To view the microacoustical domain is to confront a scienti®c dilemma that has confounded physicists for centuries: the wave versus the particle nature of signal energy. Debates concerning electromagnetic signals (such as light) have motivated most scienti®c inquiries. But much of what has been discovered about these signals applies to soundÐthe domain of mechanoacoustic vibrations as well. We will brie¯y look at the debate in both domains, optics and acoustics.
Table 2.1 Electric and electronic musical instruments: 1899±1950
Instrument
Date of demon-
stration Inventor Notes
Singing Arc 1899 W. Duddell Early electric keyboard instrument
Choralcello Electric
Organ 1903 Farrington,C. Donahue, and
A. Ho¨man
Electromagnetic instrument
Telharmonium 1906 T. Cahill Rotating tone generators, massive synthesizer
Audio oscillator and
Audion Piano 1915 L. De Forest First vacuum-tube instrument
Synthetic Tone Musical
Instrument 1918 S. Cabot Rotating tone wheels to generate current, thecurrent drove metallic resonating bars
Thereminovox 1920 L. Theremin Antenna instrument played with hands in air;
based on heterodyne tone generator
Electrophon 1921 J. Mager Heterodyne tone generator with ®lter
Staccatone 1923 H. Gernsback Sharp attack, inductance-controlled keyboard
instrument
Sphaerophon 1926 J. Mager Improved Electrophon with keyboard
Electronic Harmonium 1926 L. Theremin and
?. Rzhevkin 1200 divisions per octave, designed for studiesin melody and harmony
Pianorad 1926 H. Gernsback Polyphonic, based on vacuum-tube oscillators
Violen c. 1926 W. Gurov and
?. Volynken
Light Siren c. 1926 Kovakenko Rotating optical disks and photocell detectors
Illuminovox 1926 L. Theremin Electro-optical projector with rotating disc
SuperPiano 1927 E. Spielmann ``Light-chopper'' instrument
Electric guitar
prototype 1927 Les Paul Solid body construction with electromagneticpickups
Electronic Violin 1927 E. Zitzmann-Zirini Space control of pitch like the Theremin, but switched control of volume
Spielman Electric Piano
Harp 1928 J. Bethenod Microphone and speaker feedback to sustainoscillations
Ondes Martenot 1928 M. Martenot First of many versions
Dynaphon 1928 R. Bertrand Multivibrator oscllator
Hellertion 1929 B. Helberger and
P. Lertes Vacuum-tube oscillator with feedback,continuous linear controllers
Crea-tone 1930 S. Cooper Electric piano with feedback circuits for
sustain Givelet-Coupleaux
Table 2.1 (continued)
Instrument
Date of demon-
stration Inventor Notes
Trautonium 1930 F. Trautwein Neon-tube sawtooth tone generators,
resonance ®lters to emphasize formants Magnetoelectric organ 1930 R. H. Ranger
Westinghouse organ 1930 R. Hitchcock Research instrument based on vacuum tube
oscillators
Ondium Pechadre 1930 ? Theremin-like instrument with a volume key
instead of antenna Hardy-Goldwaithe
organ 1930 A. Hardy andS. Brown Electro-optical tone generators
Neo-Bechstein piano 1931 W. Nernst Physics Institute, Berlin, piano with electrical pickups instead of soundboard
Radiopiano 1931 Hiller Ampli®ed piano
Trillion-tone Organ 1931 A. Lesti and
F. Sammis Electro-optical tone generators
Radiotone 1931 Boreau String-induced radio-receiver tone generator
with ®lter circuits
Rangertone Organ 1931 R. Ranger Rotating tone wheels
Emicon 1932 N. Langer and
Hahnagyi Gas-discharge tube oscillator, controlled bykeyboard
Gnome 1932 I. Eremeef Rotating electromagnetic tone wheels
Miessner Electronic
Piano 1932 B. F. Miessner 88 electrostatic pickups
Rhythmicon 1932 H. Cowell,
L. Theremin, B. Miessner
Complex rhythm machine with keyboard
Mellertion 1933 ? 10-division octave
Electronde 1933 L. or M.
