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Hello,

I was thinking about this.
I think the damper has to fall at least 0.5 cm when a key is released.
The falling time for the height of 0.5 cm is 32ms.
http://www.wolframalpha.com/input/?i=fall+height+0.5cm

Now, the damper cannot fall faster than the key bottom end goes down. The key itself is balanced and pushed back by the hammer.
So I think the key falls back much more slowly and should need much more time than 32ms.
The hammer has at least to fall 1.5 cm. So, if it doesnt bounce back this needs 55ms.

So I believe the shortest tone cannot be shorter than 50ms and the duration of the shortest tone depends on the keys rotational inertia. Therefore bass notes should have a longer minimum duration.

Are there numbers known about this?
(This is important to know for the design of digital pianos)

Peter

Interesting question. I have never read anything about this but that does not mean much. My thoughts are:
The properties that change the rate of falling action parts in a piano would be springs, friction and the angle or arc of the falling part. Then the distance the parts travel would also be a factor. Most of these properties will vary from time to time and I do not believe that designers would have gone to that much trouble but I could be wrong.
The other side of this is - how many pianos that we visit have optimal damper regulation and how many people complain about less than optimal damper regulation?

I've played some pianos on which I could get an extremely short tone on a few notes. Often I had to be careful not to bottom out on the key, otherwise I might risk breaking the string. If I wanted the note to keep sounding, I usually had to start releasing my hand off the key before the hammer had finished its stroke, letting inertia take it the rest of the way to the string. I should mention that those pianos usually have the checking adjusted super close, or the letoff adjusted very late.

Yes, but the hammer really does bounce off the strings, so it will take much less than 50 msec. for the hammer to get down. But this is largely irrelevant, because after the let-off, the hammer is no longer connected to the keystick. It is the falling of the whippen that is pushing the back of the keystick down, and making way for the damper to come down. And here is another complication: It is possible to tap a key so briefly that the key never goes down far enough to lift the damper at all. But even that brief tap can be enough to give the hammer enough speed to continue on up to hit the strings - while the damper is still down. Of course that would not be considered ordinary playing. But it shows that arbitrarily short notes are possible.