, the sound will be identical in timbre and volume.  If force 1 != force 2 then the timbre and volume will be different, but due to the non-linear nature of hammer hardness, they won't necessarily vary by the same amount, which would explain how the "same" volume could have different tonality.

Or, it's like when I think about cotton wool and my mouth goes dry and finger-ends can feel it.  I.e. it's all in your head.

Neil

Acceleration is simply the change of velocity with respect to time, but when the hammer hits the string, it matters little if the hammer is accelerating or decelerating.

Maybe if the hammer and string were perfectly rigid. But the hammer spends a small amount of time on the string, so I would think whether it's accelerating or decelerating at the moment of contact matters.

OK, so we're only talking about deceleration. Not sure what you're getting at with the travel distance thing. The 4th pedal on Fazioli grands I think clearly demonstrates that travel distance is significant.

Again, this seems true only if you ignore the fact that the hammer spends some time on the string interacting with its waves and is decelerating at the moment of contact... further decelerating through contact, and eventually accelerating as it leaves the string.

Then again, it could all be in my head, but I'm not convinced yet. I gotta get my hands on a grand and do a few little experiments.

Energy is a function of velocity and mass - nothing else.

The equation for the energy of a moving mass is "one half the product of mass times the square of the velocity".  This is from classical mechanics.

Acceleration is simply the change of velocity with respect to time, but when the hammer hits the string, it matters little if the hammer is accelerating or decelerating.

As a matter of fact, once the hammer escapes the influence of the key (and it does - hence the term "escapement"), the velocity decreases ever so slightly due to frictional losses, and in grands because their hammers are being slowed on their upward path by gravity.  But this is not significant as the travel distance is not long.

It is still widely believed by many pianists (most likely because that's what they've been taught - keep in mind that not many pianists are physicists), that they can influence the tone by how they stroke the key.  But the only thing that changes the tone or timbre is the velocity of the hammer when it strikes the strings.  Harder strikes (velocities) result in more harsh overtones.  This is probably more effective in the bass with longer strings that are copper wound which renders them less like a bar and more like an ideal string (an ideal string has no stiffness whatsoever).

A vibraphone's bars are relatively much stiffer, and this creates relatively more odd harmonics.

Glenn

I'm sure an experienced pianist such as yourself must also appreciate the piano action - e.g. (1) the escapement, (2) the feeling of throwing the hammer, etc... all these add to our sense of better controlling the instrument. It much easier for me to play an acoustic than a "digital" action.

This is why my idea would be beneficial. It would simulate the feel of throwing a hammer, as opposed to the feel of pushing a lever into a MIDI sensor. I believe there are some great digital piano actions out there that feel like real piano actions... until you turn on the sound.

Or it may be possible to skip the hammer modeling step and just model how changes in key position/velocity/acceleration affect the sound. I think both are feasible, though I imagine modeling keys ---> hammers ---> strings would be superior.

Coaxing a variety of tonal hues beyond the velocity-dynamic range dichotomy is not a myth. And I say key position is the only necessary variable because velocity--and perhaps more importantly, acceleration--can be calculated from key position.

Exactly. Hence my potentiometer idea. And hence the superiority of modeling key position ---> hammers ---> strings, as opposed to key position ---> strings. (And certainly superior to the current MIDI velocity ---> sound.)

I'm not so sure. Perhaps I misspoke when I said that the hammers transfer momentum to the strings. Maybe a more accurate description involves force, which entails acceleration. Obviously acceleration plays at least as much a factor as velocity, especially if you're throwing a hammer that once released is acted upon by gravity. And perhaps this is what I really meant when talking about creating different colors of sound at the same volume.

I'm sure it'd be possible to use their parameters to accomplish what I'm thinking of. And I'll bet you a ham sandwich it's key position. The real issue is how to translate that into a hammer striking a string. As etalmor pointed out, the Disklaviers don't have to worry about that because they have keys throwing real hammers striking real strings.

Consequently, if all that matters is the velocity at which the hammer hits the string, then the "loose" connection between key and hammer doesn't come into play.  In fact it is precisely because of this loose connection that the final striking velocity is all that matters.

We don't have any where near the control over our piano strings as do guitarists, violinists, harpists, etc) because they are in direct contact with the strings with very sensitive and tactile fingers.  Not that our fingers aren't very sensitive, but the action isolates our fingers from the strings.

On the matter of the entire velocity path of the hammer, I really don't think it matters - the striking velocity is all that affects the sound (except as already noted above about hitting already vibrating strings).

If the hammer isn't in the resting position, the key re-activates the movement of the hammer, and once in motion, there can be no further control over its motion - it simply flies into the string.

If someone is familiar with the Yamaha system, it would be enlightening to learn what parameters they measure.

