Re: Chimes; Transcript of the Recalcitrant URL

[brian whatcott <inet@intellisys.net>]

> > http://users.why.net/wgray/www/howto/wchime/wchime.html
> >
> > I got response: No DNS Entry for users.why.net

> The usual reason for this network message is that
> the node is not connected, or if connected is dysfunctional.

I see that this node is once more live.
I thought it advisable to test your patience no further, so I
reproduce Jim's piece below from that URL:

      Making Wind Chimes     By Jim Kirkpatrick



> From time to time people ask how to make wind chimes, especially how to
calculate the lengths of the tubes/rods. There is no precise answer to this
question! Let's discuss it. 

There was an article in Projects In Metal, December 1991, "Eight-tube Wind
Chimes" by Thomas F. Howard. This is probably also reprinted in one of the
"Metalworking" books by Village Press that
condense issues of the magazine. I'll refer to this article in a few places
simply as "Howard". 

First, there are lots of aspects of making one, other than how long to cut
the chimes. How many chimes? What kind of chord do you want (major, minor,
pentatonic, etc.). How should you arrange them? How big should the clapper
be? 

First we'll discuss the chimes themselves, and address material and length. 

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). Howard suggests hardwoods. 

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 (eg Aluminium 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: 

     f1 / f2 = (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. 

OK, so much for the theory. Let's take a look at suggested lengths,
courtesy of Howard: 

Eight Chimes: 16 7/8, 17 3/8, 18 7/16, 19 1/2, 20 3/4, 21 3/8, 22 3/4, 24 1/8.
Viewed from the top, he shows a hanging order starting at the 12:00
position of chime 1, 5, 2, 6, 3, 7, 4, and 8
For 1/2" OD tubing with a 2-inch clapper, the chimes are placed on a
4.5-inch diameter. These lengths are close to theory for a major chord, but
rounded to the nearest 16th. 

Six Chimes: 16 5/8, 17 5/8, 19 1/4, 20 7/16, 21 5/8, 23 3/4.
A six-chimer, hung with the same spacing as the one above but leaving two
gaps: (blank), 1, 4, 2, (blank), 5, 3, and 6. 

Another consideration is how/where to hang each chime. It has been reported
that hanging them .2242 X length from the end works well because this is a
node point of the fundamental frequency (in other words, it wiggles less
there!). If you hang them using nylon fishing line be certain to deburr
the hole and smooth it, and don't place anything valuable under it (like a
glass table)!. Also note the actual distance varies for each chime. 

On the topic of materials, soft metals such as copper will generate "soft"
tones, like hitting a bottle with a rubber mallet. Hard metals like steels
or certain aluminum alloys giver a sharper tone, like hitting a bottle with
a ball peen hammer (not including breakage). Sharper tones seem to be
common on very small chimes (a few inches to maybe 6 inches) which also
seem to use solid rods. Softer tones are common on large ones (a foot or
more). Also, larger OD is supposed to yield softer tones and longer-lasting
tones. 

Cutting the chimes requires some thought, especially if you make a few
hundred. Some suggest a chop saw with an abrasive blade, to get a better
finish than you'd achieve with a toothed blade.
Remember that aluminum dust is flammable and burns very hot, so don't let
it accumulate. Use a blade that is compatible with what you're cutting. 

Some people like to use electrical conduit for the chimes. Other suggest
seamless "chro-mo" 4130 bicycle frame tubing, while copper water pipe also
seems useful. Possibly plugging one end or both
will alter the sound but I'm not sure how at this point. 

Jim Kirkpatrick

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brian whatcott <inet@intellisys.net>
Altus OK