Introduction: Copper Pipe Glockenspiel
This is potentially a very educational project. Several learning objectives are possible, depending on the subject area of interest:
- Mathematics: Solve simple equations to match pipe length to notes.
- Physics: Learn about the relationship between length and first-mode vibrational frequency.
- Music theory: Learn about the relationship between frequencies and notes.
- Shop: Learn how to measure and cut wood, join it with nails or glue, and work with metal pipe.
The basic idea with this glockenspiel is that there is a wooden frame with two rows of nails sticking out of it, and rubber bands joining neighboring nails in each row. The rubber bands hold the pipes in place while giving them a lot of freedom to vibrate. The hard work is making sure the pipes are the right length and held by the rubber bands in the right place.
The amounts of material below, and measurements mentioned later, assume our nine-note range from C6 to D7.
- About eight feet of type M 1/2" nominal copper pipe. Despite being called 1/2", this has an outside diameter of 5/8", and a thickness of about 0.03". You need the total length of your pipes (see Step 2 for pipe length calculations) plus about an inch per pipe to compensate for mistakes and to allow tuning. This is the expensive part of the project. (Our Lowes sells 10' for $12.) Note: If you combine pipe from two sources (as we did--we used some old pipe that was lying around and some pipe we bought), you will have to make separate calculations and measurements for the two pipes, in case the dimensions are not exactly the same--the tuning is very sensitive to the dimensions.
- About four feet of approximately 3/4" x 2" wood. The 3/4" is best left as is, but the 2" can be varied from about 1" to 3" with no harm. Any kind of wood will work.
- 20 to 28 nails, approximately 1.5" long and 1/16" in thickness (20 nails if the wood is joined with glue, 28 if the wood is joined with nails, in between if both are used)
- 15" of some sort of tubing that can loosely fit over the bottoms of the nails to keep the rubber bands for sliding down; we used heat-shrink tubing (but didn't shrink it); in a pinch, you can cut up drinking straws; or you can go to Lowes or Home Depot and pick up two feet of some cheap plastic tubing
- Drill and drill bit for pilot holes for the nails; a drill press can make life a bit easier
- 20 rubber bands, approximately 6" circumference
- wood for one or two hammers; we used about 8" of 5/16" dowel for the handle and about 1.5" of 7/8" dowel for the head
- a phone, tablet or computer with an app that calculates the peak frequency of sound coming in through a microphone; we used an Android mini-tablet and found that the free Fourier application was best, though some of the fine tuning was double checked with gStrings; you may find that some specific music tuning applications don't work very well for this, because your initial tuning will be quite far from an official note
- a calculator or a calculator app
- pipe cutters (we were cheap and used our hacksaw--that was a ton of work, and messy)
- flat file or other sanding/trimming tool (belt sander, disc sander, bench grinder, Dremel, etc.)
- Optional: wood glue (I used Titebond II)
- Optional: paint
Here is my nine-year-old untrained daughter playing a scale and a piece.
Step 1: Some Theory
We want the pipes to vibrate in the first mode. The picture shows how that happens: there are two nodes, 22.4% of the way in from each end, that stay put, and the pipes vibrate around them, the ends going up when the middle goes down, and vice versa. The pipes will sound the best when they are flexibly supported around the nodes. In the glockenspiel, the pipes will be supported by rubber bands at the nodes. If you want to try how a pipe sounds, you need to support it at the nodes and hit it in the middle.
Once you buy your pipe, the only thing you can really control is the length of the pipes. The longer the pipe, the lower the main frequency. The formula is:
where f is the frequency, L is the length and A is a number that could in principle be calculated from the thickness of the pipe walls, the diameter of the pipes and the speed of sound in the material. The problem with that is that it is very hard to measure the thickness of the pipe walls and diameter of the pipes with sufficient precision to get A. And you can't just use my data, because every pipe will be a bit different. Instead, we will cut a test pipe section, measure its length, use a mobile phone app to measure the frequency, and then use that to calculate A in Step 4, below.
Once we've calculated A, we can choose the frequencies we want for the notes and solve the equation f=A/L2 to calculate the length of the pipe. The solution, of course, will be that L is the square root of A/f.
