Musical Instrument Design

Practical Information for Instrument Making

Bart Hopkin

• Publisher: See Sharp Press
• Year: 1996
• Print ISBN: 9781884365089
• eBook ISBN: 9781884365836
• Edition: 1
• Topic: Media & Performing Arts
• Subtopic: Music Theory & Appreciation

This is an encyclopedic, large-format book containing hundreds of illustrations. While not geared toward making conventional instruments, Musical Instrument Design provides all the information that anyone (amateur or professional) should ever need to construct an amazingly wide variety of percussion, string, and wind instruments. Includes many designs along with parts lists and detailed construction instructions.

Chapter One
MUSICAL SOUND PERCEPTION

In order to think intelligently about sound production, we need to understand certain things about how the ears and brain make sense of the sounds that reach them. This will also help us to develop better analytical listening skills, which are invaluable in instrument making.

SOME BASICS

Sound is created when something causes small, localized fluctuations in air pressure. The fluctuations propagate outward from the source as pressure waves in the atmosphere. Should there be any ears in the vicinity, the pressure waves cause movement in the sensitive membrane that is the ear drum, and, following a series of bio-mechanical and neural transmissions, the event is interpreted as sound by the brain. A single pressure pulse doesn't amount to much of a sound; it takes a series in rapid succession to give the ear something it can respond to. The arrival of a series of pressure waves causes air molecules at a given location to move back and forth with each pulse; thus the association of sound with vibration.

An important property of vibrations is frequency, normally expressed as the number of vibratory cycles per second completed by whatever it is that is vibrating. Think of frequency in terms of complete vibratory cycles: for a vibrating object beginning at some central point, moving to one side and back to the center constitutes a half-cycle. To complete the cycle it must continue through the center point and on to the other side, and return once again to the center point. The term Hertz, abbreviated Hz, is commonly used to represent cycles per second (after the 19th century physicist Heinrich Hertz). Thus, for instance, 200 cycles per second = 200Hz.

Humans ears are responsive to frequencies falling within a range extending roughly from a lower limit of about 20Hz to perhaps 16,000 or 20,000Hz for a typical young person (this upper limit drops with age). Within this range, lower (slower) frequencies are associated with low, or bass sounds, and higher (faster) frequencies are associated with high, or treble sounds. In general, through most of the range, the human ear's acuity is quite impressive: it picks up sounds representing truly minuscule amounts of energy; and at the opposite extreme it withstands sounds carrying billions of times that energy before serious discomfort or hearing damage occurs. The ear's sensitivity is not uniform through the hearing range, however. It tapers off at both ends, and has a broad peak in the range of about 2,000Hz to 5,000Hz, corresponding to a medium-high part of the range. This means that sounds within this band sound much louder than sounds carrying comparable energy at higher or lower frequencies.

When a sound vibration occurs at a single steady frequency, you hear it as having a recognizable "note" or pitch. Pitch, in other words, is the brain's way of interpreting vibrational frequency. The ascending series of notes that you hear when someone plays a scale on a musical instrument actually represents the instrument's ability to produce sounds at a series of specific frequencies, each a little higher than the one before. (Appendix 2 at the end of this book contains a chart giving frequencies for each of the pitch names used in the standard Western musical scale.) Human ears and brains are amazingly good at recognizing steady-frequency vibrations and distinguishing one frequency from another. Frequency differences of less than one percent are easily recognized by people with no special training. This acuity diminishes toward the extremes of the hearing range.

The word "interval" refers to the perceived distance between two pitches, or how much higher one pitch is than another. People in most musical cultures seem to perceive equal musical intervals between pairs of pitches when the ratios of their frequencies are the same. The best example is the octave. The musical interval of an octave is associated with a frequency ratio of 2:1. Double the frequency of any pitch, and you get the pitch an octave above. Double it again, and the pitch is now two octaves higher than the original, while the frequency is four times as great. Just as 2:1 corresponds to the octave, a perfect fifth comprises (ideally) a frequency ratio of 3:2 between two tones; a major sixth is 5:3, and so forth. Any musical interval can be defined as a frequency ratio. The tunings chart in Appendix 2 gives ratios for all of the most important musical intervals.

