Tubaphone on 3D Printed Frame

This inexpensive xylophone-like musical instrument is what what you need to build if you are a percusionist and cannot afford purchasing a concert glockenspiel to practise between rehearsals. In this instructable, you will find all details on how to become an amateur musical instrument maker. The project revolves around the wonderful capabilities 3D printing offers when combined with traditional handicraft and goes through the parametric design and finally the tuning process.

Potentially a very educational project, building the tubaphone provides students with an engaging and meaningful way to apply the equations describing the transverse vibrations of tubes whose ends are free to vibrate. For teachers it will be a fantastic opportunity to explore the physics of the musical scale and examine the frequency information contained within sound.

This DIY project started with a request from my son who wanted to play a metallophone composed of at least 2 1/2 octaves and arranged like a piano keyboard, with the black keys - aka "accidentals" - raised above and overlapping the "naturals". I accepted the challenge that presented a nice combination of great topics like : physics of music, mathematical modelling, Computer Assisted Design, manual work and 3D printing.

I ended up making a tubular glockenspiel from tube shaped hollow bars (water conduit copper pipe) which gives to this instrument a brilliant ringing tone. Obviously, there will be a lot of cutting hours, therefore patience is required to carefully tune the tubular bells to the standard 12-note chromatic scale - or any other scale of your choice.

3D-printing took a central part to this project, enabling accurate positionning of the tubes to the optimal supporting distance and making the whole instument sizeable (you will be able to play from the first few tubes and grow the instrument as you make additional ones). Modularity was achieved by designing the tube holders with a dovetail that connect each other and so that it forms a structure that can be extended with virtually no limit as the number of tubes increases.

Have a look at the video to see it in action and do drop a vote in the "Instrument Contest" if you liked the project.

Video on Dailymotion

Happy Making!

Almost any kind of metal tubing will work, and the lengths of the tubes will vary, depending on the particular metal tubing, diameter and thickness.

Tools needed

• You will need access to a hacksaw (or a pipe cutter or a metal-cutting blade on an electric saw) to cut the tubing and both a flat and round hand file to smooth the end of the tubes.
• A smartphone running a spectrum analyzer app would be of great help when tuning each tube
• (optional) Large size cutting mat with grid lines

Cost estimation

I would estimate the total cost of supplies to be around 30EUR and certainly under 50EUR, which will be highly dependent on the tube material and dimensions.

• Copper pipes : I selected size 14/16mm (inner/outer diameter) and needed to cut approximately 6.5 m to get 2 1/2 octaves. The cumulated length of tubes required for the project can be estimated using the spreadsheet provided.
• 90g of plastic filament for 2 1/2 octaves, 3g per tube (I used ABS) 3D print time, total ~10-15h for 2 1/2 octaves
• A bag of rubber rings (Ponytail Elastic Rubber bands): 2 rings needed around each tube
• Wood for the frame, rectangular cross section 36mm x 18mm and square cross section 22mm x 18mm (any wooden material but preferably hard wood)
• Hardwood dowel rod for the mallets
• Sandpaper of different degrees of coarseness
• Contact glue or neoprene glue
• Wood dye or paint (in the color you want)

Glockenspiel calculator

A calculator is attached to this section where you can customize your inputs. If you know the exact speed of sound in the material you have chosen, enter this parameter into the spreadsheet and select the outer and inner diameters of the tubes. These are the only variables that control the sound of the tubes.

Read this great article and the good introductory sources of information listed in its reference section for more details on using the equation for frequency of vibration of a pipe: Building a copper pipe ‘xylophone’, D. Lapp, Special feature of Physics Educatin on: Sound Pysics. This document lists the speed of sound in various materials including copper.

Design

Teachers will find an opportunity to study the influence of outer diameter or thickness vs resonant frequency and therefore length of tubing. Here are some rules of thumb:

• Increasing the diameter results in an increased loudness (greater radiating surface area) but also greatly increases the length requirement for a specific note.

• On the other hand, increasing the wall thickness has the opposite effect as an increase in diameter. As the wall thickness increases there is a small decrease in the length requirement for any specific note. In addition there will be an increase in sustain time from the increased mass.

• Increasing the outside diameter while keeping the length and wall thickness constant will cause a substantial rise in resonant frequency.

