Parametric Pan Pipes - any scale you like.
by sphynx, published
Pan Pipes - any scale, any temperament - takes a list of frequencies and converts it to a set of Pan Pipes.
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This thing prints out a set of Pan Pipes from a list of frequencies in Hz. This allows you to print out Pan Pipes with different tunings and completely arbitrary scales. I give the normal equal tempered C scale as an example.
<b>The tinkering bit</b>
When you design a set of pipes, make sure your machine can accommodate them! They can get quite long at the lower frequencies.
If absolute pitch is important to you, it is a good idea to print out a single pipe (say c5) and use a tuner to make sure your machine is calibrated OK.
Each pipe should give a clear, strong tone.
If a pipe doesn't sound, or only sounds with difficulty, it probably has a leak. I had problems with my first prototype with the ends of the pipes being porous. I have now made them thicker and this should not be a problem. Make sure you print with extra top layers. You can also fill the pipes with acrylic varnish then empty it out to fill in any porosity.
I print with 0.8mm wall thickness and 20% fill density. This seems to be a good compromise between density and use of plastic.
The parameters in the SCAD program are:
1) radius - the radius of the pipe. About 6mm works well. 2) wall - the thickness of the wall of the pipe. You should use at least 2mm to give the pipes some mechanical strength and allow them to resonate. 3) notes - an array of frequencies in Hz.
<b>The science bit</b>
The Pan Pipe is probably the simplest wind instrument. It is a pipe that is open at one end and closed at the other. The sound is made by blowing across the open end.
You can calculate the length of pipe for a given frequency of note quite easily:
1) The open end of the pipe must be an anti-node in the sound wave (maximum amplitude). 2) The closed end of the pipe must be a node in the sound wave (no amplitude).
Looking at a sine wave, the distance from any antinode to the next node is 1/4 of the wavelength of the note.
wavelength = velocity / frequency
pipe_length = (1/4) x ( velocity / frequency )
Given the speed of sound in dry air at 20C and 1 atmosphere is 323.2 m/s, we can calculate the pipe_length for any frequency.