______                     
                 /      |       ________     
                /       |____  /        \    
               /        |    \/   _      \   
               \       ___       /_\      \  
                \      \_/          .      \ 
                 \          /\_____/       / 
                  \________/      |       /  
                                  |______/   

[THE_EXPR_METHOD] 002 modulation

Modulation, can essentially be seen as applying the “shape” of one signal onto another. For example, modulating the amplitude of an oscillator (carrier signal) with an sawtooth wave (modulating/control signal) would create a crescendo in loudness with a sudden drop in volume at the end. Triangle wave, on the other hand would produce a crescendo and followed by a smooth decrescendo. The resulting sound thus follows the visual appearance of the modulating signal.

Visualising the control signal in such a manner can be quite a intuitive process when applying modulations in composition.

Supposing the control signal always starts with a sawtooth wave ([phasor~]), the aim therefore is to find ways to “bend” its linear ramp into other suitable/interesting shapes to be further made used of. Following examples will demonstrate some simple transformations in which a sawtooth wave is “shaped” into other useful waveforms.

• Reverse Sawtooth:

  [phasor~ 1]->[-~ 1]->[abs~]

• Triangle wave:

  [phasor~ 1]->[*~ 2]->[-~ 1]->[abs~]

• Square/Pulse wave:

  [phasor~ 1]->[expr~ if($v1<0.5, 1, 0)]

• Attack/Decay envelope:

  

Above examples may seem trivial at first, they do however provide highly functional shapes that can be very useful in many common compositional scenarios.

Exercise:

Use only [expr~] object to reverse Sawtooth and Triangle wave

The Triangle wave above is not entirely correct, how can it be fixed?

How to do simple Pulse Width Modulation from the given example above?