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!