##### The Key Force One measures continuous Down Force and Up Force values

##### across the pre-letoff keystroke, with continuous Balance Forces and Frictional

##### Forces calculated from those. Since the Key Force One measures actual - and

##### continuous - forces, new terminology had to be employed. Each of these four

##### sets of

*actual*##### forces is then averaged over the pre-letoff stroke, resulting in

##### much-improved parameters, relative to their old "weight" counterparts. The

measurements are performed autonomously by the Key Force 1 , either with

##### the action on the bench or in the piano.

##### The Balance Force line simply bisects the Down Force and Up Force lines.

##### At all points in the pre-letoff stroke, it is halfway between these two lines. The

##### Balance Force line describes exactly how all non-inertial forces (minus friction)

##### vary across the pre let-off stroke! Its average - the ABF - gives us the magnitude.

##### Its slope - the BF Slope - gives us the

*change*##### of the Balance Force per unit of

##### key travel.

The Frictional Force line is also determined indirectly. For any point
##### in the stroke, its value is the distance between the Balance Force line and the

##### Down Force line (or Up Force line). The slope of the Frictional Force line gives

##### a solid value to the degree that the friction varies throughout the pre-letoff

##### region, per unit change of key travel. A nearly universal finding from this revo-

##### lutionary parameter is that the friction almost always decreases with increasing

##### Since continuous forces are measured and graphed across the stroke, it is

##### natural to then ask "how are the forces varying?". We already know the aver-

age value of the given force: ADF, AUF, ABF or AFF. For any of these "static"

##### forces, an optimal line can be fit through the data points. The slope of such a

##### line numerically expresses how much that type of force tends to increase or

##### decrease with each unit change in key travel. Each type of static force thus has

##### both a best-fit line and a slope associated with it. The slope of the Down Force

Sline is called the Down Force Slope. The slope of the Up Force line is called the

Up Force Slope, and so on. So the average of a continuous force plot gives its

##### magnitude; the slope of that force plot's best-fit line gives the

*change*##### .

##### This product includes

*all of the Key Leveling product*##### information, and much

##### more. It also gives all the kinetically-determined, pre-letoff "static" force infor-

##### mation, for both down- and upstrokes. It also gives the continuous force data

##### for a downstroke moving all the way through escapement, to the dip point. Not

##### only are the individual notes' micrographs given, but important new "let-off

##### event" parameters are calculated from the raw force data. These parameters

deal with both the forces and "timing" of each note's let-off event. An accurate

##### measurement of Aftertouch stems directly from these "timing" calculations!

##### As you can see at the bottom of this page, macrographs of all these parameters

##### are provided with this product, for all 88 notes across the piano!

##### The following sequence of three images gives an idea how the Down Force

##### and Up Force plots are obtained. The Motion Profile is followed, so that the

##### "finger" moves down, waits, then moves back up, with both motions occurring at

##### constant speed. The forces are acquired versus time, but are automatically trans-

##### posed so the end result is the force vs. distance plot. In the third image, the

##### Down- and Up Force lines are shown superposed onto the data.

##### The following two graphs show "static" force lines vs. key travel, for two separ-

##### ate notes on two separate pianos. The raw force data is not shown, only the best-

##### fit lines. Note how the Balance Force line bisects the Down Force and Up Force

##### lines. Also notice that the instantaneous value of the Frictional Force line is

##### everywhere equal to the distance between the DF (or UF) line and the BF line!

##### The first graph is from a "normal" grand piano. The second is from a typical note

##### on a "magnetically balanced" action. It had attracting magnets between keystick

##### and frame, in front of the balance rail, with repelling magnets behind the rail.

##### The purely "static" (non-inertial) feel of these two actions is very different, but

this difference could simply not be seen before the Key Force 1 revealed these

The "measure while moving" technology of the Key Force 1 allows the

##### the forces incurred during escapement to be measured continuously, as the

##### key descends at constant speed. Of course, these forces are actual reaction

forces between the key and the moving KF1 finger. The resulting force sig-

##### nature is then used to calculate several revolutionary new parameters, per-

##### taining exclusively to the let-off event. These new parameters are:

•

*the distance along the keystroke, to the Let-Off Start Point*

•

*the distance along the keystroke, to the Jack Trip Point*

•

*the maximum force incurred by the let-off event*

•

*the duration [mm] of the let-off event*

•

*the work done by the plunger during the let-off event*

As with the Down- and Up Forces, the let-off forces are measured while the

##### finger follows a known motion profile, in this case downward and at essentially

##### constant speed. A typical Motion Profile for this is as follows:

The times t_{LO} and t_{JT} are the times to the Let-Off Start Point and the Jack Trip

##### Point, respectively. Similarly, KMLO and KMJT are the key

*movements*##### from

##### rest position to these two points. With the measured forces transposed from

##### time to distance, a typical graph from an actual piano key action is shown below.

##### An additional force parameter is shown here:

**Let-Off Increase**##### . It is simply

##### the maximum let-off force (Jack Trip Force) minus the Average Down Force (ADF).

##### This takes the magnitude of the ADF out of the equation. The Let-Off Increase

##### thus represents the amount of additional force brought on by the escapement itself!

##### The amount of work required just to get through let-off is shown by the yellow

##### hatching. The let-off forces - and work - depend somewhat on the downstroke

##### speed, with higher speeds generally producing higher forces and work values. For

##### better comparisons of this force/work, from note to note, speeds used for those

##### measurements are consistent from note to note! The Point "F" is the point where

##### the hammer knuckle falls back onto the balancier. When the Aftertouch is below

##### a certain value, this point will be hidden among the ever-increasing front punching

##### compression forces. The Aftertouch is large enough here for it to be seen.

In addition to the macrographs associated strictly with the key leveling data,

##### this product gives you a host of others. Remember, macrographs are graphs of

##### one or more parameters, versus note number across the piano. First of all, we

##### have the let-off "timing" data superposed onto the key leveling data. Note that

##### this is the same key leveling data as was shown over in the Key Leveling product.

##### The two orange dots at each note are the start (upper one) and finish of the let-

##### off event. The upper and lower red dots are the at-rest and depressed/dipped

##### key locations. The green dots are the desired at-rest and bottom positions. The

key leveling data veers upward badly in the treble, as was mentioned in the Key

##### Leveling Product section. The way in which the let-off and aftertouch were

##### set led to the jack trip point also following the veering key limits. Again, none

of this was discovered until the Key Force 1 measured the action and revealed

##### all this data graphically. Also realize that for any note, the Aftertouch is simply

##### the vertical distance between the Jack Trip point (lower orange dot) and the

##### bottom of the stroke (lower red dot). For the white keys of this piano, it varies

The other main escapement-related macrograph that comes with this product

##### is a graph of both Let-Off Increase (LOI) and Let-Off Duration (LOD). LOE is

##### given in grams-force, and is the amount of additional force created during the

##### constant-speed downstroke due solely to escapement. The LOD, given in mm,

##### states how much key travel occurs between the very start of the let-off event and

##### the Jack Trip Point. Below is an example of such a graph, for that same piano.

There are several other macrographs that come with this product, all having to

##### do purely with the "static" forces. One set involves various combinations of

##### Balance Force, Down Force, Up Force and Frictional Force. The other includes

##### graphs of the slopes of the corresponding best-fit lines for these various forces.

##### In the box below are shown examples of most of these macrographs.