Thunder let loose upon the Void. The Voice of God. And trillions of years later we are still rocking with the waves of that Big Bang. For everything is still vibrating and all is vibration, and in its broadest sense all vibration is a kind of "sound" whose primacy has been recognized by virtually every culture, including the Judeo-Christian heritage: "In the beginning was the Word, and the Word was God..." The identification of the Word, which had to be articulated through sound, with deity, the creative and sustaining spirit of God... For other cultures, the primacy of sound as a basis for existence has been even more emphatic. Marius Schneider, in an article on "Primitive Music" in The New Oxford History of Music, affirms that "sound represents the original substance of the world" as far as the historian of culture is concerned, and points out that the (East) Indian tradition emphasizes the "luminous nature of sound" in the similarity between svar (light) and svara (sound). [quoted in McClain, Ernest G., The Myth of Invariance, p.7] India's oldest sacred book, the Rg Veda, not only posits sound as the "original substance of the world," but as discussed in a study of the philosophical methodology of the Rg Veda by Antonio de Nicolas [Four-Dimensional Man], the meanings of existence derived by our sensorium, the whole sensory apparatus of the body, are organized primarily on a model of sound. "Rgvedic man (sic) was enveloped by sound, looked for centers of experience in the experience of sound, found the model of complete, absolute instantaneity and communication in sound." [McClain, ibid, p.2] These same ideas, in different guises, can be found in the sacred texts and mythologies of Babylon, Egypt, Greece and Palestine, in the Egyptian Book of the Dead, the Bible, and Plato [ibid., p.xi], particularly as sound tuning systems and music are defined by number, by mathematical relationships. And while, for most people in the present day in Western culture, sound has lost this primacy of meaning, there still occur discussions drawing us back to this fundamental level, as in the scientist/inventor Itzhak Bentov's book Stalking the Wild Pendulum: On the Mechanics of Conciousness, in which it is speculated that the "orderly pattern of atoms in matter" may be "the result of the interaction of some kind of 'sound waves' in matter." [p.11] He further says that "we could actually associate our whole reality with sound of one kind or another because our reality is a vibratory reality, and there is nothing static in it. Starting with the nucleus of an atom, which vibrates at enormous rates, the electrons and the molecules are all associated with characteristic vibratory rates. A most important aspect of matter is vibratory energy." And continuing: "When we think, our brains produce rhythmic electric currents. With their magnetic components, they spread out into space at the velocity of light, as do the electric waves or sounds produced by our hearts. They all mingle to form enormous interference patterns, spreading out and away from the planet. "They are admittedly weak, but they are there. The more finely our systems are tuned, the clearer a signal we can pick out of the general noise and jumble of 'sounds.' "Our planet itself is producing shock waves in the plasma that fills the solar system. These shock waves interact with those caused by other planets and produce resonances between the planets and the asteroids. In short, our whole reality is based on one common factor, and that is periodic change, or sound." [p.23] It is in the context of the underlying significance of sound that I wish for us to place our study of all aspects of sound's emanations, from acoustics to the structure of a symphony or a pop tune. In our most common understanding of sound as an auditory phenomenon, sound is, as has been stated, a vibration. But no simple vibration, this, for oscillographic analyses of a "large number of musical, linguistic, and environmental sounds...reveal a previously unrecognized sonic substructure of immense detail that directly determines the nature of perceived sound." [Cogan, Robert and Escot, Pozzi, Sonic Design, p.439] COMPONENTS OF SOUND In order for sound to exist, as we know it, at least three mutually-supportive components are necessary. First, something which vibrates, called the sound source. Second, a medium through which the vibrations travel from the sound source to the third element, a receptor capable of responding to the vibrations and interpreting their significance. SOURCE: David Reck, in Music of the Whole Earth, says that "there are a limited number of ways that sound can be produced, and it is unmute testimony to the imagination of man that he has discovered most of them and has used them with astounding variety." [p.61] He lists the basic ways a sound source may be set into vibration