Two readings, two different problems
Press slowly on a key with gram weights until it goes down and you have the down weight. Let the key rest at the bottom and take weights off until it comes back up and you have the up weight. Gravity acts the same way in both directions, but friction resists whichever way the key is going, so it adds to the down reading and subtracts from the up reading by the same amount.
That gives you two equations and two unknowns. The average of the readings is the balance weight, the part that is pure mass and geometry. Half the difference is the friction. With the defaults, 52 and 22 give a balance weight of 37 grams and friction of 15 grams, and the spread of 30 grams is twice the friction.
The reason this split matters is that the two respond to completely different work. Balance weight comes from the hammer, the whippen, the shape of the key and the lead in it. Friction comes from bushings, centre pins, the key pins and the surfaces they run on. A key that reads 52 down because it is heavy and a key that reads 52 down because it is tight are the same number and opposite jobs.
What a lead is worth
A lead is a mass acting through a lever arm. Put a 6.5 gram lead 100 mm in front of the balance pin and it produces a moment of 650 gram millimetres, and referred to a measuring point 125 mm out that is 5.2 grams of help. Balance weight falls from 37 to 31.8, so down weight falls to 46.8 and up weight to 16.8. Both move by the same 5.2, and the 30 gram spread does not budge.
The linearity is worth internalising. The value of a lead is its mass times its distance divided by the measuring distance, so at the default numbers each millimetre of lead position is worth 0.052 grams. Moving a lead 25 mm forward buys 1.3 grams. Two leads at the same place buy exactly twice one lead. And a lead placed behind the balance pin adds weight rather than removing it, which is occasionally what you want and much more often an error in which direction someone measured from.
The part the gram weights cannot see
Static touch weight is measured with the key barely moving. Playing is not like that. Every gram of lead that reduces the static reading also has to be accelerated and decelerated on every note, and inertia does not care which side of the balance pin it sits on. A key made light by burying a great deal of lead near the front is light on the scale and heavy in fast passages, and pianists describe it as sluggish while the technician is looking at a set of numbers that all say the action is light.
This is why lead is not a free adjustment and why heavy hammers cannot be fixed indefinitely by adding lead further forward. The static number improves, the dynamic behaviour gets worse, and at some point the answer is lighter hammers or a different geometry rather than more holes in the key. That decision is outside what any static arithmetic can settle.
Comparing keys honestly
Every gram figure on this page is referred to the point where you set the weights. A gram at 135 mm from the balance pin is not a gram at 125 mm, so two technicians measuring the same key at different points get different down weights and both are right. Before comparing anything across a set — note to note, before and after, this piano against that one — fix the measuring point, write it on the bench, and use it every time.
The same discipline applies to the readings themselves. Whether the damper is engaged, how slowly the weights are added, whether the key was tapped to break static friction: all of it moves the numbers by more than the differences people are usually trying to detect. The arithmetic is exact. The measurement is not, and the measurement is the weaker half.
Questions people ask
What down weight should a piano key have?
This page does not say, and it is not being coy. Targets differ by instrument, by maker, by the era it was built in and by what the player wants, and the number that matters for a rebuild is the one in the spec being worked to. What the arithmetic does settle is that a down weight on its own is not enough information to act on. Take the up weight too, split the pair into balance weight and friction, and then compare the balance weight against whatever target you are working to.
Why does adding lead not change the up weight gap?
Because lead is mass and the gap is friction. Lead shifts the balance weight, and the down and up readings both sit at a fixed distance either side of it — down is balance plus friction, up is balance minus friction. Move the balance and both move together, so the spread between them is untouched. If the spread is what bothers you, the work is in the centres and the bushings, and no lead placement will substitute for it.
Where should a key lead go?
The arithmetic says a lead further from the balance pin does more, in exact proportion to the distance, so the same weight change costs fewer leads the further forward they sit. Everything else about the decision — how many holes a key will take without weakening, how the leading pattern runs across the set, and what the inertia cost is of concentrating mass at the front — is outside this page. It calculates the static effect of a position you choose; it does not choose the position.
Does the measuring distance really matter that much?
Yes, and it is the commonest reason two sets of readings will not reconcile. The gram weights produce a moment about the balance pin, so their effect scales directly with how far out they sit. Reading at 135 mm instead of 125 gives numbers about eight percent lower for the same key. Any comparison across notes, across a rebuild, or between two people needs the same point, and the point needs to be written down rather than remembered.
Can I work out the whole action ratio from this?
Not from these readings. The lever ratio the page prints is the key alone, front distance over capstan distance, and it is only part of the chain — the whippen, the shank and the hammer all multiply on top of it, and the full action ratio is measured with a different setup. What the key ratio is good for here is understanding why the capstan end of the key sees a much larger force than the front does, and why small changes at the capstan are not small at the keyboard.