Background Hearing is not a purely mechanical phenomenon of wave propagation, but is also a sensory and perceptual event. When a person hears something, that something arrives at the ear as a mechanical sound wave traveling through the air, but within the ear it is transformed into neural action potentials. These nerve pulses then travel to the brain where they are perceived. Hence, in many problems in acoustics, such as for audio processing, it is advantageous to take into account not just the mechanics of the environment, but also the fact that both the ear and the brain are involved in a person’s listening experience. The inner ear, for example, does significant signal processing in converting sound waveforms into neural stimulus, so certain differences between waveforms may be imperceptible. MP3and other audio compression techniques make use of this fact. In addition, the ear has a nonlinear response to sounds of different loudness levels. Telephone networks and audio noise reduction systems make use of this fact by nonlinearly compressing data samples before transmission, and then expanding them for playback. Another effect of the ear's nonlinear response is that sounds that are close in frequency produce phantom beat notes, or intermodulation distortion products. Limits
Perceived Human Hearing Graph
The human ear can nominally hear sounds in the range 20 Hz to 20,000 Hz (20 kHz). This upper limit tends to decrease with age, most adults being unable to hear above 16 kHz. The ear itself does not respond to frequencies below 20 Hz, but these can be perceived via the body's sense of touch. Some recent research has also demonstrated a hypersonic effect which is that although sounds above about 20 kHz cannot consciously be heard, evidence suggests that ultrasonic sounds can induce
changes in EEG (electroencephalogram) readouts of listeners in controlled test environments. In addition, though we are unable to perceive sounds above 20 kHz, listeners in the same study gave qualitatively different judgments of sound when ultrasonic frequencies were present. Frequency resolution of the ear is 0.36 Hz within the octave of 1,000–2,000 Hz. That is, changes in pitch larger than 0.36 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a (low-) frequency difference pitch. This effect of phase variance upon the resultant sound is known as 'beating'. The semitone scale used in Western musical notation is not a linear frequency scale but logarithmic. Other scales have been derived directly from experiments on human hearing perception, such as the mel scale and Bark scale (these are used in studying perception, but not usually in musical composition), and these are approximately logarithmic in frequency at the high-frequency end, but nearly linear at the lowfrequency end. The "intensity" range of audible sounds is enormous. Our ear drums are sensitive only to variations in the sound pressure, but can detect pressure changes as small as 2×10–10 atm and as great or greater than 1 atm. For this reason, Sound Pressure Level is also measured logarithmically, with all pressures referenced to 1.97385×10– 10
atm. The lower limit of audibility is therefore defined as 0 dB, but the upper limit is
not as clearly defined. While 1 atm (191 dB) is the largest pressure variation an undistorted sound wave can have in Earth's atmosphere, larger sound waves can be present in other atmospheres, or on Earth in the form of shock waves. The upper limit is more a question of the limit where the ear will be physically harmed or with the potential to cause a hearing disability. This limit also depends on the time exposed to the sound. The ear can be exposed to short periods in excess of 120 dB without permanent harm — albeit with discomfort and possibly pain; but long term exposure to sound levels over 80 dB can cause permanent hearing loss. A more rigorous exploration of the lower limits of audibility determines that the minimum threshold at which a sound can be heard is frequency dependent. By measuring this minimum intensity for testing tones of various frequencies, a frequency dependent Absolute Threshold of Hearing (ATH) curve may be derived. Typically, the ear shows a peak of sensitivity (i.e., its lowest ATH) between 1 kHz and
5 kHz, though the threshold changes with age, with older ears showing decreased sensitivity above 2 kHz. The ATH is the lowest of the equal-loudness contours. Equal-loudness contours indicate the sound pressure level (dB), over the range of audible frequencies, which are perceived as being of equal loudness. Equal-loudness contours were first measured by Fletcher and Munson at Bell Labs in 1933 using pure tones reproduced via headphones, and the data they collected are called Fletcher-Munson curves. Because subjective loudness was difficult to measure, the Fletcher-Munson curves were averaged over many subjects. Robinson and Dadson refined the process in 1956 to obtain a new set of equalloudness curves for a frontal sound source measured in an anechoic chamber. The Robinson-Dadson curves were standardized as ISO 226 in 1986. In 2003, ISO 226 was revised as equal-loudness contour using data collected from 12 international studies. Overview The term psychoacoustics describes the characteristics of the human auditory system on which modern audio coding technology is based. The most important psychoacoustics fact is the masking effect of spectral sound elements in an audio signal like tones and noise. For every tone in the audio signal a masking threshold can be calculated. If another tone lies below this masking threshold, it will be masked by the louder tone and remains inaudible too. Masking
