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.