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Wind Chime Calculations

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  • Wind Chime Calculations

    Hello Group...

    Can anyone help locate a formula that would allow me to input tubing dimensions to find specific music tones?

  • #2
    There was an article in a back issue of Model Engineer about making windchimes that I don't have a hope of finding.

    Also, a few years ago, I picked the following info off the Internet, somwewhere:

    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

    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

    Rev.: 05/05/96
    Try to make a living, not a killing. -- Utah Phillips
    Don't believe everything you know. -- Bumper sticker
    Everybody is ignorant, only on different subjects. -- Will Rogers
    There are lots of people who mistake their imagination for their memory. - Josh Billings
    Law of Logical Argument - Anything is possible if you don't know what you are talking about.
    Don't own anything you have to feed or paint. - Hood River Blackie


    • #3
      On page 136-138 of "The Machinist's Second Bedside Reader" by Guy Lautard, is his suggestion for making a nice wind chime. He uses heavy wall brass tubing. Four are required; make from 3/4" O.D. x 5/8" I.D. brass tube, one each at 13-9/16", 14-9/16", 15-9/16", and 16-1/2".
      Richard Montgomery
      Robert, LA


      • #4
        I've made several sets of wind chimes,I call them 'Wind chimes for people that like the looks,but don't care for the racket'. I used 1/2in.foam pipe insulation,several different lengths,a wood dowel about 4in.long glued in each end.A screw eye in the top,spray paint each one silver or gold,hang them from a disk,used a goose feather for the clapper.They're music to the ears of someone that works in a noisey environment.


        • #5
          Wind chimes are not always tuned to a particular scale. Sometimes they are just randomly tuned. I made a two octave, tuned set of chromatic(12 notes per octave--includes flats and sharps) chimes out of hardened type k copper pipe. The longest ones were about 24" and the shortest were about 8" long and 3/4" diameter. I never got around to making the solonoid hammer strikers to play them with. I was going to make a circuit to store songs and play them back for Christmas time.

          I got an electronic tuner ($20)from the music store where I work and cut and tried(grinding for the fine adjustments) different lengths until I got the scale perfected. The copper chimes had alot of overtones mixed with the fundamental tone that confused the tuner sometimes.

          The pitch of a given length of tubing is determined by the length, diameter and wall thickness of the tube. Also critical is the suspension of the tubes so that you don't dampen the tone by attaching the hanging string in the wrong place. Once you get them tuned, you can test the chime for the proper attachment location by holding it in your fingers and tapping the chime with a wood dowel. Keep moving your fingers up and down the chime til you find the spot where the chime rings the loudest. When you strike the chime, it flexes at the frequency of resonance. Somewhere along the length of the chime, it moves very little(called a node point, I think) You want to attach the string where the chime moves the least. It may be 1/4 of the distance, more or less. Longer story available for the more avid chime maker. thanks-Mike.


          • #6
            I think that if you cut a chime into 2 equal parts it should be twice the frequency of the original. I know that is true of stringed instruments. Unless the tubular shape affects the situation in some way.


            • #7
              Way back when I built a few wind chimes I used a pitch pipe and a hack saw, doing the fine tuning on a 6 x 48 belt sander.

              Don't use EMT conduit or iron pipe for chimes unless you want a soft, well damped tone. For a more brilliant tone use bronze or brass tube. There are also silver bearing copper alloys used to produce bell-like tones of great vibrance and clarity.

              A simple wind chime project allowed to run wild can be a lot of fun or a PITA depending on your tolerence for detail.


              • #8
                Windswhisper and others:
                I have been looking all over for a source of tubing for another version of windchimes. This is more like a hammered dulcimer only using tubing instead of strings. Can anyone lead me to a source for this material. The tubing that I have so far purchased was totally dead in sound. The tuning I would do with an electronic tuner and using the calculations so completely given in this thread.
                Thank you


                • #9
                  Mr Whisper, Being an electrician I made a set with thin wall EMT tubing on the job site from scrap 1/2".We cut them about 9" plus 3/4" for each additional tone till we were out of little pieces.Used a golf ball as a clapper and a paper coffee cup below that as a "sail".Drilled an 1/8" hole right through 1" from top and laced with mason twine,sounded better than we expected!My co-worker brought her "woodstock wind chimes" from home for comparison and hers did sound nicer.They we're made of aluminum tube from home depot,bout .060 wall thickness,and a "tagua" nut clapper.Either way scrounge around for tubeing and experiment.The laughter was worth the noise when all the guys and girls at work either helped or contributed ideas.Worst case-you create another god-awful set of wind chimes!!Good Luck


                  • #10
                    I don't want to contribute to the proliferation of wind chimes in any way...but I saw some recently that were better than most I've heard. They were aluminium tube, heavy wall, say OD 19mm, WT 2mm with a wooden thingy doing the hitting. Made high, clear sound, not too loud thankfully.


                    • #11
                      Some of the aluminum bars that I have cast can send of tones just like a tuning fork. Might be a good choice of material cast or cut to different lengths. Then again I don't like wind chimes very much. I like to hear the wind by itself or in the rustling of the trees.


                      • #12
                        Tubular Bells - brass heavy wall tubing chrome plated - sound beautiful. Mike Oldfield seems to be the only guy that plays them - as much fun as Andreas Vollenweider's Electric Harp!