This is beginning to get interesting.  I have made a number of metal bar
"xylophones"* over the years, and my bible has been "Music, Physics and
Engineering," second edition, by Harry F. Olson. Dover: New York, 1967.

He gives the equation for the fundamental frequency of a bar as a
function of its length, Young's modulus [which relates to stiffness]
and the radius of gyration.  He calculates the nodes as being .2242 and
.7758 of the length.  This is for a bar of uniform cross-section.

Rough tuning is essentially cutting the bar to the right length.  Fine
tuning is accomplished, as several people have described, by making
small cuts or grinding at the center to lower the pitch, or by trimming
the ends to raise the pitch.  These adjustments, being very minute,
don't affect the location of the nodes significantly.

Unfortunately Mr. Olson doesn't go into the question of the gross
cutting up, as is normally done on wooden xylophone bars.  These cuts
are much, much greater than would be required for tuning.  These major
changes in cross-section would affect the location of the nodes, so if
you are making them, you should use an existing design or else
determine the node location experimentally.  This can be done by
sprinkling sawdust or metal filings on the surface, striking the bar,
and watching for the locations where the filings are not disturbed.

I have previously thought that the reasons for cutting up could be to
make the bar louder, since it would flex more, being thinner at the
center, or perhaps to control dissonant overtones.  My latest theory is
that it is done so that the frame on which the bars are mounted is on a
straight line.  As someone mentioned, the length of uniform bars varies
as the 24th root of 2, so if the bars are all of the same width, the
location of the mounting holes will be a curve.  By judiciously cutting
up the bars the location of the nodes, and therefore the mounting
holes, could be made to form a straight line.  Does this ring a bell
with anyone?


* I'm using "xylophone" here informally as a generic term.  In careful
writing the proper terms should be used.  By the way, I would translate
"glockenspiel" as playing bells.

 [ I would too, if I were careful!  ;)  -- Robbie

Fritz Gellerman