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Composing with wave interference patterns and sine waves

This research work involves an exploration of how interference patterns is experienced across different sensory and technological domains.

Published onNov 17, 2023
Composing with wave interference patterns and sine waves
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Abstract

This research work involves an exploration of how interference patterns is experienced across different sensory and technological (ie. digital audio vs video playback) domains. Pattern as embodied in very specific, concrete ways. I consider interference of pure waves an interesting topic for pattern analysis due to its continuous and spatial–temporal nature in sound.
The emphasis in this research work is on an individual artistic process of exploration. This is about a translation of the motion of ripples into sound, the translation from one ‘dimension’ to another. The translation is being made through a subjective criteria that establishes a relationship between vibrations – ripples – and sound– sine waves.

Keywords

Patterns, water ripples, sine waves, sound art, supercollider

1-INTRODUCTION

This research work involves an exploration of how interference patterns is experienced across different sensory and technological (ie. digital audio vs video playback) domains. Pattern as embodied in very specific, concrete ways. This is about a translation of the motion of ripples into sound, the translation from one ‘dimension’ to another.
The translation is being made through a subjective criteria that establishes a relationship between vibrations – ripples – and sound – sine waves.

There is a large number of relevant works exploring the areas of interference patterns for sound, and many approaches to describing relationships between synchronised audio and video materials. I recognise that the emphasis in my work is on an individual artistic process of exploration.

I consider interference of pure waves an interesting topic for pattern analysis due to its continuous and spatial–temporal nature in sound. The choice of the sine oscillator as an electronic device for a sonic accompaniment to interference patterns is a deliberate choice. Sine oscillators generate sustained tones and wave propagation is continuous. The two elements share the feature of being sustained/continuous.

The aural phenomenon where two sine tones, close to each other in frequency, cause a sensation of beating or pulsations in the ear of the listener is generally called “beating patterns”. The pulsation rate of a beating pattern is equal to the difference of the two frequencies involved (i.e., F1 - F2 = Beat Frequency).
The short wavelength variations of the initial waves are overlaid with a long wavelength modulation. This modulation occurs because two waves with slightly different wavelengths cannot remain in phase. Periods of constructive and destructive interference occur.

Figure 1

Adding two waves with a slightly different wavelength results in a beating pattern.

Alvin Lucier was an American composer (1931-2021) focusing in a series of pieces exploring the natural properties of sound and the acoustic characteristics of architectural spaces.
Lucier usually worked with the sonic results of a mutual interference between two or more systems that could be mechanical, electrical, or biological.

In order to analyse different approaches, I have selected the composer Alvin Lucier because, from my perspective, he is a key influencer in the use of sine waves as a fundamental or structural element in music.

Lucier describes that sine waves can be perceived physically, specially if the surfaces of the room do not reflect too much sound and their presence can be felt by moving around the room, even a very little movement can disturb them. He describes the experience as comparable to standing in a pool of water in which the small movements of your body are sending out ripples. (Waugh, M. 2013: 81, 82)(Error)

Influenced by Lucier’s pieces, my previous research work involved some experiments with adding sine wave interference patterns to complex sounds.

A Piece for Washing Machine and Sine Waves (2017), is an exploration of the beating patterns and beat frequencies to develop into a musical idea by controlling the level, the range and duration of the beat frequencies throughout the piece. In this piece, I have used two sound materials: the sine waves – beating patterns and beat frequencies and the recording of a washing machine centrifuge. The sine waves and the recording are different layers of sound. Nonetheless, the recording works as the structural basis for the piece and at the same time works as a layer of noise.

My previous research work also involved some experiments with adding sine wave interference patterns to video imagery of water ripples. The work was presenting a juxtaposition of audio materials that are uncommon in nature (sine interference signals) with visual materials that are common and easily perceived (water ripples).

In nature, pure sine waves in the audible range of frequencies are extremely uncommon. They can only be analytically decomposed by Fourier analysis, but without a "direct" perception. Whereas interference patterns of the kind seen in the video are common place.

Those two mediums are continuous and have a spatial–temporal nature. Both are transmission mediums for wave propagation causing interference patterns.

In investigating methods for this “translation”, a first attempt was to use the “beating patterns” between two frequencies to represent a wavy movement. Unfortunately, since the beating patterns are so mathematically exact – the beat frequency is always the same amount of cycles per second – then the sine wave is not flexible and the harmony between water ripples and sine waves does not take place.

Another investigation method was to try different combinations of frequencies and random amplitude modulation.
Instead of including a single sine wave, more sine waves with different frequencies and amplitude modulation were added to generate a more organic effect because the ripples are multiple and simultaneous so the sine waves should behave the same.