Main article: Auditory masking
Audio Masking Graph
In some situations an otherwise clearly audible sound can be masked by another sound. For example, conversation at a bus stop can be completely impossible if a loud bus is driving past. This phenomenon is called masking. A weaker sound is
masked if it is made inaudible in the presence of a louder sound. The masking phenomenon occurs because any loud sound will distort the Absolute Threshold of Hearing, making quieter, otherwise perceptible sounds inaudible. If two sounds occur simultaneously and one is masked by the other, this is referred to as simultaneous masking. Simultaneous masking is also sometimes called frequency masking. The tonality of a sound partially determines its ability to mask other sounds. A sinusoidal masker, for example, requires a higher intensity to mask a noise-like maskee than a loud noise-like masker does to mask a sinusoid. Computer models which calculate the masking caused by sounds must therefore classify their individual spectral peaks according to their tonality. Similarly, a weak sound emitted soon after the end of a louder sound is masked by the louder sound. Even a weak sound just before a louder sound can be masked by the louder sound. These two effects are called forward and backward temporal masking, respectively. 'Phantom'
Main article: Missing fundamental Low pitches can sometimes be heard when there is no apparent source or component of that frequency. This perception is due to the brain interpreting repetition patterns determined by the differences of audible harmonics that are present. A harmonic series of pitches that are related 2×f, 3×f, 4×f, 5×f, etc, give human hearing the psychoacoustic impression that the pitch 1×f is present. This phenomenon is used by some pro audio manufacturers to allow sound systems to seem to produce notes that are lower in pitch than they are capable of reproducing. Software
Perceptual Audio Coding uses the Psychoacoustics algorithm
The psychoacoustic model provides for high quality lossy signal compression by describing which parts of a given digital audio signal can be removed (or aggressively
compressed) safely - that is, without significant losses in the (consciously) perceived quality of the sound. It can explain how a sharp clap of the hands might seem painfully loud in a quiet library, but is hardly noticeable after a car backfires on a busy, urban street. This provides great benefit to the overall compression ratio, and psychoacoustic analysis routinely leads to compressed music files that are 1/10 to 1/12 the size of high quality original masters with very little discernible loss in quality. Such compression is a feature of nearly all modern audio compression formats. Some of these formats include MP3, Ogg Vorbis, AAC, WMA, MPEG-1 Layer II (used for digital audio broadcasting in several countries) and ATRAC, the compression used in MiniDisc and Walkman. Psychoacoustics is based heavily on human anatomy, especially the ear's limitations in perceiving sound as outlined previously. To summarize, these limitations are:
High frequency limit
Absolute threshold of hearing
Given that the ear will not be at peak perceptive capacity when dealing with these limitations, a compression algorithm can assign a lower priority to sounds outside the range of human hearing. By carefully shifting bits away from the unimportant components and toward the important ones, the algorithm ensures that the sounds a listener is most likely to perceive are of the highest quality. Music Psychoacoustics include topics and studies which are relevant to music psychology and music therapy. Theorists such as Benjamin Boretz consider some of the results of psychoacoustics to be meaningful only in a musical context. Applied
Psychoacoustics is presently applied within many fields from software development, where developers map proven and experimental mathematical patterns; in digital signal processing, where many audio compression codecs such as MP3 use a psychoacoustic model to increase compression ratios; in the design of (high end) audio systems for accurate reproduction of music in theatres and homes; as well as defense systems where scientists have experimented with limited success in creating new acoustic weapons, which emit frequencies that may impair, harm, or kill (see ). It is also applied today within music, where musicians and artists continue to create new auditory experiences by masking unwanted frequencies of instruments, causing other frequencies to be enhanced. Yet another application is in design of small or lower-quality loudspeakers, which use the phenomenon of missing fundamentals to give the effect of low frequency bass notes that the system, due to frequency limitations, cannot actually reproduce (see references). See
A-weighting, a commonly used perceptual loudness transfer function
Auditory scene analysis incl. 3D-sound perception, localisation
Bark scale, Equivalent rectangular bandwidth (ERB), Mel scale and other scales
Missing fundamental frequency and other auditory illusions
Loudness, that is, perceived volume, Bel, sone
Noise health effects
Sound of fingernails scraping chalkboard
1. ^ Christopher J. Plack (2005). The Sense of Hearing. Routledge. ISBN 0805848843.