My value of A was approximately 67,600,000 mm2/s. You can use this to get an approximate idea of how long your pipes should be, if you're using type M 1/2" nominal copper pipe like I was, for planning. You can look up the frequencies for different notes here. For instance, C6 is 1046.5 Hz, so the length L will be approximately the square root of 67,600,000/1046.5, or 254mm. If that's your lowest note, like it was for me, this will be the length of your longest pipe.
Step 2: Choosing Frequencies
Choose the notes you want to use in your glockenspiel and copy their frequencies from this table. I used C6, D6, E6, F6, G6, A6, B6, C7, D7, which was a C-major scale octave, plus an extra high D. Significantly lower frequencies would make for very long pipes, which I don't recommend.
Step 3: Cutting a Test Pipe
Now cut a pipe, approximately an inch (2-3 cm) longer than you want your longest pipe to be. If you're using Type M 1/2" nominal pipe with C6 as your lowest note, this will be about 270mm. You will use this pipe to measure the quantity A and figure out the lengths of all the actual pipes.
Do yourself a favor and get yourself pipe cutters if you don't have them. They're not expensive. We used a hacksaw and it was a horrible pain. If you need to use a hacksaw, tape a strip of paper around the pipe to make sure the cuts are square. Then make shallow cuts all around, flush with the pipe, and then deepen the cuts until you cut through. Pipe cutters should have a cleaner cut much faster.
Copper is toxic. Use breathing and eye protection.
Step 4: Measuring and Calculating
Measure the length L of the test pipe as carefully as you can. If all you have is a rule calibrated in millimeters, still do your best to estimate to about half a millimeter precision by eye.
After the cut, let the pipe cool off to room temperature. Otherwise its frequency will be off a little.
Now measure the frequency of the pipe. This is a step you will do many times in this project. You need to suspend the pipe on rubber bands or something else soft about 1/4 of the way (22.4%) in from each end, where the nodes will be, and otherwise let the pipe vibrate freely. In my experience, getting the suspension points exactly right won't affect the frequency that much. Start an application on your mobile device that will measure the peak frequency of the sound, and suspend the pipe close to the device.
If you're using Android and the Fourier app, make sure you put the device in portrait mode, and then you press the activation button in Fourier. Fourier is a bit buggy--I recommend rebooting your device once you're done with all the measurements lest it slow down your device, and it doesn't seem to work well in landscape. But it seems to work better than any other free app I could find in the Android Market for this purpose--it measures the peak frequency really well. There no doubt are good iPhone apps for this, and maybe a desktop app, too, but Fourier is what I used. Some applications for tuning guitars didn't seem to work that well with the sound produced by the glockenspiel, for instance.
Hit the suspended pipe in the middle with something wooden, like a piece of dowel or a pencil. To do that, you will either need to have one person hold the pipe in two rubber bands and another hit it, or find a way to put the pipe down on some rubbery supports, or find some other way. What I did most of the time was to stretch rubber bands between thumb and forefinger on each hand, attach the pipe to each rubber band about 22% of the way in from each end, and have my son tap it, making sure the pipe wasn't making any contact with my hands.
It should give a lovely bell-like tone. If it doesn't, probably you've got it suspended too rigidly or by the wrong place. Write the frequency shown on the mobile device. Sometimes several frequencies will be shown, but typically only one or two will be at all in the ballpark you'd expect based on the fact that the note should be lower than the lowest note for your glockenspiel. Just choose the one that looks reasonable and is shown for the longest amount of time. Tap the pipe a couple of times to repeat the experiment and take the average of the values shown (in my experience they will often be exactly the same).
You now have is your frequency f and your length L. Since f=A/L2, you (or your student(s) if old enough) can solve for A and find A=fL2. Just make sure to use the same units of length throughout the project. I recommend millimeters. For instance, if your length were 223mm, and you measured a frequency of 1359Hz, you would have A=(1359)(2232) = 67,581,711. The student(s) can figure out the units if old enough. A Hertz is in units of 1/s, so if your lengths are in millimeters, A will be in mm2/s.
