The Beat that isnt: was An apology--Ed Sutton

[Ric Brekne]

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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:

    "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!"

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.

http://www.pianostemmer.no/music/FTHREE.wav

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.
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 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."


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





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