Bars ready for tuning...

...in 3 weeks or so, but today the coarse woodwork on the bars has been finished, and the line oil glazing needs to dry 2-3 weeks. So here are just some impressions of the bars, after sanding, bevelling, fine sanding and applying one layer of line oil glaze.

 This is the inside of the vacuum cleaner dust bag, which got full again. I am very happy to see the red powder insider that bag, and not evenly distributed over the whole workshop!

 Nonetheless, I use a dust mask of a grade marked for hard wood sanding and lead plumbing...somewhat discomforting to find that in the same category. Here are a couple of bars ready to be glazed. Note the very smooth orange colour!

 In this closeup, the nice bevelling cut done with the router can be seen. IMHO, it really adds a stylish touch to the bars.

 Marimba bar, from front.

 Marimba Bar Lane, West.

Here are all marimba bars, drying in the garden shed, after applying line oil glaze. The colour darkened to a deep red-orange glow. In the shed, there's almost no dust, no wind, and it gets quite warm in there, so its ideal to let the bars dry for the next 2-3 weeks or so.

Next up: More woodwork, since the frame needs to be constructed. Also, I'd like to find out more about the influence of the arc shape on the sound of the bar. Finally, I've got some ideas on how to suspend the bars other than just drilling a hole through them and put them on a thread. So one of these topics will get covered, so stay tuned!

...and then, there were 4!

With the basic tuning process made relatively easy and predictable, I felt that yet more could be done. And so I remembered that Heather L Hill measured the bars of a Yamaha Marimba in her 2013 Bachelor Thesis Acoustics of Marimba Bars, and found a well tuned 4th partial. Although in Bork's paper (see previous post), the tuning process is only discussed for 3 partials, the diagrams very well show the necessary information for the 4th partial.

So another experimental spruce D-bar was made. In the course of making the bar, the benefits of using a router clearly showed: Taking the measurements of the previous D-bar, I could triple tune the bar in less than an hour, including the time to bevel the edges and sand the bar a bit. The search for the 4th partial, however, took a bit longer, but with satisfying results.

The D has a fundamental target frequency of f0=147Hz, and the second to fourth partial should be at f4=591Hz, f10=1448Hz and f20=2897Hz

Here is the bar in a state close to final.

A smaller router drill was used this time. The grooves for the f20 are the ones closest to the middle groove.

 In this state, the spectrum already looks very well (green line, red line is uniform bar). There's a nice D fundamental...

 ...and an acceptable f4...

 ...and a f10 that is too low; this was due to cutting the outer f10 grooves too early too deep again; ...A N D, here it is, number...

FOUR. A fourth partial at 2999Hz, which is a ratio of 29.5, is produced by the grooves left and right of the centre groove. It is a bit too high, but there's still wood left to remove!

 As a next step, the material between the groove of f4 and the centre was removed. This lead to the f20 raising up again to ~3500Hz, so this time it DID matter to remove the material. But, since a groove makes a spike in the spectrum ;), f20 was recovered again by adding a small groove in the new plain.
This is the final stage of this D bar (orange line). F0 a bit low...

 ...f4 a perfect D octave...

 ...f10 almost spot on!...

and a f20 almost spot on as well. The actual ratio is 20.9.

Was it worth the effort? Yes! The bar, even in spruce, now has that typical mellow, almost chiming marimba sound on the attack of the mallet (at least to my ears), which the other spruce bar has not. The difference is very noticeable, since it changes the sound at the attack, which is the predominant way our ears distinguish instruments. So yes, it now really sounds marimb-ish ;).

What follows from all this? Well, I will 

• quadruple tune bars C3 (131Hz) to G#3 (209Hz)
• triple tune bars A3(221Hz) to G#4(418)
• double tune bars A4(443Hz) to C6 (994Hz) (if at all possible)

With this, the harmonics of all pairs of bars should fit together, which is one of the main reasons for tuning the higher partials. Oh yes, and my reference A4=443Hz.

Next, plain wood work is on schedule: Bevel the upper edges of the bars, sand them and apply the first coat of glaze.

Stay quadruple tuned ;).

Router Triple Tuning

Today, I can happily write that I've developed a method to triple tune a marimba bar which is both accurate and fast. Here's how.

Background of tuning a marimba bar

The modes of vibration of rectangular bars are described in great detail across the internet. A page which directly applies the science of vibrating bars to the marimba is this one. It all boils down to this: A rectangular piece of material, e.g. wood, vibrates when given a short blow by a mallet. If the bar is simply a bar without any other modifications, the modes of vibration produce frequencies in a series that is not very musically attractive:  the bar vibrates at 1, 2.7572, 5.4040, 8.9332, 13.3446, ... times its fundamental frequency. The desired frequency relations for a marimba bar are 1, 4 and 9...10 times the fundamental frequency.

In order to achieve the 1-4-10 ratios, material is removed from the underside of the bar. Removing material evenly from a vibrating bar reduces all frequencies (e.g. when the bar is thinned evenly), removing material from some small areas only affect only specific frequencies. Ingolf Bork from the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany, investigated this in great detail in his 1994 paper "Practical Tuning of Xylophone Bars and Resonators" - IMHO a must read for anyone who wants to understand the tuning process of marimba bars.

