Tuning Tubular Resonators

This is probably my favorite part of instruments making. Maybe I'm weird, but I think this part is fun. I stayed away from it for a long time because someone once told me that it was hard. Ha! Not only is it fun, it's easy.

To do this properly, though, you need to know the frequency of the pitch you are wanting to tune to, not the letter name. I hope you have a frequncy conter, or some sort of device or chart to allow you to do the conversion (there's a program on my computer that does this for me).

Once you know this, the rest is simple arithmetic:

L = [(s/f)/4] - d/3   (for resonators closed on one end)

L = [(s/f)/2] - d/3   (for resonators open on both ends)

Where:

	L = Length of the resonator, in cm.
	s = Speed of sound, in cm/sec (ca. 34,400 cm/sec)
	f = the desired frequency, in Hz
	d = is the diameter of the resonating tube, in cm.

Example:

Say we desire a resontaor for a key with a frequncy of 240Hz, and the 
resonator is being cut from some 2 inch PVC tubing.  First we convert 
from inches to centimeters: 

	2 inches = 5.08 cm.

Then we plug the rest of the numbers into our equation:

	L = Length of the resonator, in cm.
	s = Speed of sound, in cm/sec (ca. 34,400 cm/sec)
	f = the desired frequency, in Hz
	d = is the diameter of the resonating tube, in cm.

L = [(s/f)/4] - d/3   (for resonators closed on one end)

L = [(34,400/240)/4] - 5.08/3

L = [(143.3)/4] - 1.7

L = 35.8 - 1.7

L = 34.1

So a tube of 2 inch diameter, cut to length of 34.1 cm., capped off 
at one end, will be the correct resonator for the pitch of 240Hz.

Note: I round everything off to the first decimal place. With my hand tools, I can get to the closest millimeter, and that's been close enough for every project I've done so far.