Inharmonicity

[Kent Swafford]

Jim Coleman, Sr. wrote:

>Hi to all:
>
>One of my pet peeves is the passing on of information saying that the higher
>partials run sharp because of the space which the nodes take up. Such an
>article ran in the 1949 series of the Piano Technician by George --------.

I read this post with extreme interest. Was a rebuttal ever written and 
published in a Journal to set the record straight?

>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.
>Stiffness does affect the higher partials more than the lower partials, but
>it's not because of the nodes.  The very high partials are more rod like 
>than string like. I used to demonstrate this by having a very flexible felt
>temperament strip in my hand. Its longer segments (partials) would vibrate 
>quite freely and for a longer time when held between my two outstretched 
>arms (tension being the chief restorative force).
>But, if I had just a short segment (1/2 inch) protruding from between two
>fingers, I could flip it with the other hand and it would vibrate like a
>rod (stiffness being the only restoring factor)
>
>The stiffer a segment is, the more like a rod will it vibrate. The second
>partial of a rod (tuning fork) is more than 2 1/2 octaves above the 
>fundamental. Check it out. The clang tone of an A4 fork is sharper than E7.
>Of course piano strings are not nearly that stiff, but it is a good example
>of what stiffness can do.

Is the "strings/string segments act shorter" explanation of progressively 
sharper partials inappropriate? If so, then how would you describe the 
mechanism by which stiffness causes progressively sharper partials? What 
would be different in the vibration of two strings that are similar in 
every way except stiffness?

Kent Swafford