2. ^ Lars Ahlzen, Clarence Song (2003). The Sound Blaster Live! Book. No Starch Press. ISBN 1886411735.
3. ^ Rudolf F. Graf (1999). Modern dictionary of electronics. Newnes. ISBN 0750698667.
4. ^ Jack Katz, Robert F. Burkard, and Larry Medwetsky (2002). Handbook of Clinical Audiology. Lippincott Williams & Wilkins. ISBN 0683307657.
5. ^ http://www.cco.caltech.edu/~boyk/spectra/spectra.htm 6. ^ Olson, Harry F. (1967). Music, Physics and Engineering. Dover Publications. pp. 248–251. ISBN 0486217698.
7. ^ John Clark, Colin Yallop and Janet Fletcher (2007). An Introduction to Phonetics and Phonology. Blackwell Publishing. ISBN 1405130830.
8. ^ Waves Car Audio. MaxxBass Bass Enhancement Technology 9. ^ US patent Method and system for enhancing quality of sound signal 5930373 Notations
E. Larsen and R.M. Aarts (2004), Audio Bandwidth extension. Application of Psychoacoustics, Signal Processing and Loudspeaker Design., J. Wiley.
E. Larsen and R.M. Aarts (2002), Reproducing low-pitched signals through small loudspeakers, J. Audio Eng. Soc., March, 50 (3), pp. 147-164.
T. Oohashi, N. Kawai, E. Nishina, M. Honda, R. Yagi, S. Nakamura, M. Morimoto, T. Maekawa, Y. Yonekura, and H. Shibasaki. The role of biological system other than auditory air-conduction in the emergence of the hypersonic
effect http://dx.doi.org/10.1016/j.brainres.2005.12.096. Brain Research, 1073:339–347, February 2006. External
The musical ear - Perception of sound
Applied psychoacoustics in space flight - Simulation of free field hearing by head phones
GPSYCHO - an open source psycho-acoustic and noise shaping model for ISO based MP3 encoders.
How audio codecs work - Psycoacoustics
Basics about MPEG Perceptual Audio Coding
Perceptual Coding of Digital Audio
Definition of: perceptual audio coding
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Perceptual Coding Use of psychoacoustic principles for the design of audio recording, reproduction, and data reduction devices makes perfect sense. Audio equipment is intended for interaction with humans, with all our abilities and limitations of perception. Traditional audio equipment attempts to produce or reproduce signals with the utmost fidelity to the original. A more appropriately directed, and often more efficient, goal is to achieve the fidelity perceivable by humans. Basically, this means removing the part of an audio signal we cannot hear. This is the goal of perceptual coders. Although one main goal of digital audio perceptual coders is data reduction, this is not a necessary characteristic. Perceptual coding can be used to improve the representation of digital audio through advanced bit allocation. Also, all data reduction schemes are not necessarily perceptual coders. Some systems, the DAT 16/12 scheme for example, achieve data reduction by simply reducing the word length, in this case cutting off four bits from the least-significant side of the data word, achieving a 25% reduction.
The Digital Compact Cassette (DCC), developed by Philips, is one of the first commercially available forms of perceptually coded media. It achieves a 25% data reduction through the use of the Precision Adaptive Sub-band Coding (PASC) algorithm. The algorithm contains a psychoacoustical model of masking effects as well as a representation of the minimum hearing threshold. The masking function divides the frequency spectrum into 32 equally spaced bands. Sony's ATRAC system for the MiniDisc format is similar. Perceptual coders still have room for improvement but are headed in what seems to be a more intelligent direction. The algorithms are not perfect models of human perception and cognition. Of course, while the modeling of a perceptual coder could be over-engineered in the spirit of cognitive science in order to learn more about human cognition, all that is necessary in perceptual coding is to develop an algorithm that operationally corresponds to human auditory perception, not one that physically copies it.
