I was told, early in my career, that newly molded cast iron distorts as it cools to bow a new plate in the direction we're familiar with: high in the middle, lower at bass and treble. From the action's point of view, this produces string height variations that interfere with regulation (I refer you to my first posting in this blog, Introducing Grandwork™: "Bowed-Plate Syndrome" as a Regulating Asset). But a question that has been puzzling me is why would best piano manufacturers not find a solution, if the net result of this "syndrome" is problematic? Surely, they could compensate in some way, either by modifying molds or by shape-tweaking results? And the worst manifestations happen in concert instruments.
Perhaps, however, rather than a syndrome to be tolerated, it's a feature to be embraced, even at the expense of inconveniences to the action. Instead of "bowed plate syndrome", it's "crowned plate design".
The soundboard is like a light-weight bridge that must support a heavy load across much of its surface at once with as little understructure as possible. Crowning is a means to withstand the downbearing pressure of string tension and its best configuration pays both tonal and structural dividends. An overall crowning of the agraffes and capo bar in harmony with the crowning of the soundboard could have the downbearing component of string tension directed orthogonally through bridges, soundboard, and ribs toward the center of the radius to which the board was bellied (60'?). I think, whether by serendipity or design, such a configuration between plate and soundboard maximizes stability, resistance to collapse, and sensitivity to energy transfer from the strings. The bearing meets the belly's opposing forces directly, consolidating and balancing resources, creating best resonance, power, and sustain. And best tuning stability.
The extreme degree of concert grand plate crowning, which I found in one famous maker's design, is to a much smaller radius than the soundboard it applies strings to. I conjecture that, for instance, longevity is of less concern than, say, projection, power, tuning stability, and sustain, and that possibly each of these features is enhanced by extra plate crowning. Consequent pressure ridges, or premature deterioration, or collateral annoyance to a regulator, take back seats to the stage presence it reinforces. To the small hall, living room, or practice room piano, a more conservative plate crowning would suit the owner's interests and the manufacturer's warranty better.
A next question might be how, then, to set up an action to best cash in on this double asset's value, assuming custom boring has been embraced to turn the crowned string heights into a first asset.
Sensible design choices have traditionally placed the action on a flat horizontal bed and simplified the organization of parts by lining them up from parallel rails in parallel positioning. There have been exceptions, such as Chickering, with flared whippen and hammershank positioning, but results tended to be more fussy and expensive to execute. So the vertical array of parallel parts solves organizational issues, but it also is an efficient compromise between the interests of finger, hand, and arm access and those of translating their input into a hammers-striking-strings output. Direct opposition to gravity creates stability in the parts as they transfer their loads. And vertical delivery is the shortest distance between planes of keys, keybed, and strings.
The main compromise in the vertical / parallel layout occurs in the high treble. Fitting hammers with vertical travel and vertical squaring has much to recommend it, but going into the high treble where string heights descend the most, each unison's three strings get lifted different amounts to achieve hammer-to-string mating (without hammer miss-filing): bass-side the least, middle more, and treble-side the most. There is a risk of overlifting the treble-side string, creating instability, falsebeats, and increased possibility of breakage. Also, there must be differences in the flexibility of differently lifted strings that might have voicing implications.
So what if sectionally, "vertical" was tempered to be perpendicular to strings along the strike line, instead of perpendicular to the keybed. The Grandwork Squaring Platform, with its Shank Traveler and Hammer Square, can certainly accommodate this shift in direction, coordinating with strike information in the Regulating Rack's templates. Delivery and bounce would be slightly lateral (off the line of gravity), but the system would work identically otherwise. This way the strings wouldn't have to be unnaturally "leveled" or the hammers miss-filed to achieve good mating, and probably the mating would be more stable.
Would there be noticeable conflicts in the travel, squaring, or spacing of keys or whippens? Certainly, backchecking and springs could accommodate. There would be some slight conflict between hammer crowns and strings at letoff during soft pedaling, since the high side of each hammer would be letting off under a slightly lower string, when the action is shifted one string toward the treble.
A crowned keyboard is already a feature with desirable attributes and employed by many. The standard option of .0375" over 4' is a compromise between a flat keybed and the .2875" differential I found last year in two sets of concert grand string heights, but is it close-ish to the arc of a 60' radius? The natural range of motion of hands, wrists, and arms harmonizes with this crowned layout. How about crowning the front rail (or entire keybed), as well?!
I thought I might consider implementing this idea in a Steinway O I'm working on, but the string spacing totally supports action part verticality to the keybed's horizontal. It is a Hamburg "Miniature" with no cloth on the action stop and the rough installation of new hammers traveled and hung to strict verticality fits more or less perfectly - slight tweakings only. Not happening in a natural way on this piano and "natural" is an important ingredient. Might be worth looking into, though, if you get to design or redesign for a manufacturer...?
These considerations embody a principle of accomplishing things in this universe, including piano making, assembly, and regulation. Compromise is a vital component of accomplishment. And differing degrees of success, from a particular point of view, are possible depending on the terms of each compromise. On the one hand, the overall system is only as good as its weakest link. But on the other hand, the full potential of the system is only realized in specifically creating and respecting sensible hierarchies of the interests involved. And no compromises would mean nothing gets accomplished.
Stepping back from a possible discussion of national politics, I will enjoy the benefits of "radial verticality", to the extent they are present and support the higher end goals I hope to be heading toward. An example of radial verticality we all benefit from works through gravity on planet Earth. Two people standing upright in two different places, say Boston and San Francisco, may both be vertical but they are radially vertical from the Earth's center and not parallel. The perceived compromise of one principle may be the legitimate manifestation of another.
Which produces the best results is ultimately what we're after. Which configuration is the simplest, strongest, fastest, most profitable, or results in output that is the most musical, maybe. Or sometimes, viability depends on which set of collateral outcomes is least undesirable?
It may be that vertical from keybed is the winner for simplicity of application and least compromise in the most aspects of delivery. The spacing of strings relative to action parts is important to this outcome. If the former wants to be broader than the latter, perhaps there is a natural fit. If too many arbitrary contortions are required, then redesign would be required first and that might leave radial verticality dead in the water for reasons of insufficient startup funding.
But in any case, I think a flat string plane is at odds with the needed crowning of a soundboard. There would be a tendency to crush the middle and be light on the edges. If bridge height is used to mitigate, the bridges would be tallest and stiffest near the edges where they would solidify and bind vibration in the board. Harmonizing plate crown with soundboard crown, however, would facilitate even bearing, balance overall pressure, and consolidate the natural components of string, board, and bridge stability.