An Engineering Approach to Wind Chime Design
or
What Makes Toast, Toast ?
by Lee Hite

e-mail 

 Clearly the question should have been, what makes a chime a chime, rather than what musical notes should be selected when designing a set of wind chimes. I had originally asked that question and now find that I should have also asked, "What makes a good chime"? As my good neighbor, Bob, pointed out when faced with the challenge of designing a new state-of-the-art toaster, you first determine what makes toast, toast; rather than dried bread before you design a great toaster, BTW, a fascinating story.

In 2001 it took a month to study, experiment, build, and test nine sets of pentatonic scale (CDEGA) chimes for fundamental C2 through C7 for Christmas presents. The gifts were well received and sounded okay. However, from my research, I found some internet information good and some information inaccurate, misleading or wrong. This is not surprising considering the tremendous breadth of information available on the web.

While I would not consider myself an expert by any definition, and the fact that I have absolutely no musical background, I consider my findings valuable for the understanding of tubular bells and useful if you desire to build a great set of wind chimes. My experience with this project is presented here and may help you in an effort to design a great set of wind chimes. Updates continue almost monthly as the research continues.

If you're in a hurry and just want to calculate your own dimensions, go here and download the DIY Calculator.

Another engineer, Chuck's Chimes, has made a significant contribution to the understanding of chimes and I encourage to look over his site too.

^TOP^

What Is A Chime?
First, we must ask, "what is a chime?" Tubular bells (chimes) were developed in the 1880's when using regular bells became impractical in an orchestra setting because their sound so closely imitates church bells. Now, that sounds simple enough but imbedded in that explanation resides two definitions. One definition is "a chime imitates a bell" and the other definition is that "a chime does not imitate a bell". While I found those two definitions to be true I also found that there are about three categories of chimes.

The first category ranges about fundamental C6 to C8. Not unlike other percussion instruments this category is characterized by an audible fundamental pure tone with overtones mostly absent. Any existing overtones have minimal contribution to the perceived musical note. The perceived sound is the fundamental frequency and is not particularly pleasing to the ear. This sound is definitely a "non-bell" sounding chime. The loudness is low because of the small radiation surface and the rapid attenuation of high frequencies in the environment.

The second category ranges about fundamental C4 to C6. The fundamental is mostly audible and some overtones contribute to the perceived sound. The perceived sound is not the fundamental and not the overtones but a combination of both that produce a perceived musical note. The sound is acceptable but not great. This has an "almost-bell" sound but not particularly melodious. The loudness is acceptable but not great.

The third category ranges about fundamental C2 to C4. The fundamental is present but audibly absent and there are a host of overtones. The perceived sound is not the fundamental and not overtones but an imaginary tone created by the combination of the overtones. To the ear this is very melodious and quite pleasing. This is clearly a "bell-like" melodious sounding chime. The loudness is quite good because there is adequate radiation surface for the many overtones.

^TOP^

 The overtone structure for a chime in not an integer harmonic as in string instruments but instead, non-harmonic as in other percussion instruments. When the chime is supported at the first overtone node the higher partials are dampened and the fundamental remains. Overtones are multiples of the fundamental by X2.76, X5.40, X8.93, X13.34, X18.64 and X31.87 It was interesting to learn that not all chime frequencies contribute to the perceived musical note for all notes from C1 through C7. 

For example, a chime cut at fundamental C2, the fundamental is audibly absent along with little audible contribution from the first overtone. The remaining overtones combine to produce a perceived musical note. The perceived note does not coincide with any specific overtone and is difficult to measure without a spectral analyzer.

You can see from the display to the right (click to expand) that a chime cut for 272.5 Hz (near C₄^#), that the sound has two characteristics. The first characteristic is the sound when the chime is first struck. It comprises both the fundamental and the first four overtones, and has that traditional lingering sound for a short period of time.

The 2nd, 3rd and 4th overtones are present but attenuate quickly, and have little contribution to the perceived sound.

The 1st overtone contributes for about two seconds and rapidly deteriorates. The remaining sound is solely the fundamental.  Note the long hang time for the fundamental.

In contrast to the above example, the sound for a chime cut at  fundamental C6 and up is mostly the fundamental, and the overtones are audibly absent or mostly absent.

