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<DIV><FONT face=Arial size=2>Hi all,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>But the question is one of what my =
target curve
should *really* be. Hmmmm.... My thoughts:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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???</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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? </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>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?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Peace,</FONT></DIV>
<DIV><FONT face=Arial size=2>Sarah</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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