Now that you have a value for A, go back to your table of frequencies from Step 2, and calculate a length for each frequency using the fact that L is the square root of A/f. For instance, for C6, whose frequency should be 1046.50 Hz, if A is 67,581,711 mm2/s, your length in millimeters will be the square root of 67581711/1046.50, i.e., 254.1mm. You should record your lengths up to a tenth of millimeter, even though you can't cut to that precision.
For educational purposes, you may want to first suspend the tube in different ways, say by the ends, or just lie it flat on a surface, and listen to the sound. It will sound much less resonant--it will probably be quite ugly, instead of the elegant bell-like sound when the tube is suspended by the nodes. This is a teachable moment.
Step 5: Cutting a Pipe for the Glockenspiel
You now have approximate lengths for all the pipes. If you just want to make a fun toy to bang, you can just cut all the pipes to these lengths, sand lightly, and be done with it.
Unfortunately, especially with the higher notes, the frequency depends very finely on the length (it does go with the square of the length), and so to get decent precision, you will need to tune your cuts.
I worked on the tubes one-by-one, starting with the longest (which I made from the test pipe from the preceding step). This way, I knew that if I cut something too short, I could just cut it down for the next highest note (i.e., the next shortest pipe).
I marked each pipe where to cut, and my son and I cut each pipe, typically about half a millimeter to a millimeter too long.
Step 6: Tuning the Pipe
After cutting the pipe, use a pencil to mark the nodes, 22.4% in from each end (this need not be very precise--if you get it within a millimeter or two, that's fine). Then measure the frequency, exactly like you did for the test pipe, again allowing the pipe to cool after the cut. Since you cut too long, the frequency should be a bit too low. (If not, measure your cut pipe. If the measurement of the pipe is bigger than per calculation, you mis-measured something with the test pipe. Re-do your calculation of A with your new pipe, and recalculate your pipe lengths.)
Make sure you set yourself a tolerance. Since none of us in the family are very gifted musically, 0.5% or about 5 Hz was satisfactory for our purposes. You might want to set yourself a more exactly tolerance like 2 Hz. Also, if you can get all the pipes with errors on the same side, the errors should be less audible.
If after the cut you're within tolerance of the correct frequency, you're done after a very light sanding to remove jagged edges (very light, because you don't want to de-tune), and just repeat with other pipes. If your frequency is too high, and not within tolerance, you've cut things too short. Just re-cut this pipe for your next note (so, if you're making the C6 note, just re-use this pipe for D6, cutting it a bit shorter), and cut a new one for the present note. (Of course, if this is your highest note, you've just wasted some copper pipe--maybe you can use it for another project.)
If the frequency is too low, you need to trim the pipe a bit. I found a rotary tool with a sanding drum attachment to be the best way to do it. You could also use a sanding block if you're patient, or a bench grinder if you're not. Wear safety goggles and breathing protection.
What you do is trim a tiny bit, check the frequency, if it's still too low and not within tolerance, keep on trimming. But make sure to cool the pipe off before measurements. If you over-trim beyond the tolerance, cut a new pipe, and use this for the next note.
I recommend writing in pencil on each pipe what its note is.
Step 7: Laying Out the Frame
You will want the pipes about an inch apart, laid out on a trapezoidal frame.
If you're using nine pipes like I was and the C6-D7 notes, you can cut two 420mm (16.5") lengths of your 3/4" x 2" board (neither the 3/4" nor the 2" is very critical).
Draw a pencil line down the middle of one narrow side of each board.
Put 19 evenly tick marks along the centerline of each board, spaced around every 20mm (I think I actually have more like 21mm), starting an equal distance from each end (and not too close so that a nail there won't split the board), with the odd numbered tick marks being differently marked from the even numbered ones. The odd-numbered tick marks will be approximately where the nails go and the even numbered tick marks will be where the pipes will lie.
Now, lay the pipes out on top of the frame boards, on the even-numbered tick marks (they will roll--do the best you can). Adjust the angles and spacing of the frame so the node markings on the pipes lie as close to the center line as you can. You will have to make compromises here because of the non-linearity in the pipe length sequence, but if your dimensions are like mine, you should be able to do a decent compromise.
Now measure and record the inner distances between the two ends of the frame so you can lay the frame out in the same configuration later. Measure how long the cross-pieces that go under the frame and hold the two boards in place should be. In our case, they were 160mm and 116mm.
