Key Ratio

[John Hartman]

Richard Brekne wrote:
 > I think it was John Hartman that asked me for a drawing of what I
 > meant about the key ratio changing depending on the starting position
 > and ending position. Again, here is that exagerated example of the
 > three points on the key. A is the key front, B is the capstan, and O
 > is the fulcrum. And remember we are looking at the change in vertical
 > position for points A and B.

Thanks for the drawing, I see your point. I think the contradiction can
be resolved looking at the lever arms in relation to their arcs of 
motion. Then the ratios will be correct. As I said before how you 
measure the lever arms depends on what aspect of action mechanics you 
are interested in working on. If you are investigating the static 
balance of weights it is easier to use lever arm measurements that are 
perpendicular to the force of gravity. If you are interested in the 
motion of levers (how far they move) then you should measure the lever 
arms diagonally and use arc measurements for the motion. The two are 
roughly similar but not the same.

Let me give you some examples. It is true that for a key with a front 
lever arm of 100mm and a back lever arm of 50mm (measured along the 
length of the key) a 2 gram weight on the capstan will balance a 1 gram 
weigh at the front of the key. It is only roughly true that when you 
depress the key 10mm at the front the capstan will rise 5mm (your 
drawing shows this). To measure this motion precisely you need to 
measure the lever arms diagonally and use arc measurements for the 
distances. The two will be very close (In the case of a key) but not the 
same.


John Hartman RPT

John Hartman Pianos
[link redacted at request of site owner - Jul 25, 2015]
Rebuilding Steinway and Mason & Hamlin
Grand Pianos Since 1979

Piano Technicians Journal
Journal Illustrator/Contributing Editor
[link redacted at request of site owner - Jul 25, 2015]