Category Archives: Wickstroms

Fabricating and Mounting the Tubes

Making the tubes wasn’t a big deal – really just cutting them to length and finishing the aluminum so it looked nice. However, mounting them and making the stoppers was some work and is probably worth sharing for anyone interested in building an instrument.

Making the Tubes

In discussing the construction of the xylophone tubes, perhaps it is most clear to start with an overview picture. The photo below shows the tubes mounted to aluminum rails that are in turn mounted to wooden blocks attached to the frame ends.

Tubes mounted in xylophone frame
Tubes mounted in xylophone frame

The xylophone tube assemblies are quite rigid after the tubes are  attached to the 1/8 x 1 inch aluminum rails. Here is a photo of the assemblies:

Tube assemblies
Completed tube assemblies

As shown in the top photo, the assemblies fit snugly in the slot cut into the mounting blocks shown in the top photo.

The construction of the tubes themselves was pretty straightforward, but there were a few nuggets along the way that might help someone building their own instrument, so I will describe the high points.

As noted in a previous post, I bought the tubes from Speedy Metals (again, I love this place – great prices and selection and cheap shipping) in four foot lengths of 1/16″ wall aluminum . As with the bars, I used the CutList Plus software to optimally allocate the 43 tubes into the four foot stock pieces. As noted in the previous post, I calculated the theoretical length of each tube and added two inches to allow for the stopper. This was overly conservative, because the stopper was only 3/4 inch thick, but my worst nightmare was cutting all of the tubes too short!

The tubes were cut on my sliding compound miter saw using a non-ferrous metal blade. I typically shy away from cutting metal on my woodworking tools, but I was amazed at how well it cut and how perfect the edge was. Here’s are a few photos of the cutting setup and some of the cut tubes:

Cutting operation on miter saw.
Cutting operation on miter saw.
Wax used for cuts
Wax used for cuts
Some of the cut tubes
Some of the cut tubes

Note the tube of wax next to the saw. I used that to lube the blade before the cuts. Not sure if it was required, but aluminum can gall when it is cut, so it seemed like a simple precaution.

The surface finish of the stock tubes left a little to be desired, so I decided to “brush” the aluminum. To do so, I built a mandrel to hold the tube so that it could be chucked into a hand held drill. Below is picture of the mandrel.

Mandrel for finishing the aluminum tubes
Mandrel for finishing the aluminum tubes

To make this, I cut a wood disk and drilled and tapped a hole in the center, and then inserted a threaded rod. The disk had a slot cut partway through it that could be spread somewhat by driving two wood screws into it. To attach the mandrel to the tube I simply inserted the wood disk into the end of the tube and then tightened the two wood screws. This spread the slot to make the wood disk clamp to the interior of the tube.

With the mandrel inserted, brushing the aluminum was easy. I just spun the tube with a hand drill while sanding the tube with 120 grit sandpaper. It was actually kind of fun to see the dull aluminum brighten up as it was sanded. After sanding, I blew the dust of the tube and wiped it with alcohol to remove the oil, wax and dirt from the tube. Then, while slowly spinning the tube with the drill, I sprayed gloss lacquer on each tube. Some sort of varnish is required to ensure that the tubes don’t oxidize. I used lacquer because I had it on hand and it dries quickly, but there are products specifically made to protect aluminum. I was able to carefully remove the mandrel from the tube even prior to the finish drying so that I could move on to the next tube (did I mention that there were 43 of them?!) Anyway, here is a shot of some brushed and lacquered tubes:

Some of the brushed and lacquered tubes
Some of the brushed and lacquered tubes

Making the Assemblies

With the tubes completed, I turned my attention to making the aluminum tube support rails. Here’s where I probably overkilled things. As I stated in the previous post, the short tubes add little or no sound amplification. However, at this point I didn’t appreciate that fact. So I was hell bent on getting tubes on as many of the short bars as possible. The problem was that the Mahogany frame rails get really close together at the right end of the instrument. This didn’t leave much room to fit the tubes in. Here is a photo of the aluminum support rails at the skinny end of the instrument:

The rails prior to attaching the tubes
The rails prior to attaching the tubes
The rails prior to attaching the tubes
The rails prior to attaching the tubes

