Most of the information presented in this document concerns the properties and behaviour of individual sounds or sound waves, or describes their internal composition. However, in daily experience the auditory system is constantly bombarded with a multiplicity of simultaneous sounds which must be distinguished from each other. The co-existence of sounds within an environment can be compared to the co-existence of individuals in society: they can exist in a state that is potentially harmonious, but all too often they are subject to conflict, as reflected in contemporary problems of noise pollution. Music composition can be thought of as the skilful and imaginative combination of sounds, and as such is a design art that can be emulated in the design of environments. However, before one can understand the art of design, a basic knowledge of the various ways in which individual sounds interact with each other is necessary. We present six aspects of this theme:

A) Superposition of waves: the process by which simultaneous waves combine in the same space, and the results of their interaction;

B) Mixing of sounds: some basic terms from various disciplines;

C) Modulation: the electroacoustic technique of having one sound signal "modulate" another for communicational purposes;

D) Non-linear combination: the "distortion" effects that arise when sounds do not combine linearly, that is, when simple addition breaks down;

E) Environmental sound combination: special types of interaction between environmental sounds constantly occur that have an effect on the audibility of these sounds:

F) Musical pitch combination: the organization of simultaneous pitches is a basic concern in music; recent developments in psychoacoustics now explain some of the mechanisms by which the brain reacts to such combinations.

A) Superposition of Sound Waves: the most basic aspect of sound combination is the principle of linear addition of two or more sound waves, a principle which holds in most actual cases. However, since sound waves are oscillations, containing what might be thought of as positive and negative parts, simple addition can result in reinforcement (+ with +, - with -) or cancellation (+ with -). Three results of this process can be observed: spatial cancellation or "dead spots", frequency cancellation or "phasing", and cancellation between waves of nearly identical frequency, resulting in "beats".

Law of Superposition
Phase Difference
Phase Shift

B) Mixing of Sounds: in design-oriented disciplines, such as music and electroacoustics, the combination of sounds is crucial, and several basic terms have arisen that deal with types of sound combination in each discipline.


C) Modulation: modulation is an electroacoustic technique of widespread usage, which also finds analogies in acoustics and music. Stated simply, in modulation a parameter of one signal called the carrier is made to vary according to the waveform of another signal called the modulator. The carrier when modulated can be said to "contain" the information or pattern of the modulating signal, and thus the two signals are combined in a unique manner. The various applications of the technique usually have as variables: the parameter being modulated (e.g. frequency, amplitude or phase); the amount or "depth" of modulation; and finally the frequency range in which each of the carrier and modulator lie, such as the sub-audio, audio, and ultrasonic frequency ranges. Such diverse examples as the violinist's vibrato, the synthesis of complex spectra, and the transmission of radio signals can all be explained as examples of modulation.

Modulation Depth
Amplitude Modulation
Frequency Modulation

D) Non-linear Combination: many systems, including the ear, cannot maintain linearity or simple addition in the processing of single or simultaneous sounds or signals. The result of such non-linearity is the appearance of additional frequencies or tones in addition to the original stimulus.

Combination Tones
Difference Tone
Summation Tone
Aural Harmonics

E) Environmental Sound Combination: the audibility of the components of a complex sound environment depends on many factors. If all components are sufficiently low level, they combine into the composite background sound called "ambience". If two sounds are in approximately the same frequency region but one is much louder, the quieter sound will be "masked" or made more difficult to hear. Short time delays between sounds, as in echo and reverberation, could result in confusion were it not for the brain's ability to suppress the delayed components, as described in "precedence effect". Finally, perception can be wilfully focussed by the listener to pick out one sound while ignoring others, the so-called "cocktail party effect".

Precedence Effect
Cocktail Party Effect

F) Musical Pitch Combination: distances between pitches are called "intervals"; in historical practice certain intervals between simultaneous pitches were thought to be more pleasing or "consonant" than others which seemed harsher or "dissonant". Psychoacoustic research has recently documented how the auditory processing of simultaneous tones results in subjective impressions of consonance and dissonance.

Quarter Tone