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Sound Synthesis

This chapter is devoted to concepts that are essential to the study and understanding of sound synthesis. Here, the reader will find the vocabulary and fundamentals necessary to approach the different processes that produce sound, regardless of the type of synthesis used.

A short history of the different machines that accompanied the birth of sound synthesis concludes the chapter.

1.1. The art of creating sound

Sounds surround us, propagating through air, liquids and solids, but in a vacuum, they do not exist. Each sound has an identity that allows it to be recognized. Our ear, however, is only able to perceive a part of the sound messages, included in a so-called audible frequency range to which I will return in section 1.2.5.

Sound, before being music, is primarily a means of communication for both humans and animals. Throughout time, humans invented tools to create sound using archaic methods, for example tapping on stones or pieces of wood before shaping increasingly sophisticated instruments. Through this evolution a new language was born, which can be referred to as music.

Until the beginning of the 20th century, sounds were always associated with the natural environment, even though musical instruments had become very sophisticated. The invention of the first sound recording methods led to the birth of sounds that could be described as artificial; as for the synthesis part, it was necessary to wait for the development of electronics so that it could take off.

Today, sound synthesis is a real creative tool for composers, musicians and many professionals. It has become an art, even creating new disciplines such as sound design.

In sound synthesis, the objective is not to generate musical notes but to produce a sound, whether that of a real instrument, organ, piano, trumpet, violin, cymbal and many others, or even one that characterizes a steam train, a creaking door, a police siren, a fog horn, a refrigerator, the wind, a storm, the rain, the barking of a dog and even a completely artificial audio phenomenon, non-existent in the natural environment, like an intergalactic battle in a science fiction film1.

1.2. Some reminders

To begin with, I will describe the nature of a sound, then some of its characteristics, followed by how our ears work. I will continue with an analysis of sound typology, spectral analysis and timbre.

I deliberately chose to present the different mathematical equations in clean and simple forms, without going into detail and avoiding demonstrations. However, the scientific rigor essential in all physical sciences has been retained.

Next, I will approach the fundamental aspects of sound propagation with the presentation of some common phenomena, and then in section 1.8, I will return in detail to the notion of noise.

I will conclude with a history of sound synthesis and the associated instruments.

1.2.1. Sound: a bit of theory

What is sound? Answering this simple question is not so easy. We can approach the subject in two ways: the first from a purely scientific point of view, associated with the laws of physics, and the second according to sensory feelings.

For a physicist, a sound is a mechanical wave that propagates as a disturbance in an elastic medium or in a body. A wave is considered a back and forth movement (mechanical oscillation) of particles around a resting position, unlike an electromagnetic wave, which propagates energy in the form of an electric field coupled to a magnetic field.

Figure 1.1. An example of easily representable mechanical waves. Here, they are created on the surface of the water, after throwing pebbles into it.

For most of us, it is much easier to define a sound as an auditory sensation.

Sounds are produced by vibrating objects. These objects are sources, and the environment in which the sound is emitted carries the sound to our ears. At this moment, our brain allows us to perceive them, become aware of them and interpret them.

Most of the objects around us can produce sound when they undergo a shock, friction, blast or deformation. Who has not had fun vibrating a plastic ruler on the edge of a table?

Figure 1.2. Ruler vibrating on the edge of a table.

In a vacuum, a sound cannot propagate because no medium is available to transmit the vibration.

Like all physical phenomena, a sound can be characterized. Many parameters such as intensity, pitch and timbre will be able to define and differentiate it; however, these are not the only ones because the listener can interpret it themselves when listening. This approach implements subjective phenomena called psychoacoustics, which are based on the physiology, culture and ethics of the individual who receives the sound message. In this case, the deciphering of the characterization process is still very complex. We are touching on areas where science does not yet have all the answers.

Over the centuries, philosophers have often asked themselves the question: does a sound exist if there is no one to hear it?

The science that physically studies sound phenomena is acoustics. Without being exhaustive, it aims to characterize the audibility of a sound, define the means implemented for its transport and transformation or determine the deformations that it can undergo. It is a science that often remains very theoretical. Acoustics is a fundamental basis but when sounds become music, it goes beyond theoretical understanding. Music is not a science; it uses many parameters that are not always measurable, and whose combination is of great complexity.

To continue, I will review certain notions that should not escape those who want to understand the foundations and the nature of sound.

1.2.2. Intensity

This parameter characterizes the strength of a sound, determining whether the sound seems loud or quiet. The term loudness is also used.

When a sound is emitted, the sound wave deforms the carrier fluid (air in most cases). This deformation causes a change or a local disturbance in the pressure around the point of emission. This disturbance moves through the surrounding material(s) at a speed (speed of sound or velocity) that is dependent on the nature of the elements crossed, their state and their thermodynamic properties. The materials traversed, whether fluids or soft or hard bodies, all have a certain elasticity so that, in most cases, they regain their initial appearance after having been crossed by the sound. Permanent deformation or destruction may occur if the generated sound pressure is greater than the elastic limit of the bodies crossed. This scenario is unlikely, given the low constraints imposed.

The pressure variation mentioned above, mainly observed in the air, is called instantaneous sound pressure. This sound pressure induces sound energy. Both are described by the acoustic sound pressure level, also called the sound level.

The scale of sound pressure is very extensive, and the unit of measurement is the pascal (Pa) (1 pascal = 1 newton/m2). Normal atmospheric pressure at sea level is defined as being 1.013 × 105 pascals, or 1,013 hPa (1 hPa = 100 pascals). To work on the acoustic sound pressure scale, standardization has retained a reference pressure close to the average absolute intensity threshold of the human auditory system between 1,000 and 4,000 Hz2, that is, 2 × 10-5 Pa, which can be translated as a power equal to 10-12 W3/m2. However, these elements remain difficult to handle and are not very demonstrative independently of the fact that the ratio between the minimum audible sounds and very loud sounds is 1/10,000,000.

Sound sensation is above all a physiological phenomenon, and it would be interesting to quantify a sensation of excitation that would consider the extent of the acoustic level of the human ear, which varies according to a logarithmic scale. The inventor of the telephone, Graham Bell4, defined a base unit, the bel, of which a tenth, the decibel (dB) is commonly used to quantify sound phenomena in a simple way:

or:

where:

• N is the sound level in decibels;
• P is the measured acoustic pressure;
• P0 is the reference acoustic pressure (0 dB);
• W is the measured power;
• W0 is the reference power.

The logarithmic progression of the decibel scale results in a doubling of the sound intensity each time it increases by 3 dB.

Table 1.1. Table of sound power