> OK, why do violin strings go false? I don't hear
> bowed string players complaining about lack of
> brilliance, (maybe they do) but they do complain that
> old strings won't play in tune. (This is a problem I
> had whether the strings were new or not:-))
Here's more than you wanted to know, probably mostly
true. But, alas, no direct answer to your question.
Maybe someone will find it interesting.
The differential equation for string vibration contains
terms for these five items:
1. tension
2. linear density (grams per centimeter)
3. stiffness (torque per degree)
4. energy dissipation (internal friction)
5. end effects (at nut, fret, and bridge)
With use, #2, #3, and #4 lose their uniformity
along the string length. For example, dirt
can "weight" the string around the first few
frets. #5 also changes with age. These changes
cause a false string.
Beyond this point, I cannot proceed because the
problem is mathematically very complicated, the
input parameters (eg, stiffness) are uncertain,
and I have little violin experience.
#1, tension, is, of course, always uniform along
the string length, regardless of how worn or
dirty the string becomes.
With regard to #3, metals do not always become more
limp with use. There is a term "work hardening" in
the metal industry.
#4 is demonstratable by bending a paper clip
repeatedly and feeling the warmth generated (say,
against your cheek or lips). Strings also heat
slightly, in the same way, with the heat being
generated at the cost of string brilliance and
sustain.
Long pianos sound better (truer overtones) partly
because #5 becomes, relatively, less important.
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