^TOP^

The perceived musical note from a chime is not simply the fundamental frequency. To gain a better understanding of the perceived note I examined a set of orchestra chimes manufactured by Premier of England. The set was 1.5" chrome plated brass with a wall thickness of .0625 inches and ranged from C5 (523.30 Hz) to G6 (1568.00 Hz). The length of C5 was 62.625 inches. The fundamental for this length is around 65 Hz, yet the perceived note is C5 at 523Hz. Measurements for other chime notes in this set of chimes indicated the perceived note to be between 7.8 and 8.3 times the fundamental. I am not certain this is the correct ratio to multiply for "Premier" chimes but clearly there is a ratio for each material and configuration involved. In fact, I believe this style of chime cannot be compared to the traditional chime tube that is "open-at-both-ends" because the orchestra style of chime is fitted with an end cap that contains a small hole in the end cap, and is supported via a cable through that hole.

^TOP^

The physics of a perceived note:
To make a great set of wind chimes it is not necessary to understand why a chime note behaves as it does, but in my case I find it necessary. It turns out that several other people have spent time investigating the "missing fundamental" and the "perceived note' from a chime.
Some sources are:

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/subton.html#c2

http://ccms.ntu.edu.tw/~karchung/Phonetics II page thirteen.htm

http://en.wikipedia.org/wiki/Missing_fundamental

I spoke with the folks at Musser Chimes and confirmed that indeed the process of tuning a chime is a complex process of accounting for all frequencies from the fundamental through the many overtones. 

An integral part of the "perceived note" effect is the sensitivity of the human ear to loudness and to frequency. You can see the loudness sensitivity range and frequency sensitivity range of the ear by viewing the Fletcher/Munson "Equal Loudness Curves" found HERE Clearly the ear has more sensitivity in the range from about 300 Hz to about 4 KHz than at other frequencies. 

^TOP^

Chime Emulation:
There is a terrific piece of shareware software "Windchime Designer V1.0" by Greg Phillips that will emulate a chime for any note in many different scales. It will help you determine what notes sound good on chimes and what scale to use. In addition, there is a comparison calculator that can determine the length of tube once you have a measured length as a reference. An updated version (2006) is available HERE. The older version requires a sound card, is for older computers and is no longer available on the web. If you want a copy of the older version you can download from my site Chime.exe. 

If you have trouble unzipping Greg's new version here are the two files you need. Chime32A.exe and TUNING.DAT
Place both files in the same folder and run the exe file.

^TOP^

 Note Selection
Note selection is mostly a personal choice. I selected the pentatonic scale to build the nine sets of chimes; however, I discovered later in the year that there is probably a better choice. The pentatonic scale was a safe choice and sounds very good close to the chime set but not so good at a distance. A set of chimes designed for the C2 or the C3 octave have very good acoustic radiation properties and can easily be heard at a distance of 150 feet. The problem is that at that distance the ear has difficulty detecting the separate notes of the pentatonic scale (CDEGA). All notes (CDEGA) had a strong tendency to sound alike at a distance of 150 feet. The next set of chimes will be designed for notes that have considerable separation but maintain an overall coordinated sound. (More work is required to determine the correct notes for this approach.)

For much more on Scales & Chords in all Keys see Michael Furstner Jazclass at www.jazclass.aust.com

^TOP^

Tuning:
If you are building a "non-bell sounding" chime and attempting to excite exact notes, exact tuning is required. On the other hand, if you desire a "bell-sounding" chime then cutting a tube to the length suggested by the formula listed at the bottom of this page should be adequate. For your convenience, pre-calculated lengths for various materials and sizes are listed in the table below in addition to calculate your own dimensions in these DIY Excel sheet.

Calculating exact lengths appropriate for use in an orchestra setting is complicated and uses parameters not available to most people. Here we have selected an approach that simplifies the process and simplifies the formula.

Attempting to tune a low frequency tube to the exact frequency for fundamental C2 through C4 is largely a waste of time because the perceived sound is dependent on the many overtones and not the fundamental. Having said that, I want to emphasize that good tuning will certainly help to accurately produce the appropriate overtones for the selected note, particularly for the higher notes.

To better understand the difficulty in selecting a chime note to match a selected musical note see the Excel sheet ChimeFreq. This will give you a colored picture of the many overtones present for each note and on how any specific frequency is created by more than one chime. You can see the wide range of notes present in a single chime by observing the horizontal axis. The diagonal axis represents the many different opportunities for a specific frequency to be generated.

