Physics of Music - Notes

Make your own wind chimes

Making your own set of wind chimes is quite easy. The hardest part will be deciding which notes to include. Many commercially available wind chimes use a pentatonic scale, though there is quite a variety available. Find a piano or electronic keyboard, choose a set of notes and play them as randomly as you can to get an idea what they will sound like.

To start, you will need some metal pipe. This might be copper, aluminum, brass, steel, etc. Different pipes from different sources will ring longer or shorter. Go to your local hardware store and try some out to see which pipe sounds the best to you. If you don't have an appropriate pipe cutter, pick up one of those as well (a hack saw can be used also). Try to get a pipe which has a uniform cross-section (i.e. the thickness of the pipe is close to the same everywhere). The nicest ringing pipes I have found so far were originally intended as commerical grade electrical conduit and chrome plated piping for sink drains. The metal pipe for my vacuum cleaner also sounds pretty good, though that would be an expensive way to go.

Cut one length of pipe to a length which gives you a nice note. If desired, trim it to match a note on your piano. This pipe can be anywhere from a few inches (for narrow pipe) to a couple feet. After figuring out the other notes you want (or the musical intervals you want) then you can cut the other pipes using the fact that the frequency is proportional to 1/(length)2, or equivalently, the length is proportional to the inverse of the square root of the frequency, 1/(frequency)1/2 (valid if the pipe isn't too short compared to its diameter).

Example: Your first pipe has a length L0 = 30.0 cm. Suppose you want to cut a pipe which is a major third above this. The frequency ratio for a major third is 5/4 = 1.25 (see chart for various intervals or table for notes of the equal tempered scale). Hence the length of the new pipe should be L0/(1.25)1/2 = 26.8 cm.

The pipes are supported 22.4% from the end. This is at the node of the vibration. The simplest type of support is obtained by drilling a small hole all the way through the pipe and using string. For the two pipes above, the holes will be 6.7 cm and 6.0 cm from the end respectively.

Now add one or more clappers which will strike the pipes near the middle as they blow in the wind. The softer the clapper, the more mellow will be the sound.

You can also make wind chimes out of wood (hard woods like maple or oak work better than soft woods). Due to the variability of the properties of wood, you may need to do some fine tuning to get the notes you want. Sanding them at the ends (so they are shorter) raises the pitch. Sanding them lengthwise (so the wood is thinner) lowers the pitch.

The above example assumes you use the same type of material for all of your chimes. If you don't, you're on your own.

You can use the same relations to make a simple xylophone, but you will need to trim the boards since the properties of wood vary significantly from place to place even within one board. Commercial Xylophone (and marimba) bars also are "undercut" to make them sound nicer. See American Journal of Physics, vol 69, page 743 (July 2001) for more information about xylophone and marimba bars.

Here's a chart to help out.

Interval Ratio to Fundamental
Just Scale
Multiply Longest
Chime Length by
Unison 1.0000 1.0000
Minor Second 25/24 = 1.0417 0.9798
Major Second 9/8 = 1.1250 0.9428
Minor Third 6/5 = 1.2000 0.9129
Major Third 5/4 = 1.2500 0.8944
Fourth 4/3 = 1.3333 0.8660
Diminished Fifth 45/32 = 1.4063 0.8433
Fifth 3/2 = 1.5000 0.8165
Minor Sixth 8/5 = 1.6000 0.7906
Major Sixth 5/3 = 1.6667 0.7746
Minor Seventh 9/5 = 1.8000 0.7454
Major Seventh 15/8 = 1.8750 0.7303
Octave 2.0000 0.7071

To get notes an octave higher, than shown, multiply the value in the chart by 0.7071. To get an octave lower, multiply by 1.414. For example, to make a chime an octave plus a major third higher than your longest chime, multiply the longest length by 0.8944 x 0.7071 = 0.6324 .

Questions to: suits@mtu.edu

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