The Beat that isn't -- Don

[Don]

Hi Ric,

If two sine waves can have a secondary resultant that beats, then an A440
fork to F3 on piano would have lots going on too.

Frequency of F3 is about 174.61 hertz. In approximate numbers not allowing
for inharmonicity (cause I don't know how to)

f4 = 349.23
c5 = 523.25
f5 = 698.46
a6 = 1760.00

Frequencies (except a6) taken from:

http://www.contrabass.com/pages/frequency.html

If one subtracts 440 from each of these then the only really strong
resultant may be at e6 (~1320 hertz). This fits rather nicely with the
error that Dave Renauld "discovered" at the tuning exam--rather than the
1.2 was calculated before based on a5--which doesn't exist for f3 nor an A4
fork.

It certainly also means that proper results can only be achieved by using
A3 if f3 is going to be the "test" note.

I'll let someone else do the subtraction--and the addition of inharmonicity
to the figures above.

Any ideas anyone out there?

At 09:31 PM 1/12/2006 +0100, you wrote:
>Hi Don
>
>So your take on this is resultant tones rather then coincidents ?  Thats 
>the direction I am leaning as well.  I did a few tests with my handy 
>dandy pitch fork and pocket tunelab today.  Basically trying out what 
>kind of inharmonicity readings I get on the fork when I place it on 
>different types of objects.  I found that anything that conducted the 
>fork really well resulted in no overtone until around the 6th. Sometimes 
>the 5th would pop up depending on what I grounded the tuning fork on.  
>Putting it directly on the mic I dont get anything until the 10th 
>partial. All of which is in keeping with the descriptions I've found on 
>the net and in a couple books I have.  Interestingly enough... when the 
>fork was placed on sidegrain of a table the forks sound was quite 
>reduced, and I got very high readings (50-80) on a second partial. When 
>I placed it on end grain I got low but significant (10-20)  Both 
>readings showed 0.0 offset at 880.  This is in keeping with a couple 
>experiments I found on the net entitled "Forceing a tuning fork to have 
>overtones"  Seems like it has more to do with the what you place the 
>tuning fork on.  I tried grounding it on a metal note stand... really 
>loud result and no 2nd partial.  Glass was the same even tho the overall 
>loudness was much quiter.  All this points me in the direction that the 
>apparent overtone some folks are reporting is being generated by the 
>thing the fork is grounded on .... and not the fork itself.
>
>As to the wave file I posted... I thought I might show you a couple 
>other perspectives.  The wave was a one second sample. The two pics 
>below show a 1:4 resolution and a 1:10 resolution.  Note the presence of 
>another beat. The inside peak you see in the 1:10 resolution happens 
>exactly 7 times in the full one second sample. Thats the resultant beat.
>
>http://www.pianostemmer.no/images/fourtimes.jpg
>http://www.pianostemmer.no/images/tentimes.jpg
>
>Now look at the same 1:10 resolution for a mix of 440 and 447 which is 
>analogous to what happens with coincidents.  Interesting eh ?
>
>http://www.pianostemmer.no/images/tenxcoincident.jpg
>
>Seems to me like we are dealing with beats that are origionating in 
>absence of simple coincident partials.
>
>Cheers
>RicB

Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.P.T.
Non calor sed umor est qui nobis incommodat

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