Plan by Number?

The Grandwork System favors trial-and-error and go-nogo procedures over formulas and numbered measurements. Tapping on the frontrail of a grand action in its piano can alert us to a crowned fit or confirm a full fit. This same go-nogo procedure works for sampling keyframe bedding with Keysteps. The fastest way to fit a non-fitting frontrail to its keybed involves sanding places of contact until the whole rail has contact, tapping until all tapping back is eliminated. Tapping on a bedding sample key for its tapping on the Keystep machine screw below as it's turned up until there's no tap is a trial and error procedure that comes so close to finding the exact place of key and Keystep just touching that + or - .001" seems a rough tolerance. Same with the tolerance of detecting fit or no-fit for a keyframe's frontrail. You can't pay a machinist enough money to guarantee this close a tolerance. In general, numbers and math empower designers and manufacturers but slow down piano technicians. We are skilled at estimating, verifying, and getting on with the job but likely less skilled at the math.

So, why feature numbers in my discussion of grand weighoff? When all is as-expected, measuring, recording, and crunching numbers costs time. But if knowing the sense of some pre-crunched numbers expands our range of what is expected, we can proceed more directly to sensible sampling and better-aimed trial and error.

Our weight formula gave us a view of what changing hammer weight does to upweight, downweight, and inertia. And the distance formula helped us look at what changing knuckle placement does to key dip and/or blow distance. But what if such spec choices are already in place and our customer wants to know what we can do to improve the outcome? How well we understand what can be changed, what must be changed, and what cannot be changed becomes important, and knowing which changes will definitely better what is falling short becomes invaluable. Pre-crunching some numbers, then, can prepare us for troubleshooting, assessing, and proposing a course of action that we can have confidence in and that our customer will be pleased with.

I think many of us have a combination of impatience with numbers and an obsession with them. Numbers are a naming system. They are names describing the thing, they are not the thing. So we are impatient with numbers when the thing is right in front of us. On the obsession side, we'd like to name it once and add it to what we know. But the beauty, the complexity, and the quirkiness of things as they are transcends any naming system. And whether impatient or obsessed, when the team of things cooperates, who cares? So how do we become a team leader who gets such cooperation to happen with regularity? 

If we take naming as a process of metaphor and revelation, a something that sheds light on things rather than tries to define them, then we move from impatience and obsession into a world of utility. This utility has no problem adapting to what really happens - it's looking for it. The errors and the synchronicity become equally useful and our work benefits.

Mechanical tolerance describes the range of a measurement's acceptability. How close can letoff be before it encounters interference? How far away before affecting playability? The boundaries of a well-considered tolerance lie just in from the chance of a problem. But how accurate can we be within the tolerance we name? Probably less than we'd like to think but good enough for what is needed. Sampling will generally find the practical tolerance where trying to name an exact number may prove too difficult.

To play my own devil's advocate, having a suitably accurate concept of the number needed can help. An example of lame results from fuzzy thinking presented itself to me this morning:

I start my day with some lemon water. A whole lemon is too much and a quarter seems too little, so I'm cutting them in thirds. The view as I cut shows the line of slice but not the segment shape I'm creating. I made the first cut down into the center of the lemon and the second around past a quarter but less than a half. Clearly, the resulting remainder was less than two thirds and three days ago I did the same thing. I, the customer, was not happy with this, so when I did it again today, I reflected in my head on the math of what I should be looking for. More than .25", less than .5". Well, .33", if I round down. .08" more than .25" and .17" less than .50". Let's see: .08" x 3 = .24", so I need to estimate adding about a third of the second quarter to the first quarter. Right: three quarters plus three 1/3 quarters will add up to a whole lemon. The fact that the numbers of an actual third go to infinite decimal places is annoying and indicates one limit to how accurate a number can be. But the rounded .33" will work fine as center of the lemon-cutting tolerance and I'll probably do a better job next time.

