SuperCollider CLASSES

LFGauss

Gaussian function oscillator
Inherits from: UGen : AbstractFunction : Object

Description

A non-band-limited gaussian function oscillator. Output ranges from minval to 1.

LFGauss implements the formula:

f(x) = exp(squared(x - iphase) / (-2.0 * squared(width)))

where x is to vary in the range -1 to 1 over the period dur. minval is the initial value at -1.

Class Methods

*ar (duration: 1, width: 0.1, iphase: 0, loop: 1, doneAction: 0)

*kr (duration: 1, width: 0.1, iphase: 0, loop: 1, doneAction: 0)

Arguments:

duration

duration of one full cycle ( for freq input: dur = 1 / freq )

width

relative width of the bell. Best to keep below 0.25 when used as envelope. (default: 0.1)

iphase

initial offset (default: 0)

loop

if loop is > 0, UGen oscillates. Otherwise it calls doneAction after one cycle (default: 1)

doneAction

doneAction, which is evaluated after cycle completes (2 frees the synth, default: 0). See UGen done-actions for more detail.

Inherited class methods

Instance Methods

-minval

Returns the lowest value for the given parameters, which is exp(1.0 / (-2.0 * squared(width)))

-range (min: 0, max: 1)

Scales the output to the given range. This can be convenient when using LFGauss as an envelope (see example below).

{ LFGauss.ar(0.01, 0.6).range }.plot;
{ LFGauss.ar(0.01, 0.6) }.plot; // starts at about 0.25

Inherited instance methods

Examples

Some plots

s.boot ;

// a 0.1 second grain
{ LFGauss.ar(0.1, 0.12) }.plot(0.1);

// shifting left
{ LFGauss.ar(0.1, 0.12, -1, loop: 0) }.plot(0.1);

// moving further away from the center
{ LFGauss.ar(0.1, 0.12, 2) }.plot(0.2);

// several grains
{ LFGauss.ar(0.065, 0.12, 0, loop: 1) }.plot(0.3);

Some calculations

assuming iphase = 0:

minval for a given width: minval = exp(-1.0 / (2.0 * squared(width)))

width for a given minval: width = sqrt(-1.0 / log(minval))

width at half maximum (0.5): (2 * sqrt(2 * log(2)) * width) = ca. 2.355 * width

// minval for a width of 0.1:
(exp(1 / (-2.0 * squared(0.1)))) // 2e-22

// maximum width for a beginning at -60dB:
// we want the beginning small enough to avoid clicks
sqrt(-1 / ( 2 * log(-60.dbamp))) // 0.269

// minval for width of 0.25
(exp(1 / (-2.0 * squared(0.25)))).ampdb // -70dB

// maximum is always 1:
{ LFGauss.ar(0.1, XLine.kr(1, 0.03, 1), 0, loop: 1) }.plot(1);

// a gauss curve in sclang:
(0..1000).normalize(-1, 1).collect(_.gaussCurve(1, 0, 0.1)).plot;


// rescale the function to the range 0..1
(
{
    var width = XLine.kr(0.04, 1.0, 1);
    var min = (exp(1.0 / (-2.0 * squared(width))));
    var gauss = LFGauss.ar(0.1, width, loop: 1);
    gauss.linlin(min, 1, 0, 1);
}.plot(1)
);

// range does the same implicitly
(
{
    var width = XLine.kr(0.04, 1.0, 1);
    LFGauss.ar(0.1, width, loop: 1).range(0, 1);
}.plot(1)
);

Sound examples

// modulating duration
{ LFGauss.ar(XLine.kr(0.1, 0.001, 10), 0.03) * 0.2 }.play;

// modulating width, freq 60 Hz
{ LFGauss.ar(1/60, XLine.kr(0.1, 0.001, 10)) * 0.2 }.play;

// modulating both: x position is frequency, y is width factor.
// note the artefacts due to aliasing at high frequencies
{ LFGauss.ar(MouseX.kr(1/8000, 0.1, 1), MouseY.kr(0.001, 0.1, 1)) * 0.1 }.play;

// LFGauss as amplitude modulator
{ LFGauss.ar(MouseX.kr(1, 0.001, 1), 0.1) * SinOsc.ar(1000) * 0.1 }.play;

// modulate iphase
{ LFGauss.ar(0.001, 0.2, [0, MouseX.kr(-1, 1)]).sum * 0.2 }.scope;

// for very small width we are "approaching" a dirac function
{ LFGauss.ar(0.01, SampleDur.ir * MouseX.kr(10, 3000, 1)) * 0.2 }.play;

// dur and width can be modulated at audio rate
(
{     var dur = SinOsc.ar(MouseX.kr(2, 1000, 1) * [1, 1.1]).range(0.0006, 0.01);
    var width = SinOsc.ar(0.5 * [1, 1.1]).range(0.01, 0.3);
    LFGauss.ar(dur, width) * 0.2
}.play
);


// several frequencies and widths combined
(
{
    var mod = LFGauss.ar(MouseX.kr(1, 0.07, 1), 1 * (MouseY.kr(1, 3) ** (-1..-6)));
    var carr = SinOsc.ar(200 * (1.3 ** (0..5)));
    (carr * mod).sum * 0.1
}.play;
)

// test spectrum
(
{
    var son = LeakDC.ar(LFGauss.ar(0.005, 0.2));
    BPF.ar(son * 3, MouseX.kr(60, 2000, 1), 0.05)
}.play;
)

Gabor Grain

NOTE: The gaussian function doesn't start with 0 – it asymptotically approaches it at -inf and inf. When using it as an envelope, it has to start at some smaller value, and it has an offset for this value. You can remove this offset by explicitly setting the range, e.g. to 0..1 (this is the default).
(
var freq = 1000;
var ncycles = 10;
var width = 0.25;
var dur = ncycles / freq;
{

    var env = LFGauss.ar(dur, width, loop: 0, doneAction: 2).range;
    var son = FSinOsc.ar(freq, 0.5pi, env);
    son
}.plot(dur);
)


(
SynthDef(\gabor, { |out, i_freq = 440, i_sustain = 1, i_pan = 1, i_amp = 0.1, i_width = 0.25 |
    var env = LFGauss.ar(i_sustain, i_width, loop: 0, doneAction: 2).range;
    var son = FSinOsc.ar(i_freq, 0.5pi, env);
    OffsetOut.ar(out, Pan2.ar(son, i_pan, i_amp));

}).add;
)

// modulating various parameters
(
Pdef(\x,
    Pbind(
        \instrument, \gabor,
        \freq, Pbrown(step:0.01).linexp(0, 1, 100, 14000),
        \dur, Pbrown().linexp(0, 1, 0.004, 0.02),
        \legato, Pbrown(1, 3, 0.1, inf),
        \pan, Pwhite() * Pbrown()
    )
).play
)

// modulating width only
(
Pdef(\x,
    Pbind(
        \instrument, \gabor,
        \freq, 1000,
        \dur, 0.01,
        \width, Pseg(Pseq([0.25, 0.002], inf), 10, \exp),
        \legato, 2
    )
).play
)

// compare with sine grain.
(
SynthDef(\gabor, { |out, i_freq = 440, i_sustain = 1, i_pan = 1, i_amp = 0.1, i_width=0.25 |
    var env = EnvGen.ar(Env.sine(i_sustain * i_width), doneAction: 2);
    var son = FSinOsc.ar(i_freq, 0.5pi, env);
    OffsetOut.ar(out, Pan2.ar(son, i_pan, i_amp));

}).add;
)