<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=US-ASCII"> <META content="MSHTML 6.00.6000.16414" name=GENERATOR></HEAD> <BODY id=role_body style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial" bottomMargin=7 leftMargin=7 topMargin=7 rightMargin=7><FONT id=role_document face=Arial color=#000000 size=2> <DIV><FONT size=5>  The header should a been re titled a ways back guys</FONT></DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"><FONT style="BACKGROUND-COLOR: transparent" face=Arial color=#000000> <DIV><FONT size=5>.</FONT></FONT><FONT size=5>Dale</FONT></DIV></BLOCKQUOTE> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"><FONT style="BACKGROUND-COLOR: transparent" face=Arial color=#000000 size=2> <DIV> </DIV> <DIV><STRONG><FONT face=Arial size=2>IF YOU WANT TO KNOW THE TRUTH, STOP HAVING OPINIONS!</FONT></STRONG></DIV> <DIV> </DIV> <DIV> </DIV> <DIV>In a message dated 02/20/07 02:04:30 Central Standard Time, ricb@pianostemmer.no writes:</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"> <DIV> <STYLE type=text/css> .aolmailheader {font-size:8pt; color:black; font-family:Arial} a.aolmailheader:link {color:blue; text-decoration:underline; font-weight:normal} a.aolmailheader:visited {color:magenta; text-decoration:underline; font-weight:normal} a.aolmailheader:active {color:blue; text-decoration:underline; font-weight:normal} a.aolmailheader:hover {color:blue; text-decoration:underline; font-weight:normal} </STYLE> Hi Dave <BR><BR>Jims Article was entitled "Unisons - The effect of tuning on persistence <BR>and timbre"  September 1982</DIV></BLOCKQUOTE> <DIV>Dave, as Ric says above, the article is from...:-) (thanks Ric).</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"> <DIV>. <BR><BR>Its a good read and it shows (I think) where the present idea that the <BR>pin is the kind of support the article refers too in the pendulum <BR>analogy, and that falseness is caused by horizontal movment of same <BR>support.  Give it a read. <BR><BR>My take is that, well aside from the obvious observation that loose pins <BR>and the presence of false beats do not occur simultaneously more then <BR>what can be called randomly, the article just shows how a termination <BR>for an oscillating object can alter the period of the object. A better <BR>interpretation to translate to pianos IMHO would be to say that the <BR>bridge and pin assembly as a whole can come to oscillate in phase with <BR>one (or more) frequencies of the string and in one (or more) direction.</DIV></BLOCKQUOTE> <DIV>I would love to see some really carefully constructed experiments with the right optics, metrics, etc. to see the movement of the string at a point in its length as close to the bridge as possible with the hypothesis that it is not only rotating transversely, but in small arcs of rotation in the plane of the string plane as well because of the springiness of the termination, and possibly cycloidal effect combined. I know that this has longitudinal effect, and that this is an extension of Jim's article. Birkett's high speed films show quite clearly, particularly the bridge-end films, significant movement of the strings not only in and out of phase, but right up to the pin, which I would dearly love to see more closely. Some of these questions are not answerable by math alone but by better observational technique, even though I've always believed that the right question, properly asked, contains the best, if not only, answer. In some man! ner, the principle of parsimony needs to work here better; there are too many factors possibly involved in the cause of real beats and we need to shave away the least likely.</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"> <DIV><BR>This fits better with the more technical article in the 5 lectures, and <BR>explains why loose pins can not be statistically associated with false <BR>beats.  It also eliminates the whole problem with this horizontal motion <BR>of the pin thing.</DIV></BLOCKQUOTE> <DIV>I agree, Ric. Can we yet shave loose pins from the "cause" plot?</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"> <DIV><BR><BR>Your comments relative to longitudinal modes are interesting, and I see <BR>where you are going. Tho the longitudinal modes are very much higher <BR>frequencies then the transverse we ultimately hear in much of the <BR>piano....especially where the classic false beat is usually a big <BR>problem... there is perhaps no reason why these could not create a false <BR>beat.... if and only if there are two horizontals at nearly the same <BR>frequency... and I dont think they function this way... but perhaps I am <BR>wrong.</DIV></BLOCKQUOTE> <DIV>I think maybe you're right. Particularly since we cannot correlate any given longitudinal mode with a  "real" beat speed with any accuracy at all. So statistically unlikely.</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"> <DIV><BR><BR>In anycase one is still confronted with some clear observational data <BR>that as I mentioned cant be ignored. <BR><BR>Cheers <BR>RicB <BR><BR><BR>   Ric, Paul, & All - <BR>   Shooting from the hip, so to speak. I've been accurately (but <BR>   well-meaningly) chastised in the past for not actively trying to find <BR>   the answers to the questions I ask.  I'm coming to accept that <BR>   answers are not my roll. Perhaps something to aspire to.  In any <BR>   case, I'll pick through Ric's post below and refer to one item of <BR>   Paul's.  For the sake of space, I'm deleting all but the specific <BR>   quote, so it would be necessary for a reader to access the original <BR>   post to fully understand (if that ware possible)' <BR><BR>   At 06:41 AM 2/18/2007, you wrote: <BR>    >Hi Paul. <BR>    > <BR>    > !  Jim Ellis's article from way back. <BR>   Can you better identify the source? <BR></DIV></BLOCKQUOTE></FONT></BLOCKQUOTE> <DIV></DIV> <DIV> </DIV></FONT></BODY></HTML>