along with examples of musical instruments from various cultures that use these methods: "A solid object may be hit (like a log drum), scraped (like a comb), whirled through the air (like a bull- roarer), shaken (like a rattle), plucked (like the metal prongs of an mbira), or rubbed (like a glass harmonica...). A stretched skin may be beaten, rubbed, or scraped (as in the drums of the world); or stretched strings may be made to vibrate by plucking them (like a guitar), by the friction of a bow or stick rubbed across them (like a fiddle), or by striking them (like a hammer dulcimer). Reeds set in an enclosed chamber with air forced across or through them (by breath, bellows, or bag) will vibrate into sound (like a harmonica, oboe, or bagpipe), as will breath (or air) split across the edge of a hole and into an enclosed space (like blowing across the top of a bottle or a flute). Air buzzed through the tightened lips into a tube also causes sound vibrations (like trumpets, horns, trombones). And finally, sound can be produced by electronic means." MEDIUM: The medium through which vibrations are normally carried to our ears is, of course, air. We know, however, of other materials through which vibrations may be propagated: wood, metal,water.... any substance other than a vacuum. Water, in fact, is a far better medium than air for transmitting vibrations. Whales can hear their amazing "songs" over distances of hundreds of miles because of this. [SONIC ACTIVITY #1: Tie the two ends of an arm's length of thread to the bottom sides of a common wire coat hanger. Wrap the thread around index fingers a couple times, leaving enough space between hands to fit around head. Stick index fingers in ears, lean over to allow hanger to be suspended, and swing hanger to strike against any solid object, a desk, for instance. Listen carefully. {A student in one of my classes once called this activity "ridiculous." Aside from this failing, by thus labeling the activity, to hear how incredible this sound actually is, he demon- strated a deeper ignorance of the processes by which discoveries are made. The mind at play, often even in seemingly "ridiculous" or "silly" activities, is in, or borders on, that mode of receptivity to experience in which previously unnoticed things may be noticed, and more importantly, in which disparate "facts" may be drawn together to arrive at unique and creative syntheses.}] RECEPTOR: A receptor is properly called a transducer, which is a device for converting one form of energy to another. The chief receptor by which we perceive sound is the ear. The ear converts acoustic energy, the vibrations of air molecules, into electro-chemical impulses which the brain in turn converts into sonic sense. A microphone is another example of a sound receptor or transducer. It functions similarly to the ear, only its electrical impulses are directed to some other electronic processing device, like a tape recorder or an amplifier. Each one of these components, the sound source, the medium, and the mechanism of the human ear, would provide fit study for a complete book, but for the moment we want to take a closer look at the sound source, the origin of the vibrations we eventually "hear." VIBRATION By vibration is meant some kind of back and forth motion (oscil- lation). In order to vibrate, the sound source must be, as it is known in the jargon of acoustics, an "elastic body." A good and obvious example of an elastic body is a stretched rubber band. [SONIC ACTIVITY #2: Try the index-finger-in-the ear trick with a rubber band, for yet another amazing sound. (See p.8)] To set the rubber band into vibration, it must be displaced from its position of rest--usually by pulling it or plucking it. Being elastic (and here don't confuse the word elastic only with material like rubber--anything is "elastic" that returns to its original state after being "disturbed" or displaced), when released from displacement, its molecules seek to return to their original place of "rest." But since a certain amount of energy has been invested in its displacement, it is carried by the force of momentum, a carrier of that initial energy investment, beyond its original point of rest until the strictures of its molecular structure balance the momentum and pull it back toward the original position. The rubber band thus vibrates back and forth until the forces of molecular cohesion and friction have complete- ly absorbed the original energy, converting it into heat and sound. When the rubber band is displaced and released, as it makes its first vigorous snap back in the direction of rest, it pushes the air molecules surrounding it in the direction of its movement, disturbing them, pushing them in fact, to- gether, compacting them, making what is called a condensation. At the same time, the air molecules behind the rubber band are dragged