The Basic Blown Pipe

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Blown pipes include flutes, recorders, and many organ pipes. A blown pipe is probably the simplest wind model, so it’s a good place to start. Below is a basic blown pipe patch.

The patch contains three basic parts:

Noisy air source: This is an envelope generator that creates a voltage which represents the air pressure going into the pipe. For added realism, a small amount of noise is added to the signal.

Jet driver: This is a waveshaper that sums two inputs: the air coming into the pipe, and the air being reflected back from the pipe. It represents the mouthpiece, and implements the function Y=X^3-X, or Y=X*X*X-X. What does this do? The waveshaping function looks like a “hump”. When the input is either 0 or 64, the output is 0. Between these points, it rises in a hump-like shape, rising to about 20 when the input is about 40. This shape is the key to creating an oscillation in the pipe.

Pipe: This is just a tuned delay line with a lowpass filter. A zero-feedback comb filter is used, because it can be tuned to the keyboard very easily. The lowpass filter smoothes the signal, rounding off the edges. A highpass filter after the pipe removes the DC offset (discussed below).

How does it work?

So, what happens when you press a key?

1. The envelope generator rises, admitting noisy air into the pipe.
2. Because the air pressure is close to the top of the waveshaper’s “hump”, the waveshaper lets the air into the pipe.
3. When the air returns to the front of the pipe, it’s added to the incoming air. This kicks the waveshaper down past the hump, near to zero, and prevents more air from entering the pipe.
4. When the “lack” of air returns to the front of the pipe (via the delay line), this means that nothing is added to the incoming air. So the incoming air level is again near the top of the waveshaper’s “hump”, and the waveshaper again lets the incoming air into the pipe, like step 3.

As long as the envelope generator is admitting new air into the waveshaper, steps 3 and 4 are repeated over and over again, causing an oscillation that is shaped like a square wave. The oscillation time is determined by the length of the delay line. By making the delay line longer, the pitch is lowered (and vice versa). The lowpass filter smoothes the edges of the square wave, softening the sound.

Some observations are:

• The pitch is an octave lower than expected. For example, if the delay is tuned to 1ms, you might be surprised to find that the tone’s frequency is 500 Hz instead of 1 kHz. This is because it takes two trips through the delay line to make a waveform.

• A highpass filter is required to remove the “thumping” sound heard at the start of a note. This is because there’s a positive DC offset in the waveform. In fact, the entire waveform is positive. Although sometimes considered a problem with waveguide models, it reflects a reality in wind instruments: there’s always air coming out of the instrument. A highpass filter between the pipe and the output (but not in the loop!) can get rid of the thump.

• The instrument is out of tune, going especially flat when playing high notes. This is because there are a few samples of “overhead” when the signal goes through the loop, making each pass through the loop a few cycles longer than expected. The lowpass filter is a big contributor to this. A few overhead samples don’t make much of a difference on a low note that’s 1000 samples long. But on a high note that’s only 40 samples long, a 4-sample delay will drive the pitch flat by 10%, almost two semitones. A correction for this will be addressed later.