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Wind Chimes
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Different materials react in different ways. The tone will depend on the material (steel, aluminum, brass, the exact alloy, heat treatment and so on), whether you are using a solid cylinder or a tube, and if a tube, the wall thickness. It may also depend on the hanging method, and the tone quality will depend on how you strike a tube (with a hard object or a soft one, for example, like a hardwood.
Note that with a whistle, such as an organ pipe, the pitch is determined primarily by the length of the air column. It is the air that vibrates. The pipe material helps determine the "timbre" or "voice" of the pipe, but the air column determines the pitch. In a wind chime, the pipe itself is being struck and the air column has little to do with things (especially if the pipe is a solid cylinder!).
Generally you will need to cut by trial and error, using a piano or some other reference if you want to get close. You can also do it by ear if you're either good or tolerant. But we can help you get close.
If a chime is cut in half, the new tone will be *four* times the frequency, or two octaves up in pitch. To progress from one standard musical note to the next, each note is different in frequency by the twelfth root of 2, or about 1.059463. For chimes, we need the square root of this number, which is about 1.0293. In other words, if our "reference" chime is 1 foot long, the next lower note in the equal-tempered scale would be 1.0293 feet or 1 foot and .3516 inches or close to 1 foot, 23/64 inches. Many people can detect notes out of tune (relative to another) by a few percent of one note. So, cutting the chimes to proper length is important.
One formula was presented in a book, "Music, Physics and Engineering" by Olsen, for a tube, free at both ends:
f=1.133 pi K v / (l^2)
K=sqrt(a^2 + ai^2) / 2
{radius of gyration of a hollow circular cylinder}
Here pi=3.14159... f is frequency (in Hz), l is length (in cm) and v is the velocity of sound in the material of the tube wall (e.g. Aluminum is 5.1E5 cm/s). Note that K is different for different cross-sections (I think it is K=a/2 for a solid circular bar). a and ai are the outer and inner radius of the tube (in cm).
See also "Basic Acoustics" by Donald E. Hall, Harper & Row, NY, 1987. This book points out that for two bars being identical except in their lengths, their frequencies are related as:
f2 / f1 = (L1 / L2)^2
There are several different musical scales to choose from. In the Western world, scales revolve around 12 equally spaced tones (equal tempered) but most music uses only 8 of the twelve. Which 8? This determines whether the scale is "major" or "minor" (or one of several less common scales). Another scale for wind chimes is the pentatonic scale (5 tones) used by eastern music. The advantage here is that no combination of pentatonic notes is considered dissonant (displeasing).
Construction details: The chimes and clapper should be spaced so the clapper will hit either one chime, or two chimes, and no more. The order of the chimes is important for two reasons: It helps keep the weights distributed so the whole thing does not tilt, and it ensures that any pair of chimes will sound nice when struck together.
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(shamelessly stolen from some
web site years ago,
and subsequently saved as a file deep within the bowels of the computer)
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