Copper pipe glockenspiel

Build a great-sounding glockenspiel out of copper pipes!  The pipes, when correctly mounted, have a lovely bell-like tone.  This glockenspiel (a glockenspiel is like a xylophone, but with metal slats or tubes) is based on a project in this book, but with a larger range and tuning information based on theory from this excellent article.  

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.

I built this project with my six-year-old son.  The exact amounts of material you need depend on what musical coverage you want the instrument to have.  After consultation with my nine-year-old daughter as to what music she wanted to play on it, I opted for nine notes, covering a C-major octave, plus an extra D at the top, namely from C6 to D7.  The lower the notes, the longer the copper pipes will need to be, and hence the more copper pipe you will need.  On the other hand, the higher the notes, the more precisely the cuts will need to be made.  

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

The next step will describe the basic theory and mathematics behind the project.  As Plato insisted, music is very mathematical, but the mathematics is not very hard.

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:

• f=A/L²

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.  In theory, you could measure the diameter of the pipes and the thickness of the pipe walls, and then precisely calculate A and figure out how long your pipes should be for the desired frequencies.  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.  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.

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.

Comments

[newbiepapercrafter]

Wonderful! More proof that you can make music with ANYTHING!

[dchall8]

This works with steel pipe conduit, too. Only problem with that is that it is welded and the sound is slightly dulled. But if you want to prove the concept and the math, steel is much less expensive.

[arpruss]

You could also get non-welded steel pipe or tube. I checked on onlinemetals.com, though, and their mild steel tubes seemed slightly more expensive than Lowes' copper pipes which are $1.18 per foot.

[arpruss]

Does anybody know a good iPhone app to use for checking the peak frequency? Or good desktop apps?

[mikeasaurus]

Fantastic project! Glockenspiel gefaellt mir!

[arpruss]

Thanks! I really like the color scheme the kids and I came up with.

For Christmas, one of the gifts for our six-year-old was the ingredients for several woodworking projects, and this was one of them. We've got a couple more projects to go!

[stumitch]

NICE!!! now I have a new project to try with my metal/wood classes. very well done!

[wilgubeast]

This looks absolutely fantastic. I particularly like how you made the connection with more than one subject's learning objective. More glockenspiel.