Let's Build an Organ Pipe!

Part one here!

In this post, I'll go step by step through my process for creating an (unpainted) PVC organ pipe! An organ pipe has two parts: the resonator, which is most of the length of the pipe as a simple empty tube, and the fipple, which creates oscillations.

THE RESONATOR 

The resonator takes vibrations (or perhaps more accurately, oscillating air vortices that I don't entirely understand) from the fipple and resonates at a fixed, controllable wavelength, allowing specific tones for music. Each pipe is going to produce one fundamental tone, just like individual strings in a piano. A single pipe will create several other tones at once when sounded, equaling integer multiples of the fundamental frequency (harmonics). The smaller the pipe, the more prominent the harmonics, but the fundamental is always the strongest.

Here are some different harmonics fitting into a single pipe (top three waves) and a fundamental of a longer pipe (bottom), with distance from midline being relative min and max pressure for each one:

However, less so than composers, we don't need to concern ourselves much with harmonics for building the organ. The pipe will sound like the fundamental frequency when you play it. So what matters more for us is the bottom of the image above: When you make a longer pipe, it will naturally resonate at a longer fundamental frequency. Longer waves are heard as lower tones. So by making different length pipes, we make different notes.  One half the length of pipe = one octave lower, and other notes vary by even logarithmic steps in between. In other words, human perception varies logarithmically with frequency.

So the resonator, at the end  of the day, is just an empty tube of the correctly calculated length. I'm making mine out of PVC pipe. For tuning purposes, I also have slightly larger pieces of pipe on top that can slide up or down to make fine adjustments to the lengths for tuning.

Middle C is an open pipe of about 2 feet in length, as a point of reference. A concert tuner of the A above middle C at 440Hz is about 1.28 feet long. 

Closed pipes (with a stopper at the end) have twice as long of waves, roughly, because the wave has to "reflect" the length of the tube then back again from the fipple. A closed pipe sounds one octave lower than it normally would, so middle C would be about a 1 foot long closed pipe. This is useful if you want to fit big pipes in an apartment building.

THE FIPPLE

The fipple is the vibration producing part of the pipe. I'm going to be routing air to my pipes by plastic tubing, so it needs to convert a stream of pressurized air from a circular tube into a consistent vibration. The fipple is much harder to make than the resonator.

Briefly, the concept of a basic flue pipe fipple (meant to sound something like a flute) is:

1. You somehow shape incoming air into a laminar air flow (a flat, non turbulent sheet of air).
2. You get that flow to pass right into a thin knife of rigid material, which will then vibrate.
3. The vibration resonates in the resonating chamber.

The way we make those things happen is by building something like this:

The pipe (red) has a cap on the end (black) with a hole for the air hose (green). There's also a plug in the pipe (orange). Air comes into the cavity in the back and has nowhere to go, except for a narrow section of pipe cut away at the top. This forces the air into a sheet, which passes over and under a knife shape cut in the pipe (red also). This vibrates, which then causes resonation in the pipe (left off the edge of this image). Again, I think it is more like oscillations of swirling air systems in a much more complicated way than just vibrating, but that's close enough for me to build it.

So without further ado, let's build it! We begin with a PVC plumbing pipe:

First, we need to cut a notch out of the end. The width of the notch is related to the diameter of the pipe, something around 2/5 the diameter. The depth of the notch depends on the system you're using for a cap. I used this tool here, a dremel with a grinding fiber/ceramic/something wheel:

Here's the notch cut out:

Then I used a much wider grinding stone (seen below), 100 grit sanding drum (not shown) and finally manual 220 grit sandpaper (not shown) to grind a sharp, gradual "knife edge" on the inside of the notch. Grinding stone:

Knife edge after all the dremeling work:

Knife edge after hand sanding:

We need a laminar sheet of air now. I achieved this by using the thickness of the PVC pipe wall itself as a guide for a sheet of air. So I need to block off the inside diameter, AND the outside diameter. The inner diameter is blocked using this section of a solid plastic dowel rod:

The corner is sanded down to aid aerodynamics (the air needs to be smoothly guided toward the knife). The plug fits into the pipe snugly. Notice how the pipe walls stick above the plug, so that when the cap goes on later, there will be a thin slice of opening:

A hole is drilled in the middle of the pipe cap. This is where plastic tubing will go to deliver the air supply:

And finally, the cap is attached. If you look closely, you will be able to see the thin slice of empty black space in between the plug and the cap nearest the camera. This is the guide for the airflow to make it into a sheet of air. It will then pass right into the knife edge, creating the musical vibrations, which resonate in the remainder of the organ pipe:

Again, here's the schematic now that you've seen the real thing:

NEXT TIME

In the next installment of this series, I will explain how the air system works, and I think I'm going to actually try out a new idea, different than my original plan, for how to activate air flow to individual pipes. I will try experimenting with homemade electric solenoids, versus the alternative of manual springs and levers and things.  If the electric version works, then the whole organ could be played either manually OR by computer program, potentially!