Tweaking action geometry has similar, if far more expensive, hazards and solutions. My view is be methodical but flexible but disciplined but thoughtful, and joyful but timely, but insisting on best quality, but realistic. Does such a philosopher-technician's approach require numbers? No, as long as things work. Can it benefit from numbers? Yes, if they speak a truth that we can hear.

So, rather than an exhaustive (and exhausting) list of what happens when each detail is changed, I'll offer a summary of our models. For this purpose, let's eliminate the weight-specific and distance-specific modifiers. They give us more accurate answers but confuse the relationships. In their place, adding 14% to the action leverage (AL = SL (shank leverage) • WL (whippen leverage) • KL (key leverage)) for weight and subtracting 14% for distance make the Welte numbers match the final specs I ended up with after contracting spread just a little more. The trial and error spread tweak was prompted by a slight disappointment in results after so much work and it magically improved feel and playability, bringing all specs into the expected (hoped for) zone.

This summary uses numbers from the Welte naturals (the sharps have taller whippen heels and a different key ratio but similar relationships).

      leverage = RA (resistance arm) ÷ EA (effort arm)
      SL = 5.62 ÷ .87 = 6.46
      WL = 3.75 ÷ 2.61 = 1.44
      KL = 4.50 ÷ 8.50 = .53
      AL = SL • WL • KL
      AL = 6.46 • 1.44 • .53 = 4.93
      ALW (AL for weight) = AL + .14 • AL
      ALW = 4.93 + .69 = 5.62
      ALD (AL for distance) = AL - .14 • AL

      ALD = 4.93 - .69 = 4.24

Downweight (DW) vs hammerweight (HW) simplified:     
      DW =  HW • ALW
      DW = 8.9 • 5.62 = 50.02
      HW = DW ÷ ALW
      HW = 50.02 ÷ 5.62 = 8.9
      UW (upweight) = 20.0 (minimum/maximum for low bass)
      BW (balanceweight) = (DW + UW) ÷ 2 
      BW = (50.0 + 20.0) ÷ 2 = 35   
      F (friction) = (DW - UW) ÷ 2

      F = (50.0 - 20.0) ÷ 2 = 15

Key dip (KD) vs blow distance (BD) simplified:
      KD = BD ÷ ALD
      KD = 1.75 ÷ 4.24 = .413 
      BD = KD • ALD

      BD = .413 • 4.24 = 1.75  

At the front of the key, at the player's finger, we have key dip and downweight, and at the striking end, we have blow distance and hammerweight. In between are the three levers and friction. Embracing all are action balance (weighoff) and inertia. The puzzle of how best to push and pull the details into a better configuration becomes unavoidable when one or more elements are unacceptable. Fortunately for the problem solver, some of the elements must remain the same or become very specific alternatives, limiting the possibilities.

For both musical and mechanical reasons, standard dimensional and tonal expectations should remain our priority guidelines. The published specification is of secondary importance. Key height, for instance, must provide enough front keypin in the front bushing and enough balance keypin protruding from the balance bushing combined with no visual gap between top of keyslip and bottoms of keys and enough gap between tops of keys and bottom of fallboard - regardless of a discrepancy with the spec sheet. 

If our customer wants a change in the way their action plays, a series of changes may be required. On the other hand, if a shallow dip and a long blow distance have aftertouch in a piano with a heavy action, one change may solve a series of problems! The tradeoffs form a spectrum of possibilities that mostly involve choosing priorities. The numbers, when they fall within the expected range and have continuity and consistency, disappear from view. Whatever the balance of considerations, weighing off will help to assure customer happiness.  

Part 1 "Why Weigh Off?" 

Part 2 "My Strategy" 

Part 3 "Method and Style"

Part 3a "Regulation Strategy Review" 

Part 4 "Pragmatics"

Part 5 "Trials and Errors"

Part 6 "Levers"

Part 7 "Playing with Proportions"

Part 8 "Weight, Friction, Inertia, and Distance"

Part 10 "Best Balance for Best Art"