In addition to the many overtones present for each chime we have the difficulty of knowing which overtones are prominent for each note because of the ear's sensitivity as represented by "The Equal Loudness Curves". As you might suspect, the prominence of a particular overtone changes as we move up the scale. For a typical ear sensitivity range of 300 Hz to 3 KHz, see the sheet named 300Hz-3KHz. Obviously this is not the entire audible range of the ear but is presented as a simple example of the limited ability of the ear to hear all the frequencies generated by the overtone structure. In particular, the range of C2 to C3 contain a large number of audible overtones while the range of C5 to C7 contains very few. The range of C2 to C4 produces the most melodious sound and is the easiest set of chimes to build. Precise tuning (+ or - .1Hz) is not required.

^TOP^

Location for chime tube mechanical support:
Chime support is at either of two locations. The more tubular bell sounding chime is when the chime tube is supported by a hole in an end cap. The end cap lowers the fundamental frequency and some associated overtones. For  1/2" copper pipe, type L, the fundamental is lowered by about 3% to 6% from calculated values on this page. For 3/4" type L copper pipe, the fundamental is lowered by about 11% to 12%. The good news is that the end cap noticeably increases the hang time for the first overtone and the chime has a much more bell-like sound. Look at these two spectral waterfall displays and specifically compare the hang time of the 1st overtone.  You will notice the a considerable increase in sustain time for the end cap supported tube.

Waterfall display for a chime tube supported at the traditional 1st overtone node	Waterfall display for a chime tube supported by a hole in the end cap. Similar to the traditional orchestra chime

The second support method is the traditional 1st overtone node which is 22.42 % from the either end. See the Free Bar Vibrational Modes at the right I found it easy to destroy the Q (hang time) of a hi-Q chime by improper support. Thin wire, rubber grommets and plastic inserts all worked but contributed to a lowering of the Q. Nylon plumb line with no inserts worked best and the line is available in a variety of colors. Of course it is necessary to de-burr and burnish the drilled support holes to minimize wear and tear of the line. Sources for rubber or plastic grommets include Radio Shack, Home Depot, Lowes and your local model airplane & hobby store.

You can support the chime at the second or third overtone nodes but it is not recommended.  All charts and calculations on this page are for support at the first overtone node. See reference at right.

BTY, for acoustics, it is easy to confuse overtones and harmonics. "Overtones" = Harmonics -1, or "Harmonics" = Overtones + 1. This acoustic harmonic relationship has no connection to the Radio Frequency definition of harmonics.

1st Overtone                             2nd Overtone                               3rd Overtone
 Animations courtesy of  Dr. Daniel A. Russell  at Kettering University, Flint, Mi

A variety of methods can be used for 1st node mechanical support

Method 1	Method 2	Method 3	Method 4
Most typical and the most stable in high winds.	One support point and somewhat less stable than method 1. More difficult to de-burr the inside support hole.	May be more pleasing to the eye with less visible string. Less stable that method 1. More difficult to de-burr the inside support hole.	A mounting pin eliminates the string knot and provides a cleaner look.

Centering the support line on the pin for this example I used #12 copper wire but you can use what works best for you.

Method suggested by Chuck from Columbus

^TOP^

Frequency measurement:
We can measure the fundamental frequency and the overtone content with DSP (digital signal processing) via FFT (Fast Fourier Transform Analysis), but from a practical view I found it of little value in determining the actual musical note. Having said that, the FFT measurement is quite valuable in understanding the characteristics of the chime spectrum.  I Use a couple freeware versions available here.

DL4YHF's Amateur Radio Software: Audio Spectrum Analyzer ("Spectrum Lab")

OscilloMeter

A commercial electronic music tuner by Krog worked well for fundamental measurements but can be tricky because of the short hang-time from the chime.

A good software solution for frequency measurement is to use a tuning program. I found a shareware program "Tune Lab Pro" worked well once you were close to the desired frequency. Tune Lab Pro version 4 is available HERE. This is good for frequency measurements but completely ignore the musical note display because it's set up for string instruments which are integer harmonic, chimes are non-harmonic.

^TOP^

Mechanical support for frequency measurement:
I had good success supporting the chime horizontally at both nodes, one by a rubber band, and at the other node by a thin wire attached to an accelerometer. The accelerometer eliminated the annoying background noise when using a microphone.

