<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> </head> <body bgcolor="#ffffff" text="#000000"> Hi Susan and others. Nice post by the way Susan.  In particular I would like to snip out two quotes and comment on them as they relate to the general discussion. First: <blockquote>"I find it encouraging that several of the people writing most earnestly about this supposedly crucial inaccuracy had the direction of it wrong ... good for Bob Davis!" </blockquote> Its really goes a bit deeper then what Bob pointed out if you stop and think about it.  As Ed hinted at, there is something amiss with the whole <<second partial>> of the tuning fork to begin with. A few people threw out a couple statements.. one even declared that tuning fork manufacturers dont spend any time tuning this frequency around 880Hz.  The truth of the matter is that it simply doesnt exist.  A bit of time looking at the physics of tuning forks reveals that they function more or less like clamped bars, and that the first overtone is found somewhere between 1/5 and 1/6 the length of the tines.  The relevant frequency is wayyyy up there.  In short... the tuning fork has no frequency around twice the fundamental. It aint there period. At least one post more or less pointed that out, and Ed was on this tact as well I think. But to the point.  The fact is that when playing F3 and sounding the Tuning fork at the same time... a definite and unmistakable beat circa at 880 Hz is heard. Less obvious is a much slower beat at 440... difficult to discern but there.  Now since the fork does not sound at 880, and F3 does not have a frequency at 440... neither of these beats can be explained in terms of coincident partials. Period.  All argumentation using coincident for or against using F3 are then simply invalid ! We have to first explain where the unmistakable beating comes from.  Now I cant do that.. beyond a bit of honest speculation.  What I think is happening is that we are hearing the forks 440 Hz being interfered with by F3's 5th partial at around 880 Hz. Whether its something akin to a difference tone or some similar phenomena I cant say. But it seems clear that the reference frequency must be the forks 440Hz. THAT is what F3 is beating against one way or the other ! As such, the control intervals relative beat rate to this is of no consequence whatsoever.  What is of consequence is the partial of the note being tuned then.  If its A4 then we are dealing with its second partial which ends up at exactly twice 440Hz. The resulting A3(2) will be flat after the transfer.  If however A3 is tuned directly from the fork and F3 then its second partial will be at 440.  This explains why Susan and others get so close every time, and why David Renaud's experiment resulted in A3 being flat by the exact degree of inharmonicity A4's 2nd partial Listen to the following wave file which is comprised of 2 sine waves of equal strength. Frequencies of 873 and 440 Hz. <a class="moz-txt-link-freetext" href="http://www.pianostemmer.no/music/FTHREE.wav">http://www.pianostemmer.no/music/FTHREE.wav</a> Now these are sine waves with no overtones per se...  yet there are at least 2 easily discernible beat rates. This should be proof enough that beat relevant beat rates can occur in the absence of coincident partials. For what its worth.. here is a screen shot showing the combined wave form of these two frequencies. <a class="moz-txt-link-freetext" href="http://www.pianostemmer.no/images/FTHREE.jpg">http://www.pianostemmer.no/images/FTHREE.jpg</a> Second: <blockquote>"On the other hand, I (sometimes) am happy that people with minds put together somewhat differently than mine enjoy taking unreasonably exact technical devices, and working out _exactly_ where the gnats like to hang out. It's nice, on general principles, to know these locations, and have a grounding in general gnat-anatomy, though I will always depend on my ear instead -- so it ends up as kind of an academic pursuit. Never mind, we all have our roles in life ... we all make our various contributions." </blockquote> Thats the intended spirit of this list. Those who succeed in letting go of accepted so called truths and maintain a questioning posture even in the face of "accepted fact" are liable in the end to contribute more to that spirit then otherwise.  And this last discussion is a perfect example of just that.  As to whether or not F3 is usable at all with a tuning fork... one can only say that arguments citing the lack of coincident partials simply do not bear on the subject at all, and a clear explaination of what is the exact source and frequency range of the beats that occur between F3 a 440Hz tuning fork is needed before one can discount it. When all this is shown, and put up against the fact that Susan,,, like so many many others, is able to achieve a <<beatless>> (for all audible purposes) rate between A3 and the fork... then it seems to me that its premature to condemn F3 as unusable with a 440 fork.  We also clearly establish beating phenomena in abscence of coincident partials here.... This should be of particular interest to adherents of the Virgil Smith natural beat.  Maybe its in this direction we should really be looking for tuning purposes in the first place... and that coincidents are at best only a guideline.  Cheers RicB </body> </html>