Router Triple Tuning a Marimba Bar

Based on the findings in Ingolf Bork's paper, I developed the following technique to quickly and accurately tune a marimba bar. I call it Router Triple Tuning, because the essential tool to work on the bar is a router (Oberfräse in German). Here's how I do this:

The test bar is the one for the lowest D with the desired frequencies 147Hz, 591Hz and 1448Hz. The bar is 430x56x20mm, spruce wood. The router is a cheap DIY router, and a 12mm routing drill was used. The spectrum was measured using a Gericom Webboy (Celeron 600Mhz) running Linux Slackware, and the program baudline. A dynamic microphone from Hama, the DM20, was connected to the Laptop.

 With the bar cut to length, a 12mm routing drill is used to cut grooves into the bar. The position of the grooves are the center of the bar (lowers the fundamental), then left and right to this (lowers the frequency which will become the 4*f0), and then at the ends (lowers the frequency which will become the 10*f0). The positions are taken from Bork's paper.

 Here is a close up of the grooves made for the f0 and f4. On the left side, the wood between the grooves has been removed, where on the right it is still there. The wood in this area does not affect the frequencies at all!

 The following 3 pictures show the spectrum of the bar at an intermediate state of tuning. The measurements are from the blue line, and show the frequencies. The bar is still way to high, but already the influence of the grooves is clearly visible.

The red line shows the spectrum of the bar without any grooves. The frequencies show the above mentioned ratios for a uniform bar. The green spectrum shows a very early state of tuning, with the grooves only a few millimeters deep. However, the spectrum now only shows three peaks, and these peaks are roughly at those frequencies we need.

 

 Here is the router at work. Step by step, the grooves are deepened by 0.5..1mm in each step, the then the spectrum was inspected again.

First the f4 grooves were deepened to lower the frequency to the desired area. Then, the f1 groove was deepened to lower the f1 and f10. Before working on the f10 groove, the f1 should be 2-3 tones above the target note. Then, the outer grooves for f10 can be deepend, to bring f10 almost to pitch. Then, f1 is finished, which lowers both f1 and f10.

 Here is the final bar and its spectrum.

 Fundamental: It's a D!

 F4: 4 times f1, that makes 2 octaves, so a D again.

 f10: 3 octaves and 3-4 semitones; Bork suggests a ratio of  9.8, here we have 9.7, so this should be fine.

 

Another technique mentioned for tuning marimba bars was applied here: When the fundamental gets too low (e.g. too much material was removed from the center), it is possible to raise the fundamental again by removing material from the very ends of the bar. With this bar, it was found that the pitch was raised approx. 50 cents. 

 Here is the final D-bar. Removing all the wood between the grooves for f4 and f1 did not affect the frequencies, however, a large increase of the decay time was observed, so that even this spruce bar produces quite a pleasant sound!

The benefit of using a router compared to sanding is that 1) the router can be set to precisely cut 0.1...5mm deep, and does this evenly, and 2) it produces almost no dust, but small flakes of wood. The router used also has a tube where a vacuum cleaner can be attached. The amount of material that must be removed is quite a lot, as can be seen in the picture - imagine all this wood converted to red Padouk dust - no, thank you :), not my cup of tea.

So next, this method will be applied to a Padouk bar. Stay triple tuned!

Tuning experiments

The first try tuning a Padouk bar was not very successful: It should have been a G#, but it ended up as the F below, and the 2nd and 3rd overtone were not quite where they should be.

Also, cutting the arc with the jigsaw was not accurate, and sanding such a big amount of wood has never been an option for me.

So I bought a router!And tried my tuning skills on some spruce bars. Results look promising: Routing at the node positions for f1, f4 and f10, the removal of material provided an immediate effect on the frequencies. More tests to come, here are just some pics from the workshop.

My name is Robot, Router Robot :)

Practice on spruce bars. More about the groove on the ends later, when I cover the theory and method in more detail.

The first Padouk bar, not quite there where it should be.

Cutting to length

Today, the bars were cut to their final lengths.

Measuring from each side the length of the bar.

The improvised chop saw cutting table.

You DON'T want your fingers to be here when it's on!

Chop saw view, as seen as a bar.

If it looks like a marimba, it sure is a marimba...not yet :).

Every bar is now labeled with its dimensions and the pitch it will be tuned to. Oh, and did I forget to mention that the lengths were checked again?

The cross section shows the beautiful structure of this wood (African Padouk).

Next, the fabulous ARC will be cut into each bar. There are some calculations to do, and these, as well as the literature and instructions used, will be the topic of the next post(s).

Stay tuned!

Cutting...red dust!

The package with African Padouk arrived today, so it was cutting time! The bars had a width of 67mm, so they had to be cut lengthwise to the desired widths. I used a chop saw...scary, loud, but makes a perfect cut.

The raw bars, sorted and double-checked.

The chop saw setup. The "tent" in the background caught most of the dust, and the vacuum tube in the background created at least a direction for the saw dust to go.









Underneath the blade, red saw dust accumulated. It felt like powder!

Here's a closup of the saw dust debris. A beautiful ocher colour, and it smelled burnt and nutty ;).

The result of today's work: Bars cut to width, sorted, and of course checked and rechecked against the instructions. More on the instructions and literature in later posts...stay tuned!