^TOP^

The Wind Chime Striker:
Orchestra chimes, of course, need a human to strike the chime and a rawhide-covered rubber mallet works well for that application. However, for wind chimes there is little strike energy available from the wind catcher so preserving and applying that energy is the challenge. I tested a number of strikers and found that considerable strike energy can be applied by using a 2" diameter oak disk machined to a knife-edge and loaded with about 1oz of weight. I also used a small 1/16-inch brass tube about 5 inches long as an axle for the disk. The axle keeps the disk horizontal during rapid and sudden movements from high winds.

If you live in a area with little wind then eliminating the 1oz weight may be desirable. See the next section on striker location for more info on striker weight and location.

The small diameter disk was used to minimize the striker from contacting more than one chime at a time. Attempting to strike several chimes simultaneously to produce a chord was a waste of strike energy and ineffective. There is little strike energy available to start with and attempting to strike a musical cord with the striker is, at best, disappointing. A larger diameter disk may be preferred as it is less likely to be blown to the outside of the chime circular mounting profile during high winds.

There are two locations on the chime that work well for striking. If you are building a "non-bell sounding chime" for fundamental C6 and up, striking at the center or the end works equally well. Striking the center assures excitation of the second harmonic but, you run the risk of not exciting the odd harmonics.

On the other hand, if you are building a "bell sounding" chime it is important to excite all possible modes for good overtone representation. This is easily accomplished by striking at the very end of the chime. Striking at the end will assure the excitation of all modes since all modes exhibit high impedance at the end of the chime.

^TOP^

A Better "Ringer Dinger"
Update 2009, The traditional striker described above works well, however, I was looking for an approach that would produce a more consistent sound. To my surprise I believe there is a better way. Striking the chime at the very end consistently produced a much better sound that striking near the end or in the center. As mentioned above, you run the risk of not exciting the odd harmonics by striking at the center.  This should not have been surprising since orchestra chimes are struck at the end. Try it for your self. On most chimes it made a difference except on the high notes where few overtones exist.

A tapered striker was used to accomplish this goal and to assure the striking of all chimes at the very end. If you have access to a wood lathe, it's an easy task to machine a tapered striker from wood. I used pressure treated stock but any hardwood would work. It is important to under-cut the inside to minimize excessive weight which will inhibit striker resonance.

This heavier striker made it more difficult to resonate. (see Striker Location, below). As described in "Chuck's Chimes" the choice of material depends on the note selection. For lower frequency chimes a soft, heavy striker is best and for higher frequency chimes a harder, lighter striker works better.

^TOP^

The Wind Chime Striker Location a new approach "The Resonate Striker"

I happen to live in a wooded area with little wind and have struggled to achieve good strike energy with low winds. With that in mind, I set out to improve the low wind performance of the striker.

The objective is to maximize striker movement with little input energy. The easy solution was to resonate the line holding both the striker and the catcher using the second mode bending principle. This resonance will help to amplify and sustain the motion of the striker with little input energy from the wind.

You can easily recognize this movement by using both hands to hold a string vertically and have a second person pluck the center of the string. The natural resonance of the string will cause the center to move back and forth horizontally. If you position the striker at the exact center between the top support and the catcher you can achieve this resonance.

Jack Maegli, on Chuck's Chimes page mentions that the catcher/sail should have a weight equal to about 25% of the striker. For medium to high winds and for a non-resonate mounting, I completely agree with that suggestion. In this instance when you attempt to resonate the support line, I suggest a light weight striker to assist with good resonance. A heavy striker would not resonate.

When resonance is working well you will notice as the catcher comes to rest, the striker will continue to bounce off the chimes for a few more strikes, an indication of dissipating the stored energy from resonance. See this Resonant Striker VIDEO WMV, for a demo. Notice the large movement of the striker compared with little movement from the catcher.

^TOP^

The Wind Chime Wind Catcher, a new approach. "The Unstable Catcher"

Traditional wind catchers work well, hang vertically, and can be configured in a variety of materials, sizes and shapes. The objective of a better catcher is to cause the catcher to become unstable and to move the striker in a more circular motion from the force of single-direction winds and to better capture the effect of turbulence.

First, my dissatisfaction with the traditional wind catcher is that in single-direction winds it has a tendency to cause the striker to swing to and from the direction of the wind and not strike adjacent chimes. Much like the periodic motion from the pendulum effect and sounding like ding-dong, ding-dong, etc.

