Pitch at breaking points

[Richard Moody]

Ric rote
> > OK, within 0.489 cents for one (specific) size to the next.
> >
> Something funny with that value Ric.  Take say #12 to #13 wire. That's 0.8
> mm vs 0.75 mm, or 1.12 semitones diameter difference. Breaking tensions in
> my Roeslau data sheet are 121 kg vs 108 kg, or 0.98 semitones difference.
> Subtract these two to get 0.14 semitones of pickup from #13 to #12 wire.
> Or 14 cents if you prefer working in smaller units.

Doesn't  Roeslau give a range of breaking Tensions for each size?
The .489 cents for one specific size to the next means from one guage size
to the next.
of a specific pair.  If #22.5 to #23 is specified the difference in breaking
tension the Freq is 0.485 cents apart.    If you choose the high breaking
point of one string and use against the lower breaking point of the other
you can get a cents
that is smaller or larger depending on how you arrange your choices. It is
very possible the strings could break at these tensions than any other in
the range. However In the
example I just gave I used the two lower breaking points of both wires.  If
262lbs is used for wire #112.5 (.031) and 279  for #13 the cents difference
of frequency at breaking is .5 cents.
    You suggested #12 to #13 wire. The English sizes are .029 and .031
respectivly.   When you say that is a 1.12 semitone diameter difference, how
do you arrive at that?  Or there is .98 semitones between 108kg and 121kg.
I don't understand how the ratio of two Kg's gets a cents value.

    To calculate the frequency of the wire at its breaking tension I use
F=T^(1/2) / L*d*.0479896.
    Since we know the tension, and the diameter, all we need now is the
length. I used 100 inches.   for #12 that will give a F of 112.9....cps.
For #13 the Freq at breaking tension  is 110.1cps  The cents difference is
29.4 cents. (WOW you wouldn't think 3cps is that much!)   You said 14 cents.
One is twice as much as the other.  Does
this mean we are 1200 cents different?  Seriously, I was doing it in inches,
and you are using metric.  I could set up a spread sheet in metrics but that
is for another time.
    The difference between the breaking freq of #12 and that of #23 is160
cents.  You said 1.1 semitones I guess that means we 112 cents apart?
    There is another significance to this frequency of breaking points.  I
did a spread sheet using .029 through .051 in increments of .001.  I
obtained the frequencies at breaking point, then did a cents difference
between each size. These show no
pattern at all, and a larger variation then expected from looking only at
the frequencies.They go (starting at #12.5)---21, 14, 3, 7, 13,
3 , 11,13,4,5 (cents) and so on.
    So one can choose a  pair to suit his argument. ; )    We can both be
right ---ric

> Careful mixing data like this or you fall into Koster's trap. In this kind
> of comparison you must compare apples to apples to make meaningful
> conclusions. Using mean breaking tensions is reasonable, or compare low
> to loe or high to high for an estimate of tensile pickup. But you should
> not compare highest to lowest.

Sorry, I just did.  I was curious to know the range of frequencies at
breaking points.   Each size has a range of breaking points.  From comparing
the higest to lowest  I learned that wires of different sizes  might indeed
break at the same frequency, or they might snap at 50 cents apart.
    Regarding "traps"   What is a trap but a capricious restriction on the
use of data?
I won't  get ensnared in that. As long as one reports his data and shows
where it stands in where it comes from. If the mean of data is being used
you should report that, or if you are using highest or lowest or a
combination. ---ric