The Beat that isn't -- or is it?

Kent Swafford kswafford@earthlink.net
Wed, 11 Jan 2006 16:33:11 -0600


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On Jan 11, 2006, at 12:38 PM, Ric Brekne wrote:
> ...
> Its really goes a bit deeper then what Bob pointed out if you stop =20
> and think about it.  As Ed hinted at, there is something amiss with =20=

> the whole <<second partial>> of the tuning fork to begin with. A =20
> few people threw out a couple statements.. one even declared that =20
> tuning fork manufacturers dont spend any time tuning this frequency =20=

> around 880Hz.  The truth of the matter is that it simply doesnt exist.

This is incorrect, in practice. Attached here is a spectrum analysis =20
of the same John Walker fork that I measured earlier with RCT =20
Pianalyzer. The 2nd partial may have vanishingly low amplitude, but =20
it is there. It exists.


=EF=BF=BC
> A bit of time looking at the physics of tuning forks reveals that =20
> they function more or less like clamped bars, and that the first =20
> overtone is found somewhere between 1/5 and 1/6 the length of the =20
> tines.  The relevant frequency is wayyyy up there.  In short... the =20=

> tuning fork has no frequency around twice the fundamental. It aint =20
> there period. At least one post more or less pointed that out, and =20
> Ed was on this tact as well I think.
>
> But to the point.  The fact is that when playing F3 and sounding =20
> the Tuning fork at the same time... a definite and unmistakable =20
> beat circa at 880 Hz is heard. Less obvious is a much slower beat =20
> at 440... difficult to discern but there.  Now since the fork does =20
> not sound at 880, and F3 does not have a frequency at 440... =20
> neither of these beats can be explained in terms of coincident =20
> partials. Period.

This is not as not as clear cut as your "period" suggests.  8^)

>   All argumentation using coincident for or against using F3 are =20
> then simply invalid !

No, a weak 2nd partial is not the same thing as no 2nd partial.

> We have to first explain where the unmistakable beating comes from.

As noted by at least one, this beating can be weak, consistent with =20
the fifth partial of the piano's F3 beating against the weak 2nd =20
partial of the A fork.

> Now I cant do that.. beyond a bit of honest speculation.  What I =20
> think is happening is that we are hearing the forks 440 Hz being =20
> interfered with by F3's 5th partial at around 880 Hz. Whether its =20
> something akin to a difference tone or some similar phenomena I =20
> cant say. But it seems clear that the reference frequency must be =20
> the forks 440Hz. THAT is what F3 is beating against one way or the =20
> other !

Doubtable.

> As such, the control intervals relative beat rate to this is of no =20
> consequence whatsoever. What is of consequence is the partial of =20
> the note being tuned then.  If its A4 then we are dealing with its =20
> second partial which ends up at exactly twice 440Hz. The resulting =20
> A3(2) will be flat after the transfer.  If however A3 is tuned =20
> directly from the fork and F3 then its second partial will be at =20
> 440.  This explains why Susan and others get so close every time, =20
> and why David Renaud's experiment resulted in A3 being flat by the =20
> exact degree of inharmonicity A4's 2nd partial

This is a bit mixed up. If you tune a piano's A4 to zero beat with an =20=

A440 fork, you don't necessarily need any check at all if you are =20
very skilled. The same would be true of the piano's A3; if you tune =20
it to zero beat with an A4 fork, you may not need a check note at =20
all, which is a good thing since the coincident partial between the =20
piano's F3 and A3 are at F5, the 4th partial of A3 and the (weak) 2nd =20=

partial of the A4 fork. In other words, if you are skilled at zero =20
beating a fork with an piano's A3 or A4, you may tune an accurate A =20
in spite of using an inappropriate check note.   8^)   I suggest that =20=

this is a reasonable explanation of Susan's success.

> Listen to the following wave file which is comprised of 2 sine =20
> waves of equal strength. Frequencies of 873 and 440 Hz.
>
> http://www.pianostemmer.no/music/FTHREE.wav
>
> Now these are sine waves with no overtones per se...  yet there are =20=

> at least 2 easily discernible beat rates. This should be proof =20
> enough that beat relevant beat rates can occur in the absence of =20
> coincident partials.

No, Ric. Sine waves, at least the way I was taught 30 years ago are =20
more imaginary ideals than they are real, kind of like equal =20
temperament.   LOL

It is extremely likely that the waves in your example actually have =20
partials. The most likely explanation of the beats then is simply the =20=

2nd partial of the 440 tone at 880 beating 7 bps against the 873 =20
tone. That's the way I hear it, anyway.


> For what its worth.. here is a screen shot showing the combined =20
> wave form of these two frequencies.
> http://www.pianostemmer.no/images/FTHREE.jpg
>
> Second:
> "On the other hand, I (sometimes) am happy that people with minds put
> together somewhat differently than mine enjoy taking unreasonably =20
> exact
> technical devices, and working out _exactly_ where the gnats like =20
> to hang
> out. It's nice, on general principles, to know these locations, and =20=

> have a
> grounding in general gnat-anatomy, though I will always depend on =20
> my ear
> instead -- so it ends up as kind of an academic pursuit. Never =20
> mind, we all
> have our roles in life ... we all make our various contributions."
>
>
> Thats the intended spirit of this list. Those who succeed in =20
> letting go of accepted so called truths and maintain a questioning =20
> posture even in the face of "accepted fact" are liable in the end =20
> to contribute more to that spirit then otherwise.  And this last =20
> discussion is a perfect example of just that.  As to whether or not =20=

> F3 is usable at all with a tuning fork... one can only say that =20
> arguments citing the lack of coincident partials simply do not bear =20=

> on the subject at all, and a clear explaination of what is the =20
> exact source and frequency range of the beats that occur between F3 =20=

> a 440Hz tuning fork is needed before one can discount it.

You maintain that there is a mystery, but I believe there is no =20
mystery. Sine waves gots partials, and so do forks.   8^)

> When all this is shown, and put up against the fact that Susan,,, =20
> like so many many others, is able to achieve a <<beatless>> (for =20
> all audible purposes) rate between A3 and the fork... then it seems =20=

> to me that its premature to condemn F3 as unusable with a 440 =20
> fork.  We also clearly establish beating phenomena in abscence of =20
> coincident partials here...

No such observation is established at all, since there is a clear and =20=

simple alternate, and conventional explanation.

> This should be of particular interest to adherents of the Virgil =20
> Smith natural beat.  Maybe its in this direction we should really =20
> be looking for tuning purposes in the first place... and that =20
> coincidents are at best only a guideline.

Sigh. Above you claim as desirable the "letting go of accepted so =20
called truths". In science, they put it differently. While it is =20
certainly desirable to be open to new explanations, it is still =20
essential to maintain skepticism of new theories until they can be =20
shown to provide a better explanation of observed phenomena than the =20
old theories.

Ric, you haven't even come up yet with an alternate theory for the =20
source of beats. They come from coincident partials. If you think =20
otherwise then you bear the burden of explaining an alternate source. =20=

I say there may be no alternate source.

Coincidentally yours,

Kent




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