On Tuning Marimba Bars - (Discussions with Joerg Boettcher)
-----Original Message----- From: "Joerg Boettcher" Sent: 3/03/04 6:32:13 PM To: email@example.com Subject: 2nd overtone on marimba barsHello Jim!
I am building a marimba with 4 1/2 octaves, beginning from A1 (220Hz). My Questions are:
1. In which way does the thickness of the marimba bar affect the pitch of the 2nd overtone (3 octaves and a major third above the fundamental)? Is it so, that the more thick the bar the higher the pitch? I have realized, that my bass bars are too long according to the 2nd overtone, because the tone is from beginning to to low. My idea is, to use thicker bars. Or is it than difficult, to tune the fundamental low enough?
2. From your website I understood, that in order to hear the 2nd overtone, you hold the bar at 1/3 of the length of the bar. Okay, I can hear the tone. But now my question: At which position I have to remove material in order to tune the 2nd overtone lower or maybe higher?
Thanks in advance!
Joerg (Germany, Berlin)
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Ok - yes the 2nd overtone is 3 octaves and a major third above the fundamental.
While the absolute thickness of a plank of wood will effect the pitch, it is best to think more in terms of the ratio of thickness in the middle to thickness at the ends. The thinner the bar is at the antinodal positions (middle for the fundamental) COMPARED TO at the ends the lower those notes will be. So really you can lower any of the frequencies produced by removing timber from the antinodal area or raise the pitch of all the frequencies by removing timber from the end. If you do this, don't simply cut the bar shorter, as this will change your main nodes (string holes) as well. What you do is cut a little triangle shape (in cross section) from the bottom edge of the bar - so just like carving the middle, you are only removing timber from the bottom of the bar.
You could also use thicker bars to start with, if the 2nd harmonic is way too low. If you use thicker bars, be sure to do a test bar first as the effect is a little unpredictable, and will depend on the timber you use. You could also just redesign the whole instrument so that the lower bars are shorter. Once again, be careful if you go for this approach though as this will mean those low bars have to be thinner in the middle to get the fundamental low enough. Make a test bar first to ensure that the bar is robust enough at that thickness. Using thicker bars of course will have the opposite effect - the bars will end up thicker in the middle as well, and this my decrease the amount of vibration the bar produces because it gets less flexible.
When tuning the various frequencies coming from the bar, its really important to get the ratios right as early as possible, then lower them all to pitch together. This is because its impossible to effect one without also changing the others.
To lower the pitch of any vibrational mode you carve timber from the antinodal area of the bar for that mode. The closer to the exact antinode, the bigger the effect.
To understand where the nodes and antinodes are in the bar is pretty easy. You already have the idea of holding the bar in one spot to hear a particular harmonic. This works because you are holding the bar at a nodal position for that mode which is also in the antinodal area for the fundamental. You are effectively stopping the fundamental while encouraging a different mode by holding its node still. The string holes on the bar work on the same principal - they are at the nodes of the fundamental, so they can hold the bar here without stopping the fundamental mode of vibration. When we hit the bar in the middle, the middle of the bar vibrates downward while the ends vibrate upward. This position - the exact middle between the fundamental's nodes (string holes) - is the fundamental's antinode.
If we divide the area between the string holes in two we also get the node for the first harmonic. The other nodes are of course still the string holes. Dividing these areas in two ie. halfway between the bar middle and string holes, will be the antinodes for the first harmonic. To lower the 1st harmonic, we carve here. This will of course also lower the fundamental, as it is still in its antinodal are, although not as much as the middle of the bar.
If we divide this space between the string holes into 3, we end up with 2 nodes between the string holes for the 2nd harmonic. Halfway between these nodes is of course the antinodes. We tend to avoid tuning the 2nd harmonic using the antinode in the very middle of the bar, as this also has a huge effect on the fundamental. The other 2 antinodal areas for the 2nd harmonic are very close to the string holes, so will have very little effect on the fundamental - they can tend to effect the 1st harmonic a bit though. One trick - if lowering the fundamental is also lowering the 2nd harmonic too much, try removing timber not from the very center of the bar, but closer to the 2nd harmonic's nodes. This will tend to lower the 1st harmonic more though, so its a bit of a "try as you go" trade off.
Hope all this is of some help - feel free to ask if you have more questions.
answers by Jim MCCarthy - 03/03/2004
For more help on instrument building you can email Jim.