In reply to Mr. Cris Forster

My Dear Ozan,

Please tell your correspondent that I thank him for the care he has shown to write to me directly (regardless of the fact that he has done this publicly)... I am glad to encounter someone as experienced as him. Yet, it is clear to me, that our mathematical languages and worries are not the same. This is normal. At any rate, as far as I recall, it was over the technical assistance I have given you, upon which he argued that your string tension equation was only an approximation. I have proven to you mathematically, that your equation and his are identical. Now, I am pleased to behold, that by posting your equation together with his, he accepted both of them as equally valid expressions.

Thus, there seems to be nothing further to discuss.
My best wishes and regards to him, as well as to all of your colleagues on the tuning list.

Cordially...
Papa Tolga

tyarman@isikun.edu.tr

----- Original Message -----
From: Cris Forster
To: tuning@yahoogroups.com
Sent: 28 Mayıs 2005 Cumartesi 19:25
Subject: [tuning] Re: Different ways of expressing the same tension equation

>My Dear Ozan,
>His Equations (1) and (2) are identical, since obviously, the
>diameter is twice the size of the radius. For this reason, I would
>say, they are redundant.

Dear Ozan's Father,

As a builder of traditional and original acoustic musical
instruments, I find little redundancy in the mathematics of
vibrating systems. I am passionate about the subject of _musical
mathematics_ because it is my life's work. This commitment
leaves very little on my redundancy plate. I have simply
attempted to be thorough.

I have communicated with builders of acoustic musical
instruments for 30 years. Some builders prefer to measure
tension with a diameter variable, others prefer to measure tension
with a radius variable. I know no better way to dispel confusion
than to be thorough.

>However, these equations are correct for the "first harmonic"
>only. Else, one should multiply the tension (or the "weight" that
>will create the tension) by n^2, where n, being an integer, points
>to the nth harmonic.

Builders of musical instruments only consider the tension of the
fundamental mode of vibration, or of the first harmonic. Here's
why: most strings are tensioned between 40% and 50% of their
_break strength_. If the tension falls too much below the lower
limit, the strings are too loose and will sound weak. If the
tension rises too much above the upper limit, the strings are too
tight and will break prematurely. To calculate a string's break
strength, we must know the _tensile strength_ of the stringing
material. Tensile strength refers to the maximum tension a material
can withstand without tearing. I won't digress with detailed break
strength calculations. Suffice it to say, the tensile strength of
spring steel music wire varies with diameter.

>His equation (3) too is identical to his equation (1); recall that
>I have previously explained that the mass per unit length is
>nothing else but D^2 x pi x rho.
>Anyway, I am glad he finally agrees with you about the fact that
>equation (3) (the one you had furnished sometime ago), is not an
>approximate relationship, but is as rigorous as his first equation;
>they are in fact, as I keep on saying, identical relationships...

In Ozan's original text, and I quote,

******************************

The middle strings are manufactured from stainless steel such
that each weigh about 20 grams per unit meter, or 8 grams (0.008
kgs) per 0.4 meters.

******************************

the diameter of the sample string is not included.
Hence, no one is able to verify the accuracy of this physical
property of the wire.

>His last equation too is correct, but, although he defined it, I
>would have used another symbol for the total mass so as not
>to confuse it with `mass per unit length`. Nevertheless, after
>writing eqation (3), his equation (4) is again a triviality, and
>for this reason, redundant.

Again, I believe it is better to be thorough than to be terse.
Also, Equations 3 and 4 are highly interesting to me because they
would enable a prospective instrument builder to contemplate
these kinds of calculations without owning an expensive
micrometer. An accurate postage scale could be used to measure
either the mass per unit length (M/u.l.) or the total mass (M) of a
string. Personally, I find this kind of approach, especially in a
classroom where for financial reasons a precision micrometer may
not exist, highly interesting and most relevant.

>On the whole, I am glad to see that he has tacitly agreed with
you in the end...
>My best wishes to him...
>
>Pap T.

Dear Distinguished Professor at MIT,

My best wishes to you as well.

Cris Forster, Music Director
www.Chrysalis-Foundation.org