Finding nodal points in marimba bars (Qs Len Clark)
-----Original Message----- From: Len Clark Sent: Tuesday, 23 October 2007 10:02 AM To: firstname.lastname@example.org Subject: marimba helpHi Jim.
I just read some of your articles, They are great. I am a music teacher, and I build the Madin style Marimbas, with a few changes.
I am frustrated by the Xylophones that don't have a high B and C note, so 2 children have to share certain aspects of their playing, so I wanted to design an instrument like a bass xylo. I have the measurements for the bars on standard xylos and Marimbas, but I am puzzled by the relationship of the bar length and the 2/9 point. If I calculate the bar length divided by 9 and multiplied by 2, they often are different results than the ones in the book.
I am not the best at maths, but can you assist me with the principles I need to know to design different instruments please? Thanks.
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I'll do my best to help you, so feel free to keep asking questions as they arise. (they seem to when building instruments!)
Firstly, Although I've met Jon and seen/heard many of his instruments all over the country, I've never seen his book. I can't therefore comment much about what those measurement contained therein might be, or on their accuracy. I've heard people talk about the 2/9 rule for calculating nodes, and as a fairly general method I guess that would usually produce reasonably accurate results. I would suggest it only as a starting point though. The basic problem with "calculating" nodal points, is that you can't - not with precision anyway. Because wood is a non-uniform material, the speed at which the waves travel through the wood can vary from one part of the bar to another, and this can place the actual genuine nodal points in slightly different ratios of the bar lengths.
My advice to you if you are building/designing from scratch, is this: START by cutting and tuning the bars. Bar lengths are not crucial because the carving will do the tuning, so just use another instrument as a guide and extrapolate if including a bigger range. As long as your bar lengths form an even graduation from the top bar to the bottom bar you will be ok. Measure out the 2/9 spots and just put a small mark on the bars (both ends) on those spots with a pencil. These will be used only as a guide to help you tune the bar. I also mark out the spot in the middle of the bar, and the spots 1/3rd of the distance between the nodes - these are used as a guide for where to carve/sand the arch when tuning the second and third longitudinal modes, although you are most likely only wanting to tune the instrument fundamentally ie. The first longitudinal mode.
Don't drill any holes in the bars yet - wait till the bars are ALMOST tuned. Let's say get them to a semitone from where they should be. Now we find where the nodes actually are in the bars. I have a couple of scrap bits of wood with string tensioned between the heads of 2 sticking up screws. I balance the approximate nodal points (which we marked) on the strings. Just lay the stringed planks on the ground or bench and weigh them down with something heavy once you have adjusted their relative position. Of course you could use an existing marimba frame with the string in place, but no bars, and simply use the best matching slot for whatever bar you are working with. Once the bar is in position, sprinkle some fine sawdust or salt over the top and gently strike it with a small mallet - harder one is better usually. After striking it a few times - not hard enough to bounce the bar out of position - the dust or salt should begin to accumulate at the nodal points. Pretty soon you should be able to see a fairly distinct line of dust at each end. It might even be at an angle - don't worry if it is - remember wood is non-uniform. Next use the pencil to mark the center of each nodal line with a firm X. (ie wherever the nodal lines intersect half the widths of the bars) Now lay the bars all out on a flat surface WITH THE CORRECT AND EXACT SPACING that they will have when in position on the frame - this means you need to know what the gap is going to be between bars etc. Use a big ruler or other straight edge to mark a heavy pencil line across the bars through all the nodal Xs we found. This line might have to be a line of best fit, and the bars might benefit from being shifted slightly one way or the other in their length direction to put the Xs closer to the best fit line.
Now you drill the holes in each bar using the line exactly as a drill-line. Depending on your instrument design, either one end or both ends of the bars will have these lines at a slight diagonal to account for the graduated bar lengths. With the holes drilled, you are safe to finish tuning each bar exactly without any risk of the holes altering the final note.
Now you have a set of bars with the nodes in the best possible positions, it should be a simple matter to make your frame so that the bar support timbers follow those same "lines of best fit".
If for whatever reason you really don't want to start with the bars, then go ahead and work out your frame assuming 2/9 nodes, BUT make sure you use wide bar support timbers so that there is some adjustment possible in the final nodal line by means of having the string holders off center in the timber.
Feel free to ask if you get stuck!
UPDATE - check out this video on finding nodal points in marimba bars.
answers by Jim MCCarthy - 01/12/2005
For more help on instrument building you can email Jim.