The kind of optimal sonic materials by closed consideration of the nature of the water as a medium for interference patterns are the sine waves altered by random amplitude modulation.

Sine waves propagate in space causing beating patterns and phase interferences. Water ripples are a very good visual representation of the propagation of sound in space. Water ripples are in constant movement and collide one to each other creating a complex pattern, very clearly appreciable on the surface of the water.

The following audiovisual developed during the previous research using sine waves with random amplitude modulation as a mapping of the images of water ripples.

Video 1

Water Ripples and Sine Waves (2017), audiovisual, (05’48’’ excerpt)

The current research work explores how pattern is experienced across different sensory and technological (ie. digital audio vs video playback) domains. Throughout this research work I put emphasis on an individual artistic process of exploration. In this framework, I have decided that I want to schematically represent the invisible interference patterns through an illustration of concentric circles in motion. The concentric circles are a graphic resource used throughout the piece. The graphics are created in p5live.

The following video showcases a layer of concentric circles that symbolically illustrate the water ripples.

Video 2

Water Ripples and Sine Waves (2023), audiovisual demo to showcase the idea.

The pattern's experience in nature extends to other environments such as air. In the following video, moving air causes two objects to oscillate on a table. In this system, the two objects are disturbed by the air in motion and at the same time are disturbing the air themselves with their visible oscillations. The interference patterns propagating in space are invisible to our eye. The concentric circles illustrate an emulation of the invisible waves resulting from the oscillations propagating in the air.

Video 3

Moving air causes two objects to oscillate on a table.

2. Materials and methods in SuperCollider

Throughout this piece, I am exploring with different patches in SuperCollider to achieve a rich texture for the sonic mapping of the ripples.
The beating patterns are generated with a sine oscillator function.

The following patch showcases a beating pattern with a beat frequency/pulsation rate of 1.2 beats per second.

(
Ndef(\x,
	{
		var sig;
		sig = SinOsc.ar([300, 301.2], 1, 0.1);
		sig = sig * LFNoise2.kr(0.6);
		sig = sig * 0.3;


}).play;
)

The random amplitude modulation is achieved with the modulation of the noise function.

The following patch showcases the noise function modulating the amplitude of the signal. Although the possibilities are odd, at low frequencies, two of these signals could cause distortion.

(
Ndef(\x1,
	{
		var sig;
		sig = SinOsc.ar([202, 260], 1, 0.1);
		sig = sig * LFNoise2.kr(1);
		sig = sig * 0.2;


}).play;
)

Other sources to control the signal involve the replacement of some parameters by a sine oscillator function to achieve a more complex texture.

(
Ndef(\x2,
	{
		var sig;
		sig = SinOsc.ar([300, 301.2], 1, 0.1);
		sig = sig * LFNoise2.kr(SinOsc.kr(3).range(1,11));
		sig = sig * 0.3;


}).play;
)

The following code block showcases the code generated in p5live for the images of the video and the concentric circles in motion.

let grow = 1;


function setup() {
	createCanvas(windowWidth, windowHeight)
	
}

function draw() {
background(255);

noFill();
strokeWeight(4);
stroke(0);
  

for (let i = 0; i < 3; i++){ 
if (i == 0){
  s = 0;
} else if (i == 1){
    s = 30;
} else {
  s = 60;
}

circle (0, 800, s+grow);
 grow+=0.2; 
  grow=grow % width;
  
  for (let i = 0; i < 3; i++){ 
if (i == 0){
  s = 0;
} else if (i == 1){
    s = 30;
} else {
  s = 60;
}
}
circle (600, 700, s+grow);
 grow+=0.2;
}

}

Bibliography

Hermann, Thomas, Andy Hunt, and John G. Neuhoff. The sonification handbook. Vol. 1. Berlin: Logos Verlag, 2011.

JITLib, An overview of the Just In Time programming library. https://doc.sccode.org/Overviews/JITLib.html

Lucier, Alvin, Gisela Gronemeyer, Reinhard Oehlschlägel, and Alvin Lucier. Reflections: Interviews, scores, writings = reflexionen. MusikTexte, 1995.

O'Modhrain, Sile, and Georg Essl. "PebbleBox and CrumbleBag: tactile interfaces for granular synthesis." In Proceedings of the 2004 conference on New interfaces for musical expression, pp. 74-79. 2004.

Rohrhuber, Julian, and Alberto de Campo. "Just in time programming." The SuperCollider Book. MIT Press, Cambridge, Massachusetts (2011).

Waugh, Michael. “Music 109: Notes on Experimental Music. By Alvin Lucier”. Middletown, CT: Wesleyan University Press Press, 2013. 215 Pp

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