From CNBH Acoustic Scale Wiki
Roy Patterson , Etienne Gaudrain, Tom Walters
This Chapter is about the sounds made by musical instruments and how we perceive those sounds. The Chapter is intended to explain the basics of musical note perception, such as, why a particular instrument plays a specific range of notes; why instruments come in families; and why we hear distinctive differences between members of a given instrument family, even when they are playing the same note. The answers to these questions might, at first, seem obvious; one could say that brass instruments all make the same kind of sound because they are all made of brass, and the different members of the family sound different because they are different sizes. But answers at this level just prompt more questions, such as: What do we mean when we say the members of a family produce the same sound? What is it that is actually the same, and what is it that is different, when different instruments within a family play the same melody on the same notes? To answer these and similar questions, we will examine the relationship between the physical variables of musical instruments, like the length, mass and tension of a string, and the variables of auditory perception, like pitch, timbre, and loudness. The discussion reveals that there are three acoustic properties of musical sounds, as they occur in the air, between the instrument and the listener, that are particularly useful in summarizing the effect of the physical properties on the musical tones they produce, and explaining how these musical tones produce the perceptions that we hear.
The remainder of the introduction sets out the aspects of tone perception to be explained, namely, the perception of pitch, instrument family and instrument register within a family. The second section describes the acoustic properties of tones as they pertain to music perception, and sets out some of the terminology used in the Chapter. The third section explains the relationship between the physical variables of tone production (length, mass, tension, etc.) and the acoustic variables observed in the sounds. The fourth section describes the internal representation of musical sounds in the auditory system to show how the acoustic properties of sound appear in the auditory representation of musical tones. The fifth and final section reviews the relationship between the acoustic variables of sound and the auditory variables of tone perception, and suggests how the standard definitions of pitch and timbre might be revised for use in discussions of the perception of musical tones and musical instruments.
1.1 Pitch, Instrument Family and Instrument Register Within a Family
The Chapter focuses on the sounds produced by the sustained-tone instruments of the orchestra and chorus, that is, the families of instruments referred to collectively as brass, strings, woodwinds, and voice. Table I shows four of the instruments in each of the families, ordered in terms of their size or their register. With just a little training, most people can learn to identify these sixteen instruments from a simple monophonic melody (van Dinther and Patterson 2006). With regard to family and register, the purpose of the chapter is to explain how auditory perception enables us to distinguish the main families and the different instruments within a family.
Imagine the sequence of tones you would hear if a trombonist, a cellist, a bassoonist, and a baritone vocalist took it in turns to produce the same tone, say C3 (the C below middle C on the keyboard). What is the ‘same’ about the four tones is their pitch. What is different, and what allows us to distinguish the tones, is the distinctive timbres of the different instrument families. This is the traditional distinction between the perceptual variables, pitch and timbre. The pitch of a musical tone is effectively determined by the repetition rate of the sound. The sound waves produced by the sustained-tone instruments of the orchestra (brass, string, woodwind and voice) are complex and their spectra are complex; nevertheless the tones are essentially periodic and the pitch that they produce is very closely related to the number of times that the sound wave repeats in the course of one second. This aspect of music perception is entirely straightforward for sustained-tone instruments. Psychoacousticians have developed models to explain how the auditory system extracts pitch from sound waves, and the models have become increasingly elaborate as they attempt to explain the pitches produced by exotic, computer-generated waveforms, and the relative salience of these esoteric pitch perceptions. The models fall into two groups: those that follow Helmholtz (1875) and attempt to explain the perception of pitch on the basis of the frequency spectra of the sounds, and those that follow Licklider (1951) and emphasize the distribution of time intervals observed in the firing patterns that pitch-producing sounds generate in the auditory nerve. A brief overview of the debate is presented in Section 4 of this chapter; more extensive discussions are provided in a recent paper by Yost (2009) and a recent chapter by de Cheveigné (2005). Despite the passion of the debate between the spectral and temporal modellers, for readers who are simply interested in the relationship between the physics of note production and perception, the pitch of the notes of the main orchestral instruments is simply the psychological correlate of the repetition rate of the waveform that the instrument produces.
With regard to timbre, the instruments of a given family have similar physical shapes, they are made of similar materials, and they are excited in similar ways, so it is not surprising that the instruments of a family produce tones with a similar sound quality, or timbre, that distinguishes the family. The categories of timbre associated with instrument families are labelled with words that describe some physical aspect of the source. So, the trumpet is a brass instrument, the clarinet is a wood-wind instrument, and the violin is a string instrument. The family aspect of timbre is largely determined by the shape of the envelope of the magnitude spectrum of the tones that the instrument produces. This aspect of musical perception is also relatively straightforward for sustained-tone instruments.
Within a family of instruments, the different members are distinguished physically by their size, and perceptually by the effect that the size of the instrument’s components has on the tones they produce. There are two different aspects to instrument size and they jointly determine our perception of the register of an instrument within its family. In the string family, register distinguishes the violin, viola, cello, and double bass, and the instrument names are normally used to specify the instrument’s register. In the string family, as the size of the instrument increases from violin to double bass, the lengths and masses of the strings increase, and so the tones of the larger instruments have lower pitches (on average). The range of pitches that an instrument produces is one of the properties that determines the register we perceive and what instrument we hear within a family. The second aspect of instrument size is the size of the body and it also affects the register we perceive and the instrument we hear; larger bodies go with lower registers. The fact that register depends on two acoustic variables means that the perception of register is somewhat more complicated than the perception of pitch and family timbre. Nevertheless, the principles, as they pertain to the perception of musical tones, are readily comprehensible and they are a prominent topic in this chapter. To begin with, register can be regarded as the perceptual property that enables us to distinguish the size element of instruments within a family (Table I) including the categorization of humans as sopranos, altos, tenors, baritones, or basses. Note that children, when they begin to sing, are sopranos and they progress down in pitch to their eventual range as they grow up.
In summary, the main purpose of this chapter is to describe how the physical variables of tone generation are related to the acoustic variables of tones as sounds in the air, and how these acoustic variables are related to the perception of melodic pitch, family timbre, and register within an instrument family. There is a secondary aspect of register, associated with the perception of individual instruments, that allows us to distinguish the upper and lower notes by the sound of the tones themselves, and we refer to the tones as coming from the upper or lower ‘register’ of a particular instrument, or voice. We will return to this secondary aspect of tone perception later in the chapter, once the acoustic properties of sound, and their primary role in perception, have been set out.