Trying to get a grip on a mechanics problem

[baaa]

greetings forum members, a first post.

I belong to a pianists forum. Many of us are using a digital piano (DP) these days - limited budget, space, privacy (you can use headphones), low maintenance (no need to tune!) are the drivers.

The DP industry is still under the spell of the real thing, the acoustic piano (AP) upright or, even better, a grand. Relatively few of us get to own or even use one. So DP manufacturers are doing their best to emulate the 'action' of an AP - that is, to make it FEEL like one is playing the real thing, irrespective of sound (that's another story entirely). In fact the DP action is a radically different, grossly simplified version of the AP action but these days, in the modern DP, it's not at all bad.

(sorry to be droning on...)

In the DP forum of pianoworld we like to get stuck into the ins and outs of DP actions, the heavy ones (slower), the light ones (fast) and we have several 'theories' about what is happening mechanically when we play one.

Let me cut to the chase. Here (scroll to about 1/3 down the page) is an animation of one of the better DP actions.

We're trying to get an idea of the work required to play this particular keyboard. So we've coined terms like 'down weight' 'up weight' 'dynamic weight' and' inertia' but there appears, to me anyway, to be a half-cocked understanding of what is going on. Where is the inertia? How do we measure friction. How about inertia...etc.etc.

Could someone offer a lead for this enquiry? The questions raised may not be interesting enough here. Might there be a better forum? Does anyone here have any ready insight?

thanks for reading, and thanks for any suggestions...

 

[thankz]

maybe a book on conceptual physics would help you. ;P

 

[olivermsun]

Where's the pianists' forum?

 

[baaa]

Where's the pianists' forum?

http://www.pianoworld.com/

http://www.pianoworld.com/forum/ubbthreads.php/topics/2308145/Questioning_the_Wisdom_of_Heav.html#Post2308145 a thread (it's typical of many that crop up from time to time) that's got a few trying to grapple with the definitions. I don't think anyone understands the mechanics but it looks as though it would be simple to formulate. Perhaps I'm wrong.

 

[baaa]

(ooops! is my query a textbook type problem, in which case I'm in the wrong forum?...please could some kind soul advise.)

 

[olivermsun]

Thanks for the links.

It's an interesting but open-ended problem, so it might help generate responses if you can pose specific questions.

P.S.: Also, there's always the possibility (as with many discussions that mix an art with an instrument/technical aspect) that people are overthinking things. :)

 

[baaa]

- many thanks for looking. Overthinking - definitely! I'm also guilty of this.

I have in mind a question or two but I'll need to think about it in order to avoid going round the houses.

I'll report back over the weekend...

 

[Stephen Tashi]

I suggest you study how to measure the force (or pressure) between fingers and keys as a function of time. Even if you develop a mathematical model, you'd need to measure something objective in order to test it. The engineering section would be the place to ask about sensors for such an experiment.

 

[baaa]

I suggest you study how to measure the force (or pressure) between fingers and keys as a function of time. Even if you develop a mathematical model, you'd need to measure something objective in order to test it. The engineering section would be the place to ask about sensors for such an experiment.

thanks for your input.

The piano forum has long been preoccupied by the range of light to heavy actions and interestingly (for us!) there's no consensus yet on what is best, nor is there any apparent correlation between the requirement for a particular action-weight with experience/ability.

Newcomers none the less like to try and get a blind idea of what to purchase so to that end we've been talking on and off about key weight in an attempt to quantify a light or heavy action

We're been talking (perhaps improperly?) about static weight and dynamic weight.

Static weight, even if this isn't the right term to use, seems intuitively easy to measure.
We know that friction comes into this too but if I simplify this for a moment I can tell you that at 60grms the keys on my board are more or less in equibrium with the mechanism, i.e. a single key can be depressed to any point in it's moveable range (10mm at the key tip) and it will remain at that position using a 60g weight. We see actions with static weight as low as 40g and perhaps as high as 70g. Horowitz never traveled without his own custom Steinway (40g+ I seem to remember).

Dynamic weight...everyone in the forum see this as the inertial component. This is where we need most help since even 'technical' papers on piano mechanisms talk about the difficulty of quantifying it.

So;

I vaguely remembered and did a quick google check for this simple formula

work done = force x distance.

On the face of it that seems to go a long way to explain the difference between the physical effort required to play at ppp or fff since to get fff we need to apply a great deal more force to move the key, and thus the hammer, quickly.

I've no idea what sort of formula would describe how to bring together the relevant variables - unless it's a simple refinement of the one above (higher static weight requiring greater force) - but I do wonder at this stage if 'static weight' as defined above is the greater part of the sense of 'feel' of the weight of the action or if it is otherwise, is it perhaps the inertial part...the bit we can't measure (apparently!)? Maybe the sensor you mention in your post, if it exists, is the way to quantify this. Is there no theoretical way based on the geometry and weight of the keys and the hammer together with static weight?

I don't want to try anyone's patience so I'l leave that question hanging, if I may, to see if it leads anywhere.

Or if this is more up the street of another forum (or branch of this one) I'll be content to move there.

 

[olivermsun]

Well first of all as a I don't think you're ever going to determine by using physics what is the "best" weight for a given player. I flipped through some of the comments in that thread, and I agree with much of the "experience-based" commentary: a heavy action can give you more control, a light one may be easier to play fast passages on. The choice probably depends in part on your playing style as a musician. Practically speaking, I agree with the people who find it a little easier to go from a heavy action to a light one than the other way. It probably is almost always bad advice to have a beginner choose something very unusual because he or she believes this will be suitable for their intended style or whatever.

That being said, sure, there is a difference between "dynamic" and "static" weight, and you'll have to take that into account when you think about how a certain keyboard plays. The engineers at Kawaii or wherever surely have modeled, measured, and refined all of this in excruciating detail.

The simplest physics model might be a seesaw.

The dynamic weight would probably be quite hard to measure. Someone just posted a question in one of the forums about a force sensor — this might work but seems like a lot of effort to get it set up with repeatable key actuations and stuff.

Maybe I'll add more thoughts later, got to run for now!

 

[Stephen Tashi]

What's a link to a good diagram of how a piano action works?