SW heresy?

[Sarah Fox]

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Hi all,

Thanks for the advice about techniques to even out the SW curve!  That =
should give me a variety of techniques to use/combine in order to even =
out the jags.

But the question is one of what my target curve should *really* be.  =
Hmmmm....  My thoughts:

The unmodified SW curve is obviously very linear.  (Yes, I know what =
linear means.  I "minored" in mathematics, sort of -- except that my U. =
didn't officially recognize minors).  Stanwood's curves, OTOH, are all =
concave downwards.

I was advised off list that I shouldn't force the hammers to =
artificially conform to a standardized Stanwood curve but to simply even =
out the jags to make the action smooth from bottom to top.  There's =
something to be said for this idea.

But as I got to thinking about the SW curves, I was wondering, where do =
they REALLY come from?  That is, where does the shape come from?  I =
suspect the hammer manufacturing people might be able to enlighten me as =
to this.  (Ray???)  I'm *guessing* that the felt is denser than the =
molding, and when the hammer becomes skinnier, it loses more felt than =
molding, resulting in a more precipitous dropoff in weight at the higher =
end.  This would occur with a constant hammer length and a linear =
variation in hammer and molding (and felt) width.  Am I anywhere close =
on this idea???

Contrast this function with other functions that might actually relate =
to optimal hammer mass:  String length and mass both decrease with the =
note number, with a function that is concave upwards.  Note frequency =
increases with a function that is concave upwards.  Note period (inverse =
of frequency) increases with a function that is concave upwards.  The =
Stanwood curve seems rather meaningless with regard to any of these =
functions.  For instance, it might be good to match hammer mass to =
string mass by some proportion.  Right?  As the scale goes up, string =
length and mass approach an asymptote of zero.  Therefore, shouldn't =
hammer mass approach an asymptote of zero?  Instead, the curve starts =
taking a dive in the treble.  If the scale went up well past 88, hammer =
mass would eventually crash to zero.  Because these curves do not have =
the same form, the relationship between hammer and string mass is =
anything but constant.  That doesn't make sense.

So is this something that is the way it is just because of tradition -- =
because the cauls are built that way, and that's what ya' get? =20

Now that I look at my linear SW curve (with jags), I'm wondering if this =
isn't REALLY a closer match to something meaningful (like string mass) =
than the idealized Stanwood curves.  Any thoughts, y'all?

Peace,
Sarah



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