Secondly, with turbulent winds the traditional catcher does not do a good job of contacting all the chimes. Certainly, the wind is random in direction and the catcher will eventually cause the striker to contact all chimes, but I wondered if there might be a better way?

Thirdly, as you know, winds vary considerably across the country from low speed to high speed and from predominately single-direction winds to mostly turbulence winds, and in any combination. The best solution for you will depend on your type of wind. You may need to try a few different catchers for your best success..

From some windmill research I did several years ago I recall that wind, close to the ground, can behave quite differently than winds aloft. As you know, wind can be quite turbulent and often does not blow horizontally as intuition would suggest. Instead, it is a two dimensional force simultaneously blowing in both the horizontal direction and the vertical direction. Swirling and blowing uphill, downhill, and horizontally. Wind sheer is a common occurrence close to the ground and perhaps we can exploit that force to make a better wind catcher.

To better understand wind turbulence mixed with single-direction winds watch this 20 sec WMV,  Bi-Directional Wind Vein VIDEO showing a bi-directional wind vein mounted on my deck. You probably noticed the swirling motion mixed with single-direction winds and the random uphill and downhill movement, pitch & yaw. Let's take advantage of this movement to create a striker movement that is somewhat rotational in nature and does a better job of striking all the chimes.

To better capture turbulence the solution is quite simple. Mount the catcher at 45^O to the horizontal so as to catch the pitch and yaw forces. See the picture to the left and right for an easy solution. Thread the support line through two small holes next to the center of an old CD disk and tie the knot slightly off-center to create the 45^O slope. You may need to glue the line in place for the long term.

A second approach to capturing turbulence and to cause the striker to move in a more circular motion is to hang the catcher perfectly horizontal. Counter intuitive, I agree, but depending on your particular type of wind it can work surprising well.

^TOP^

Solving the "Ding-Dong"

With a single direction wind there is little one can do to avoid the annoying ding-dong sound despite all the innovative catcher designs I have seen. The above "angle-mount catcher" works and attempts to solve the "Ding-Dong" problem, but is not the ultimate answer. The real answer is to accept the "ding-dong" effect and rotate the chime set to take advantage of the periodic motion from the striker.

Rotation is easily accomplished by inserting a few paddles about the circumference of the support plate. As my wife says, "they look like "Mickey Mouse Ears". Hang the top support plate using a sturdy but flexible line. For light weight chimes I use nylon plumbing line from the local building supply store. Heavy chimes require a more reliable material. You can either double up the nylon line or in my case, I use 1/8" nylon pull-line used for pulling wires through electrical conduit.
 

This approach has a tendency to self regulate the amount of rotation. The chime set will wind-up until the support line can no longer accept twist and then un-wind as the striker continues to function. In addition, the higher the wind velocity the less the chimes seem to rotate, which is good for high winds.

As an example, here is a "Rotating Wind Chime Part 1 of 2  Video", WMV,  taken with normal winds. Notice the bi-directional wind vein indicates little turbulence with winds from a single direction.

Here is "Rotating Wind Chime Part 2 of 2  Video", WMV, taken with very high winds. Notice the chimes tend not to rotate out of control with the high winds.

^TOP^

Choice of Material for Wind Chime Tubes:
As I am sure many already know, the choice of material makes a considerable difference in the timbre of the chime sound. I tuned three tubes of the same diameter and wall thickness made from brass, copper and aluminum to the same fundamental frequency of C2. The resulting timbre was as different as day and night. I suspect the difference in perceived sound is because of the varying ability of the material to support overtones in varying degrees of loudness. Researching this effect was way beyond the scope of the project. Aluminum had the very best overall sound for fundamental C2.

For the "non-bell sounding" chime tuned to fundamental C6 there was little noticeable difference among the three materials. This is not surprising because of a lack of overtones at these frequencies and the chime approaches a pure tone at the higher frequency. Tubing sources seems to becoming more scarce at time goes on. Here are a few I found but I have no personal experience with them. I have had considerable success in locating brass and aluminum tubing at my local metals recycler.

