This video was created by WGBH Public Television Boston for the Annenberg Network series on Mathematics as an example of someone who has put Algebra to use in the real world in service of world culture.
There are three additions I’d like to make:
When using 1 gram blocks simulating the piano hammer out on the far end of a see saw, the movie shows me placing the block on the table instead of on the end of the beam.
The reason, which is not shown, is that I place weights along the beam to simulate all the parts of the key. When they are in place then I place the 10gram weight on the end of the seesaw and slide it along until this beam is balanced.
How far out the weight is on the beams tells the weight ratio of the action.
Finding the position for a known weight on a see saw so that the see saw balances level is an analogy for solving an equation for a single unknown variable.
When displaying the hammer weight analysis of a Hamburg Steinway D in Jordan Hall, New England Conservatory of Music. The data shows a big dip in the weight.
This is the way it came from factory and it’s usually the hammer weights are found to be smoother in these pianos but you never know until you measure them..
What the video does not say is that the dashed lined on the graph just above the hammer weights is the new Precision Touch Design specification after modifying and upgrading this action.
Lead weights were inserted into the wooden portion of the piano hammer to bring the weights up so specification.
The result is a more even and predictable result in the response of the keys and more evenness in the tone. Bringing the weight level up also increases the projection of the sound and fullness of the tone which is important in a concert hall.
After showing a graph of how much lead weight is in the keystick from the factory and how the equation is used to smooth out the weight inconsistencies, I mention that we use a wippen support spring added to the existing parts.
A combination of spring tension and lead weight is used to create a faster, quicker action without giving up hammer weight and tone.
It should be noted that we do not do this to all Stanwood Action jobs. It is what we call a “High Performance Option”.