Taubman Battery-powered, space control of pitch likethe Theremin, with volume pedal
Cellulophone 1933 P. Toulon Electro-optical tone generators
Elektroakustische Orgel 1934 O. Vierling and
Kock 12 vacuum-tube master oscillators, otherpitches derived by frequency division
La Croix Sonore 1934 N. Oboukhov Heterodyning oscillator
Ethonium 1934 G. Blake Emulation of the Theremin heterodyne
oscillator
Keyboard Theremin 1934 L. Theremin Bank of tone generators controlled by
traditional organ keyboard
Table 2.1 (continued)
Instrument
Date of demon-
stration Inventor Notes
Polytone 1934 A. Lesti and
F. Sammis Electro-optical tone generators
Syntronic Organ 1934 I. Eremeef and
L. Stokowski Electro-optical tone generators; one-hour ofcontinuous variation
Everett Orgatron 1934 F. Hoschke and
B. Miessner Ampli®ed vibrating brass reeds
Partiturphon 1935 J. Mager Five-voice Sphaerophon with three keyboards
Hammond electric
organ 1935 L. Hammond andB. Miessner Rotating tone generators
Photona 1935 I. Eremeef 12 electro-optical tone generators, developed
at WCAU radio, Philadelphia
Variophone 1935 Y. Sholpo Photo-electric instrument in which the
musician draws the sound on sprocketed ®lm
Electrone 1935 Compton Organ
Company Based on design of L. Bourn; electrostaticrotary generators
Foerster Electrochord 1936 O. Vierling Electromechanical piano
SonotheÁque 1936 L. LavaleÂe Coded performance instrument using
photoelectric translation of engraved grooves Kraft-durch-Freude
Grosstonorgel 1936 O. Vierling andsta¨ of Heinrich- Hertz-Institut, Berlin
Played at 1936 Olympic games
Welte Light-Tone organ 1936 E. Welte Electro-optical tone generators
National Dobro VioLectric Violin and Supro Guitar
1936 J. Dopyera Commercial instruments with electromagnetic pickups
Electric Hawaiian
guitar 1936 L. Fender Commercial instrument with electromagneticpickups
Singing Keyboard 1936 F. Sammis Played electro-optical recordings, precursor
of samplers
Warbo Formant organ 1937 H. Bode and
C. Warnke Four-voice polyphonic, envelope shaping, keyassignment, two ®lters
Oscillion 1937 W. Swann and
W. Danforth Gas-discharge tube oscillator
Krakauer Electone 1938 B. F. Miessner Early electric piano
Melodium 1938 H. Bode Touch-sensitive solo keyboard
Table 2.1 (continued)
Instrument
Date of demon-
stration Inventor Notes
Sonor c. 1939 ?. Ananyev Moscow, ribbon controller on a horizontal
®ngerboard; violin-like sound
Kaleidaphon 1939 J. Mager ``Kaleidoscopic'' tone mixtures
Allen organ 1939 Jerome Markowitz Vacuum-tube oscillators
Neo Bechstein piano 1939 O. Vierling and
W. Nernst First commercial version of the electric piano
Ampli®ed piano 1939 B. Miessner Variable tonal quality depending on the
position of the pickups
Novachord 1939 Hammond
Company Several tube oscillators, divide-downsynthesis, formant ®lters Parallel Bandpass
Vocoder 1939 H. Dudley, BellLaboratories Analysis and cross-synthesis
Dynatone 1939 B. Miessner,
A. Amsley Electric piano
Voder speech
synthesizer 1939 H. Dudley Voice model played by a human operator
Violena 1940 W. Gurov
Emiriton 1940 A. Ivanov and A.
Rimsky-Korsakov Neon-tube oscillators
Ekvodin 1940 A. Volodin,
Russia
V-8 c. 1940 A. Volodin,
Russia
Solovox 1940 L. Hammond Monophonic vacuum-tube oscillator with
divide-down circuitry
Univox c. 1940 Univox Company Vacuum-tube sawtooth generator with diode
waveform shaper circuit
Multimonika 1940 Hohner GmbH Lower manual is wind-blown, upper manual
has sawtooth generator
Ondioline 1941 Georges Jenny Multistable vibrator and ®lters, keyboard
mounted on springs for vibrato
Melotone c. 1944 Compton Organ
Company Electrostatic rotary generators Hanert Electrical
Orchestra 1945 J. Hanert Programmable performance controlled bypunched paper cards
Joergensen Clavioline 1947 M. Constant
Martin Monophonic, three-octave keyboard
What is a wave? In acoustics it is de®ned as a disturbance (wavefront) that propagates continuously through a medium or through space. A wave oscilla- tion moves away from a source and transports no signi®cant amount of matter over large distances of propagation.
