The Basic Flute
A flute is a kind of “blown pipe”, so it’s closely related to what we’ve already done. It’s a pipe with 12 toneholes along its side, corresponding to the notes on a chromatic scale. These holes are almost as wide as the pipe itself, so opening them has the effect of shortening the pipe.
This is how the lowest octave is played. Higher octaves are achieved by adjusting the player’s embouchure, which changes the angle and velocity of the blown air. This forces the note to jump to one of the flute’s higher vibrational modes.
Our first flute patch, while not an exact model of a flute, will add one significant new feature that our blown pipe lacked: it can jump to higher vibrational modes, just like a flute. The patch is below.
The patch contains four basic parts:
Noisy air source: This is identical to the noisy air source in our blown pipe.
Jet driver: This also is identical to the jet driver in our blown pipe, and once again is the key to creating an oscillation in the pipe.
Embouchure delay: This is new, and is a tuned delay line. It’s going to be tuned to one octave above our desired pitch. Its input comes from the jet driver, and its output goes to the bore.
Bore: Like the blown pipe, this is a tuned delay line with a lowpass filter. But there are some differences. For one, the delay is tuned to the desired pitch, instead of one octave above the desired pitch. Also, notice that there are two feedback loops instead of one. The first feedback loop, called “Bore Fdbk”, is added to the output of the embouchure delay, and the result goes back into the bore. The second feedback loop, called “Emb Fdbk”, is added to the incoming air pressure, and the result goes into the jet driver.
How does it work?
The operation is similar to our blown pipe. Once again, the combination of the jet driver and a delay (in this case, the embouchure delay) creates a square wave whose period depends on the length of the delay.
But the bore delay makes something interesting happen. Remember that in our blown pipe, it required two trips through the jet driver and delay to make a waveform. This model has the same effect: it requires two trips through the jet driver and embouchure delay to make a waveform. This means that while we’ve tuned the embouchure delay to 659 Hz, the final waveform is half that frequency, or 329 Hz. This frequency matches the frequency of our bore delay, and the two delays work together to boost that frequency, making an oscillation.
So far, so good. But why bother? Our blown pipe model did the same thing, and didn’t require as many parts.
Here’s the reason. Notice the “Emb Pitch” knob? It can raise the resonant frequency of the embouchure delay. As you slowly move it from 0 to 12 (semitones), what happens? The sound first becomes noisy and unfocused, then refocusing again one octave higher. As you continue to move it from 12 to 24 (semitones), the sound again becomes noisy and unfocused, refocusing at 1 ½ octaves and at 2 octaves.
What’s happening? As the knob moves away from zero, the two delays no longer reinforce each other (since the bore delay isn’t being changed). When the pitch of the embouchure delay doubles (at 12 semitones), the delays reinforce each other again, since the pitch of the embouchure delay is now the second harmonic of the bore delay. Likewise, when the pitch of the embouchure delay triples or quadruples (at 19 and 24 semitones), the delays reinforce each other again, since the pitch of the embouchure delay is now the third or fourth harmonic of the bore delay.
So, this “Emb Pitch” parameter lets us play overtones that the blown pipe didn’t.
Not quite like a real flute
We’ll point out that our model doesn’t do exactly what a flute does. For example, the length of a flute’s bore is fixed at the lowest octave, and all higher notes are harmonics controlled by the player’s embouchure. In our model, both the bore and embouchure delays track the keyboard, and harmonics are used as special effects.