^TOP^

Source of Tubing:

Aluminum and brass tubing tend to exactly follow their stated ID and OD dimensions, however, copper tubing does not. See the table below for actual dimensions for Type L copper tubing. More on type K, L, and M here
 

^TOP^

Measuring Tape:
I found it much easier to work in millimeters rather than inches. The problem was finding a tape measure that uses mm here in the USA. I found one made by The L.S. Starrett Company, model # CS1-8ME12. Lowe's Home Improvement carries the item but only at their web site. It cost about $10-. Another possibility is L.S. Starrett model # CH12-10DME

^TOP^

Conclusions:
Clearly there is more to a chime than I had anticipated and I am sure I did not learn all that there is to know about the physics of a chime. This was a Christmas present project and not a focused research project. I am convinced that it is not necessary to tune a set of "bell-like" chimes designed for a musical note from fundamental C2 through C4 because the formula achieved the desired frequency within 2 Hz. Tuning to achieve an accuracy closer than 2 Hz was a waste of time. However, for a fundamental note from C5 and up, tuning is required.

Having said that, I am not convinced that selecting a musical note for the range of C2 through C4 by choosing the fundamental frequency is the correct approach. The actual musical note depends upon the configuration of the overtones and they are dependent on the choice of metal used to manufacture the tube. Therefore, the correct length is not the length for the fundamental note but a length longer than the fundamental. I leave the determination for the correct tube length to achieve an exact musical note for another time. However, building a set of chimes for fundamental C2 or C3 sounds very melodious and is definitely worth the effort. Also, for or a chime set between C2 and about C4 I believe it is necessary to spread the notes apart so they maintain their individuality at a distance.

My favorite design configuration is a.) end cap support b.)striking the tube at the verry bottom using a taper striker c.) rotating the chime set with wind veins. Your particular wind-type (single-direction or turbulent) and wind speed will determine the best choice for both the wind catcher and for the chime striker. Rotating the chime-set works well to solve the "Ding-Dong" sound caused from low velocity single directions winds.

^TOP^

Calculations:   If your looking for DIY calculations or pre-calculated dimensions, scroll down to here.

Chuck at Chuck's Chimes has already provided the application of Euler's* equations to a thin wall round tube.
For your convenience that information is enhanced repeated below. Also reference a paper by Tom Irvine

The bending natural frequency of a tube is predicted using Euler's* equation.  w = (B X l)2 X √ (E X I/(rho X l4))

w - frequency radian per second  -  for frequency in cycles per second (Hz),  f = w/(2 X π)
E - modulus of elasticity
I - area moment of inertia = π X d³ X t/8 for a thin wall round tube
d - mean diameter
t - wall thickness
rho = mass per unit length = Area  X  mass per unit volume = π X d X t X density
l - length of tube

w= (B X l)² X (d/l²) X √ (1/8) X √ (E/density)

(B X l)²  - Constants based on the boundary conditions for a wind chime (Free-Free Beam)
(B X l)²  = 22.373 for the first natural frequency.
(B X l)²  = 61.7 for the second natural frequency.
(B X l²  = 121 for the third natural frequency.
(B X l)²  = 199.859 for the fourth natural frequency.

To get the units correct you must multiply the values inside the square root by gravity (g).
g = 386.4 in/sec² for these units.

For a given material then the frequency of a thin wall tube reduces to  f = constant  X  d / l²

Implementation follows like this:
Units
OD =  inches
ID  =  inches
Density =  Lbm / in³
Modulus of Elasticity =  Lbm / in²
f  =  Hz
Area Moment of Inertia =  in⁴
Area = in²
Gravity Constant = 386.4 in/sec²

The formula reduces to this:

Area Moment of Inertia = π X (OD^⁴ - ID^⁴)/64
                          Area = πX(OD^² - ID^²)/4
                              K = √((Elasticity X Moment X Gravity)/(Area X Density))
      Length (inches) = √(22.42 X K/(2 X π X f))

If you're curious about the circular mode (not considered here) see this http://paws.kettering.edu/~drussell/Demos/radiation/radiation.html

^TOP^  

Calculate your own dimensions DIY
Requires any of the following to view and execute:
MS Excel Viewer (Free) Get it here; or Sun Open Office (Free) Get it here; or MS Excel (Cost $) Get it here;

Download  DIY Wind Chime Calculator in Excel

All dimensions calculated are based on OD, ID in inches and Material type.
OD = outside dimension of tubing (inches), ID = inside dimension of tubing (inches),
Material type = Aluminum, Brass, Cast Iron, Copper, Steel and Stainless Steel.
Note selection by frequency in Hz.
The calculator uses nominal values for material properties; however, if you know the exact material density and the exact modulus of elasticity, you can enter that data for your specific material.