along with it, thus spreading them out, causing a rarefaction. These disturbances in the air occur with every back-and-forth motion of the rubber band, creating a series of con- densations and rarefactions which are transmitted in all directions around the rubber band as molecules of air knock together and pull apart, creating waves of air. Thus a series of pressure waves is created in the air which causes our eardrums to vibrate in response, and hence, sound. FREQUENCY We know that if we stretch the rubber band tauter, we'll hear a different sound, which we describe as "higher," although this is purely a metaphorical term. What we have just done is to make the molecules of the rubber band seek their original point of rest with greater intensity, causing the rubber band to vibrate faster. Frequency is the technical term for rate of vibration. We subjectively perceive the frequency as pitch, the "highness" or "lowness" of a sound. Frequency is measured by the number of times something vibrates back and forth per some given time unit, which, when measuring acoustic vibrations, is the second. The proper designation for the frequency of a sound is cycles per second (abbrviated c.p.s) or hz (pronounced Hertz, named for a 19th century physicist who studied the nature of vibration). A cycle is one complete "trip" of the vibration. This can be illustrated by observing the action of a swinging pendulum. The cyclic motion is usually measured in terms of movement from the state of rest to maximum point of displacement, back through the resting point to maximum point of displacement on the opposite side, and back to the resting point. Actually, one may start from any point and measure to the analogous point in the cycle, and this is done in examining the phase of one vibration in relation to another. If a pen were to be attached to the bottom of the pendulum and a roll of paper moved from right to left underneath the pen, a picture of the pendulum's motion could be drawn. If the distance between the starting line and ending line were to represent one second, then the frequency here is 1 c.p.s., or 1 Hz. If the distance between the starting line and ending line were to represent one second, then the frequency here is 2 c.p.s., or 2 Hz. The human ear responds to acoustic frequencies within the general range of 20 Hz to 20,000 Hz (sometimes abbreviated 20K Hz). Some people can hear somewhat beyond these ranges, and other animals are capable of much wider response, which signifies that human perception of reality is actually very limited. You can now enter frequencies at the prompt to test your hearing, as well as the frequency response of your computer. Hit 'E' to enter. THE OCTAVE [ to hear sound discussed below, any key to stop ] The sound you are hearing as you read this is a sweep of frequencies from 20 Hz to 4K Hz and back down to the lowest frequency on a standard piano (whose frequency you will be asked to calculate in a minute). Then the frequency jumps by octaves up to 440 Hz, which, since the 1920's has been used as the international tuning standard. The distance from one frequency to another can be expressed as a ratio. When we hear one frequency in relation to another, their difference (or ratio) produces a perceived difference in pitch, which is called a musical interval. The term octave refers to what is perhaps the most important musical interval, which is a ratio between two frequencies of 2:1. The word octave is derived from the fact that most common tunes in Western music employ 7 different pitches (labeled A,B,C,D,E,F,G), within the frequency ratio of 2:1. The eighth pitch (thus octave) is the same letter name (in this case "A") at a frequency ratio of 2:1. This ratio is possibly the only universally common interval, forming the basis for the world's diverse tuning systems. Since we'll be referring to the octave again and again, a thorough understanding of this interval is important. Here are a series of octaves, with their frequencies given. Note that octaves have a similarity of sound. They are just "higher" or "lower". They all form 2:1 ratios. OCTAVE PRACTICE AND PROBLEMS 1 & 2 You may again enter frequencies as you did on page 16. This time focus on listening to frequencies with rations of 2:1. ['E' TO ENTER, '+' FOR NEXT PAGE, '-' FOR PRIOR. HIT 'R' TO GOTO TO PROBLEM #1]. ENTER FREQUENCY (no commas): EQUAL TEMPERAMENT [ to hear sound mentioned below ] As you read this sentence, the 7 basic pitches deployed within the octave, which are common to Western music, are being sounded. You have no doubt heard this scale before, and its particular pattern will be described in greater detail later. An incredible variety of music has been produced using only these pitches, but by adding just a few more the possibilities for pitch combinations increase geometrically. 