<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><DIV>On Jan 23, 2007, at 10:19 AM, Jim Busby wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><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; "><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Thanks Fred.</SPAN><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "> </SPAN></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Thant’s exactly what I was looking for. When I first heard this Al Sanderson was in the class and agreed that it was a good formula. I guess the reason the FAC measurements are taken the way the SAT “manual” says is because Dr. Sanderson chose a particular piano faculty to “test” their taste of stretch (Harvard??) and came up with their recipe. Yours seems to give much more stretch, and when I compare my aural tunings with what you suggest below it comes out much closer than the “out of the box” SAT tuning</SPAN></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Thanks for your work. I’ll buy lunch in Kansas!</SPAN></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; ">Jim Busby BYU</SPAN><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "></O:P></SPAN></FONT></P><P class="MsoNormal"><FONT size="2" color="navy" face="Arial"><SPAN style="font-size: 10.0pt;font-family:Arial;color:navy; color: rgb(0, 0, 128); font-size: 13.3333px; "><O:P style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "><SPAN class="Apple-style-span" style="color: rgb(0, 0, 128); font-family: Arial; font-size: 13.3333px; "> </SPAN></O:P></SPAN></FONT></P></SPAN></BLOCKQUOTE></DIV>Hi Jim,<BR><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>It shouldn't increase the stretch at all, at least consistently, to measure the way I do. It just helps eliminate problem readings, coming up with more reliable inharmonicity constants. And, as a side effect, it means that A4 will be right at A4 every time (assuming no operator error <G>). And, in fact, that's what got me started measuring the A number that way. Sometimes you would end up, after tuning precisely to the calculated tuning, with A4 being significantly sharp or flat. The literature that came with the machine more or less said "Live with it [pianos aren't perfect], or, if you care, tune A4 according to the calculated tuning, measure it, and create a pitch offset to account for the difference." I preferred a third approach, where the A number input reliably put A4 fundamental right at 440.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>The problem arises when, say, there is a "false" reading for the 2nd partial of A4. It could read sharp or flat (presumably due to some kind of coupling with a resonance in the whole soundboard/strung back system). The formula relies on the difference between A4 and A5 being in the predicted ratio of 1:4 to the difference between A5 and A6. Sometimes the ratio of the measured partials is different. The FAC formula predicts where A4 will be based on that 4:1 ratio. If the reading of the 2nd partial isn't at that precise point in comparison to the 1st and 4th partials, the prediction will be wrong.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>Sanderson's FAC stretch (pre-SAT III) is basically somewhat wide 4:1 throughout, aiming at some amount of cents wide double octaves. At some point, early on, I think I heard he altered the formula for the bass to give it a bit more stretch. This mathematical fix, I think, may have been a source with the "F problem" I complain about. I'm not familiar with the first generation FAC, so I'm just speculating based on a few snippets of memory of things I read some time or other, maybe 15 years or more ago.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>The C number is basically used to place C7 to C8, starting with a target C8, at just wide of 4:1 to C6. Again, it relies on that 4:1 ratio between the C7C8 cents difference and the C6C7 cents difference. Again, there are occasionally (and fairly often) pianos where the measurements won't be in that ratio. If you actually measure the C8 partial, and do the calculation I outlined, the FAC formula will reliably give you that slightly wide 4:1 stretch up through that top octave.</DIV><DIV><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>Dr. Al says he personally prefers a wider stretch. If you want more stretch (I did), you need to add to those FAC numbers. I added a fairly constant 0.5 cents to the A number (and decided I didn't care if I was consistently tuning all pianos 0.5 cents sharp), and I think I added about 2.5 to 5.0 to the C number. And then I checked the top notes as I tuned, playing notes a 12th, double octave, 19th and triple octave below, and comparing (looking at the lights for each), coming up with a compromise usually pretty close to 19th and triple octave.<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></DIV><DIV><BR class="khtml-block-placeholder"></DIV></BODY></HTML>