As you can see, I had to carefully bend the rails to get them to fit correctly. I’m not gonna lie – getting those rails bent just perfectly was a bitch! Once they were bent, I was able to mark the angled slots on the wood support blocks, but getting the bends right was tough. So if anyone out there is still listening, here is the lesson: don’t bother making or mounting the short tubes. They don’t change the sound, and its also not an aesthetic consideration because you cannot even see the short tubes since they are mostly obscured by the Mahogany rails. If I had to do this over again, I would skip the shortest tubes and just use straight rails, thus avoiding the bends and all of the tight clearance issues. Live n learn…

Attaching the Tubes to the Rails

Now, I racked my brain on how to mount the tubes to the rails. There are two challenges. First, attaching a round tube to a straight rail is tricky, since the tubes want to roll and slide along. Originally, I was thinking of making a big jig to hold everything in place, but that was going to be a lot of work. Second, I wanted a constant standoff between each tube end and the bottom of its corresponding bar to maximize the tube/bar resonant coupling. Because the undercuts on the bars are all different thicknesses, this means to tops of the tubes are not in a plane – some are higher and some are lower. It is possible to measure the standoff for each tube and transfer that to the jig, but I was sure I would screw up all of that bookkeeping.

Ultimately, I converged to an approach where I glued all of the tubes to the rails and then later added screws to make the bond stronger. Let me elaborate a bit.

As the photos above show, the tube rails hang in slots that are cut in wood blocks attached to the frame. With the rails in place, and the xylophone bars strung, it is possible to slide each tube between the rails, from the bottom, and set both the position on the rail and the height of the tube. To set the height, I cut a ring from a scrap piece of tube that was ~1/4 inch tall. Then, I would sit the ring on top of the tube, like a spacer, and raise the tube until the spacer just touched the bar. At this point I would slide the tube left and right until it was aligned with the bar. Now, without moving the tube, I would mark small index marks on the tube and rail so that it could be re-positioned later. This process was repeated until I had marks for all of the tubes.

At this point, I was able to remove the xylophone bars from the frame and start to mount the tubes. Friction between the rails and the tubes was insufficient to hold the tubes in place, but I found that I could use wooden clothes pins to hold the tubes in place. (Remember clothespins? I had to buy them on Amazon because it had been years since we’ve had any in the house). Here is a photo of some of the tubes in place:

Tubes with clothespins holding them in place
Tubes with clothespins holding them in place

That’s Jack helping in the background.

Once the tubes were in place, I just needed to add epoxy to temporarily hold them. I mixed up some West Systems epoxy and added a silica thickening medium to make the glue more viscous so that it didn’t drip. Then, using a toothpick, I very carefully made a little epoxy gusset on each of the four crevices around the tube. This was a little tricky, but all of those years as a kid playing the board game Operation paid off! Here is a picture of the glued tube:

Close up of tube with glue
Close up of tube with glue

For a few of the last tubes, I used a syringe to inject the glue into the tight crevices. The epoxy was too thick to pass through the syringe, so I used superglue instead. This was much easier and cleaner, and I was able to get the glue deep into the crevice so that the glue didn’t run much. I also sprayed the glue with accelerator to further avoid runs. Wish I had thought of that first. Here is a picture of the syringe and glue I used:

 

Syringe and superglue used for some of the bars
Syringe and superglue used for some of the bars

In any case, the glue is just temporary. While the bond is actually stronger than I expected (I made a test piece and broke it apart,) I wouldn’t want to count on it for the life of the instrument. So once all the tubes were glued in and set, I was able to gently pull the whole assembly out for the next step – adding mechanical fasteners to each tube.

I found some 4-40 screws that were 3/16 long so that the end of the screw was just flush with the inside of the tube. Here is a picture of the completed assembly, so you can see what I am talking about:

Close up of screws holding tubes to rails
Close up of screws holding tubes to rails

Drilling and tapping the screws was tedious, but I made a jig to help.

The jig was just a little T-shape of wood with wings that straddled each bar. It had two holes in it to guide the drill for each pair of holes. This made drilling the holes pretty speedy even though there were a lot of them. The drill I used was for the 4-40 threads. After these holes were drilled, I put in a body drill and just drilled 1/8th of an inch, which was the thickness of the rail. This ensured that the screws pulled up tight to the tube.

I tapped each tube by using a tap, a battery powered drill and a bit of lubricant. Tapping 1/16th inch aluminum is pretty easy, but you do have to be very careful not to break the tiny tap. I did break one during the operation, but had some spares on hand.

