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<DIV><FONT face=Arial size=2><EM><FONT size=1>> Let me see if I =
understand
this graph correctly tho.. its built on actually sampled frequencies ? =
Or how
did you arrive at them ?</FONT> </EM></FONT></DIV>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman" =
size=3>Yes . . . and
no: I sampled a few notes (A2, A3, A4, A5, and A6) to calculate =
"inharmonicity
constants," and then filled in the rest of the unsampled tones =
with a
[linear] progression. If I understand correctly, this is similar to what =
TuneLab
uses when constructing a tuning curve. While a 'real' piano might not be =
as
steady with the inharmonicity progressions, I think it accurately takes =
in to
account some of the complexities of dealing with
inharmonicity.</FONT></FONT></DIV>
<DIV> </DIV>
<DIV>I should make one point about calculating an "inharmonicity =
constant" [for
one string]: there is really no standard way of making a calculation =
like this.
The "constant" is an amount by which the partials increase =
exponentially. The
problem with this is that strings do not exactly increase at a constant
exponential rate. In general, the first few partials are unsteady; the
predictability increases with the higher partials. One way to do this is =
to
average the results together, but you could also do a weighed average, =
or even
develop a more complex means of distributing the "inharmonicity =
constant"
between the partials.</DIV>
<DIV> </DIV>
<DIV>This is an excellent method of predicting the location of each =
partial, so
it is extremly useful when dealing with theoretical situations; I also =
think it
is a very efficient means of doing normal everyday kind of tunings. But =
for
concert level tunings, it is much more important to know the actual =
location of
each partial, not the theoretical location of where the partial =
should
be.</DIV>
<DIV><FONT face=Arial size=2></FONT><FONT face=Arial =
size=2></FONT><FONT
face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><BR><EM><FONT size=1><FONT face=Arial>> Strange behaviour by =
the
4:2, 6:3 and 8:4 that I am sure has a good explanation. :)
</FONT></FONT></EM></DIV>
<DIV><FONT>There might be more going on that I haven't thought about, =
but the
noticeable "change" in each of the lines comes from switching from the
A4/D3^(1/19) linear division, to a system of pure 12th progressions. It =
is very
strange though: especially the 4:8 and the 6:3. </FONT><FONT =
face=Arial
size=2></FONT><FONT face=Arial size=2></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><BR><FONT face=Arial size=2><FONT size=1><EM>> I perhaps =
may get time to
do a fairly complete tuning, sampling and graph this week. This is =
actually
quite fun !<BR></EM></FONT><FONT face="Times New Roman" size=3>Good =
luck, I'm
interested to see how things turn out!</FONT></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT =
face=")t3"><STRONG></STRONG></FONT> </=
DIV>
<DIV><FONT face=")t3">In general, what do =
you do with bass
strings? Like I said before, I still have a problem with doing bass =
strings for
a very fine, concert level tuning. I really dislike that the =
"fundamental" is
missing. Do you do anything to try and counteract this phenomenon, or do =
you
just do it the normal way?</FONT></DIV>
<DIV><FONT =
face=")t3"><STRONG></STRONG></FONT> </=
DIV>
<DIV><FONT =
face=")t3"><STRONG></STRONG></FONT> </=
DIV>
<DIV><FONT face=")t3">Bradley</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV></BODY></HTML>