By Jim McCarthy | June 14, 2009
Hi all… well last time I left you it was almost two weeks ago and I’d just got to the interesting stage of putting the marimba together. I’d tuned a few of the easier resonators in the middle octaves and layed the bars out on the basic frame structure.
The previous weekend was a “long weekend” with an extra public holiday, so I had a little extra time to play around with the next few steps. Here’s what I managed…
- I finished the experimentations with the new “clustered resonator” designs and finished the top octave of resonator tuning.
- I finalized the design for the resonators in the lower octave, and cut and tuned them.
- I finalized the nodal lines on all the bars and drilled them through – followed by the fine tuning of the bars to exact pitch and a final polish.
- I designed the “string holders” to suspend the bars and came up with a way to easily produce them “en mass” with just a drill and an angle grinder. I made a few this way to prove that you can actually do a reasonable job of it in a reasonable time which I’ll show you – I may use a milling machine in the end however as the result will be a little more refined and quicker. In the past I’ve simply had these types of pieces manufactured to dimensions for me, but the idea of this project is to create the whole instrument from basic readily available materials and tools.
- I also decided on the resonator bank “splits” – cut the horizontal support aluminium strips for the banks, and built the “cross bars” between the timber struts to support the ends of the resonator banks. These tasks seem small, but actually take up a lot of time when designing from scratch as there are some calculations to be made! Of course, if you are building this instrument later on from the plans, you will simply be able to follow the steps of the building guide.
Ok – so lets go through these things one step at a time…
What I really WANTED to do was to get on with tuning the resonators, but experience told me that for the top octave and the bottom octave, there would be difficulties. The middle three octaves are quite easy to tune, simply by hitting them on the bottom with your fingers or a mallet and using a digital tuner or stoboscope to test the pitch. I’m very quick at this these days and know the approximate length of the pipes anyway. SO what I do is simply cut them a fraction shorter, then slide the end cap off a fraction till the correct pitch is read – then mark the position of the cap on the tube with a a texta, apply the glue and make the join. It also pays to check the pitch and adjust the end cap in the ten seconds or so you have as the glue is setting to make sure it is right on.
The top and bottom octaves tend to be more difficult to produce measurable tones from though, so what you really need is the actual tuned marimba bar to test how it sounds over the resonator. Here is a photo of me doing this type of thing to the left using my special rubber band and open box system to suspend the bar. I can move the resonator in and out of position under the bar whilst striking it and listen for the effect in amplification and pitch.
Before I could do any of this however I needed to do the fine tuning of the bars, and before I could do THAT, I needed to drill the nodal holes for the suspension strings. You may remember I kinda mentioned this order of events in my last post. Remember I had just ruled the nodal lines over the bars? So I spent a day drilling all the bars, then fine tuning them down to the last few cents.
So now at last I could get on with my experiments for the new clustered resonator idea!
You see, the problem with normal resonators under the bars in the top octave, is that they are SO SHORT! Firstly, they have a diameter about the same as the height, so they don’t sound very well when you activate them. You cannot actually hear a pitch when you hit them on the bottom, so the only way to tune them is by testing them for effective resonance under the matching bar. This is a hit n’ miss affair which is difficult to get accurate as you are relying on the ear’s ability to detect very subtle differences in resonances. The other way which is common to get a correct resonator length, is to calculate it. Essentially this is done using the equation v=fw where v is the velocity of sound in air (at average temperature) – f is the note’s frequency – and w is the wavelength. As we are using quarter wavelength resonators the basic calculation for resonator length is: (v/f)/4. There is also a factor called the “end correction”. Essentially the effect of the confining resonator wall continues a little way past the actual end of the resonator mouth making it effectively a little longer. This means that you have to make the 1/4 wavelength resonator measurement a little shorter for it to be in tune. Officially this is calculated at 0.61r (where r is the tube radius). In practice however, it is extremely difficult to calcualate this accurately as the effect changes with proximity to the marimba bar etc.
My cool idea to help deal with these issues was to use a “cluster” of very small diameter tubes instead of a single large diameter tube. The idea is that by using a smaller diameter you are reducing the amount of end correction. Therefore a slight calculation error in the end correction factor accounts for a much smaller percentage of the tube length and creates less variation from the correct target pitch. Of course to achieve the same volume from the resonators, the equivalent cross-sectional area must be preserved, which is why yu will need a cluster of the smaller tubes. By using extremely thin tubes, the end correction could be cut down to a amount so small as to be not worth factoring into the calculation – BUT… the problem with this approach, is that air close to the tube walls tends to resist movement because of cohesion. In a large diameter tube this accounts for a very small percentage of the total volume of air, but in a very thin tube it is actually the greater portion of the air, and the result is a resonator which produces very little sound volume. So I reached a compromise for my main tests… I used 15mm PVC pipe which strangely actually had an internal diameter of about 19mm. By using four of these together arranged in a square, I had a cluster which fit nicely under the high marimba bars and had only slightly less cross-sectional area in total than the 40mm pvc pipe normally used.
