On Tuning Slit Drums (Qs from Matt)
-----Original Message----- From: Matt Sent: Sunday, 12 August 2007 6:20 AM To: firstname.lastname@example.org Subject: Slit DrumsHello Jim,
My name is Matt and I am a percussion craftsman. Although I have built over 300 slit drums I would like to improve my work by learning to properly tune the overtones of my notes. The nodes and tuning is similar to a marimba but different because the end of the tine or tongue is fixed.
Can you help at this?
I would also like to know if you have seen an air volume calculator that would help me create individual bodies for each tongue that would be properly tuned. This would be a box version of the tubes used in other instruments.
I would really appreciate your help,
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Hi Matt - thanks for your email.
I am very impressed by the pics you sent - not only do you have some wonderful and truly unique designs, but clearly there is no compromise in your workmanship either.
I have no experience specific to instruments of the type you build - well, only playing them - but as you have pointed out, the theories are the same as those used in marimba constuction.
As for the resonator....
Well we are talking about a helmholtz resonator system, so a quick google on helmholtz should get you the equations you need, but in practise they probably won't help you much. The equation s a fairly simple relationship between the volume and the area of the opening. Both are a factor. With a modern marimba resonator we use cylindrical pipes so the opening is always easy to work out - the eaquations get modified to use the pipe diameter. With the central American traditional marimbas, the lower notes often have resonators that "balloon" out at the end - in other words the opening is smaller in relationship to the volume, which lowers the resonant pitch, but decreases the resonant amplitude. The thing is that if you place the bar too close to the resonator opening, the resonator "thinks" it's opening is getting smaller - it thinks the bar is closing off the opening, so the resonant pitch lowers. Some instruments even have a facility to raise or lower the lower end of the set of bars by a cm or so to compensate for temperature variations. Things are a little different for your instruments because there is no gap between the tines and then cavity - the only gaps are between the tines - incidently I have seen slit drums with the whole top piece of timber with the tines, raised from the box on short pegs so there is a small gap all the way around the edge - might be worth looking into - my guess is that this would increase the volume of the resonance, decrease the length of the resonance and make the required box bigger.
If your resonating box/tube has a uniform cross section, then the length can basically be 1/4 wavelength of the fundamental frequency. Look up the velocity of sound in air (I forget what it is offhand - I think its about 340 something m/s) Use v=fw where v=velocity - f=frequency and w=wavelength. Because v is a constant, and you know your tine's fundamental frequency, you should be able to work out 1/4 wavelength. Your box tube will need to be just a tad shorter than this. To quote from my own paper --which in turn is quoted - (bibliographed underneath)- "At the open end of an air column containing a standing wave, the air is moving in and out of the open end, and its motion actually extends a little way past the end. This makes the tube appear longer than it actually is by an amount called the end correction. For a cylindrical pipe of radius r, the end correction has been calculated to be 0.61r"3.
You could modify that to reflect a surface area calculation based on LxW dimensions instead.
As I said - its not going to work quite the same anyway, because your tines do not sit above the opening, they sit IN the opening. In practise I suspect, that once you get the boxes the basc size you want, you could tune them by simply drilling/carving to open out the opening more, or closing it off more somehow.....
I really hope these thoughts are of some use to you - as previously stated, much of this is educated guesswork because I've never actually built this type of instrument, but perhaps there is some usefull theory there.
answers by Jim MCCarthy - 01/12/2005
For more help on instrument building you can email Jim.