5 additional pitches are common to Western music. A tuning of pitches within an octave has been developed which is called equal temperament. A temperament is another name for a way of relating one pitch to another within an octave. Any equal temperament is a tuning in which an octave is divided into equal increments. The temperament of Western European music, which was only codified within the past 300 years, divides the octave into 12 equal parts. To hear these 12 increments, hit 'H'. What you have just heard is a pattern of intervals, each one of which is called a half step. Whereas the frequency ratio of the octave is 2:1, the ratio of a half step is much smaller. It can be calculated as the 12th root of 2, which results in an irrational number (1.0594531...). The starting frequency of the series just sounded was 220 Hz. Each successive pitch was arrived at by multiplying the previous pitch by this small amount. If you consider that our hearing range is from 20 to 20K Hz, and that this represents a little over 10 octaves, you can calculate that 12-tone equal temperament makes available somewhat more than 120 distinctly different frequencies. It has been calculated that "...the total of perceptible pitches...within our hearing range...is about 1400..." [Cogan & Escott,p.442] We therefore are capable of hearing many more pitches than we are used to hearing in the music we are familiar with. Many cultures other than our own employ much finer gradations of pitch difference. This is true especially in the Orient, India, and Southeast Asia. At least from the time of Pythagorus, scientists and musicians have experimented with many tuning systems. We will hear later on some of the music of Harry Partch, a composer in our own century who used a tuning which employed up to 43 increments within an octave. Just within the past year, the latest synthesizers (including the "industry standard" Yamaha DX7II) have added the feature of alternative tuning systems, so you will no doubt be hearing more music containing smaller divisions of the octave. You can now experiment with hearing varying divisions of the octave. The standard way of dealing with small pitch differences is to divide up the half step into 100 parts, each one of which is called a cent. At the prompt, you can enter the number of cents, from 1 to 100, you wish to hear as the smallest frequency change. [ 'E' TO ENTER, . TO HEAR 1ST TIME, ALT/P TO HEAR AGAIN. ENTER AS MANY TIMES AS YOU WANT WITH 'E'- SEQUENCE. ] Frequency changes, along with varying lengths of tones, are the basis for melody, which is the foundation of Western music. One final issue regarding frequency before moving on: A musical tone may be properly conceived of as vibration which is periodic, that is, whose frequencies are consistent. If fluctuation of frequency is very rapid, the vibration is aperiodic and results in noise. Noise is technically defined as erratic, intermittent, or statistically random oscillation. For an example, hit . AMPLITUDE The amount of energy invested into setting the vibrating source into oscillation determines how loud a sound is. Loudness is how we subjectively perceive amplitude. The farther something is displaced from its resting state, the greater is the amplitude. Whereas frequency is represented along the horizontal axis , as we saw with the representation of a pendulum's swing, amplitude is measured along the vertical axis. The farther out the swing, the greater the displacement, thus the louder the sound. Another term used to describe loudness is intensity. The common meas- urement of intensity is the decibel. The decibel is a logarithmic num- ber in which 0 decibels represents the threshold of hearing (for a frequency of 1000 Hz). Every 3 decibels represents a doubling of perceived sound intensity; every 10 decibels represents an increase of pressure by a factor of 10. From 0 to around 40 db (as the decibel is abbreviated), sounds are very quiet indeed. It is not until a sound reaches this level that it said to cross the threshold of intelligibil- ity. Sounds approaching and louder than 120 db achieve the distinction of crossing the threshold of pain. The difference between 0 and 120 decibels is a one trillion (1,000,000,000,000) increase in intensity. Since there is no programable control of loudness on this computer, we cannot demonstrate changes in amplitude with good aural examples. You may have noticed, however, that during the frequency "sweep" in the unit on pitch, some frequencies seemed louder than others. This is due to the whole computer vibrating along with its tiny speaker, with some components (like side wall) having particular frequencies more likely to vibrate than others. This computer has its own resonance frequencies, and you'll have the chance later on to try to find out what they are. For the moment, we'll rely upon this phenomenon to illustrate differences