<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><DIV>On Jan 17, 2007, at 10:35 AM, James Ellis wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">The Conn stroboscope that I believe Robert Young used for his measurements</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">was pleaty good for showing the inharmonicity trends that he discusses,</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">despite the fact that we can make more accurate measurements now.</FONT></P></BLOCKQUOTE>Yes, accurate enough for laying a foundation. But it was limited to +- 1 cent resolution, and B7 top pitch. It would be interesting to see if the top end is as predicted, or if things change, for instance, especially with the shortest strings.<BR><BLOCKQUOTE type="cite"> <P style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; min-height: 14.0px"><BR></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">There is the fact that a string in a real piano is subject to the</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">characteristics of the piano's acoustical system being reflected back into it.</FONT></P></BLOCKQUOTE>Yes, precisely. There seems to be a wide variance from the predicted in real pianos, due to all sorts of effects. For example, I find that measured inharmonicity fairly consistently becomes lower after a piano is tuned, setting aside pitch. Ie., if a piano is basically at pitch but out of tune with itself, it will measure higher inharmonicity than after a fine tuning. I wonder whether different stretches might also affect measured inharmonicity.<BR><BLOCKQUOTE type="cite"> <P style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica; min-height: 14.0px"><BR></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">Regarding bass strings:<SPAN class="Apple-converted-space"> </SPAN>Fred mentions anomalies in inharmonic ladders that</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">Dean Reyburn has discussed.<SPAN class="Apple-converted-space"> </SPAN>I have not seen Dean's work, but I can say</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">those anomalies are very real.<SPAN class="Apple-converted-space"> </SPAN>They are NOT from faulty measurements.</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">They come form the fact that it is IMPOSSIBLE to wind a PERFECT bass</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">string.<SPAN class="Apple-converted-space"> </SPAN>The very slightest irregularity of ANY kind in the winding or core</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">wire will cause it.<SPAN class="Apple-converted-space"> </SPAN>I have been measuring and plotting inharmonicity</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">curves of bass strings for nearly two years now, using a monichoord I</FONT></P> <P style="margin: 0.0px 0.0px 0.0px 0.0px"><FONT face="Helvetica" size="3" style="font: 12.0px Helvetica">designed just for that purpose, and some state-of-the-art analysis programs.</FONT></P></BLOCKQUOTE>I don't think Dean has ever documented or published results. I think he has just observed the phenomena in the process of developing his software, which relies heavily on partial ladders. In order to obtain good calculated tunings, he had to find a way to account for irregularities (I don't know what he came up with, but presumably some kind of averaging). </DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>I don't think they occur only on bass strings. Plain wires can also have anomalies, as I discovered when I first started tuning with an SAT a little over ten years ago. I found that results were "odd" often enough that I looked into it a bit. SAT relies on the discrepancy between two partials to predict a virtual partial ladder. I found that I could get a better calculated FAC tuning if I measured the distance between the A4 and A6 partials of A4, and between C6 and C8 partials of C6 (as opposed to A5 and A6 partial of A4, C6 and C7 partial of C6), and extrapolated a result. The distance between 1st and 4th partial seemed to "average out" the anomalies in the measurement between 2nd and 4th, 1st and 2nd, and yield a result that calculated better tuning spreadsheets. </DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>I have had similar "strange" experiences with RCT on a few pianos, where I have got wide variances in calculated tunings on measurements made the same day. (I look particularly on the values for G#4 and C8 in comparing, as they are good benchmarks). Unfortunately, the partial ladders that RCT automatically measures are hidden from view, so I can't come to any useful conclusion other than to keep my eyes and ears open for anomalistic numbers and patterns (looking at the charts in the Custom EQ window helps a lot). Where do the anomalies come from? Perhaps the biggest factor is termination, though that is just an educated guess. There can certainly be a wide differences is termination from piano to piano and from string to string.<BLOCKQUOTE type="cite"> </BLOCKQUOTE></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><BR></BODY></HTML>