^TOP^

Pre-calculated lengths for some common materials used in chimes are in the table below.
For different materials or sizes use the DIY Excel sheet above.

^TOP^

Suggested Reading

An interesting physics class, student project, authored by Professor G. William Baxter and Assistant Professor Keith M. Hagenbuch, both from Penn State, Erie

Thanks to the suggestion of a visitor (Larry) here is a book "The Physics of Musical Instruments by Neville H. Fletcher, Thomas D. Rossing" available at eBay HERE that has a great chapter on chimes and bells.  
The missing fundamental effect
The missing fundamental (Hanover College)
Fletcher/Munson Curves   Fletcher/Munson Curves with ISO 
 

Software:

Windchime Designer V1.0" by Greg Phillips
If you have trouble unzipping Greg's new version here are the two files you need. Chime32A.exe  and TUNING.DAT
Place both files in the same folder and run the exe file.

Tune Lab Pro software

DL4YHF's Amateur Radio Software: Audio Spectrum Analyzer ("Spectrum Lab")

OscilloMeter

Some good links:

http://www.hibberts.co.uk/index.htm This site has not only nice pages on bell sounds and tuning but offers free software that lets you listen to the effects of overtones and allows you to tune your bell or chime using a sound card and microphone. Really nice.

http://www.msu.edu/~carillon/batmbook/index.htm Chapter 5: The Acoustics of Bells is a nice introduction to bell physics.

http://www.mmk.ei.tum.de/persons/ter/top/pitch.html Psychoacoustics of pitch perception.

http://www.mmk.ei.tum.de/persons/ter/top/strikenote.html The strike note of bells.

Not exactly related but an interesting video Steam Driven Chimes   

^TOP^

A Few Sources for Chimes

SQUIDOO

^TOP^

FAQ's

Q Some chimes are anodized or appear to have a clear coat type finish for weather resistance or aesthetics I assume. Does a coating (powder coat, anodize or paint) affect the tone quality, tuning, or note sustain of the pipe?
A In general the answer is NO. However, if you were to paint it with a thick latex paint or some such coating, it would have a considerable affect. But a powder coat or anodizing will have little affect.

Q I have measured some different chimes and the hang point is usually close but far from exact. Should you drill the hang point hole at the center of the calculated measurement or is the hang point where the string actually contacts the tube (upper edge of the hole)?
A An excellent question. The answer is yes, the location of the hole should allow the string to touch the upper edge of the hole at the hang point. I drill just slightly below the mark to hang on the mark. With a small hole, there is enough flexibility in the location that even drilling on the mark won't seriously degrade the Q.

Q Does the hole size that you drill for the hang point matter?
A Yes, if it is large relative to the diameter of the tube it would affect the modes but a small hole has no affect. I personally use 1/8 inch or smaller.

Q I recently bought two not cheap wind chimes – and they do not chime in the absence of hurricane gale winds!!! Is there anything we (read – my husband) can do to get them to catch any breeze that happens by? Would the CD section in your article be all he needs? I have spent a long time on the internet looking for some quick fix but can’t find anything. The power company recently cut down all of the shrubs we have been carefully tending for years and now we have dreadful road noise. The chimes were an optimistic detraction to that new situation
A This is a typical problem in that the wind catcher is often too small and too heavy. Without seeing the set of chimes directly I might suggest you replace the wind catcher with something larger and lighter weight. I use an old CD just to make the point that it needs to be light weight and fairly large in size. Often an old CD is not large enough. You can use anything that pleases your eye and meets the size requirements, like a decorative aluminum pie pan or any such item.

Q Where do I get the mounting pins and what size is recommended?
A I typically use 1/8 inch brass pins and that stock is available at my local hobby store where a person can buy model airplane parts, model trains, model cars and the like. I have also seen 1/8 inch round stock at Home Depot.

Q How are they held in position in the tubes?
A If you put a 1/8 inch rod in a 1/8 inch hole it can be loose. I will take a hammer and slightly flatten one end of the pin for a force fit.

