Sub-harmonic tuning


Gold Member
Recently, I have been trying to tune frame drums, tamborim and tambourine/pandeiro. There isn't much to the shell for resonance, so tuning is very important to take advantage of whatever resonance there is... Mind you.

I did some calculations based on the Helmholtz equation, this time I assumed that the entire shell was behaving as a port, and that the spring constant was negligible. This yielded some counter intuitive results, since the tamborim and tambourine have the same depth, but different radius, you would expect the larger drum to have a higher shell frequency. Which isn't the case. IE ports with larger areas have higher frequencies. Since I like a lower tuned tambourine, I just tuned it to one of the higher modes of the circular membrane. However for the tamborim an F#3 is too low. I tuned it to that note, and indeed there is some resonance there however there were barely any tension on the tensioners, then I tried tuning it an octave higher. Which sounded good and was about the right range.

My question is for turnings like this what happens? I suspect that the resonant frequency of shell reinforces every other oscillation of the fundamental, every third oscillation of the (1,1) mode every fourth oscillation of the (0,2) and so on, but also perhaps causes the energy to radiate and decay faster, which gives it that sharp echo-ee sound.