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[Clansgian AT wmconnect.com]

> I'm assuming that your question is rather a rhetorical one, but here goes.
> 

Thanks for answering anyway.  But, no, it's not really rhetorical.  I ask it 
here to illustrate the 'gap in knowledge' thingie, but let me explain that 
the 
question has a very practical side.

> First of all, your question is not a practical one, because I would not 
> replace a string with one twice the diameter, because of tonal changes, and 
> increase in tension on the instrument.   So it isn't a real world example.



Right, not per se.  And you wouldn't, not ever, replace a string with one 
twice the diameter.  There is no practical value in the literal application 
of my 
example, but it illustrates a property of musical strings that is invaluable 
in dealing with them,



> 
> Secondly, just because a string broke on a particular pitch does not mean 
> it 
> would do so again on the same pitch.   It may have broken there simply 
> because a weak point in the string gave way at just that particular moment. 


Remember in the example we broke it on purpose.   Now, I've had a bit of 
hands on experience with strings, designing and building instruments that 
have 30 
or more of them.   A new string from industrial spring steel (music wire) or 
spring phosphor bronze has very little variation and will break at exactly 
the 
same pitch string after string.

As you point out (correctly) it is the tonality we are concerned with.  A 
string of a given material, I am most familiar with bronze but it applies to 
all 
materials including nylon, will have the desired tonality at some percent of 
it's maximum tensile strength, that is, the point at which it would break.  
That ranges in circumstances but is between about 35% and 75% of maximum 
strength.  For example, a treble bronze string will not have a fudamental 
(all 
harmonics) at less than 70% maximum tensile strength.

Since percent of maximum strength is so important to instrument design, it 
follows that maximum strength is as important.  Hence the point at which a 
string will break is not rhetorical nor academic. You can't predict its tonal 
properties without knowing that (by calculations, not glibly breaking 
strings).

> 
> Thirdly, I have absolutely no idea, off the top of my head.   My initial 
> response would be an octave lower.   I could figure it out, I suppose, but 
> I 
> would find it a more practical use of time to look it up, should I actually 
> need 
> the information.  
> 

That was my initial response too and small wonder because it is intuitive.  
But the acutal answer is this.  He string and it's double diameter 
replacement 
will break at exactly the same pitch!  The diameter of the string is 
irrevelant.  If the string is .0001 diamter or one inch in diamter, it will 
break at 
exactly the same pitch.  I will supply the fomulae if your interested.

I said it was a practical exercise, the practical side is that you cannot 
change the percent of maximum tension by changing the diameter of the string, 
so 
you cannot change the tonality by doing so either.  If a string sounds tinny 
or mushy, replacing it with a string of larger or smaller diameter will not 
change that.  It will change the deviation of the string, but not it's 
tonality.


> And yes, I would considerthat a "gap" in my knowledge.   However, There 
> will always be "gaps" in my knowledge.  

Everyone will have gaps.  But I submit I've made my point that wagging one's 
head over homeschooling or unschooling as leaving 'gaps' in one's knowledge 
is 
a moot point.  Everyone has gaps in their knowledge.

>   That has always been a bone of contention between me, and many of my 
> colleagues.   far better, I feel, to know how and where to obtain an 
> answer, if 
> necessary.

I'm going to go you one better here, Ray, and say it is far better to feel 
that the knowledge and answers are never far from one.  You don't have to 
have 
had a college course in this or that math, or this or that subject, else you 
are doomed in ignorance all of your days.  Schools instill in the child the 
feeling of hoplessness that unless the adept opens the gate to knowledge, he 
can 
in no wise expect to take part in it.  Unschooling dispells this myth and the 
unschooled never feels that whatever knowlede or skills he/she needs are not 
right at their elbow.