in loudness. By holding down the UP/DOWN arrows, you can sweep up and down from approximately 50 to 4000 Hz. Listen for subtle varia- tions in loudness. These are actually the result of the original vibrations in the speaker being reinforced and not by any actual increase of amplitude within the speaker itself. Nonetheless, you should be able to hear what probably could be measured as a 3-4 decibel difference overall. Sound loudness measurements are complex because the human ear responds to different loudnesses at different frequency ranges and with differing qualities of sound. Greater pressure is needed in the extremities of the hearing range in order to produce a given loudness, than in optimum response ranges of the ears. The optimal response range is from 1000 to 4000 Hz. "Human hearing is variable. It is affected, for example, by culture: some Africans hear sounds that, to 20th-century urban North Americans, are remarkably soft. In industrialized cultures, the young are able to hear a wider range of frequencies than the old. We are still ignorant of the exact roles that culture, habit, and environment play in affecting human hearing equipment and ability." [Cogan & Escott, p.442] Sound Level Reference 0-40 db:.........barely perceptible sounds, not clearly identified--distant wind sound, for instance 40-50 db:........whispering at 5-10 feet distance rustling leaves, 10-20 feet away cat purring, 5 feet distant 50-60 db:........normal conversation, 5-10 feet away central air conditioning unit in big building your own footsteps on concrete, hard-soled shoes 60-70 db:........orchestra, moderate passage, 30-40 feet general din, dining hall light traffic at 30 feet 70-80 db:........truck traffic, 30 feet stereo, 3/4 gain, 10 feet shouting 80-90 db:........lawnmower, 20 feet loud orchestral passages, 20 feet 90-100 db:.......hammering nails, 5 feet thunder, half mile to mile 100-110 db:......jackhammer, 10 feet table saw, 5 feet 110-120 db:......Rock concert, 20-30 feet airplane taking off, 200 feet TIMBRE The diagrams we've seen illustrating the swinging of a pendulum are pictorial representations of wave forms. The pendulum swing creates a simple curvilinear form because as it swings out to the positive side of displacement it slows down until it reaches the turn-around point, then regains speed as it passes the resting point, slowing down on the opposite swing, and so on. This simple motion is similar to the way a piano string or a violin string vibrate over their overall length. The resultant wave form is a sine wave. The tone such a vibration would produce is called a sine tone. No acoustic vibration is quite this simple, however. The vibration of a piano string can illustrate this. When it is set in motion, it not only oscillates back and forth over its whole length, but also vibrates in parts, each one of which vibrates at its own rate. This occurs because the molecules of the string are knocking against each other, waves of kinetic energy are flowing along the string, being reflected back from the stopped ends of the string, and reinforcing or cancelling each other. You've seen this happen if you've ever thrown a pebble into a small pool of water. A circle of waves radiates outward, reflects back off the sides and crosses on-coming waves. Reinforcement and cancellation of the waves' energies create an overall wave structure called an interference pattern. The interference pattern in a vibrating string was discovered at least as long ago as the 6th century BC, by Pythagorus. At exactly whole-number (integer) divisions of the string, points of no energy occur. These are called nodal points. The result is that the string vibrates over its whole length at the same time as it is vibrating over half its length, over a third of its length, over a quarter of its length, and so on. Each of these subsidiary vibrations occur at frequencies inversely proportionate to the lengths and with varying amplitude relationships. The vibration over the whole length is called the fundamental. It is the frequency of this whole-length vibration which we have been referring to in describing pitch. If this frequency is 100 Hz then the half-length vibration of the string is 200 Hz, the third- length vibration is 300 Hz, the quarter-length vibration is 400 Hz, and so on. ( for illustration ). These subsidiary vibrations are variously described as overtones, partials, or harmonics. They are audible, and every acoustic vibration produces them. We generally do not perceive them discretely, however, but rather coalesce them into a composite sound whose quality varies from sound to sound, instrument to instrument, depending upon their particular configurations. The pattern of harmonics is different for virtually every sound, and thus we can distinguish between one kind of sound and another. This is what is called timbre (pronounced "tam-ber"), or "tone color." Together with the manner in which a tone is initiated (called onset), timbre allows us to distinguish whether we are hearing a flute, oboe, human voice, and so on. Depending upon overtone constituency, a sound may be described on a continuum from relatively pure to relatively harsh. The fewer the audible overtones, the more pure the sound, the greater the number of partials the harsher the sound. The purest sound would be a sine tone, and the closest instrumental sound to a sine tone is a flute in its higher register. Electronic instruments can produce sine tones within their circuitry such that they appear as simple pendulum-swing curves on an oscilloscope, but when they are made audible through a speaker, the membrane of the speaker itself generates harmonics and thus a tone which is not entirely pure. The timbre of the tone generated by this computer is not quite pure and varies, like the amplitude, with different frequency ranges. We again have no programable way of altering the timbre here, but with some programming manipulation we can approximate a variety of tone qualities. Listen first of all for the quality of the unaltered tone and hear if you can perceive the slightly buzzy quality indicative of the presence of overtones. Then imagine that your ears are capable of focusing toward the bottom of the frequency spectrum being sounded and, like a flashlight beam, capable of being swept upward. Focus in on successively higher frequency territories and try to isolate the pitches which cause the buzzy sound. Do this with each example. With practice, you should be able to hear discretely varying frequencies within the framework of what, at first "glance", appears to be a single sound. There are 7 examples. You may hear them as many times as you wish by hitting 1-7. Each of these sounds is distinctly different, and examples 5-7 sweep up and down through the harmonic series in the way you can imagine doing when listening to a single sound. Harmonics are so named because of the whole-number relationships they bear to one another. Some sounds, like a cymbal crash, generate partials whose relationships are inharmonic, non-whole number ratios. When sounds produce harmonics (as opposed to in- harmonics), their ratios are simply calculated. The fundamental is harmonic number 1. The next highest is number 2, and so on. The number in the series also indicates proportion. Number 2 is 2x1 (or 2:1). Number 3 is 3x1 (or 3:1). Ratios also may be determined between any two harmonics. The ratio from harmonics 2 to 3 is 2:3, and so on. Our pictorial representation of a vibrating string only illustrated 4 divisions of the string, but actually the divisions continue on to a theoretical infinity. We are capable of hearing up to 16 harmonics, but as you can determine that the proportions become smaller and smaller the higher one goes in the series, hearing discrete upper partials becomes difficult. The frequency sweeps in the preceding examples focused on the first 8 harmonics, which are easily perceived. To facilitate calculation, all of the examples used a fundamental of 100 Hz. Thus the second harmonic is 200 Hz, the 3rd is 300 Hz, and to continue on: 4=400 Hz, 5=500 Hz, 6=600 Hz, 7=700 Hz, and 8=800 Hz. Listen now to these frequency relationships with each pitch sounding for about one second. When a single note on a piano is struck, these pitches are component parts of what we normally designate as a single sound. Some common sense analysis can lead to realization of why our ears focus in on the fundamental as the indicator of frequency. First of all, it is the loudest, having the greatest displacement. But second, within the first 8 harmonics, it is replicated in octaves 3 more times. The second harmonic is an octave above the first (2:1 ratio, remember!). The 4th harmonic is 2 octaves above the fundamental, and the 8th harmonic is 3 octaves above the fundamental. (There is yet one more octave relationship within the first 8 harmonics--the relationship of the 3rd harmonic to the 6th forms a 2:1 ratio). PROBLEM 3: Given a fundamental of 55 Hz (3 octaves below tuning "A"), what are the successive harmonics up to the 8th? Wave Form We have seen an image of a sine wave, with its simple curvilinear form. If one started superimposing one sine wave upon another, the resultant reinforcement and cancellation of oscillations would produce other patterns. This is exactly what the 18th century mathematician, Joseph Fourier, determined. He devised a theorem which states that any wave can be written as a unique sum of sine waves. This principle was employed in the early development of electronic music, since all that was available to composers at that time (the 1940's) were sine wave generators. Some present-day synthesizers use this technique also, in a procedure called additive synthesis. Many