Q How does the string stay in the middle of pin and not slide off to the side?
A A spot of hot glue or epoxy will do the trick. A knot works well too.  Click here to see a mechanical method

Q What type of string is recommended to hang the pipes?
A I have had good long term endurance with the nylon plumbing line from Home Depot and available in several colors. To reduce the UV effects I most often will dip the white nylon line in a dark wood stain to help reduce the deterioration over time. Nylon fishing line works well but be sure to deburr the mounting holes. For the heavy chimes I use 1/8 inch cable-pull nylon line used in the electronic data transmission business. I found an ample supply at a Hamfest one day. Not sure where to buy it over the counter. Might try an electrical supply store?

Q You mentioned that aluminum makes the best chimes. What type of aluminum and what wall thickness? As you can see from the above web page, you can get 6061 and 2024 aluminum from these folks and many different wall thickness.
A When I made that comment about aluminum in 2001 I still had a lot to learn. It turns out that now, when I make chimes for friends which I do quite often, I use 2.0 inch diameter aluminum with a wall thickness of 1/8 inch. One of the key factors that contribute to a good sound is the "High Q' or "long hang time". Depending on the energy of the strike the hang time can be as long as two minutes for that tubing. I still prefer aluminum because of the light weight and the low cost.

However, I am now convinced that good sounding chimes can be made from most any material if care is taken to select the right notes, and that takes some experimenting. I have a set from regular 3/4 inch copper pipe right from Home Depot that sounds just great. A friend made a set for use in a public park in Colorado from iron pipe and they too sound good.

A second element contributing to a good sound is selecting a note that is low enough in frequency so as to allow many overtones.

A third element is one that Chuck addresses and that is selecting the length to match the acoustical length. See his site for the calculator. I have made a few using that approach and they all sound good.

The striker is also an important factor. I am currently revisiting the subject of the best striker and wind catcher combination.

^TOP^

Projects by site visitors click picture to expand

Commissioned Chime Set by Kenny Schneider, 2003,  plays Bach's, "Joy of Man's Desiring" when struck.
 See https://artistsregister.com/artist_image.phtml?slideId=13395&backlink=artists&number=CO201

By David from Alaska, Dec-09
The set is contains 20 chimes from 1-1/2" EMT (electrical metallic tubing) with a range from C4 to G above C5. The chimes are mounted in a frame of jacoba wood (sometimes called Brazilian Cherry). The frame construction is a combination of mortise/tenon and screwed connections.

By Chuck, from Columbus, Ohio  Dec-09  Nice use of chains.
I made six set of chimes based on the information on your site and gave them away as Christmas presents. They sound great. Although, I'm not too sure about using the chain to support the ringer and wind catcher. It's probably much too heavy. See his  Chime Video WMV

One bit of information you didn't explain is the need to create notes within the same chord in a given key. That way, any two or more notes that chime together will sound great together. My music teacher friend helped me select an F major 9th cord and a G major 9th cord.

I also found a given type of pipe has a limited range of notes that will ring well. I put a copper wire through the tube and through the last link of the chain. Then I used a long stick that just fit inside the bottom of the pipe with a point cut on the end in the middle. I pressed the stick against the copper wire to put a bend in the middle so the chain will center itself. It is much prettier, more heavy duty, and more permanent than string. Finding the brass chain was the most difficult part. I used Trex decking to make the top support and ringer so they will never decay.

Hip Chimes by John, Troy, NY,  Jan 2010
Tubular not, but none the less, they are chimes. Yes, these really are Chimes made from old orthopedic and dental implants that I have in my collection from 32 years, e.g., hip stems, knee prostheses, acetabular cup prostheses, dental blade-type implants, etc. Two of the hip stems are Ti (one is actually just a scrap piece from machining a hip stem) and the other 2 stems are  Co-Cr-Mo alloy. When they are made out of Vitallium (a very hard Co-Cr-Mo alloy, usually cast, but sometimes wrought), the ringing is terrific. (Ti-6Al-4V alloy sometimes also rings pretty well.) (See the (Hip Chime Video Here) WMV

The middle clapper thing is an old-style Co-Cr-Mo acetabular cup replacement, which was meant to screw into the pelvis. The small rectangular plate above it is a little Ti plate, which will hopefully catch the wind a bit.

The Biggest Intel® Chime Set

  ^TOP^

Links:

* Equations from paper by Tom Irvine

http://www.eng-tips.com/viewthread.cfm?qid=152064

http://www.educypedia.be/education/physicsjavasound.htm

member

Leland L. Hite, K8CLI, Loveland, Ohio
Last updated on 02/08/2010