The short answer to the question about why the center of a xylophone
bar is scooped out is that this increases the volume and resonance of
the bar while decreasing the pitch.  If, for example, the center
section of a bar is one-half the overall thickness, then its pitch will
be an octave lower than it would have been without the scoop.  The bar
will have much better tone and volume for a given pitch than the longer
full-thickness bar of the same pitch.

If you are trying to tune a bar, you can increase its pitch by sanding
off the length, and you can decrease the pitch by sanding the scoop a
little deeper.  It is amazing how little material needs to be removed
to change the pitch, especially on the thickness.

Several years ago, I built a large xylophone using some red oak I had
in my shop, based on an article I read in the American Woodworker
magazine dated December 1990.  Because I was expanding the size of the
project from the magazine, I needed to understand how to calculate the
bar dimensions.  I started with stock that was 0.75 inch thick and 1.5
inch wide.  I was mounting the bars at two points, which should
theoretically be placed one-quarter of the overall length in from each
end.

Unfortunately, there are losses and other problems in real materials,
so the best point is actually 0.2235 times the overall length for the
position of the supports from each end.  I made the scooped out section
equal to half the overall thickness (0.375 inch) and 1 inch narrower
than the distance between the supports.

Now I needed to determine the length of the bars.  Since every species
of wood behaves differently (as do different pieces of wood from the
same species), experimentation turns out to be the best method of
determining the length of a starter piece.  After that, the lengths
follow a simple mathematical progression, which can be fine-tuned with
minor sanding, as described in the first paragraph.

For me, A(440) had a length of 8.25 inches.  The support points were
1.9 inches in from each end and the scoop-out length was 3.7 inches
long.  The ratio between adjacent half-steps in a chromatic scale is
2^(1/12), and the length ratio between adjacent half-step bars is
2^(-1/24).  Thus, bars two octaves apart are twice as long as each
other.  This is probably more information than was needed to answer
the original question, but it may come in useful for anyone wishing to
either fine tune existing bars or to replace missing ones.

The attached Excel file "XYLOPHN1.XLS" is an example of bar
calculations for your information, in case anyone wants more details.

Thanks for your great publication which I thoroughly enjoy.

John J. Breen
Granuaile Rd, Southboro, MA  01772

 [ Thanks for the fine treatise, John.  I'll ask Jody to place the
 [ Excel spreadsheet file at the MMD Archives.  Interested builders can
 [ also write to the author at his e-mail address above.  (Don't forget
 [ to remove ".geentroep")  -- Robbie