[CAUT] calculating change in pitch for change in lengths / Mitch

[Richard Brekne]

Hi Mark

Just a quick note on the <<competing formulas bit>>. They are not really 
competing at all. They are simply different perspectives, looking at the 
problem from a completely different angle. I've been working through 
this side pin displacement bit a bit more and find what looks to be a 
big hole in the reasoning concerning the effect of increase in the 
length of the string segment on the bridge surface due to strings being 
forced up the pins and hence having their offset angle increased.

The problem is that this increase in length primarilly affects the 
segment on the bridge itself. The speaking length is only changed by the 
actual vertical rise component. And this is lengthened mind you, which 
in itself contributes to a lowering of pitch.  The resulting total 
tension increase however compensates for this but must be figured over 
the entire length of the string... including front lengths, lengths up 
to the bridge pins, back lengths and bridgesurface lengths in addition 
to the speaking length. This tension increase must be then applied to 
the very slight increase in speaking length within the standard formula 
for frequency. All this assumes no friction for simplicity.

The net increase in frequency then for long strings at lower tensions is 
not nearly so dramatic after all,  tho the impact from an increased 
offset angle does dominate the picture.

The formula sheet  provided by Dr Galembo looks a lot more comlicated 
then it is. Its really simple triangle trig for figureing the lengths, 
and Hooks law for finding the resulting increase in tension.  The 
formula used for calculating frequency once these two are done is the 
same, taken from the Calculating tension.

For a given a wire of 1390 mm speaking, 100 mm backlength, 1.1 mm Ø with 
a 20 mm wide bridge and 10 ¤ offset and 10 ¤ pin angle all at 127,5 lbs 
starting tension and 0 vertical deflection, a 1 mm rise in soundboard 
results in a 1,029 cent rise in pitch.  Add a 0.2 mm rise in the bridge 
surface with all that implies for lengthening the bridge surface 
segement and a very slight increase in speaking length.. you get an 
additional 2.82 cent rise... or a grand total of a 3.85 cents rise in 
pitch.  Not so dramatic after all. Brings me back again to what I 
started off saying... the affect on long strings is minimal... and next 
to nothing if the starting tension is reasonbly high.  On shorter 
strings however... the change for bridge surface rise gets dramatic

None of this includes the length from the front termination to the 
pin... which further reduces the net change in tension and hence pitch 
due to the fact that tension disperses over the entire string.

Cheers
RicB


    I think this has been a great discussion. There have been many aspects
    effecting the pitch change of strings that I had never considered
    and are
    very relevant to my work.

    Now those last few jabs concerning the competing formulas may not
    have been
    necessary. I didn't sit down and try to understand either formula so
    I'll
    never know who was at fault. The fact that there are formulas out there
    designed to clarify these things is all I need to know right now.

    I say go ahead and hash it out. But change the subject line so I can hit
    the delete button if things get too obstinate.

    Mitch Staples

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