--On Friday, March 14, 2003 9:49 AM +0100 Richard Brekne <Richard.Brekne@grieg.uib.no> wrote: > [ ... ] > [...] I had thought that Jim was outlining some > requirement for the momentum of the hammer crown to be perpendicular to > the string at impact at the same time as a hammer with a 90 degree rake > was to be perpendicular to the string. Of course I couldnt make this add > up :) > > But I do still have a little itch on my left temple. Jim mentioned that > it would be desirable to put the center pin on the string plane for both > grand and uprights. That would indicate to me he's got something else in > mind then just the gravity assist on rebound for an upright. This question about having the same, or different, conditions for grands and uprights seems to take the discussion of travels along arcs into the important area of hammer/string interaction during the (microseconds-long) duration of contact, before the joint action of string return, hammer felt (and other) resilience, and gravity has brought about the final loss of contact. I don't have knowledge in this area, but recently saw it discussed in the piano section of The Physics of musical instruments, ed. Neville H. Fletcher and Thomas D. Rossing (New York: Springer, c1991; 2nd edition, c1998), which refers to previous published research. It is certainly quite interesting. My guess was, that the importance of the arc travel of the crown striking surface (and underlying layers) referred to had to do with the changing geometric relationship between felt layers and string surface points (and string interior) *after* the instant of first contact; I didn't think of the related question of force of blow at that instant, which seems to be, at least when taken narrowly, what is brought out further by Ric below. In Fletcher and Rossing (and, probably, even more pointedly elsewhere), it becomes clear that in this event of (briefly)enduring contact, the tone--and even the initial-transient, "non-continuing" part of the tone--is only in the beginning stage of the process of its formation. But, it seems at least reasonable to expect that the changing geometry of this contact, between its beginning and end, might be influential. And, in this regard, a difference between a standard modern vertical and a standard modern grand suddenly seems to take on relevance: the "contact-arc" of the grand, throughout some of its range--more or less of it, depending on string length and other elements of design--has its center (the hammer flange center) forward of the capo or agraffe, while the "contact-arc" of the vertical has its center in back of (below) the strike line, in the region of (or even beyond) the upper node of the second partial of the speaking length. Therefore, if we assume that, for example, a thousandth-of-a-millimeter segment of string material, initially contacted by the axial center of the hammer crown, *becomes* a slightly longer segment whose own center is *closer to* the capo/agraffe, when it has reached its initial maximum amplitude as part of the first or second partial (or better, a "future" part of the first or second partial that is in the process of formation), than it is when at rest, or at zero amplitude, then it will be seen that the "contact-arc" of the (standard modern) grand is always "approximately congruent with" the arc that is travelled by the contacted string segment around the capo/agraffe termination as its center, while the "contact-arc" of the (standard modern) vertical can never be even approximately "congruent with" the corresponding arc travelled by the contacted string segment of the vertical's string: the latter two arcs are always "opposed to" one another. What this geometric fact might *mean* in terms of transient or continuant tone production, is, of course, the design question. Related questions appear at the other end, at the bridge termination. If I understand the German correctly, Junghanns et al. (Piano- und Fl"ugelbau, Frankfurt am Main: Verlag Das Musikinstrument, various editions in the 1970's) point out that it has sometimes been thought -- e.g., by a Feurich designer -- that the longitudinal pull, or longitudinal vibration, of the struck or vibrating string on the bridge termination is able to influence tone by causing the bridge momentarily or periodically to "tilt" (kippen). For this reason, Feurich was said at one point to have favored straight bridges, rather than curved bridges. Of course, what kind of "travel" the bridge termination point might take from this particular cause would require an analysis of what kind of "fulcrum" the bridge, as part of such a "lever", might have in the whole system of the flexible, and tensioned/compressed, board assembly, at any given instant of total tone (or silence). *Perhaps*, we are dealing with movements that fall below a certain threshold of significance for the kind of theory we need at this point. (Cf. what Del Fandrich has said, on his web site, about the theory of wood species tonal properties that was based on the finding of microscopic "resonators" within the interior of the tissues of spruce, in the conferences organized by F. Morton et al. in the period around 1916, and reprinted by Vestal Press.) Randy Jacob University of Michigan Library [The thread included further] : > I think the diagram below shows what I am confused about here. While the > tip of the hammer would certainly have its momentum orientented > horizontally, the angle of the hammer itself is far from perpendicular to > the string at impact. And the longer the hammer bore the larger that > angle would be. Isnt that going to cause several other problems ? It > would have an increased tendancy to stress the joint of hammer and shank. > The hammers center of gravity wouldnt be perpendicular either... or what ? > > Perhaps it is a misconception, but it has always been my understanding > that the maximum amount of energy that the hammer can impart to the > string occurs when the shank is paralle to the string, and the hammer > perpendicular to both. Jims post seems to be saying something else. Or > what ? > > > Cheers, and thanks > > RicB > > [Image] > > Keith Roberts wrote: > > > Try this. Take a hammer/shank/butt and with a pin, affix it through the > > centerpin to a piece of paper. Scribe the arc made by the end of the > > shank, Then drill a hole through the center of mass of the hammer and > > scribe that arc. You can see that the center of mass is moving down at > > an angle to the strings when the bore distance is set up at the center > > pin distance. If you cut loose this missile (which is sort of what > > happens when let off occurs) it would immediately begin to tumble...... > > Keith Roberts > > > > > Ric: > > The crown of the hammer would move in a different arc than that of the > > shank. When the hammer shank is vertical, and the arc it travels in is > > at it's apex, the tip of the hammer is on a downward descent. Draw a > > straight line between between the tip of the hammer and the hammer > > center pin. When that line is vertical, the tip of the hammer is > > moving straight into the string. The shank would be tilted back. > > Thus, putting the center pin closer to the string means that the tip is > > hitting the string on a > > more horizontal plane. It makes sense. Maybe it's a question of which > > arc you want to worry about. > > > > Roy Peters > > -- > Richard Brekne > RPT, N.P.T.F. > UiB, Bergen, Norway > mailto:rbrekne@broadpark.no > http://home.broadpark.no/~rbrekne/ricmain.html >
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