Optical Wave versus Particle Debate
The wave±particle debate in optics began in the early eighteenth century, when Isaac Newton, in his Opticks (published in 1704), described light as a stream of particles, partly because ``it travels in a straight line.'' Through experiments with color phenomena in glass plates he also recognized the necessity of ascrib-
Table 2.1 (continued)
Instrument
Date of demon-
stration Inventor Notes
Wurlitzer electronic
organ 1947 WurlitzerCompany Based on the Orgatron reed design, latermodi®ed according to B. Miessner's patents
Conn Organ 1947 Conn Organ
Company Individual oscillators for each key Electronic Sackbut 1948 Hugh LeCaine Voltage-controlled synthesizer, pitch,
waveform, and formant controllers
Free Music Machine 1948 B. Cross and
P. Grainger Electronic oscillators and continuousautomated control
Mixturtrautonium 1949 O. Sala Trautonium with noise generator, ``circuit-
breaker'' sequencer, frequency dividers
Heliophon 1949 B. Helberger
Mastersonic organ 1949 J. Goodell and
E. Swedien Rotating pitch wheels
Connsonata 1949 Conn Organ
Company Oscillators designed by E. L. Kent
Melochord 1947±9 H. Bode Later installed at North West German Radio,
Cologne
Bel Organ c. 1947 Bendix Electronics 12 vacuum-tube oscillators, other pitches obtained by divide-down circuit
Elektronium Pi 1950 Hohner GmbH Monophonic vacuum-tube oscillator with
divide-down circuitry
Radareed organ 1950 G. Gubbins Ampli®ed reeds ®tted with resonators
Dereux organ c. 1950 SocieÂte Dereux Electrostatic rotary generators, waveforms derived from oscillogram photographs
ing certain wavelike properties to light beams. Newton was careful not to speculate further, however, and the corpuscular or particle theory of light held sway for a century (de Broglie 1945; Elmore and Heald 1969).
A competing wave theory began to emerge shortly afterward with the experiments in re¯ection and refraction of Christian Huygens, who also per- formed experiments on the wave nature of acoustical signals. The early nine- teenth century experiments of Thomas Young reinforced the wave view. Young observed that a monochromatic beam of light passing through two pinholes would set up an interference pattern resembling ``waves of water,'' with their characteristic patterns of reinforcement and cancellation at points of intersec- tion, depending on their phase. Experiments by Augustin Fresnel and others seemed to con®rm this point of view. The theory of electromagnetic energy proposed by the Scottish physicist James Clerk Maxwell (1831±1879) described light as a wave variation in the electromagnetic ®eld surrounding a charged particle. The oscillations of the particle caused the variations in this ®eld.
Physicists resolved the optical wave±particle controversy in the ®rst two decades of the twentieth century. This entailed a uni®ed view of matter and electromagnetic energy as manifestations of the same phenomena, but with di¨erent masses. The wave properties of polarization and interference, demon- strated by light, are also exhibited by the atomic constituents of matter, such as electrons. Conversely, light, in its interaction with matter, behaves as though composed of many individual units (called photons), which exhibit properties usually associated with particles, such as energy and momentum.
Acoustical Wave versus Particle Debate
What Atomes make Change
Tis severall Figur'd Atomes that make Change, When severall Bodies meet as they do range. For if they sympathise, and do agree, They joyne together, as one Body bee. But if they joyne like to a Rabble-rout, Without all order running in and out; Then disproportionable things they make, Because they did not their right places take. (Margaret Cavendish 1653)
The idea that a continuous tone could be decomposed into smaller quantities of time emerges from ancient atomistic philosophies. The statement that all matter is composed of indivisible particles called atoms can be traced to the ancient
city of Abdera, on the seacoast of Thrace. Here, in the latter part of the ®fth century BC, Leucippus and Democritus taught that all matter consists only of atoms and empty space. These Greek philosophers are the joint founders of atomic theory. In their opinion, atoms were imperceptible, individual particles di¨ering only in shape and position. The combination of these particles causes the world we experience. They speculated that any substance, when divided into smaller and smaller pieces, would eventually reach a point where it could no longer be divided. This was the atom.