The Future of Perceptual Coding It is probable that all future coding schemes that make any claim to sophistication will make use of psychoacoustical principles. While the present commercial systems, PASC and ATRAC, were instituted in the interest of economy of storage, there are other valuable functions for perceptual coders. Transfer over networks, presently a time-consuming function when sending large, high-quality audio files, is a prime example of where perceptual coding is needed. Consider a case with a relatively fast connection to the Internet: a T1 line, able to transfer data at approximately 1.3MB/sec., requires almost three minutes to send five minutes of CD-quality stereo digital audio. Assuming the 25% efficiency of PASC, the same amount of digital audio could be sent in under two minutes. Additionally, the perceptually coded material may sound better if dynamic bit allocation were used. If the coding was performed in real time, as some are, then the speed of transfer between the central processing units and the Internet connections at each sending and receiving point would also be increased. Other applications include stand-alone converter modules for conversion to any media and, eventually, software encoders. The need for standardization soon becomes apparent, and hopefully it will be met. The long explanation of masking and perceptual coding
Next Section: Future audio and Internet developments: Client-Server Systems Audio on The Internet
Perceptual Coding Compression schemes often operate on signal values like the amplitude of speech at a specific instant (sample) or the intensity of an image at a specific location (pixel) without regard to the way that the final reproduced signal will be heard or seen by a human user. This is appropriate for some data such as measurements or text, but it fails to take advantage of potentially useful information when reconstructing a signal intended for subjective perception by humans. If, for example, greater compression can be achieved at the cost only of loss imperceptible by the human ear or eye, then a lossy system can appear to have as high a performance as a lossless system with far inferior compression. Compression methods taking advantage of the nature of these phenomena are referred to collectively as perceptual coding, and seminal work during the past decade promises significant improvements in compression. Perceptual coding can be accomplished by a variety of means, but it usually involves using models of human perception, such as a human auditory system or human visual system model. These models can be quite complex and their incorporation into compression algorithms quite involved, often involving cooperative work among psychologists, computer scientists, and engineers. The potential gains have been estimated at 10-50% improvements in efficiency of compression with no perceptual distortion. One approach is to transform the raw data
using the perceptual model into features deemed important for perception. It is these features that are then explicitly compressed and used to reconstruct the signal. Another approach is to incorporate the perceptual knowledge into the measures of distortion and fidelity used to design the codes. Regardless of the specific method, sensible incorporation of quantitative aspects of human perception is likely to provide substantial improvements in compression performance for speech, audio, images, and video with a modest increase in cost or complexity.
Psychoacoustics Psychoacoustics is essentially the study of the perception of sound. This includes how we listen, our psychological responses, and the physiological impact of music and sound on the human nervous system. In the realm of psychoacoustics, the terms music, sound, frequency, and vibration are interchangeable, because they are different approximations of the same essence. The study of psychoacoustics dissects the listening experience. Traditionally, psychoacoustics is broadly defined as “pertaining to the perception of sound and the production of speech.” The abundant research that has been done in the field has focused primarily on the exploration of speech and of the psychological effects of music therapy. Currently, however, there is renewed interest in sound as vibration. An important distinction is the difference between a psychological and a neurological perception. A song or melody associated with childhood, a teenage romance, or some peak emotional experience creates a memory-based psychological reaction. There is also a physiological response to sounds, however. Slightly detuned tones can cause brain waves to speed up or slow down, for instance. Additionally, soundtracks that are filtered and gated (this is a sophisticated engineering process) create a random sonic event. It triggers an active listening response and thus tonifies the auditory mechanism, including the tiny muscles of the middle ear. As a result, sounds are perceived more accurately, and speech and communication skills improve. While a psychological response may occur
with filtered and gated sounds, or detuned tones, the primary effect is physiological, or neurological, in nature. Research on the neurological component of sound is currently attracting many to the field of psychoacoustics. A growing school of thought — based on the teachings of the Dr. Alfred Tomatis — values the examination of both neurological and psychological effects of resonance and frequencies on the human body. Thanks to the ground breaking findings of Dr. Tomatis (1920-2001), we have come to understand the extraordinary power of the ear. In addition to its critical functions of communication and balance, the ear's primary purpose is to recycle sound and so recharge our inner batteries. According to Tomatis, the ear's first function in utero is to govern the growth of the rest of the physical organism. After birth, sound is to the nervous system what food is to our physical bodies: Food provides nourishment at the cellular level of the organism, and sound feeds us the electrical impulses that charge the neocortex. Indeed, psychoacoustics cannot be described at all without reference to the man known as the “Einstein of the ear.” In the realm of application-specific music and sound, psychoacoustically-designed soundtracks revolve around the following concepts and techniques:
• • • • •
Intentionality (focused application for specific benefit) Resonance (tone) Entrainment (rhythm) Pattern Identification (active listening or passive hearing) Sonic Neurotechnologies (highly specialized sound processing)
Resonance & Entrainment Consider the following: Anything that moves has a vibration. Though invisible, every aspect of our material world at the atomic level moves constantly. Wherever there is motion, there is frequency. Though inaudible at times, all frequencies make a sound. All sounds resonate and can affect one another. In the spectrum of sound — from the movement of atomic particles to the sensory phenomenon we call music — there is a chain of vibration:
• • • •
All atomic matter vibrates. Frequency is the speed at which matter vibrates. The frequency of vibration creates sound (sometimes inaudible). Sounds can be molded into music.
