<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META content="MSHTML 6.00.2900.3020" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: #ffffff" bgColor=#ffffff> <DIV>My take on this, Julia, would be that calculus *is* used in scale design.  Within the models that are used to derived equations, certain assumptions ( that a value is a constant or there are negligible interrelationships of different values for instance) are made that reduce the calculus into a discrete formula that can be more easily used.  </DIV> <DIV> </DIV> <DIV>What may increase the accuracy, as you suggest might be the benefit of using calculus, might be to more realistically develop the model and the assumptions inherent in it.  For example, I'm not sure that we have accurate models of string vibration, given the effects of at least one end point moving in space and time relative to the influence of the vibration (forcing function) other strings, the bridge, soundboard, etc.  Similary I'm not sure that we have accurate models of the effects of the non-speaking lengths of the string on the speaking-length vibration.  And these two models influence each other.  This gets just way to complicated.</DIV> <DIV> </DIV> <DIV>Probably, if we had such models, we would be too confused mathematically to get a handle on solving it.  It would be fun to try, and it would be nice to be smart and rich enough to undertake such endeavors.</DIV> <DIV> </DIV> <DIV>Just my late-night thoughts.</DIV> <DIV> </DIV> <DIV>Mark Ultsch, RPT</DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B> <A title=KeyKat88@aol.com href="mailto:KeyKat88@aol.com">KeyKat88@aol.com</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, February 14, 2007 9:12 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Is calculus ever used in scale design?</DIV> <DIV><BR></DIV> <DIV>Greetings, </DIV> <DIV> </DIV> <DIV>     Is calculus ever used in stringing/scale design? If not, why not?</DIV> <DIV> </DIV> <DIV>Julia Gottshall</DIV> <DIV>Reading, PA</DIV></BLOCKQUOTE></BODY></HTML>