• Unfortunately, not all of the fundamental tones and/or all of the overtones can be adequately radiated as an auditable sound by the chime tube for all possible lengths. For a typical ear sensitivity range of 300 Hz to 3 KHz and in particular, the range of C5 to G7 contains very few auditable overtones.

These are some aspects that can be studied using the provided spreadsheet when making design variations on tube material and diameters.

Tube holder parametric Design

The design intent of the plastic tube holder is to ensure that the tubes are positioned with their nodes in the standing wave for the first mode of vibration. Also for modularity reasons, the design involve a dovetail fitting and each tube holder is modelled as a standalone part.

The code for generating the 3D model of the tubaphone modular holders was developped in Openscad format and is placed in the Public Domain. This code is self explanatory with its comments and can be downloaded from this section.

Just make sure that the tubegap percentage is set the same in the spreadsheet and the Openscad code and simply type the angular value and offset value that is found on the last two columns of the spreadsheet for the chosen geometry.

For the set of 4 white key tube holders including note A6, you can type :

white(nb=4,anglt=15.53,offst=2.93);

And the corresponding 3 black keys tube holders will be generated with the following syntax :

black(nb=3,anglt=15.53);

Check in the spreadsheet the number of tubes with the same angular value : either 3 (group beginning with C) or 4 (group beginning with F).

The offset value is used to produce the discontinuity between the white keys having the smallest frequency interval (B-C and E-F) whilst keeping the inter tube spacing equal.

The Openscad code provided in the previous step is used to export the models as STL files. Now is the time to take the STL files to the 3D printer. Best is to proceed by group of tube holders requiring the same angular orrientation to avoid mixing different designs but if you feel good with it, you can fill the bed with several groups. It could be a good idea to print the tube holders for the "acciddentals" in black and the "naturals" in white to mimic a piano keyborad.

I used the following settings for ABS printing:

Layer height: 0.2mm
Speed: 70mm/s
Filling: 35%
Travel speed: 150mm/s
Nozzle temp: 230
Bed temp: 105
Retraction: 3mm
Retraction speed: 10mm/s
Brim/raft: none

There is no need to reorrient the parts and no support is required. The printer geometrical accuracy need to be reasonnably good to meet +/- 0.5mm accuracy on the dovetail details.

Once the prints have completed you can take some time to clean the edges in contact with the bed and prepare the parts for assembly so that the female slot and its male complement can fit together properly.

If you attempt to create exact notes for an orchestra setting, accurate tuning is required and the use of an electronic tuning device or a good tuning ear may be necessary. On the other hand, if you desire a good sounding set of chimes but do not need orchestra accuracy, then carefully cut and finish to the length suggested by the pre-calculated spreadsheet.

Instead of using professional spectrum analyzers we can use a standard smartphone, sacrificing a little in accuracy. The uncertainty factors stem from the lack of absolute level calibration of the microphone which is not going to be an issue in our situation. In particular, these experimental instructions are worked out using an Android-based smartphones, but various other handheld recorder can play the trick.
The starting point is to install an app called “Spectroid for Android” from Google Play. There are many similar apps available, and these can equally apply to tuning the tubes using these hints as a reference. This app produces a spectrogram, where the vertical axis shows dBFS (decibels below Full Scale), and the horizontal scale is a logarithmic frequency scale. A logarithmic scale suits us well, because we are interested in frequencies ranging 400 to 4,000 Hz.

The following settings in the Spectroid app have given satisfying results when it comes to analyzing music.

Audio:

• Source: Microphone
• Sampling rate: 96000Hz
• FFT size: 4096
• Decimations: 5 [=0.73Hz/bin; this is the frequency resolution of our spectral analysis.]
• Window function: Blackman-Harris
• Desired transformation interval: 50ms
• Exponential smoothing factor: 0.30

Display:

• Frequency axis scale: Logarithmic
• Waterfall: Off
• Max-hold trace: On
• Peak markers: 1 marker
• Stay awake: On

Miscellaneous:

• Subtract DC: Off
• Test signal: Off

Adjust the screen (by two-finger moves and pinching/spreading) to show approx. 400...4000Hz on the horizontal scale, and approx. -20...-130dB on the vertical scale. It is easier to adjust the vertical scale while in vertical screen mode, and the horizontal scale while turning the phone into horizontal mode. If some green "jumping" lines appear, click the "X" in the upper right corner of the screen. This adjustment takes a bit of patience, but the app remembers it once it is done. Use horizontal screen mode for recording, since we are more interested in the frequency than the absolute levels in dB.