Making the Stoppers

I gave a lot of thought to how to build the stoppers. Again, there are a lot, so I was trying to find the most efficient way to bang these out. The stoppers had to fit snugly in the tube and have some means of locking them. I figured I could use the same screw-spreading-split idea that I had used for the mandrel, but I still needed to make 43 disks. I considered a hole saw (couldn’t find the right size,) 3D printing (I don’t own a printer…yet,) slicing a dowel (couldn’t find a vendor to make a custom size dowel,) turning a dowel (I suck at wood turning,) casting the plugs using urethane (slow and expensive,) and a few other ideas. In the end, I made the wood disks using my band saw and router. Let me explain.

I started by cutting 43 squares of 3/4 melamine. Melamine seemed good because it has a nice hard and flat surface to reflect the sound.

Squares of melamine that will become stoppers
Squares of melamine that will become stoppers

Next, I set up a quick jig on the drill press to drill a shallow 1/4 inch hole directly in the center of each square.

Drilling pilot hole
Drilling pilot hole

The plug will be flipped over and this hole will slip onto a 1/4 inch steel pin protruding from a sliding jig. The following photo might make this more clear.

Jig to rough cut round disk on band saw
Jig to rough cut round disk on band saw

In this photo the wood disk has been inserted on the pin (not shown, because it is hidden under the disk). The jig then is slid up to a stop such that the block can be rotated to cut a rough oversized disk, as shown in the following photo.

Cutting disk on band saw
Cutting disk on band saw

Once the disks are roughly sized, I moved the jig over to the router table. This operation was similar – slowly slide the jig up to a stop and then rotate the disk into the router  bit to trim the edge. Here is a picture of that operation:

Fine routing of disk to final size using router
Fine routing of disk to final size using router

This was pretty dusty, hence the dust collection. This all worked pretty well, and was pretty speedy, but was a little nerve-racking as my fingers were pretty close to that big-ole router bit. But alas, I finished with all of my digits intact.

The next step was to drill the hole for the “spreader screw.” So I went back to the drill press as shown in the following pic.

Drilling spreader holes
Drilling spreader holes

I used a tapered drill so that the screw started more easily. Finally, I cut the slot on the band saw as shown in the following photo.

Cutting spreader slot
Cutting spreader slot

When I was all done, I had a bunch of stoppers that looked like these:

A swarm of stoppers
A swarm of stoppers

I forgot to mention it, but I also tapped a 1/4-20 hole in the center. This is to insert a long machine screw that was used as a temporary handle to adjust the stopper up and down during tuning. This screw along with the spreader screw is shown in the stoppers at the lower left.

In the end, the stoppers worked pretty well. Here is a picture of the a few of the tubes with the stoppers installed.

Tubes with stoppers installed
Tubes with stoppers installed

Not sure if you can see clearly in the photo, but the stopper fit is pretty tight.

The Final Post

Our little xylo-adventure has just about come to an end. In the final post, I will describe making the legs. This is mostly just straightforward woodworking, but I will discuss a few design considerations that may be if interest.

 

 

 

Tuning the Tubes

The resonator tubes are an important part of the xylophone. They boost and shape the sound produced by the bars. There is lots of information on the web about resonator tubes, so I won’t repeat that, but I will discuss our approach to making, mounting, and tuning the tubes.

The Physics

It is not hard to find info about “quarter wave stopped resonator tubes” on the web (in musical parlance these are sometimes called “stopped pipes.”) This is the type of resonator tube that is used for xylophones and marimbas These tubes basically resonate at a fundamental frequency of c/4L, where L is the length of the tube and c is the speed of sound. In simple terms, the tube boosts the bar sound amplitude by utilizing the normally wasted downward-directed sound energy in a way that boosts the upward facing energy (which is what you mostly hear). It shapes the sound too, because it does not boost all frequencies equally. In particular, it only boosts the fundamental and the odd harmonics. Because xylophone bars are tuned to a 1:3:6 frequency relationships, the fundamental and second partial will be boosted, but the third partial will not. This is another reason why I wasn’t too concerned about tuning the 3rd partial – its already puny energy is swamped by the boosted energy of the first two partials. Additionally, while we haven’t discussed it much, real xylophone bars “ring up” not just the “transverse modes” that dominate the sound, but also lesser “longitudinal” and “torsional” modes. Because these modes are not typically odd harmonics of the fundamental, they do not get amplified. So, at the end of the day, when tubes are added to the instrument, you mostly hear the fundamental and the second partial – all the other frequencies get dwarfed.