Cut the cross-pieces.
Sand if needed. I used a friend's miter saw and it did such clean cuts that sanding wasn't needed. If you use a hand saw, you may want to sand. Don't want splinters.
Step 8: Attaching Cross Pieces
You now have two long pieces of wood, two short cross-pieces, and measurements of how far apart the two ends of the long pieces should be.
Turn the long pieces upside-down, with the tick marks down, and space them according to the measurements. You now need to attach the cross-pieces, while keeping the long pieces the right distance apart. What I did was to use a combination of nails and wood glue, two nails per cross-piece. I drilled pilot holes for the nails (I tried without that, and got splitting), put glue on where the jint would be, and nailed the first cross-piece in place. Then before the glue set (don't use a fast-setting glue like Super Glue!), I adjusted the angle of the frame for symmetry and for the correct spacing at the other end. Then I glued and nailed the other side.
Then clamp and wait for drying.
Step 9: Laying Out Where the Nails Go
Once the glue is set (if you use nails and glue and Titebond II, you can probably start on this in an hour or so), set up the frame right-side up, with the tickmarks on top and the cross-pieces on the bottom. Now arrange the pipes on the boards again in their places.
Now you need to figure out how to place the nails that will be joined with rubber bands. If all the nodes were right on the center line, you could just put all the nails on the center line, on their tick marks. However, because some of the nodes will be off the center line, you will need to shift the nails in such a way that a rubber band across two neighboring lines will cross the pipe as close as you can make it to the node line on the pipe.
You can eye-ball it. In my experience if the rubber band is a few millimeters away from the node, you'll be fine. Mark locations for the nails, offset to one or the other side of the center line near the odd-numbered tick marks. Make sure the locations aren't too close to either edge or the wood will split.
Now, make an indentation at each mark to help you drill. I used a center punch, but you can also just press down with a small Phillips screwdriver.
Step 10: Stops for Rubber Bands
The nails will have rubber bands on them. But we don't want the rubber bands to slide down the nails. So we will put some stops on the nails. Basically, you want some sort of tubing that can go over the nails, fairly loosely, so that the rubber bands can rest on top of it. We used some heat shrink tubing I happened to have that was the right thickness (I didn't shrink it), but in a pinch you can cut up drinking straws.
Cut twenty 14mm lengths of the tubing.
To figure out how long the tubing I needed as well as how far the nails should stick out (next step), we experimented with a mockup of the attachment of one pipe on a piece of scrap to see how it would all work.
Step 11: Attach the Nails
Drill pilot holes (while wearing safety goggles), with a drill bit smaller than your nail, for the nails in the indentations you made in the earlier step.
Then put the pieces of tubing onto the nails, and hammer the nails into their holes, trying to keep them straight, and make sure they stick out close to 25mm. To do that, we used a small piece of cardboard cut to size as a template to check that the nails were far enough in. Then straighten the nails.
I used ribbed nails, about 2mm thick and about 40mm (1.5") long. This allowed the nails to get anchored well.
Step 12: Paint
We painted the long boards with red latex house paint. The cross boards we painted with black acrylic craft paint mixed 1:1:1 with water and Titebond II to make it a bit less matte. It's all up to you. You don't even have to paint at all.
We were careful when painting to clean paint off the nice black tubing on the nails. Paint the top side first, as then you can nicely lay the whole thing down on the nails to dry while you paint the bottom side.
Step 13: Attach Rubber Bands and Pipes
Now, string rubber bands between neighboring nails, sitting above the stops made of tubing on the nails. With the size of bands we used, we first doubled up each rubber band or it would have been too loose, and then attached it. Then we just inserted the pipe into the rubber band, shifting it so that the node mark on the tube is as close as possible to the rubber band.
Step 14: Hammer
You can now make one or two hammers. You could just cut pieces of 1/2" dowel and use those.
We went slightly fancier. We cut an 8" length of 5/16" dowel and approximately a 1.25" length of 7/8" dowel. We drilled a 5/16" hole in one face of the 7/8" dowel length and glued the 5/16" dowel into it. (As always, use safety goggles.)
For two-handed play, you might want to make two.
And now you're done!
Music education could be the next step...