On Tuning Slit Drums (Qs from Matt)

-----Original Message-----
From: Matt
Sent: Sunday, 12 August 2007 6:20 AM
To: jim@percussionclinic.com
Subject: Slit Drums

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,
Thank you,

Matt Collins

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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.
I would guess that each note, having a fixed end and a free end would act in 1/4 wavelength mode, 3/4 wavelength mode, then 5/4 then 7/4 etc.. - Sound right?? This would follow the fixed end being a forced nodal point in the tounge, and the free end being a forced antinode. With a marimba bar one simply removes material in the area of the bar between the suspension points (forced nodes) to lower the pitch. More specifically you measure along this length to find the antinodal position of the vibrational mode you wish to lower. Ie the fundamental is right in the middle - the 2nd harmonic is also right in the middle but is usually tuned from the other antinodal points 1/6th of the length from the nodes because here it affects the fundamental pitch very little. The first harmonic is in the 1/4 from the nodes position. I'm going to suggest that there is likely a similar type of system with a vibrating "tounge", but with some important differences. You might need to experiment a bit to test out my guesses here...... I suspect that removing timber from the very end of the tounge - even though it is the antinode - would actually raise the fundamental because of the reduced mass on the moving section - this would be similar to raising the overall pitch of a marimba bar by removing timber from under the free ends. There is also another major difference - a marimba bar is a freely vibrating bar, but the tounge's vibration is controlled to a certain extent by the flexibility of the timber at the non-free end. I suspect you could lower the pitch of the fundumental considerably by thinning the bar right on the joining point. I also suspect this technique would decrease the relative strength of the secondary tones and emphasize the fundamental - my thinking is that the "forced nodal point" becomes a bit more free - ie less forced. As for tuning the secondary tones - I personally would start by trying the same theory used with marimba bars - my feeling is that it would hold true - once again I can't be sure without trying it, but thats where I would start. SO - that would mean lowering the 1st overtone would require removing timber from the position 1/3 from the attatched end of the tounge, and lowering the second overtone would require removing timber from 1/5 or 3/5 from the attatched end.

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.

3. John Backus.

The Acoustical Foundations Of Music. (New York: W.W. Norton & Company Inc. 1969) 65.

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.
All the best...

Jim McCarthy

For more help on instrument building you can email Jim.

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