TIMBRE AND OVERTONES

Most sounds in the real world are complex, and are comprised of vibrations of many frequencies. The ears do not generally hear a complex sound as a group of separate pitches at different frequencies, however, but as a single sound possessing a characteristic timbre, or tone color. That tone color results, in part, from the blend of frequencies present. In some cases the blend creates a sensation of pitchless noise. In other cases the ears and brain hear a multi-frequency sound as a single "note" or pitch, focusing on one frequency from among the many present as the defining tone.

Let's look at these phenomena more closely. We can start by describing several general vibration types.

No steady frequency present:

In some sounds no recurring pattern arises — just flurries of disordered air movement. The ear hears such unpatterned sound as unpitched noise. The noise may seem trebly or bassy, depending upon the general frequency trend. Maracas (shakers) provide one example of this sort of sound. Try shaking a maraca and humming back the note you've heard. You can't do it, because in that rush of shaker sound there is no steady, dominant frequency.

One steady frequency present:

In most natural sounds there are one or more recognizable steady frequencies present. Steady-state vibrations need not maintain the same frequency more than a tiny fraction of a second; the ear is very quick about recognizing them.

Where there is but one frequency present, the aural effect is a well-defined pitch and a timbral quality which is not unpleasant, but rather colorless. Sustained vibrations at a single pure frequency are hard to achieve by acoustic means, although some flutes or blown bottles may come fairly close. Sounds that are much closer to the one-frequency ideal can be produced electronically. Some of the beeps and boops of early electronic music are examples.

Several steady frequencies present:

If there are many frequencies present as components of a single sound from a single source, the listener usually does not get a sense of plurality, but hears the blend as a single tone having a particular timbre. The nature of that timbre depends in large part on the relationships between the frequencies within the tone. Here things become rather complex, and some key questions arise. Will the ear interpret the multi-frequency sound as having a defined pitch? What qualities in the timbral blend allow the ear to do so? And which factors determine what the perceived pitch will be? In answering these, we begin by defining some terms.

Sidebar 1-1

WAVE FORMS

Most sounds are blends of many different frequencies sounding simultaneously. It might be difficult to envision how this actually happens physically. One can easily picture a particle of air vibrating back and forth at a particular frequency, but how can a single particle vibrate at two or more frequencies simultaneously?

To express multiple frequency vibration, the particle engages in a complex movement which can be mathematically interpreted to be the sum of the several frequencies it is supposed to be manifesting. This mathematical interpretation may seem like an artificial contrivance. (Is the complicated dance the particle is performing really the same as vibrating at multiple specific frequencies?) But this interpretive model does correspond to the ear's subjective response. Presented with a complex vibratory motion that can be shown mathematically to represent the sum of several frequencies, the ear and brain do indeed hear those several frequencies.

To aid in the study of such motions, acousticians draw graphs, plotting the pattern of vibratory movement through time. Different types of vibration yield different graphic patterns, called wave forms. The wave form for a single, pure frequency is a wavy line of very regular and smooth curvature, known as a sine wave (because it matches a graph of the sine function in trigonometry). Sounds with strong harmonics show wave forms that are more angular, but still quite regular. More complex timbral blends, with non-harmonic frequencies or added noise components, have correspondingly more complex and irregular wave forms. With highly complex wave forms it becomes difficult for the ear and brain to recognize the recurring patterns and perceive the constituent frequencies. Sounds with complex wave forms are perceived as musically confusing, noisy, or dissonant.

In a sound with multiple frequencies present, the individual frequencies are called partials. The lowest of those frequencies can be called the fundamental. Additional frequencies arrayed above are overtones. Overtones fall into two important categories: harmonic and inharmonic. Harmonic overtones are those that have frequencies equaling some integral multiple of the fundamental frequency. This defines a series of harmonic overtones. For a fundamental frequencyƒ, the harmonic overtones have frequencies 2ƒ, 3ƒ, 4ƒ, 5ƒ... and so on indefinitely. That is the harmonic series (illustrated in Figure 1-3); and you will be hearing a lot about it before you finish this book. In their aural effect, harmonic overtones blend closely with the fundamental to create the feeling of a single tone. Inharmonic overtones (those whose frequencies are not multiples of the fundamental frequency) do not seem to blend as closely into the overall tone, giving the resulting composite timbre a spicier, edgier, or more dissonant quality.

