Inharmonicity

[Jim Coleman, Sr.]

Hi Roger:

For some who do not know what a sine wave is, I'll try to illustrate in
asci format:


                         x
                   x           x

               x                    x
---------------------------------------------------------------------
                                        x                   x 

                                            x           x
                                                  x


The full sine wave as illustrated pictures the 2nd partial as we think.
Now, to answer your question a little more completely. All complex 
sounds can be broken down into simple sine waves according to Fourier
Analysis. In the illustration above, where the sine wave crosses the
zero point or null point is where the node is. You can see from this
illustration that there is little or no bending at the null point. The
greatest bending occurs at the peak of the loop. This is where most of
the bending occurs. There are two other places where bending occurs and 
that is at the two terminiation points. This may be why the lowest partials
have more erratic behavior. The effect of the end points comes into play
in a greater percent of the bending. In the case of the fundamental, there
are three bending points: the one loop and the two end points. In the case
of the second partial, there are four bending points; two loops, and two
end points. In the case of the third partial: three loops and two end 
points. From this you can see that the lower partials are affected by the
end point in a higher percentage than are the higher partials. The 10th
partial has 12 bending points. 

>From all of this, you can clearly see that the higher partials are affected
more by the wire stiffness than is the fundamental. But the fundamental does
have more relation to the bending of the end points than the loop point.

This may be an explanation of the erratic behavior of the lower partials.
I still suspect though that the board and bridge may contribute to this to
some degree.
    
Since you mentioned Harold Conklin, I thought you might like to know that
Michael Wathen keeps in touch with him on a fairly regular basis. Harold
retired to Dundee, FL. He was one of my two best friends at Baldwin.

Jim Coleman, Sr.




On Sun, 16 Aug 1998, Roger Jolly wrote:

> Hi Jim, 
>        What node points in a sine wave???? A sine wave by definition has a
> constant rate of change, therefore bending would imply something that is
> not constant!!!!!
>   However I agree with the overall valuable contributions that you are
> making to this discussion, sure tell you worker around H.Conklin. A pity he
> is not here helping out'
> Regards Roger
> 
> 
> 
> >If you simply look at the nodal point of any sine wave, the bending takes
> >place at the loops, not at the nodes. The nodes are the pivot points.
> 
> Roger Jolly
> Baldwin Yamaha Piano Centre
> Saskatoon and Regina
> Saskatchewan, Canada.
> 306-665-0213
> Fax 652-0505
>