This chain explains the omnipresence of sound. Resonance is the single most important concept in understanding the constructive or destructive role of sound in your life. Entrainment, sympathetic vibration, resonant frequencies, and resonant systems all fall under the rubric of resonance. Resonance can be broadly defined as “the impact of one vibration on another.” Literally, it means “to send again, to echo.” To resonate is to “re-sound.” Something external sets something else into motion, or changes its vibratory rate. This can have many different effects — some subtle and some not so. From iceburgs to airport construction to the human body, soundwaves have the capacity to alter, to actually shift frequency. Simply put, sound is a powerful — yet often ignored — medium for change. Another fascinating and important aspect of resonance is the process of entrainment. Entrainment, in the context of psychoacoustics, concerns changing the rate of brain waves, breaths, or heartbeats from one speed to another through exposure to external, periodic rhythms. The most common example of entrainment is tapping your feet to the external rhythm of music. Just try keeping your foot or your head still when you are around fun, up-tempo rhythms. You will see that it is almost an involuntary motor response. However, tapping your feet or bopping your head to
external rhythms is just the tip of the iceberg. While your feet might be jitterbugging, your nervous system may be getting a terrible case of the jitters! Rhythmic entrainment is contagious: If the brain doesn't resonate with a rhythm, neither will the breath or heart rate. In this context, rhythm takes on new meanings. Not only is it entertaining, but rhythmic entrainment is a potent sonic tool as well — be it for motor function or other autonomic processes such as brainwave, heart, and breath rates. Alter one pulse (such as brain waves) with music, and the other major pulses (heart and breath) will dutifully follow. When it comes to the intentional applications of music, the entrainment effect completes the circle of the chain of vibration: Atomic matter —> vibration —> frequency —> sound —> sympathetic vibration (resonance) —> entrainment. Music alters the performance of the nervous system primarily because of entrainment. Entrainment is the rhythmic manifestation of resonance. With entrainment, a stronger external pulse does not just activate another pulse but actually causes the latter to move out of its own resonant frequency to match it. Understanding the interlocking concepts of resonance and entrainment enables us to grasp the way external tone and rhythm can heal or create havoc. Sound affects glass and concrete as well as brain waves, motor response, and organic cells.
Pattern Identification Simply put, pattern identification is one of the brain’s analytical processes. Identifying a pattern (visual, auditory, odiferous, kinesthetic) enables cerebral attention to shift from active awareness to passive acknowledgement. Listening and looking are active functions; hearing and seeing are passive. In active listening mode, the middle ear function is highly engaged while the brain seeks to identify a pattern. Once an auditory pattern is found, passive hearing begins. Habituation sets in and the brain focuses on other things. There are specific times when active listening or passive hearing is preferable. Active listening stimulates the nervous system. Passive hearing is neutral or “discharging.”
