Adding Partials 'Manually'

A simple example, well suited for approaching the idea of additive synthesis in Faust is given by Romain Michon within a CCRMA workshop:

import("music.lib");
import("filter.lib");

freq = hslider("freq",300,20,2000,0.01) : smooth(0.999);
gain = hslider("gain",0.3,0,1,0.01) : smooth(0.999);
t = hslider("attRel (s)",0.1,0.001,2,0.001);
gate = button("gate") : smooth(tau2pole(t));

process = osc(freq),osc(freq*2),osc(freq*3) :> /(3) : *(gain)*gate;

Within the process function, three oscillators are called in parallel by comma-separating them. The :>_ operator collects their outputs, which are subsequently devided by 3 and amplified.

Fourier Series in a Loop

The example fourier_series.dsp in the seminar's Faust repository makes use of the parallel directive within a loop, allowing the use of more partials.

// fourier_series.dsp
//
// Generate a square wave through Fourier series.
// - without control
//
// Henrik von Coler
// 2020-05-06

import("stdfaust.lib");

// define a fundamental frequency
f0            = 100;

// define the number of partials
n_partial = 50;

// partial function with one argument ()
partial(partIDX) = (4/ma.PI) * os.oscrs(f)*volume
// arguments
with {
f = f0 * (2*partIDX+1);
volume = 1/(2*partIDX+1);
};

// the processing function,
// running 50 partials parallel
// mono output
process = par(i, n_partial, partial(i)) :> +;

The Faust Website Examples

The Faust website lists two examples for additive Synthesis. Here, each partial is represented in the graphical user interface with individual control for temporal envelope parameters. This allows playing a triggered sound with a dynamic timbre.

Expressive Timbral Control

For using additive synthesis in an expressive way, metaparameters are essential. It is desirable to control the behaviour od all partials and thus the timbre with few meaningful controls.

The following example, found in the semiar's Faust repository, controlls the decrease in energy towards higher partials with a single parameter:

// exponential.dsp
//
// Additive synthesizer with controllable
// exponential spectral decay.
//
// - continuous
// - stereo output
//
// Henrik von Coler
// 2020-05-05

import("stdfaust.lib");

// define a fundamental frequency
f0           = 100;

// define the number of partials
n_partial = 50;

slope     = hslider("s", 1, 0.1, 7, 0.01);


// partial function
partial(partCNT,s) = os.oscrs(f) * volume
// arguments
with {
f = f0 * (partCNT+1);
volume =  0.3 *  exp(s * -partCNT);
};

// the processing function,
// running 50 partials parallel
// summing them up and applying a global gain
process = par(i, n_partial,  partial(i,slope)) :>_ * hslider("Master Gain",0,0,1, 0.1) <: _,_;