Make sure you are in a quiet environment, place the phone on a pillow or on a sound-absorbent material to eliminate possible vibrations to be recorded.

Before you start working with an audio spectrum analyzer, you should familiarize yourself with this instrument and its ability to pick the natural frequency of the tubes. To confirm that the settings listed above fit for purpose, I used a standalone tone generator to check that the frequencies I am interested in are properly detected by the device. This can be achieved using a tone generator PC software or similar app from a spare smartphone or even a tuning fork and other diapason.

When you feel comfortable using the spectrum analyzer, position the rubber rings at 22.4% of its free extremities (the exact length is calculated automatically in the spreadsheet) around the tube you want to tune and place the tube on a flat surface.

When ready for sound analysis, strike the tube with a mallet and press the record button immediately after (to avoid picking the complex spectrum that develops when hitting the tube). Be absolutely still and quiet, and observe the emerging spectrum picture. When you have a more or less stable diagram after a few seconds, click "pause" symbol to freeze the picture and store the screenshot. It should look something like the screenshots attached to this section.

A marker should be visible (highest peak) at the fundamental frequency of the tube which is exactly the information we have been looking for in this step. Knowing this frequency will help making a decision on wether a tube is acceptable or should be reworked, as discussed in the next section.

This approach allows to analyze the brilliant ringing tone of the tube and isolate its fundamental frequency also known as the first harmonic.

Start with the note of your choice but preferably a long one which will lead to a higher accuracy when estimating a correction factor. Use either a pipe cutter or a hacksaw to cut the conduit according to the chart measurements from the spreadsheet provided in the previous sections. Don't divide more than a piece to start with. This first tube will be used to check how close we are from the theoretical frequency for this length of the particular tube we are using and ultimately apply a correction if required.

Obviously, the length of each tube determines its pitch, so try to match the measurements as precisely as possible but allow a little extra when you cut to permit tuning adjustments as follow:

• If the pitch is flat (too low), you can saw off a little more to correct it. Very small discrepancies can be fixed later by extra filing. It's a good idea to err on the side of too long, since it's impossible to add length to a tube.
• If you do find that the pitch is sharp (too high), cut a new piece of tube for that tone, and shorten the "mistake" for use as the next highest note in the scale.

Measure in 22.4% of its length from both ends of each tube and place a mark. These are the positions of the nodes in the standing wave for the first mode of vibration. If you want to convince yourself that these are the optimal location to hold the tube, have a look at the videos available at this link on tubular glockenspiel. Position the rubber rings at these marks around the tube you want to tune and place it on a flat surface. When ready for sound analysis, strike the tube with a mallet and record the frequency you get.

After the pipe has been sawed to the specified lengths and tuned, its cut ends should be ground smooth. Use a round metal file inside the mouth, and a flat file for the outside surface. You'll probably also want to finish those areas with fine black (silicone carbide) sandpaper. When you are done, check the tube's extremities with your finger to ensure that there are no sharp edges left.

Make sure you set yourself a tolerance for accepting/rejecting tube tunining. I used -8 cents/+8cents which is quite demanding, but can be achieved when done carefully.

Final check is to make sure one more time that the tube is tuned to the required frequency within the specified tolerance in the spreadsheet.

Apply a correction factor

This step is required after the initial tube to recaculate the predicted cutting length based on the experience acquired from the first tuning step. Normally you don't have to come back again to this step but in some circumstances you may wish to apply a further correction if you feel something has drifted along the way for instance when several tubes do not behave the same.

The tube length calculated in the spreadsheet may be - slightly - different to the actual length of tube that allowed to meet the frequency of the note we have chosen. Indeed, several inputs in the formula are not been accurately estimated for the exact material you have in hands. If the difference in length is not too large, you can change the correction factor set to 1 by default so that you get a better prediction of the cutting length to consider for the next few tubes.The value of the correction factor can ba calculated as follow: (actual length) / (predicted length). If the length was initially predicted too short, this should be greater than 1 and vice versa. Now type the result in cell L15 of the spreadsheet, print the table and bring the cutting list to your work station to avoid being too far off with the next few tubes.