Sonic Neuro-Technologies Representing two distinct approaches to therapeutic sound, filtration/gating (F/G) and binaural beat frequencies (BBFs) currently define the growing field of “sonic neurotechnologies.” This phrase was coined by Joshua Leeds to describe the arena of soundwork that depends on the precise mechanical manipulation of soundwaves to bring about desired changes in the psyche and physical body. Two diverse approaches to the processing of sound frequencies hold great interest and are used on some of the audio programs in Sound Remedies. Filtration/gating (F/G) techniques have been honed in Tomatis clinics worldwide. By gradually gating and filtering out the lower range of music (sometimes up to 8000 Hz), and then adding the frequencies back in, a retraining of the auditory processing system occurs. The effects of filtration and gating are felt on a psychological, neurodevelopmental, and physical level. The application of sound stimulation has been effective in the remediation of many neurodevelopmental issues. Children and adults with learning/attention difficulties, developmental delays, auditory processing problems, sensory integration and perceptual challenges have experienced profound improvement. Another approach to sound processing is the field of binaural beat frequencies (BBFs). By listening through stereo headphones to slightly detuned tones (i.e., sound frequencies that differ by a prescribed number of Hz), sonic brainwave entrainment takes place. Facilitating a specific range of brainwave states may assist in arenas such as pain reduction, enhanced creativity, or accelerated learning. These two sonic neurotechnologies — used separately — have roots in neurology, physiology, and psychology. They must be used carefully and wisely. BBF and F/G soundtracks can be powerful tools. Consequently, proper consideration must always be afforded. Please note: Sound products with BBFs or F/G contribute to health and wellness, but they are never
intended to replace medical diagnosis or treatment. Do not drive or operate machinery while listening to sound programs that use these methedologies. The therapeutic use of sound, like any new tool, requires discipline, education, and strict observance of ethical standards. There is currently no established licensure in the use of sonic neurotechnologies. Therefore the onus of responsibility for handling the changes that occur as a consequence of the application of these methods (most specifically, filtration/gating) falls on the practitioner. Sound is a marvelous adjunct to an existing profession. Therapists and educators will do well in performing due diligence and acquiring proper training.
Sound Stimulation with Filtration/Gating In the broadest definition, sound stimulation can be defined as the excitement of the nervous system by auditory information. Sound stimulation auditory retraining narrows the focus. In this context, a precise application of electronically processed sound, through headphones, can have the effect of retraining the auditory mechanism to take in a wider spectrum of sound frequencies. An ear that cannot process tone properly is a problem of great magnitude. As discussed in previous chapters, sufficient auditory tonal processing is a prerequisite to normal auditory sequential processing.
Auditory tonal processing (ATP) may be defined as the ability to differentiate between the tones utilized in language. Auditory sequential processing (ASP) is the ability to link pieces of auditory information together.
Auditory tonal processing is a basis for more complex levels of auditory sequential processing. ASP is the ability to receive, hold, process, and utilize auditory information using our short-term memory. As the foundation for short-term memory, ASP is one of the building blocks of thinking. Sequential processing functions are fundamental to speech, language, learning, and other perceptual skills. The ability to interpret sound efficiently provides the neurological foundation for these sequential functions. Per neurodevelopmental specialist Robert J. Doman Jr., “many people who have experienced auditory processing deficits have seen their sequential functions return and/or improve when proper tonal processing is restored.” The primary sound application used in the remediation of impaired tonal processing was created by Alfred Tomatis. Further discussions cannot take place without absolute acknowledgment of his pioneering research. The current field of sound stimulation auditory retraining evolves from Tomatis's discoveries of the powerful effect of filtration and gating of sound. In the context of auditory retraining, let's summarize these terms:
Filtration means the removal of specific frequencies from an existing sound recording, be that the music of Mozart or a recording of a voice. Through the use of sound processing equipment, it is possible to isolate and mute certain frequency bandwidths. With filtration, any part of the low, mid, or high end of a recording can be withdrawn and reintroduced at will. On a visual level, imagine erasing the bottom part of a picture and then eventually drawing it back in. This is filtration. Gating refers to the creation of a random sonic event. This is accomplished by electronically processing a soundtrack so it unexpectedly jumps between the high and low frequencies. While not always pretty to listen to, the net effect of this sound treatment is an extensive exercising of the muscles of the middle ear. The combined process of filtration and gating creates a powerful auditory workout. And for good reason! The middle ear mechanism must work very hard to translate the complexity of the “treated” incoming sound.
“Psychoacoustics” is a brief excerpt from The Power of Sound, published by Healing Arts Press. © 2001 Joshua Leeds. All rights reserved. Further information about psychoacoustics can be found in The Power of Sound and other fine books at Sound-Remedies.com.