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xylophone
Calculations for Xylophone Bars
by Jack Breen (980321 MMDigest)

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 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
21 Mar 1998 14:55:26 -0500 (EST)

Excel spreadsheet file: breen_xyloph3.xls (26 kb)


breen_xylo.gif (3 kb)

XYLOPHONE BAR DIMENSION CALCULATIONS
   Material: Red Oak
   Width: 1.5 inches
   Thickness: .750 inches (half of width for harmonics)
   Thinned Section Thickness: .375 inch (half of thickness for harmonics)

Nodes are the mounting points for the bars.

             OVERALL     NODE    THIN
NOTE   FREQ   LENGTH LOCATION  LENGTH

A    55.000   23.335   5.232  11.871
A#   58.270   22.670   5.083  11.505
B    61.735   22.025   4.938  11.149
C    65.406   21.398   4.797  10.803
C#   69.296   20.789   4.661  10.467
D    73.416   20.197   4.528  10.141
D#   77.782   19.622   4.399   9.823
E    82.407   19.063   4.274   9.515
F    87.307   18.521   4.152   9.216
F#   92.499   17.993   4.034   8.925
G    97.999   17.481   3.919   8.643
G#  103.826   16.983   3.808   8.368
A   110.000   16.500   3.699   8.101
A#  116.541   16.030   3.594   7.842
B   123.471   15.574   3.492   7.591
C   130.813   15.131   3.392   7.346
C#  138.591   14.700   3.296   7.108
D   146.832   14.281   3.202   6.878
D#  155.563   13.875   3.111   6.653
E   164.814   13.480   3.022   6.435
F   174.614   13.096   2.936   6.224
F#  184.997   12.723   2.853   6.018
G   195.998   12.361   2.771   5.818
G#  207.652   12.009   2.692   5.624
A   220.000   11.667   2.616   5.436
A#  233.082   11.335   2.541   5.252
B   246.942   11.012   2.469   5.074
C   261.626   10.699   2.399   4.902
C#  277.183   10.394   2.330   4.734
D   293.665   10.098   2.264   4.570
D#  311.127    9.811   2.200   4.412
E   329.628    9.532   2.137   4.258
F   349.228    9.260   2.076   4.108
F#  369.994    8.997   2.017   3.963
G   391.995    8.741   1.960   3.821
G#  415.305    8.492   1.904   3.684
A   440.000    8.250   1.850   3.551
A#  466.164    8.015   1.797   3.421
B   493.883    7.787   1.746   3.295
C   523.251    7.565   1.696   3.173
C#  554.365    7.350   1.648   3.054
D   587.330    7.141   1.601   2.939
D#  622.254    6.937   1.555   2.827
E   659.255    6.740   1.511   2.718
F   698.456    6.548   1.468   2.612
F#  739.989    6.362   1.426   2.509
G   783.991    6.181   1.386   2.409
G#  830.609    6.005   1.346   2.312
A   880.000    5.834   1.308   2.218
A#  932.328    5.668   1.271   2.126
B   987.767    5.506   1.234   2.037
C  1046.502    5.349   1.199   1.951
C# 1108.731    5.197   1.165   1.867
D  1174.659    5.049   1.132   1.785
D# 1244.508    4.905   1.100   1.706
E  1318.510    4.766   1.068   1.629
F  1396.913    4.630   1.038   1.554
F# 1479.978    4.498   1.009   1.481
G  1567.982    4.370   0.980   1.411
G# 1661.219    4.246   0.952   1.342
A  1760.000    4.125   0.925   1.275



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