<html>
<body>
<br>
Sarah,<br><br>
Now, thar ya' be goin' agin with all that there thinkin' and observin'
and such....doncha know that's where all the trouble starts?<br><br>
Horace<br><br>
<br>
At 10:30 PM 8/21/2004, you wrote:<br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Hi
all,<br>
</font> <br>
<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.<br>
</font> <br>
<font face="arial" size=2>But the question is one of what my target curv=
e
should *really* be. Hmmmm.... My thoughts:<br>
</font> <br>
<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.<br>
</font> <br>
<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.<br>
</font> <br>
<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???<br>
</font> <br>
<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.<br>
</font> <br>
<font face="arial" size=2>So is this something that is the way it is jus=
t
because of tradition -- because the cauls are built that way, and that's
what ya' get? <br>
</font> <br>
<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?<br>
</font> <br>
<font face="arial" size=2>Peace,<br>
Sarah<br>
</font> <br>
<br>
</blockquote></body>
</html>