Marimbas have an arch, and for a reason!

Finally, there is progress, in understanding the arch as well as in tuning the bars. After much frustration with the upper A, G# and G (which are currently lost), I finally arrived at a scheme that works consistently. If it works, it works like a charm: double tuning the bars takes approx 20 minutes now (not kidding!), and the process is very predictable and repeatable.

Here's how:

In the pic above, today's result is present. The arch is now cut starting at the position influencing f4 the most down to the middle. The terasse is formed by stepping the router approx 0.7mm down in each step, resulting in a final depth of approx 5mm. With this initial arch, the f4 is almost spot on (typically +100Hz), and by increasing the steps by 0.5mm again, f4 can be brought exactly to match. The fundamental in that stage is high by 3-4 tones, and can be brought to pitch by deepening the centre groove alone. Since this does not really affect f4, the tuning is stable.

And here it is, my 5 semitone-marimba:

And it sounds like this :)

My understanding of the arch is that it serves 2 purposes:

• bringing the frequencies 
• down
• to specific pitch
• prolonging the decay time

The decay time gets longer with an arch present, probably due to the overall reduced stiffness of the bar. The frequencies of the fundamental f0 and the f4 are influenced at regions along the arch:

• f4 at approx 30% of length
• f0 all the way from 30% to the middle

This means that when the arch starts at approx 30% of the length, both the f4 and f0 are lowered. Most of the arch between 30% and 40% lowers f4, and all the way from 30% to the middle lowers f0. So when the first arch is cut, both f0 and f4 drop. Then, by deepening the grooves around 30-40% of length, the f4 can be brought to pitch, also further deepening f0. However, f0 is still high enough. The final tuning step of lowering f0 can be achieved by cutting right in the middle, where the influence on f4 is practically zero (it isn't but I think it does not matter). That is why you need and arch and grooves ;).

I wonder how things work out when I triple and quadruple tune the lower bars...much head-scraping, I think!

Stay tuned!

Influence of the arch on decay time

It's been a while since the last post, now there should be again some time to work on the marimba. In this post, 2 topics will be discussed: A final tuning experiment, and the planned procedure for tuning the bars.

Influence of the Arch on Decay Time

The arch depicted in Bork's paper extends towards the edges beyond the areas of influence for f4. I was wondering whether removing this material in an arch like shape would influence decay time or pitch.

Before working on the arch, the decay time was measured in the following way: Strike the bar 3 times hard, and measure the time from maximum to 30dB below, as displayed by the current baudline setup. I am only interested in detecting any influence, and not in determining the actual T60 of the bars, so this should be ok. Measured this way, the average decay of the original bar was 731ms on the fundamental.

The straight-edge shows the how the arch would extend towards the end of the bar.

 Material was removed in steps with a 6mm router drill.

On both sides, the typical marimba bar arch is now present.

Then, the decay time was measured again, as shown in the images above. It was found to be 772ms after removing the material. Even after flattening the whole area to the level of the innermost step, the decay time remained approximately the same (745ms).

Results

By removing the material in an arch like shape lead to

• a small increase in decay time of the fundamental (+5%)
• a small decrease of f10
• no other effects noticed

So, I don't consider it worth the effort to finish the arch from the position of f4 outwards.

Tuning strategy

I am going to tune the bars in the following way:

• start at the C6 bar, work from highest pitch downwards
• double tune bars C6 (994Hz)  to A4 (443Hz)
• triple tune bars G#4 (418Hz) to A3 (221Hz)
• quadruple tune bars G#3 (209Hz) to C3 (131Hz)

Inspecting the archs of  a commercial marimba, I found that the thickness at the middle of the arch decreases with decreasing pitch. So starting at the top pitch, I can use the higher bar as a guide to set the router, this should speed up things a bit.

Let's see!