Tuning the tubes is done by adjusting a movable stopper that effectively changes the length of the tube. This is what determines the length L in the equation above. So you might think that tuning the tubes is just a matter of computing the tube length via the equation above and then setting the stopper to that length (I did,) however, like most equations from physics, the formula above is only approximate. It is very accurate under certain conditions, such as when the tube length to diameter ratio is large and the sound input to the tube is a “plane wave.” However, neither of these assumptions is true for the xylophone. In particular, the shorter tubes have a relatively low length-to-diameter ratio; and the sound wave coming off the bar is likely not planar, since the bottom of the bar is curved.

Dr Entwistle pointed me to a book called “The Physics of Musical Instruments,” by Rossing and Fletcher (ISBN-13: 978-1441931207,) that had some interesting comments about xylophones and ¼ wave resonators. In the section on resonator tubes, they note that the resonant frequency of the tube is a weak function of the distance between the tube end and the bottom of the bar. However, they state that “As yet, the theory describing the coupled bar-resonator system has not been worked out in detail,” which basically means that there is not a simple equation to compute the actual stopper position as a function of the desired frequency.

Additionally, the Rossing book describes a few topics of practical importance. First, the it describes something referred to as the “end correction factor.” It turns out that the equation above must be tweaked somewhat due to the fact that the standing wave in the tube does not end exactly at the pipe mouth but is rather a bit beyond it. The more accurate equation for the resonator frequency is f =c/[ 4(L+0.61r)], where r is the radius of the tube. I found other references to the end correction online and there appears to be some debate in the literature over the correct value of the correction factor (i.e., the value of 0.61).

As noted above, the book notes that the tube frequency is affected by the spacing between the tube end and the bar bottom. I had already seen that some xylophones allowed for adjustment of the height of the tube assembly (i.e., the assembly of all of the tubes locked together into a rigid structure) to compensate for temperature changes. It makes sense that if the tube-bar spacing is less than the 0.61r factor, then it will affect the tube resonance since the bar is effectively serving as a stop at the top of the tube.

At the end of the day, it became clear that the bars must be tuned in situ to obtain accurate tuning. However, I couldn’t resist the urge to check out the physics, so I did a few experiments and built some tuning curves that I hoped might at least guide the resonator tuning. However, in the spirit of full disclosure, I must note that I mostly ignored the results from this effort and just tuned the tubes by ear! Nevertheless, I will describe these experiments, if for no other reason than to perhaps save others the folly of this endeavor. You can safely skip this section without regret if you just want to git-er-done…

Tuning the Tubes

I started out by doing experiments with a piece of PVC as I awaited the delivery of the aluminum. I was particularly interested in verifying the resonant behavior of the tubes as a function of spacing distance to the bar. It wasn’t clear to me how to establish the correct tube-bar spacing. Intuitively, it seemed to me that the best coupling might result from close spacing, so that the spacing would be dictated by physical constraints, like avoiding contact if the bar should sag.

In order to start my experiments, I needed a value for the speed of sound. The speed of sound is a function of the density of the air, which is a function of the temperature. I found an online calculator here that computed the velocity. During my experiments, I measured the temperature at 19.2 C, and the the online calculator gave me a velocity of 343 m/s.

I must admit that I struggled a bit with how to find the resonant frequency for my PVC resonator pipe. I fabricated an adjustable stop and set it to yield a 15.0 cm tube. Per the standard 1/4 wave calculation (with a 0.61*r end correction,) the computed frequency was about 525 Hz. I experimented with several methods of exciting the bar. I tried whacking the end of the tube, and attempted to measure the impulse, but the resonance died out rather quickly. Here’s an example where you can see that the pulse dies out in about 25 ms:

Measured decay of 15 cm tube after being whacked.
Measured decay of 15 cm tube after being whacked.

I did some decayed sinusoidal fitting to this, but wasn’t able to get accurate results. Ultimately, I used a small speaker to excite the tube as shown in this photo:

PVC tube with small speaker used for excitation
PVC tube with small speaker used for excitation

The tube was excited by the speaker at the right, and the resulting audio was recorded with the microphone.

Next, I tried exciting the tube with white noise. Interestingly, you could easily hear the “coloring” of the noise due to the modes. This gave PSD plots like this:

PSD of white noise response.
PSD of white noise response.

However, I found that identifying the peaks was unreliable. Ultimately, I wrote some Matlab code to generate and play a frequency sweep while recording the response. Here is an example of one of the PSD curves:

 

PSD of 15 cm tube excited with frequency sweep.
PSD of 15 cm tube excited with frequency sweep.

