The formula for calculating the hammer/key leverage ratio is as follows;

Hammer to key ratio = (B/A)*(D/C)*(F/E)


B - Balance pin hole to capstan/heel contact point
A - Key front, measured over front pin, to balance pin hole
D - Wippen flange center to jack/roller contact point
C - Wippen flange centre to capstan/heel contact point
F - Hammer centre to hammer strike point
E - jack/roller contact point to hammer centre

Hammer/key ratio diagram
Image was made prior to PCT stage of our patent application, hence the missing detail.

When taking measurements off an action, please note the following;

  • Be sure that the regulation is somewhere near specification, particularly regarding the hammer blow distance for actions with a significant offset of the jack/roller contact from the line of centers when at rest. See diag. below of a standard early Steinway setup (1906).

  • The most critical measurement is E (jack/roller contact to hammer center distance). An error of only 0.5 mm will cause a ratio error of 2.5%. Therefore, the size of the roller and the distance of the roller slot to the hammer center will have a significant effect on the hammer/key ratio. Watch out for poorly and unevenly fitted rollers - a major problem which causes note to note action geometry variation.
  • The contact point between the jack and knuckle will be nominally 1 mm away from the rear edge of the jack face. The rear edge of the jack should be aligned with the rear edge of the wood centre of the roller. Be sure that this is correctly adjusted prior to taking any measurements.
  • We take the front key lever measurement from the key top over the front pin, to the balance pin hole at the bottom of the key. Many others take the measurement from the very front edge of the key. I believe this is not representative of the real world conditions in which a pianist plays a piano. The front pin position would seem to be a more practical point from which to take ratio measurements. Since the 20 mm nominal distance from the key front the centre of the front pin is pretty much an industry standard, the validity of ratio measurements taken in this way will hold from piano to piano.

  • Measurements should also be taken from the black notes. There are many examples where the ratio of the black notes varies considerably from that of the whites.

Please email me if you require further explanation, or if something is not clearly explained.
Ron E. Overs
1 Dec. 2001

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