<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><DIV>On Jun 13, 2007, at 3:37 PM, Richard Brekne wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">All of this assumes that nothing else is going on... purposely... so as to shed light on what looks plausible or not.<SPAN class="Apple-converted-space"> </SPAN>To me, I agree right off that it does not seem plausible that the soundboard can actually rise or fall enough strictly vertically to effect pitch directly in any significant way.<SPAN class="Apple-converted-space"> </SPAN>I find the <<string climb>> up the pin interesting enough... as it is certainly looks doable from the perspective of what load the soundboard can bear... but if you apply the results to all strings... you end up with a steep climbing curve that is very much more related to speaking length then anything else. To be sure... lower BPP's will be affected more then higher ones... but if you run the numbers it ends up looking like the shorter the string the bigger the effect. Since we don't see pitch changes in that follow this pattern in real life pianos... this tells me something else must be a far more dominant factor.</FONT></DIV> </BLOCKQUOTE></DIV><BR><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>I know this discussion last June wasn't the most popular we've ever had on this list <G>, but I'd like to add a belated something to the topic. Not about calculations, but about physical causes. Ron Nossaman has said that he thinks the changing offset of the string through the bridge pins is the major cause of pitch change due to humidity change. But as Ric Brekne points out, if the change in offset between bridge pins is the major cause, it would make sense that the high treble would have the largest pitch change. Why doesn't it? There would have to be a factor acting in the opposite direction, affecting the high treble the most.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>I'll offer a couple possible explanations. First, the bridge expands in width at the same time it is expanding in height. If we take the bridge as fixed in position, the middle of the bridge will stay fixed, with the edges moving away from it. The front/speaking length side of the bridge will be expanding toward the tuning pins (more or less, more directly in the high treble), and it will carry the bridge pins with it. This will cause the speaking length to shorten, hence lowering pitch. (Obviously there will be an opposite effect with shrinking due to lower humidity, but for simplicity, I'll just talk about swelling and increased humidity here). And the pin closest to the edge of the bridge will move the most, meaning that in notched trichords, the string toward the bass will be flattened the most (true of the design of both grands and uprights). I noted this as a possible cause of the unison effect a while back. This effect needs to be seen as counteracting the overall rise in pitch. And the effect will be proportionally greatest in the high treble, as the speaking lengths are shortest there.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>A second factor is movement of the bridge itself. The soundboard wood is expanding when exposed to humidity, whether or not it presses the string plane upward enough to cause the measured pitch changes. There are forces at play which will cause given portions of wood to move relative to others. In the high treble, there is a lot more soundboard behind the bridge than to the front. Hence, it makes sense to speculate that the high treble portion of the bridge would move (relative to the plate and rim) toward the speaking length when the soundboard absorbs moisture.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>So here are two factors counteracting the side-bearing effect of the bridge pushing strings up the angled bridge pins. It's pure speculation, but it seems to hold together, and has the added plus of possibly explaining the way unisons behave. Also might explain why certain sections of unisons go flat while the rest of the piano goes sharp. It takes very little change in speaking length to cause a major change in pitch. </DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>There is an additional possible effect having to do with the bridge expanding/contracting in width: there is often a marked difference in pitch change (humidity induced) between unisons below and above plate struts. I have attributed it in my mind to curvature of the bridge there, or to changes in scaling. But it occurs to me that many pianos have a notching pattern that moves the speaking length pins closer to the center of the bridge in the unisons above a break, then jumps toward the outside of the bridge below the break. This is done for scaling reasons, but it could also provide a partial explanation for that pitch change difference. I've been trying to notice which pianos have that feature, and see whether they are also pianos that have that acute pitch change difference. So far, they seem to match fairly well, but it's early to say anything for sure.</DIV><DIV> <SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>I'm beginning the annual mass pitch lowering before fall semester, shoveling sharpness out of pianos as fast as I can, so this subject is acutely in my consciousness at the moment. Semester starts in a week and a half, and Monday at the private school I service. Summer's over. Why is it still hot?</DIV><DIV><BR><DIV><DIV>Regards,</DIV><DIV>Fred Sturm</DIV><DIV>University of New Mexico</DIV><DIV><A href="mailto:fssturm@unm.edu">fssturm@unm.edu</A></DIV><DIV><BR class="khtml-block-placeholder"></DIV></DIV><BR><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV></BODY></HTML>