The Basic Reed Woodwind
Reed woodwinds include saxophones, clarinets, oboes, and bassoons. Other reed instruments include harmonicas, accordions, and some organ pipes. These pages will concentrate on monophonic instruments, like saxophones.
Our discussion will assume some familiarity with the blown pipe model. In fact, we’ll borrow some pieces of it.
Reed woodwinds can have two kinds of reeds: a single reed, as used in a clarinet or saxophone, or a double reed, as used in an oboe or bassoon. Since I can’t find a double-reed model, we’ll model a single reed, and then use EQ to attempt to mimic oboes and bassoons.
Reed woodwinds can have two kinds of bores: a cylindrical bore, as used in a clarinet, or a conical bore, as used in saxophones, oboes, and bassoons. Our bore will be able to simulate both kinds of bores.
The basic model
The basic model is below. It doesn’t sound like much yet, but don’t be discouraged. There are many improvements to be made.
How does it work?
The operation is similar to our blown pipe. Once again, the combination of the jet driver and a tuned delay is the basis of the model. In fact, the jet driver is identical to the one in the blown pipe model.
It’s the delay line that’s different. In fact, there are two delays, one each in the Left Side Pipe and Right Side Pipe.
Let’s trace the signal flow. We’ll begin with the Left Side Pipe. This section contains a delay line, a lowpass filter, and a gain control. The output then goes to the Right Side Pipe, and is inverted as it enters. The Right Side Pipe is identical. It contains another delay line, a lowpass filter, and a gain control. The output then returns to the Left Side Pipe, and is again inverted as it enters. Notice that the lowpass filters and gain controls have matching characteristics, but that the delay lines can have different lengths.
It turns out that this loop is, in fact, the standard physical model of a string. One delay represents the length of string from the pick to the bridge, and the other delay represents the length of string from the pick to the nut. The lowpass filters and inverting gain controls represent the reflections and energy losses at the bridge and nut.
But instead of “plucking” the string by injecting a noise pulse into it, we’ve placed a jet driver at the pick point. We’ve summed the outputs of the delays, divided them in half, and then added them to the input air pressure. This feeds the jet driver. The output of the jet driver goes back into both delay lines. This kind of model is called a “blown string”. It’s an attempt to model a conical bore in an inexpensive way.
Cylindrical and conical bores
It’s the cylindrical bore of a clarinet that gives it that “woody” sound. This is because the straight bore supports only odd harmonics (more or less). The conical bores of saxophones, oboes, and bassoons are the reason that their sounds include even harmonics.
There are two common ways to model conical bores. The “physical” way is to create something called a Kelly-Lochbaum filter, containing dozens of tiny delay lines, adders, and multipliers. Using this method, any shape of bore can be created.
We don’t have a Kelly-Lochbaum module in the G2, so we’ll use the “non-physical” way: the blown string. It can’t do everything a Kelly-Lochbaum filter can do, but it’s enough to create even harmonics, and we can do the rest with EQ.
We’ll control the “shape” of our bore by controlling the ratio of the delay line lengths, via the Pan knob on the “Splitter” Pan module. If the knob is in the center, the two lengths are equal, and our pipe sounds woody, like a clarinet. But if one length is longer than the other, the sound begins to include even harmonics. Varying this control is a lot like varying the pulse width of a pulse-wave oscillator. Regardless of the position of the Pan knob, the total length of the loop remains the same, and this is why the pitch doesn’t change when the Pan knob is moved.
The delays are tuned using an old trick from the original Nord Modular: the Level Scaler Module. This module can be linked to the keyboard and adjusted to output a -6dB/octave slope. Since -6dB represents a 50% reduction, and since we want the delay line to become 50% shorter with each increasing octave, this module is perfect for the task.
The control parameters
This model has 5 control parameters. They are: