<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Hi Ric,<DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>Very interesting to read the original paper. Thanks for finding it. It is also interesting that all of this work was done on the basis of measurements made with a Conn Stroboscope. I wonder if additional work has been done with more refined measuring devices, and, if so, if the results have been the same. <DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>The figures (as in charts/diagrams) referred to in the article don't appear in the link Ric gave. The original article (including the figures) can be seen in pdf via <A href="http://scitation.aip.org/jasa/">http://scitation.aip.org/jasa/</A> (The Journal of the Acoustical Society of America - search Young (author), Inharmonicity (keyword title/abstract). </DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>There are the usual scattershot results in Young's research, which he "resolves" to neat curves, as seen in those figures. As a practical technician, I often find that there seem to be strange anomalies in inharmonicity, and often separate measurements of the same string will vary markedly, in my experience and that of others (Dean Reyburn talks about "false" inharmonic ladders - I forget his term for them). All those formulae make it seem that pianos are more predictable than they are. <BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><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><BR class="Apple-interchange-newline"></SPAN></SPAN> </DIV><BR><DIV><DIV>On Jan 16, 2007, at 2:23 AM, RicB wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hi again... for easier reading then the scrubbed doc attached to my last please see:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://www.afn.org/~afn49304/youngnew.htm">http://www.afn.org/~afn49304/youngnew.htm</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Cheers</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">RicB</DIV> </BLOCKQUOTE></DIV><BR></DIV></DIV></BODY></HTML>