All in a row

[John Delacour]

At 10:48 PM -0500 11/10/01, Bill Ballard wrote:

>But even doing this relocation of the balance line (by moving the 
>sharps), the consequences to the leverage of the key such as David 
>has observed is difficult to ignore. David's metrology may seem to 
>exist in a universe parallel to that of linear measurement of key 
>lever ratios: in fact, it is simply measuring the leverage by 
>weight. I like my keyboards at .51, and I have seen key lever ratios
>  of .59. But I am not looking forward to meeting at keyboard with 
>.79 ratio, especially the group of .79's was in fact the sharps, and 
>I was supposed to set aftertouch and not worry about dip, and 
>furthermore, to expect to rebalance a set of keys whose leading had 
>to answer to a 5.5 total leverage on the naturals and (way up there) 
>7.5 on the sharps.


Hello Bill.  Since the only thing I have at home to play with 
(besides my own action model, of course) is a Kawai one-key model, I 
thought I'd see what the result would be of having the pins all in a 
row on that, and the results give a far less gloomy picture than you 
are painting.


    Centre to normal from ivory front____242.00 mm
    Height of ivory_______________________25.00 mm
    Height of ebony_______________________34.00 mm
    Front lever ivory____________________243.29 mm
    Centre to normal from ebony corner___186.00 mm
    Front lever ebony_____________________189.08 mm
    Centre to pilot top (back lever)_____127.00 mm
    Mechanical advantage (ivory)___________1.92 %
    Mechanical advantage (ebony)___________1.49 %
    Reciprocal (ivory)_____________________0.52 %
    Reciprocal (ebony)_____________________0.67 %
    Touch depth (ivory)___________________10.00 mm
    Key travel_____________________________0.04 radians
    Key travel_____________________________2.37 degrees
    Touch depth (ebony)____________________7.69 mm
    Static touch weight (ivory)___________50.00 grams
    Static touch weight (ebony)___________64.33 grams

As you will see, I am giving the sharps a starting height of 9 mm. 
above the ivory which will leave them 1.3 mm proud when fully 
depressed, roughly as in a normal keyboard, so that the height of the 
sharps is a full 1/8" lower.  I am assuming a 56 mm. difference 
between white front and black front.  I'm not familiar with the local 
jargon fostered by the list or the PTG, so my terms may need 
interpreting but I'm guessing that my 0.52% is equivalent to your "I 
like my keyboards at .51".

In the usual set-up there is, of course, slightly more loss due to 
circular motion in the back levers of the sharps, which loss is 
transferred theoretically with usury to the front lever in the 
Chatwall configuration, but in either case I'm not considering it 
significant.

We arrive at a lever ratio of 0.67 % for the sharps which would 
require us to use say  an extra two lead weights in the sharps IF we 
consider it necessary to achive usinform 50 gram weighting throughout 
the scale and IF we do not use helper springs or magnets.  The excess 
of 14 grams will almost certainly need to be reduced -- since the 
difference would be palpable -- but to what point?  Suppose we 
discover that a 54 static down-weight is acceptable, then we have 
only 10 grams to remove, and this is almost within range of a helper 
spring, without talking of the magic ferrite, of which I have no 
practical experience.


>Ron's challenge that David should refute each of Riemann's reported 
>advantages is not required.

And I hope I'm not required to change my name to Ron either :-)

>  I agree that what Riemann says in is fact there for the pianist to 
>enjoy. The issue is a little larger, namely whether the side-effects 
>of such a redesiging of the keyboard is a reasonable price to pay 
>for it.

I think I've shown that the disadvantages, even in theory, are less 
than has been suggested, and Ron (a real one) will be delighted that 
I've actually used a SPREADSHEET to show it.

The real test is reaction from a broad range of competent players, as 
in all matters, but the theory must come first and even player 
reaction must be scientifically assessed.

JD