Happy cutting !

You don't have to wait until all parts have been printed before starting the assembly. Interconnect the tube holders and slide the corresponding tube with the rubber band on at 22.4% of the extremities and slide it into the central groove.

Make sure you follow the sequence listed in the spreadsheet so that the pieces with the correct angles and offets are installed at the right place. Then, you can insert the longest tubes to the left hand side and orient all tube holders so that the male dove tail is facing the right hand side. Finally make sure that the tubes are arranged parallel to each other to confirm that the mounting was done properly.

You may want to lay out the plastic tube holders on a more rigid wooden frame. The nice thing with this project is that you don't have to make compromises here because of the non-linearity in the pipe length sequence since this is already controlled by the groove being accurately positionned in the 3D printed part. Also remember that the tubes sounds best when it is supportedaround the two nodes, 22.4% of the way in from each end. Make sure to mark some of the tubes at their nodes to optimize the spacing between the pieces of wood. Then, all you have to do is to make sure you select a thick piece of wood on which the plastic tube holders can be glued. A rectangular cross section would be perfect as it allow to offset the two rows of tubes. Position the central piece of wood supporting the "naturals" so that it is perpendicular to the tubes. Now measure and record the inner distances between the two ends of the frame and find the best possible fit for the other 3 long pieces in a trapezoidal shape with the highest on the double back row, as shown on the pictures.

Measure how long the side-pieces that hold the boards in place should be. Cut the side pieces. Sand if needed and glue/nail the frame in place. You can finish wood with the product and method of your choice. I used a clear varnish and let it dry for several hours before proceeding to the final step of assembly.

Place the lower tubes first, mark positions and glue the plastic tub holder structure to the wood. Finally, glue the upper tube holders so that the "accidentals" fall perfectly in the middle of the "naturals".

If you do not have any mallet to play this instrument, you might want to 3D print a sphere and mount it to a hardwood dowel rod.

I created the attached script to print half the sphere of diameter 28mm with a 8mm hole in the center. Once printed, the flat surface of both half spheres must be grinded with sandpaper.

Cut two pieces of length ~300mm from a diameter 8mm dowel rod.

Glue the two halves onto the rod and keep the pieces pressed firmly together to achieve proper adhesion.

Finish the ball using a file.

I have summarized more information below on this fairly rare musical instrument.

Definition
Musical instruments consisting of vibrating pipes or bars are known as idiophones. Tubaphone (tubuscampanophone or tubuphone) - set of metal tubes arranged in a keyboard fashion and played with spoon-like wooden mallets padded with leather. A metallic hollow sound is produced. The tubes can also be suspended on a thin cord and struck to get a slight vibrato effect.

History
The Tubaphone’s history can be traced back to a musical instrument called the "tubuscampanophone" originating from Germany and eastern Europe. In the beginning of the 20th century, the tubaphone was adapted to military band music.

Other Instructables

This project is a revisited version of an other instructable available here: Copper pipe glockenspiel by arpruss on January 14, 2012

One other feature I would like to add is a damper bar mounted on springs and actioned with a pedal. This damper bar, which would have some sort of material such as felt fastened to it would naturally rest against the tubes but if one presses down on the pedal, the damper bar would be pulled down, allowing the tubes to ring freely (in other words, to sustain). I am still at design stage on this feature but I am confident a prototype will be tested anytime soon.

If you want to go further, you can continue experimenting the subtle but obviously not so harmonic overtones produced by this instrument. With the second and third mode vibration frequency respectively 2.76 and 5.40 times greater than that of the first mode the perceived note does not coincide with the Equal Tempered scale. Luckily, the limited ability of the ear to hear all the frequencies generated by the overtone explains that this phenomena is audibly mostly absent and do not prevent this instrument to produce melodious sounds.

On a more personal note, I really enjoyed writing these instructions and sharing the many steps I had to sort out to get to a satisfying end product. Now that I am done with my first Instructable, I will have to think about what my next project could be...

Keep me posted if you made a tubaphone and do not hesitate to ask questions if you decide to embark on the same project.