There is no good source of practical information available regarding the construction of pan pipes, so I did a couple of tests to establish some general principles for pan-pipe scaling. The question I was trying to answer was:
Given a pitch, what is the ideal internal length and diameter of the pipe.
Since cane is a natural material, it will not conform to the precise dimensions defined here, however these numbers should provide a reasonable starting point for experimentation.
Acousticians say that the sounding length of a stopped tube (such as a panpipe pipe) is 1/4 the wavelength of the sound produced. In actual practice, the open end of the pipe "loads" the resonating chamber, and the formula I have come up with, (based on simple tests using Lucite tubes of various lengths) is this:
Sounding length = 2.4123*Wavelength
The wavelength of a pitch can be determined as follows:
Wavelength = speed of sound / frequency
Given a sea level speed of sound of 345 meters per second, this produces the following graph. The red line is an idealized curve of all notes between F#3 (261.63) and A#6 (1864.66). The dark blue indicates values physically determined from cut Lucite tubes, and the green line are the intervals from Henry Thomas's Bull Doze Blues, which is a early blues recording featuring the rare American panpipe, the Quills.
This is the table used to calculate the values for the idealized curve shown in the graph above.
|Note||Frequency (Hz)||Calculated wave length (mm)||Pipe length (mm)||Pipe width (mm)|
I've found that a ratio of between 10 to 1 and 15 to 1 for length to bore works well. I have been using 11 or 12 to 1 in my experiments. 11 to 1 is used in the example above. Good sounding pipes can diverge from this value and still sound well, which is a good thing because cane is rarely exactly the size you need.
For a practical example of how I've applied this information to the practical construction of a set of pipes, see this page: The Quills