The PVC end caps would have been quite expensive in total considering the amount needed – and also they were quite thick and would have meant that too much space would have been needed under each bar – so clearly I had to find another way to seal off one end. Ordinary wine corks ended up providing a good solution. I sanded back a cork just a fraction so it could be force a couple of millimeters into the tube, then used a hacksaw to cut away the remaining cork and sanded the bottom flat. The cork was glued into the pipe using the normal pvc pipe glue – I also found that by dripping two drops of glue into the bottom of the tube, it sealed off the cork and made a nice hard floor to the tube.
Now after a fair bit of playing around with this idea, I did in fact get some of these clustered resonators sounding really good – probably even a small fraction better than a regular resonator! The problem was that to get four of these smaller tubes tuned was taking just as long as the single bigger tube. There were still problems with tuning the smaller ones, and there were other problems as well which I considered would come up when building them into the resonator banks themselves. I came up with various solutions for these, and I may pursue this further at a later date on a different instrument – perhaps a super high pitch instrument???? – but in the end I realised that for this marimba, the standard single-tube approach despite being troublesome in the top octave, was still the all round most practical method. So I fiddled for ages with short 40mm tubes, testing them for relative resonance under the actual bars they would amplify – and eventually came up with the set for the top octave.
So now I had all the resonators tuned except the lowest few. So it was a matter of tuning the bottom octave of resonators which are the longest and actually require some design because they are too long to fit under a normal height instrument without putting some bends in the tube. Fitting them all in and having them suspended properly can be an issue, especially if you want to have resonator tubes on the wider side like myself.
I came up with a design and tuned all the lowest tubes. The bottom C and D I tuned, but did not glue all the joints as I wanted to leave some room for later adjustments. So with all the tubes tuned, it came time to actually assemble them. Before that though I needed to decide how the resonator banks would be split – if each row of notes had one single long bank of resonators, it would be terribly difficult to dissemble and transport the instrument, so it is common to make the resonator banks in sections. For a four octave plus sixth instrument or smallet it is usually quite acceptable to simply divide each row into halves. For a full five octave instrument with wide bars like this however, that would make for sections which would not easily fit in your average family car – something I feel very strongly that a design should allow. So I split each row of tubes into three sections. Where to make the splits ended up being quite easy as the diameter of the resonator tubes changed at the points roughly a third of the instrument length anyway, so it was obvious to make them there. This has the advantage that it cuts down on bending the aluminium strips which hold the tubes together.
I measured the distance between the timber struts at these points that I’d decided on, and cut lengths of 50mm wide aluminium flat to these lengths. I also came up with a cool way to bolt them to the timber so that there was no bits protruding up towards the bars, or more than 19mm from the timber of the struts. Also so there is no bare metal attached to the timber struts, which is a design flaw which means that during transport your nice estapol finish to the timber tends to get scratched up by the metal bits unless each piece is individually wrapped in a blanket! The design is extra good I think because in one simple structure these pieces perform both the task of providing the resonator bank support, as well as providing structural support between the timber struts and keeping their distance fixed – a needed part of any marimba design with long spans like this. You can see from the photo here that I’ve also cut the 25mm wide aluminium strips which will rivet to the top of the resonator tubes and hold them up.
Whilst I had the aluminium grinding wheel on the angle grinder, I also tried my hand at producing a few of these string holders. As I said in my last post… In the past I’ve simply had these produced by a third party business with computer controlled milling machines – which is certainly a time saver although of course at a cost! I really wanted to show that you CAN actually make these quite easily however with nothing more than a drill and angle grinder (with a special wheel for aluminium – a normal metal wheel will NOT do it!) The photo here is my FIRST effort… NOT my best! However you can see that it will work just fine and actually look ok too. The slighly messy bit at the bottom will be embedded into the timber strut and unseen, and there will be some rubber tube over most of the rest of it anyway, so even if these are a little scratched and imperfect, it will not really be visible.
Well that was pretty much the result of that long weekend and some bits from the week. Since then I’ve had almost another week and I’ll post about that pretty soon, so keep watching!