Learning: was Violin

[Richard Brekne]

Ron Nossaman wrote:

> >Richard,
> >McFerrin gives you a fine and authoritative formula for computing string
> >inharmonicity. Compute for me please, using that formula, the inharmonicity
> >of a B-1 string with 0.037" diameter core, and 0.093" total outer diameter
> >of the wrapped section.
> >
> >Ron N
>
> My apologies, that's a B-1 string 1238mm in length.
> Ron N

McFerrins inharmonicity formula are on page 43 section 4.5 and are really only
good for unwound strings. This has been up on the Nordic list a couple times and
I have a formula for them and I will hunt it down. It is in my saved emails in
one of my three mail accounts and I will get it and compute the value for you it
you wish.

McFerrin also gives a formula for calculating tension in wrapped strings (page
30 section 3-10), tho nowhere in his book as far as I can tell does he mention
if the two formulars could be combined to give the inharmonicity of wound
strings.


Be that as it may... we have the Inharmonicity formula for plain strings given
as

I = ((1731 pi ^2 Q K^2 S) / 2 L^2 T) * n^2)   =  Bn^2

B can be changed to  (1731 pi^2 d^2 Q) / (2 * 64 f^2 L^2 D)

where d is the diameter of the string, f is the frequency of the fundemental, D
is density of steel in string, L is the speaking length of the string, and Q is
Youngs modulus for piano wire.

Sticking values for Q and D in the equation (misprint in the book here as it
says Q and d) and if the diameter and speaking length are taken in centimeters
then we have

B = (3.4 * 10^13 d^2)/(f^2 L^4)   Or in inches which you gave   B = (5.3 * 10^12
d^2)/(f^2 L^4)

either of these multiplied by n^2 gives inharmonicity for plain string.

Since it is my understanding that this formula doesnt work for wound strings
there is no point in plugging in the parameters you give to yeild the result.
Also I see you were nice enough to give core and diameter in inches and length
in mm. No biggie really, but an easy place to stumble.

For sake of comparison I will find that other formula I have, and calculate the
Inharmonicity useing that as well as using McFerrins formula for plain string.
Just to see how significant the difference is.

OK ?

--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:rbrekne@broadpark.no