current synthesizers make available other wave forms and present math theory contends that "...almost any waveform family will work as the basic alphabet of a wave language." [Quantum Reality, Nick Herbert, Anchor Books, 1987] There are four commonly available wave forms. The sine, which we've seen; a square wave (which is actually what this computer generates); a sawtooth wave; and a triangle wave. to see how these would appear as oscillographic images. Sine wave additive synthesis is capable of producing virtually any sound. With the added capability provided by other waveforms, composers now have entire orchestras of sound contained in desktop instruments no larger than the clavichords of the 17th century. ENVELOPE All sounds vary, to greater or lesser degree, with the passage of time. The description of the overall changes in a sound over time is called the sound's envelope. While timbre or frequency may change over time and thus may be described in terms of timbral or frequency envelope, the most usual application of the term is to amplitude. Amplitude envelope is a description of the manner in which a sound's loudness changes with the passage of time. There are four standard components of amplitude envelope: Attack, Decay, Sustain, and Release (often seen abbreviated as ADSR). Attack is the amount of time it takes for a sound to reach its maximum loudness level from the instant of its initiation. Decay is the time it may take to level off to its Sustain level (if it is cabable of sustaining). And release is the time it takes for the sound to die out once "turned off." Some sounds bypass the sustain segment, and the release cycle is equivalent to the decay. A piano, for instance, whose envelope is called a "bell" shape (since it has the same configuration as a struck bell), has a nearly instantaneous attack cycle with gradual tapering off of the sound (decay) until reaching 0 loudness. We cannot illustrate amplitude envelope with this computer, but as various pictorial representations appear, you will hear the envelope traced by the analogous frequency changes. Conclusion This discussion has been somewhat technical. The greater our un- standing of the nature of sound, the better we can hear. I can think of no better way to enhance our hearing capabilities than to develop the ability to hear harmonics. Used as an exercise, focusing in on harmonics hones our hearing equipment to a fine degree. Knowledge of other components of sound, like frequency, amplitude, and envelope, also enhances our hearing acuity by making it possible to focus on details of sound. The more detail we can take in, the richer is our experience. In depth exploration may also stimulate curiosity--the more we know, the more questions we are able to ask. The more questions we ask, the more we come to know. The more we know, the more questions.... There is, furthermore, a broader perspective here. For it is in the rather mysterious property of vibrating things to vibrate in complex ways, yet having simple harmonic proportions, that there exists a model for the relationship of the heavenly bodies one to another. This in fact led Pythagorus and others to devise theories about the so-called Music or Harmony of the Spheres. These theories manifest themselves in many ways, among the latest being Superstring theory, in which reality is conceived to consist of ten dimensions and "...the fundamental building blocks of matter and energy aren't infinitesimal points but infinitesimal strings." And "it's at this ultimate smallness that everything exists as the dance of one-dimensional strings in a ten-dimensional universe. A string vibrating and twitching in a specific fashion might manifest itself in the real world as a quark. Another string, shaking and rolling in a different fashion, might appear as an electron, or a photon, or one of the many other creatures of the subatomic bestiary. The strings are the same; only the modes of vibration change." [Gary Taubes, "Everything's Now Tied To Strings," Discover, November, 1986] Also, in sound we have a representation of the idea of the One and the Many. A single sound is all one sound, a whole, perceived as a unified entity; but at the same time it is many-voiced, a composite of an infinite number of vibrations, each unique and discrete. Hence, when you listen to sound, listen carefully. Listen not only to what is perceived at first as the fundamental pitch, but listen also for the many voices, the overtones, which coalesce into forming the overall sound. Listen with ears attuned to the harmonic structure of the universe, and maybe you will come to understand the importance of sound in the Rg Veda, sound as the basis for all else, the primal vibration upon which the whole phenomenological world floats, sound as Bentov suggested, giving structure to the very atoms of which we are made.