Another atomist, Epicurus (341±270 BC), founded a school in Athens in 306 BC and taught his doctrines to a devoted body of followers. Later, the Roman Lucretius (55) wrote De Rerum Natura (On the Nature of the Universe) de- lineating the Epicurean philosophy. In Book II of this text, Lucretius charac- terized the universe as a fortuitous aggregation of atoms moving in the void. He insisted that the soul is not a distinct, immaterial entity but a chance com- bination of atoms that does not survive the body. He further postulated that earthly phenomena are the result of purely natural causes. In his view, the world is not directed by divine agency; therefore fear of the supernatural is without reasonable foundation. Lucretius did not deny the existence of gods, but he saw them as having no impact upon the a¨airs of mortals (Cohen 1984, p. 177).
The atomistic philosophy was comprehensive: both matter and energy (such as sound) were composed of tiny particles.
Roughness in the voice comes from roughness in its primary particles, and likewise smooth- ness is begotten of their smoothness. (Lucretius 55, Book IV, verse 524)
At the dawn of early modern science in the seventeenth century, the French natural philosophers Pierre Gassendi (1592±1655) and Rene Descartes (1596± 1650) revived atomism. Descartes' theory of matter was based on particles and their motion. Gassendi (1658) based his system on atoms and the void. The particles within these two systems have various shapes, weights, or other qual- ities that distinguish them. From 1625 until his death, Gassendi occupied him- self with the promulgation of the philosophy of Epicurus.
During the same period, the science of acoustics began to take shape in western Europe. A con¯uence of intellectual energy, emanating from Descartes, Galileo, Beekman, Mersenne, Gassendi, Boyle, and others, gradually forced a paradigm shift away from the Aristotelian worldview toward a more experi- mental perspective. It is remarkable how connected was this shift in scienti®c thinking to the analysis of musical sound (Coelho 1992). Problems in musical
acoustics motivated experiments that were important to the development of modern science.
The Dutch scholar Isaac Beekman (1588±1637) proposed in 1616 a ``cor- puscular'' theory of sound. Beekman believed that any vibrating object, such as a string, cuts the surrounding air into spherical particles of air that the vibra- tions project in all directions. When these particles impinge on the eardrum, we perceive sound.
The very same air that is directly touched and a¨ected by a hard thing is violently shocked and dispersed [by a vibrating object] and scattered particle-wise everywhere, so that the air itself that had received the impulse strikes our ear, in the way that a candle ¯ame spreads itself through space and is called light. (Cohen 1984)
In Beekman's theory, the particles emitted by a vibrating string derive their velocity from the force with which the string hits them. Every particle ¯ies o¨ on its own, is homogeneous, and represents in its particular shape and size the properties of the resulting sound. If a particle does not hit the ear, it ®nally comes to rest, according to the laws of projectile motion, and is then reinte- grated into the surrounding air. Beekman ascribed di¨erences in timbre to variations in the size, shape, speed, and density of sound particles. Gassendi also argued that sound is the result of a stream of particles emitted by a sounding body. The velocity of sound is the speed of the particles, and fre- quency is the number of particles emitted per unit time.
Almost two centuries later, in 1808, an English school teacher, John Dalton (1766±1844), formulated an atomic theory of matter. Unlike the speculations of Beekman and Gassendi, Dalton based his theory on experimental evidence (Kargon 1966). Dalton stated that all matter is composed of extremely small atoms that cannot be subdivided, created, or destroyed. He further stated that all atoms of the same element are identical in mass, size, and chemical and physical properties, and that the properties of the atom of one element, di¨er from those of another. What di¨erentiates elements from one another, of course, are their constituent particles. Eighty-nine years after Dalton, the ®rst elementary particleÐthe electronÐwas discovered by another Englishman, J. J. Thomson (Weinberg 1983).