For the preliminary rounds of the Minnesota International Piano e-Competition, contestants play a Yamaha Disklavier piano - the midi information is then transmitted live to another Yamaha Disklavier piano far away where the judge(s) listens to another Yamaha piano which plays the contestant's file.  If it's real enough for judging world class talent, then it's likely real enough for most of us.

http://www.piano-e-competition.com/

Incidentally there are some very good renditions of many classical piano pieces that can be DL'd in midi format for no charge.

Glenn

I'm fairly sure that's regarded as a myth.  Given that the player has no further control once the keystroke passes the escapement point, it's reasonable to conclude that the only variable (with regard to influencing tone) is velocity.

I agree with you, - the final velocity is the only thing that counts. But the digital pianos enforce a deterministic relationship between the *average* speed of the key (time to pass between two points) and the final hammer-string collision velocity.
This is obviously a simplification of reality. Even if we knew the final velocity of the key - it wouldn't be enough, because there is a loose connection between the key and the hammer.
The entire path of the key over time should be taken into account, as well as the previous state of the hammer (if it's not in the resting position due to a previous press) - you'd need all this info, as well as a model of the action itself in order to determine the final hammer velocity...

I totally agree - here you don't need to model the hammer - because you have one!

The real reason acoustic pianos are more organic than digital pianos is that you can create different tonal colors, not based solely on velocity, but on where in the key's travel you start and end. Real piano hammers transfer momentum to the strings. Digital piano actions transfer only SPEED.

I'm fairly sure that's regarded as a myth.  Given that the player has no further control once the keystroke passes the escapement point, it's reasonable to conclude that the only variable (with regard to influencing tone) is velocity.  In physics, momentum is simply the product of mass and velocity -- and because each hammer's mass is constant, for the purpose of modeling a piano's action, momentum and velocity are equivalent descriptors.  Beyond its role in affecting the hammer's velocity, the only other function of key position that could possibly influence tone would be its role in controlling the damper.

I agree that there's plenty room for improvement the actions commonly seen in digitals.  The exception being digital-acoustic hybrids, which have "real" actions, and have two sensors per note: one at the "hammer" to capture the velocity at which the imaginary "strings" are struck, and a key position sensor to control the virtual "damper".

Voltara

I agree - but I'm sure an experienced pianist such as yourself must also appreciate the piano action - e.g. (1) the escapement, (2) the feeling of throwing the hammer, etc... all these add to our sense of better controlling the instrument. It much easier for me to play an acoustic than a "digital" action.
I know that there is work related to mimicking the touch with electromagnets that dynamically cast different forces on each key as the player depresses them. This way you can theoretically copy any keyboard instrument's touch - be it harpsichord, Hammond B3, or a Bosendorfer, at the flip of a button. Think of how cool that would be: to download the "touch" of an instrument from the internet ...!!
Here is one mention of it: http://www.actapress.com/PaperInfo.aspx...reason=500

That is true, and I think it all comes down to calculating the collision velocity of the hammer and string. Still it may be a complicated operation: one might need to model the physics of the piano action, and inject the key's trajectory (over time) into that model, to produce the hammer's trajectory, and final speed ...

-- Eran

And as far as the action on the VPiano...big deal. It's still only capable of triggering 4-5 different layers maximum

First of all, I'm pretty sure V-Piano's action--like ALL digital piano actions--sends all MIDI velocities 0-127. The "4-5 different layers maximum" refers to the sound module's interpretation of those MIDI velocities. Due to practical constrains, it's unreasonable--in fact, nearly impossible--to sample more than a fraction of the dynamic range. That's why modeling is the way forward. And I'm sure that V-Piano uses modeling to generate 127 distinct sounds per note.

That will NOT make digital pianos more organic. You could have a MILLION velocity steps and it wouldn't be any more convincing than most digital pianos' 3-4 layer sampling.

The real reason acoustic pianos are more organic than digital pianos is that you can create different tonal colors, not based solely on velocity, but on where in the key's travel you start and end. Real piano hammers transfer momentum to the strings. Digital piano actions transfer only SPEED. Heh, let's not even call it "velocity" because it's directionless--the sound module sees single digits, not vectors. In order to yield genuine dynamic and tonal ranges, a digital piano must incorporate 2 things:

1) An action that senses and communicates key position.

2) A sound module that interprets this data appropriately.

Step 1 is easy. The keys should control POTENTIOMETERS, not hit MIDI sensors. I suppose optical pots would be ideal so that there's no superfluous friction. MIDI values 0-127 should be more than adequate to cover the mere half-inch of key travel.

Step 2 is the hard part. But I'm sure the "white coats" can figure it out! Basically, the sound module or software must interpret the pot values in terms of position, distance traveled, velocity, and acceleration.

-, I should patent this idea! LOL