And now, back to the question of perceived pitch in multi-frequency sounds. There are many possibilities here, and many factors at play. Here are some governing considerations:

Rule #1: In general, lower-frequency components play a greater role in establishing the perceived pitch of a tone, while higher-frequency components contribute more to its coloration. Most commonly, the lowest frequency present, the fundamental, establishes the pitch.

Rule #2: Harmonic overtones lead to a well defined pitch sense. To whatever extent the overtone frequencies can be construed as falling into the harmonic pattern, the tone will sound coherent, full, and well defined in pitch. Familiar instruments having harmonic overtones include most string instruments and the standard woodwinds and brass. The perceived effect of the composite tone quality depends in part upon which harmonics are most prominent: where the higher harmonics predominate, the tone will be brighter, as with a harpsichord; where higher harmonics are subdued, the tone will be rounder, as with a nylon string guitar.

Rule #3: In tones possessing multiple inharmonic frequency components, the perceived results are quite variable. They depend on the relative prominence of the different components, the pitch relationships between them, and the degree of crowding in different parts of the spectrum. In such cases, the ear sometimes succeeds in picking out the fundamental as the defining pitch, but hears it as part of a peculiar timbre. Sometimes the ear tracks another tone as the defining pitch. Sometimes the ear doesn't focus on any one tone as the defining pitch, and the sound is perceived as pitchless. Figure 1-2 provides examples.

Tuned carillon bells (such as the sets used in church towers) provide a wonderful example of an instrument possessing prominent frequencies not arranged harmonically, but still interpretable to the ear as having a single defined pitch. The tone is highly distinctive — nothing else sounds like cathedral bells — and it is one that many people find enchanting. It also can be musically confusing, in that the ear may occasionally take track the wrong overtone as the defining pitch. When you have an opportunity, try listening closely to the tone of a set of big bells, mentally isolating the pitches present, making note of their relationships, and — this is an important part of the perception of the tone — observing which overtones sustain longest, and which die out quickly.

Many "pitchless" percussion instruments are better described as having ambiguous pitch. This includes most drums, some cymbals, cowbells, triangles, and so on. With a little concentration, a listener can often pick out one or more pitches in such sounds, and these pitches, even if one tries to ignore it, take on meaning in musical contexts. In addition, it is surprising just how many everyday sounds have at least some component of identifiable pitch. To test this, try knocking, banging, squeaking, and scraping everything in a room, listening as you go for pitch among the noise. Give each item a couple of tries: sometimes the definite pitch components are elusive, but you might be surprised at how often you find them.

In the ambiguous territory between clear pitch and pure noise, a great many disorienting effects occur. There can be iridescent tones, which seem to shift pitch depending upon musical context or a change in one's perceptual predisposition. There can be tones which seem to have pitch in one musical context but degenerate into pitchless jangle in another. There can be tones for which two people disagree as to what their pitch really is. There can be tones which seem to have pitch, but which have so much pitchless noise mixed in that the resulting timbre is bizarre. There can be tones in which the components blend seamlessly, and tones in which several pitches retain a degree of individuality, sounding gong-like or even chordal. And there can be anything in betwe...

Table of contents

• Cover
• Title Page
• Copyright
• Acknowledgments
• Introduction
• Preface
• Chapter One: Musical Sound Perception
• Chapter Two: Acoustic Principles
• Chapter Three: Tuning Systems and Pitch Layouts
• Chapter Four: Idiophones
• Chapter Five: Beaters, Scrapers, & Friction Makers
• Chapter Six: Aerophones
• Chapter Seven: Membranophones
• Chapter Eight: Resonators and Radiators
• Chapter Nine: Chordophones
• Chapter Ten: Special Effects
• Chapter Eleven: A Few More Thoughts
• Appendix One: Tools and Materials
• Appendix Two: Frequency and Tunings Charts
• Appendix Three: Amplification, Microphones and Transducers
• Appendix Four: More on Air Columns, Toneholes and Woodwind Keying Mechanisms
• Glossary
• Bibliography
• Index
• Back Cover