Is calculus ever used in scale design?

[RicB]

My take on this, Julia, would be that calculus *is* used in scale 
design.  Within the models that are used to derived equations, certain 
assumptions ( that a value is a constant or there are negligible 
interrelationships of different values for instance) are made that 
reduce the calculus into a discrete formula that can be more easily used.  

What may increase the accuracy, as you suggest might be the benefit of 
using calculus, might be to more realistically develop the model and the 
assumptions inherent in it.  For example, I'm not sure that we have 
accurate models of string vibration, given the effects of at least one 
end point moving in space and time relative to the influence of the 
vibration (forcing function) other strings, the bridge, soundboard, 
etc.  Similary I'm not sure that we have accurate models of the effects 
of the non-speaking lengths of the string on the speaking-length 
vibration.  And these two models influence each other.  This gets just 
way to complicated.

Probably, if we had such models, we would be too confused mathematically 
to get a handle on solving it.  It would be fun to try, and it would be 
nice to be smart and rich enough to undertake such endeavors.

Just my late-night thoughts.

Mark Ultsch, RPT