This is what the recording sounded like for this tube:

The code identifies the peaks (which of course correspond to odd harmonics). However, the first peak (the fundamental) was always a bit broad and had a sort of “shoulder” to it, which made me doubt it. So I wrote a little algorithm to find an the optimal “least common factor” for all of the identified peaks. The higher harmonics had generally broad peaks so I also ignored them, and only used the lower modes. In general the setup was somewhat fickle and the quality of the peaks that I got was a strong function of the microphone and speaker placement. In any case, here is some data for my 15 cm tube:

Temp = 19.2 deg C


>> ResonatorTune(500, 'res=15.0, spc=3.0')

res=15.0, spc=3.0 -

Fund: 509.0

, Error (Hz): 5.9, NumModes: 2

   Mode 1: Error (Hz): +10.6

   Mode 2: Error (Hz): -1.2

>> ResonatorTune(500, 'res=15.0, spc=2.0')

res=15.0, spc=2.0 -

Fund: 509.4

, Error (Hz): 6.0, NumModes: 2

   Mode 1: Error (Hz): +10.8

   Mode 2: Error (Hz): -1.3

>> ResonatorTune(500, 'res=15.0, spc=1.0')

res=15.0, spc=1.0 -

Fund: 505.0

, Error (Hz): 2.8, NumModes: 2

   Mode 1: Error (Hz): +5.0

   Mode 2: Error (Hz): -0.5

>> ResonatorTune(500, 'res=15.0, spc=0.5')

res=15.0, spc=0.5 -

Fund: 492.5

, Error (Hz): 3.4, NumModes: 2

   Mode 1: Error (Hz): +6.1

   Mode 2: Error (Hz): -0.7

These data correspond to 4 different collections with varying standoff distances from the end of the tube to the speaker (from 3.0 cm to 0.5 cm). It is interesting that the frequency doesn’t shift above about 2 cm, but there is a nearly 20 Hz shift when the tube is very close to the speaker. This clearly shows the behavior noted in the Rossing book (i.e., decreased frequency for close spacing,) which was pretty cool.

So using this technique, I set off to build a curve that could be used to set the stopper distance for each tube. I chose to set the distance at 0.5 cm, which is about as close as I could safely space the tubes from the bars without fear of contact. For each stopper distance, I performed a sweep and used my least-common-factor code to find the tube resonance. With this approach, I was able to build the following curve.

Resonator tube tuning curve.
Resonator tube tuning curve.

The blue points on the curve are the measurements and the red line was created using the frequency equation given above (including the 0.61r end correction factor). The equation accurately predicts the frequency for the longer pipes, but performs poorly for the short pipes. As a quick test, I tried fitting the equation above, but left the speed of sound and the end correction factor as free variables. This resulted in the blue curve. The fit was better for the short tubes, but resulted in poor performance for the long tubes. So I decided to skip function fitting entirely, and just set my stopper distances by interpolation between the measured points.

Next Up

This post described some of the science involved in establishing the tube resonant frequency. In the next post, I will describe the fabrication and mounting of the resonator tubes.

 

First post – and introductions…

Bear with us – blogging is entirely new for our family; we’re totally just groping around in the dark! Despite our inexpierence, we are going to give this the old college try. So here goes…

About Us

I guess introductions are in order. My name is Rich Wickstrom, and this is a site that I’ve created for my family and me.

Rich in his natural habitat (in the garage smoking a cigar)
Rich in his natural habitat (in the garage smoking a cigar)

 

The actual catalyst for creating this site was the completion of a xylophone that my son, Jack, and I built. I’ve always taken advantage of the vast information available on the internet; I am, however, guilty of not really giving back. My xylophone project was extremely unique and, therefore, had a quite limited audience. It seemed to me, however, that maybe, just maybe, there was at least one person out there who could make use of my highly-specific information. To be honest, I’m much more interested in my xylophone than I am in my family; I do, however, feel obliged to take a moment to introduce them.

Here’s we are:

IMG_0472
Powerpuff Girls (feat. Hit Girl)

From left to right, that’s Jack, Rich, Lily and Lynette. I promise my son an I aren’t usually found in drag…

Here’s a photo to prove it:

The family
The fam

Our Site Name

Oh yeah, why supermediocre.org?

One day, my daughter, Lily, and I were brainstorming name ideas; we were gravitating towards names that were quirky and sort of self-deprecating. The mashup “super mediocre” eventually came up. We liked that it was an oxymoron and sort of off-balance all at the same time; it fit our family in some twisted way.  I checked if the domain was available- it was (big shocker).

In the end, we thought the name supermediocre was… perfectly OK.