The simple modelling of the rich sounding effect of non-linear mouthpiece action on layers of the repetitive delays down the instrument tube, I found, can be applied to other pipe instruments like this simple saxophone model. Reed instruments work a little differently to trumpets though...
The hard driving action of the trumpet mouthpiece I used in the previous section does not happen so much in a reed instrument. For the valve action is by a reed this time. I realised that a reed would still vary the area of the mouthpiece aperture, perhaps again producing some kind of squaring or non-linear action, but this time mainly under the influence of the pipe resonance oscillating as a unit. I thought the reed valve aperture is much bigger relative to the pipe size this time and its geometry is quite different and complex. I also thought that the reed, being a springy valve of flexible shape and made of softish material, would have its own broad resonance and filtering action, tending to a produce a sluggish response at high frequencies. This would produce its own additional ‘fixed’ (ignoring for now lips pressure and position) frequency dependant effect to the ‘pipes’ resonant loop making a combined complex resonant system which the player persuades to start to oscillate, adding wind energy to maintain it. In the patch, to test this out as simply as I possibly could, all I used is a simple variable low pass filter 2nd./4th. order with resonance (Q) control to model the ‘reed’ that is any soft damped resonance the ‘reed-lip’ arrangement might posses. This was subtly added to the delay loop circuit and adjusted to just below unity gain. For the valve effect I used a VCA as I did before in the trumpet. Like the trumpet, this model is rather oversimplified but I didn’t have many modules to play with and I was just actually testing for a clarinet sound. I got the saxophone by mistake as I my whole delay loop ended up being in-phase (resonates at all harmonics) rather than out-of-phase (resonates at odd harmonics). It was a ‘Eureka moment when the distinctive saxophone sound came from the ‘speakers.
To make the above saxophone patch sound, the whole ‘pipe-reed system’ is made to oscillate; that is the gain round the delay line, filter, VCA loop raised to one or just slightly higher. I’ve marked this path is a deeper blue in the diagram. Uncontrolled, above one the oscillations would get bigger and bigger and it’s very hard to keep it at exactly one, so there must be some form of amplitude limiting. In reed instruments, this is a function of the limiting spring action of the reed in the mouthpiece. If you blow hard enough, it will sooner or later reach its limit of elasticity or even collide with the body. Electrically, in the model a soft amplitude limiting function built into the delay line for overload protection just happened to work nicely as a very crude reed elasticity limiting device. For once luck was on my side.
Looking at saxophones, they have conical bores while clarinets, for example, have straight cylindrical bores. This I all very well in reality, but with electronics, it is very difficult to construct a conical analogue delay line! With delay lines you can either have positive or, by electronically turning the waveform upside down, negative feedback from the output back to the input. Fortunately though with delay lines, both forms at unity gain will oscillate - when positive; at all harmonics of the fundamental, when negative; at odd harmonics only but an octave lower. In the saxophone, the conical bore does tend to act as an open pipe resonant at all harmonics, so in the model a positive delay loop is used as the nearest simple practical approach to this.
To make the model work, the overall gain has first to be set just below unity to make the ‘pipe’ live and then blowing energy (gain) is added to make it oscillate. To do this a second multiplying element (VCA) is used (bottom centre) in series with and before the (reed) low pass filter. Also a little filtered noise is added (top line) to add some breath sound and randomness. Pressing a keyboard note raises the gain as well as selecting a note. At very very close to unity this results in a sluggish breathy pipe sound, above that results in the normal saxophone sound. The remaining multiplier (CVP) introduces a small amount of tremolo to keep the sound alive. The filter frequency (‘lip-reed position’) is tracked along with pitch. Deviating from this relationship can cause the ‘reed’ to ‘over-blow’ when it goes higher than the pitch.
When performing on the model there’s a few things that do jump out at you....
1) Like the trumpet model, if the system is allowed to become absolutely static the sound became fairly lifeless.
2) Much less squaring effect is required; Z = Y(X + M) for the multiplier; setting is X<<M. So I was probably wrong about the effective size of the reed compared to the pipe as its action is more obviously subtle than I had first thought.
3) The model ‘OVER-BLOWS’ easily.
There are loads of knobs to twiddle. Here’s what some of them do....
The frequency and resonant peak of the ‘reed’ low-pass filter have a very marked effect. If they don’t track the sound becomes strained. You can hear this in the first sound clip below towards the end. Setting to a low gentle roll-off frequency, the saxophone sounds woolly, with higher notes sounding really strained while the tuning is also seriously effected. This is because of the filter’s added delay (analogue filters all add a little delay to the signal) . Set much higher, the saxophone sounds bright and crisp but unintentional ‘over-blowing’ becomes a problem. The very extreme high notes still sounded strained as the sound quality gradually changed with increasing pitch.