The Beat that isn't -- Don

[Ric Brekne]

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


Hi Ric,

You are right--it doesn't "add up" at all. It subtracts. Look at one second
of the sin wave scan. You will see the 7 "peaks" from the secondary
resultant easily visible.

At 10:46 AM 1/12/2006 +0100, you wrote:
 >Kent:
 >
 >The sine waves that I combined together to make the wave file I posted
 >show no measureable overtones using Tunelabs Inharmonicity tool. Neither
 >could Cybertuner pick anything up.  Now the phase display that Tunelab
 >has showed a very intermittent response at around 880 for the 440
 >signal.  This response faded in and out and its frequency wavered quite
 >a bit. I doubt that this is an overtone per se. I fail to see how these
 >non existing coincidents can account for the beat rate in the wave file.
 >And so I question whether or not it is there. This echos Ed's and others
 >ponderments and its a fair question. And  I dont see that  simple
 >coincident partials theory provides an answer to it.
 >
 >Every link I find that describes tuning forks describes them as
 >instruments that have (for all practical purposes) no overtones.  Such
 >as the below. Several sights which describe experiments like the one you
 >did with your cybertuner attribute (sometimes) presence of very weak
 >overtones that are not accounted for by the design of the tuning fork to
 >sympathetic vibration from surrounding material... such as what ever you
 >grounded your tuning fork on.  John Walker tuning forks make a real big
 >point out of emphazising the <<overtone free>> characteristic of their
 >tuning forks in all their advertising.   One other point. The duration
 >and strength of your <<overtone>> is not sufficient to account for the
 >long duration and intensity of the beating between the fork and the non
 >coincident F3.
 >
 >I say something doesnt add up.
 >
 >Cheers
 >Ric

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