<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; = -khtml-line-break: after-white-space; "><BR><DIV><DIV>On Jan 11, 2006, = at 12:38 PM, Ric Brekne wrote:</DIV><BLOCKQUOTE type="cite"> = ...</BLOCKQUOTE><BLOCKQUOTE type="cite">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. <BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>This is incorrect, in = practice. Attached here is a spectrum analysis of the same John Walker = fork that I measured earlier with RCT Pianalyzer. The 2nd partial may = have vanishingly low amplitude, but it is there. It = exists.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV><IMG = src="cid:76C4FEFF-2E16-4FA6-A745-A53E135C4F1F@local"></DIV><BR><BLOCKQUO= TE type="cite"> 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.<BR> <BR> 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.<BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>This is not as not as clear = cut as your "period" suggests. 8^)</DIV><BR><BLOCKQUOTE type="cite"> = All argumentation using coincident for or against using F3 are then = simply invalid ! <BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>No, a weak 2nd partial is = not the same thing as no 2nd partial. </DIV><BR><BLOCKQUOTE = type="cite">We have to first explain where the unmistakable beating = comes from. <BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>As noted by at least one, = this beating can be weak, consistent with the fifth partial of the = piano's F3 beating against the weak 2nd partial of the A = fork.</DIV><BR><BLOCKQUOTE type="cite">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 !<BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>Doubtable.</DIV><BR><BLOCKQUO= TE type="cite">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</BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>This is a bit mixed up. If = you tune a piano's A4 to zero beat with an A440 fork, you don't = necessarily need any check at all if you are very skilled. The same = would be true of the piano's A3; if you tune it to zero beat with an A4 = fork, you may not need a check note at all, which is a good thing since = the coincident partial between the piano's F3 and A3 are at F5, the 4th = partial of A3 and the (weak) 2nd partial of the A4 fork. In other words, = if you are skilled at zero beating a fork with an piano's A3 or A4, you = may tune an accurate A in spite of using an inappropriate check note. = 8^) I suggest that this is a reasonable explanation of Susan's = success.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><BLOCKQUOTE= type="cite"> Listen to the following wave file which is comprised of = 2 sine waves of equal strength. Frequencies of 873 and 440 Hz. <BR> <BR> = <A class="moz-txt-link-freetext" = href="http://www.pianostemmer.no/music/FTHREE.wav">http://www.pianostemm= er.no/music/FTHREE.wav</A><BR> <BR> 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. <BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>No, Ric. Sine waves, at = least the way I was taught 30 years ago are more imaginary ideals than = they are real, kind of like equal temperament. LOL</DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>It is extremely likely that = the waves in your example actually have partials. The most likely = explanation of the beats then is simply the 2nd partial of the 440 tone = at 880 beating 7 bps against the 873 tone. That's the way I hear it, = anyway.</DIV><DIV><BR = class="khtml-block-placeholder"></DIV><BR><BLOCKQUOTE type="cite"> = For what its worth.. here is a screen shot showing the combined wave = form of these two frequencies.<BR> <A class="moz-txt-link-freetext" = href="http://www.pianostemmer.no/images/FTHREE.jpg">http://www.pianostem= mer.no/images/FTHREE.jpg</A><BR> <BR> Second:<BR> <BLOCKQUOTE>"On the = other hand, I (sometimes) am happy that people with minds put <BR> = together somewhat differently than mine enjoy taking unreasonably exact = <BR> technical devices, and working out _exactly_ where the gnats like = to hang <BR> out. It's nice, on general principles, to know these = locations, and have a <BR> grounding in general gnat-anatomy, though I = will always depend on my ear <BR> instead -- so it ends up as kind of an = academic pursuit. Never mind, we all <BR> have our roles in life ... we = all make our various contributions."<BR> <BR> <BR> </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.</BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>You maintain that there is = a mystery, but I believe there is no mystery. Sine waves gots partials, = and so do forks. 8^)</DIV><BR><BLOCKQUOTE type="cite"> 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...<BR></BLOCKQUOTE><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>No such observation is = established at all, since there is a clear and simple alternate, and = conventional explanation.</DIV><BR><BLOCKQUOTE type="cite"> 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. <BR></BLOCKQUOTE></DIV><BR><DIV>Sigh. Above = you claim as desirable the "letting go of accepted so called truths". In = science, they put it differently. While it is certainly desirable to be = open to new explanations, it is still essential to maintain skepticism = of new theories until they can be shown to provide a better explanation = of observed phenomena than the old theories.</DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>Ric, you haven't even come = up yet with an alternate theory for the source of beats. They come from = coincident partials. If you think otherwise then you bear the burden of = explaining an alternate source. I say there may be no alternate = source.</DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>Coincidentally = yours,</DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV>Kent</DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV><BR = class="khtml-block-placeholder"></DIV><DIV><BR = class="khtml-block-placeholder"></DIV></BODY></HTML>=