In the PTG article did you cover what happens when the shank is set at an angle to the vertical? The hammer then travels in a cone instead of a plane. And for the hammer to be perpendicular to the strings when striking them, they cannot be perpendicular to the strings when at rest.
When I replaced the hammers on my own Walter Console, mostly as a project, I ran into this and decided the improvement in tone was worth it. But my, oh my, did I have to do some tapering for clearance! I did cheat on the lowest bass notes, though. They don't hit the strings quite perpendicular, but I don't think it is as important with single strings. The tone improvement is probably from the better hammer mating.
No, I did not. I don’t know of any modern pianomaker doing this. Probably for good reason. Unless the hammerbutt flanges were also angled—A nightmare I don’t even want to begin contemplating!—I should think it would increase the torsional stress on the hammershanks (introducing a lot of erratic hammer wobble) and the hammerbutt flanges introducing increased action center wear. But I must admit I haven’t really thought about this much. (Question: Without altering action center spacing on the action rails how much can you angle those hammershanks?)
The articles came about, in part, because I regularly hear from people who tell me that “good pianos” have a lot of—or very little of—this or that particular feature. Usually it is something like string length (especially in the low bass of very short pianos), string angles (again usually, but not always, in short pianos), scale tensions, soundboard area or some such. According to these claims it should be possible to come up with concert grand performance in a piano the size of a spinet. If only I would do such and such….
Briefly; as they might apply to this topic:
From a purely theoretical standpoint when laying out an overstrung scale to fit in a short piano it would seem that the more we angle the bass strings the better. Why not, after all, take full advantage of one of the only two inherent benefits of overstringing and make those bass strings as long as possible? As you discovered with your Walter, though, there are downsides to this approach that may not, at first thought, be apparent.
Side-to-side string spacing within the bi-chord unisons is a more-or-less fixed dimension. Typically bi-chord agrafe hole spacing is 6 mm. Even if we don’t use agrafes we still have to stay close to this spacing. Side-to-side bridgepin spacing varies but it is usually around 7 to 10 mm. No matter the string angles we cannot decrease either of these by much or the strings are going to start hitting each other; especially as the overall diameter of the strings increases (which it does quickly in short scales).
With the strings at 90° to the strikeline side-to-side spacing between the notes—the action center spacing
—could safely be as little as 13 mm (plus or minus some small amount) without causing any string clearance problems between notes. As the string angles increase, however, the action center spacing must be made increasing greater to keep the strings from adjacent notes from hitting each other. This is not a big deal until the string angles are made greater than about 30° – 35°. Action center spacing of around 14 mm will suffice; not a big increase. Much beyond this and the action center spacing has to be increasingly wider and once you pass 40° action center spacing has to be made increasingly wider by a lot
Making the action center spacing wider, of course, makes the piano wider and it increases the amount of keyflare required. Increasing the keyflare increases the amount of side force on the keybushings causing them to wear out faster. It also results in an increasing amount of twist to the key and this increases action saturation.
If we’re going to attempt to align the hammers with these steeply angled strings there are also going to be problems. We’re going to have serious side-to-side clearance problems through the hammer’s arc of travel. Here we have two possible solutions: we can make the hammers thinner—the opposite of what we want in the bass section for acoustic performance—or we can increase action center spacing. Once the boring angles go much beyond 15° – 18° or so clearance through the hammer’s stroke becomes a problem. (Anyone doubting this has never replaced a set of hammers on a square!) So, we either limit our bore angles or, again, we have to increase the action center spacing beyond reasonable limits.
If we limit our bore angles and don’t align the hammers to the strings then once again action center spacing will have to be increased or the hammers will begin striking the neighboring strings of the adjacent unisons.
Etc. (Does anybody notice a trend here?)
The point of the article was that it is easy to focus on one or two scale or design parameters and say that this or that should be done to make a good piano. The reality is somewhat more difficult; choices must be made and compromises must be found. The best pianos will be those in which the designer has made reasonable and artful choices that result in a suitable balance between all of these.