As the particle theory of matter emerged, however, the particle theory of sound was opposed by increasing evidence. The idea of sound as a wave phenomenon grew out of ancient observations of water waves. That sound may exhibit analogous behavior was emphasized by a number of Greek and Roman philosophers and engineers, including Chrysippus (c. 240 BC), Vetruvius
(c. 25 BC), and Boethius (480±524). The wave interpretation was also consis- tent with Aristotle's (384±322 BC) statement to the e¨ect that air motion is generated by a source, ``thrusting forward in like manner the adjoining air, so that the sound travels unaltered in quality as far as the disturbance of the air manages to reach.''
By the mid-1600s, evidence had begun to accumulate in favor of the wave hypothesis. Robert Boyle's classic experiment in 1640 on the sound radiation of a ticking watch in a partially evacuated glass vessel gave proof that the medium of air was necessary for the production or transmission of audible sound.
Experiments showed the relation between the frequency of air motion and the frequency of a vibrating string (Pierce 1994). Galileo Galilei's book Mathe- matical Discourses Concerning Two New Sciences, published in 1638, con- tained the clearest statement given until then of frequency equivalence, and, on the basis of accumulated experimental evidence, Rene Descartes rejected Beekman's corpuscular theory of sound (Cohen 1984, p. 166).
Marin Mersenne's description in his Harmonie Universelle (1636) of the ®rst absolute determination of the frequency of an audible tone (at 84 Hz) implies that he had already demonstrated that the absolute-frequency ratio of two vibrating strings, radiating a musical tone and its octave, is as 1:2. The per- ceived harmony (consonance) of two such notes could be explained if the ratio of the air oscillation frequencies is also 1:2, which is consistent with the wave theory of sound.
Thus, a continuous tone could be decomposed into small time intervals, but these intervals would correspond to the periods of a waveform, rather than to the rate of ¯ow of sonic particles.
The analogy with water waves was strengthened by the belief that air mo- tion associated with musical sounds is oscillatory and by the observation that sound travels with a ®nite speed. Another matter of common knowledge was that sound bends around corners, suggesting di¨raction, also observed in water waves (®gure 2.1). Sound di¨raction occurs because variations in air pressure cannot go abruptly to zero after passing the edge of an object. They bend, in- stead, into a shadow zone in which part of the propagating wave changes di- rection and loses energy. This is the di¨racted signal. The degree of di¨raction depends on the wavelength (short wavelengths di¨ract less), again con®rming the wave view.
While the atomic theory of matter became the accepted viewpoint in the nineteenth century, the wave theory of sound took precedence. New particle- based acoustic theories were regarded as oddities (Gardner 1957).
Waves versus Particles: a Contemporary Perspective
The wave theory of sound dominated the science of acoustics until 1907, when Albert Einstein predicted that ultrasonic vibration could occur on the quantum level of atomic structure, leading to the concept of acoustical quanta or phonons. Einstein's theory of phonons was ®nally veri®ed in 1913.
In his own way, the visionary composer Edgard VareÁse recognized the sig- ni®cance of this discovery:
Every tone is a complex entity made up of elements ordered in various ways . . . In other words, every tone is a molecule of music, and as such can be dissociated into component sonal atoms. . . . [These] may be shown to be but waves of the all-pervading sonal energy radiating throughout the universe, like the recently discovered cosmic rays which Dr. Mil- liken calls, interestingly enough, the birth cries of the simple elements: helium, oxygen, silicon, and iron. (VareÁse 1940)
The scienti®c development of acoustical quantum theory in the domain of audible sounds was left to the physicist Dennis Gabor (1946, 1947, 1952). Gabor proposed that all sound could be decomposed into a family of functions
Figure 2.1 Zones of audition with respect to a sound ray and a corner. Listeners in zone A hear the direct sound and also the sound re¯ected on the wall. Those in zone B hear a combination of direct, re¯ected, and di¨racted sound. In zone C they hear a combination of direct and di¨racted sound. Listeners in zone D hear only di¨racted sound (after Pierce 1994).
obtained by time and frequency shifts of a single Gaussian particle. Gabor's pioneering ideas have deeply a¨ected signal processing and sound synthesis. (See chapters 3 and 6.) Later in this chapter, we present the basic idea of the Gabor matrix, which divides time and frequency according to a grid.
Today we would say that the wave and particle theories of sound are not opposed. Rather, they re¯ect complementary points of view. In matter, such as water, waves move on a macro scale, but water is composed of molecules