The Light and Sound Dictionary… continued
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Beats are amplitude variations that result when pure tones spaced close together in pitch are mixed. When tone pitches are far enough apart, the result of mixing tones is consonance (sounds okay). As the mixed tones get within an octave of each other, they sound good only if the tones form good chords. When they get still closer, the effect shifts to beats. A trigonometric formula, long since forgotten by many, expresses the addition of two pure tones as:
sin(a) + sin(b) = 2*(sin((a+b)/2)*cos((a-b)/2))
Interpreting the formula, beats are perceived as the average pitch (a+b)/2 modulated (pulsed) at the difference frequency (a-b). If you are paying close attention and noticed the disappearing 1/2, cos(a-b)/2 has two amplitude peaks per cycle, so the modulation is perceived to be at frequency (a-b) not (a-b)/2. When you listen to a mixture of slowly changing tones on a dual binaural beat instrument, fascinating beat effects are heard.
Beta brainwave frequencies are associated with are normal waking state. Beta frequencies range between 13-34Hz.
Binaural beats result when pure tones at different beats are simultaneously heard by both ears. For instance, say one tone of 200Hz is heard predominantly by the left ear. Another tone of 190Hz is heard predominantly through the right ear. These two pure tones are heard and processed separately, depending upon their arrival time, by our auditory center. If these two tones are of the same pitch, the resulting sound will be perceived as being inside our head. But if both tones have slightly different pitches, the resulting effect will sound more like a back and forth movement. Binaural beats result when pure tones at slightly different pitches are heard by the two ears. The effect is different from a mixed tone beat phenomenon, because the tones are heard and processed separately by the auditory apparatus. Our mechanism for localizing the source of a sound depends on detecting differences of arrival times of the sound waveform — two tones of the same pitch but at different phases will be perceived as being inside the head, closer to the ear in which the sine wave peaks first. Tones of slightly different pitches appear to have constantly shifting phase, and the source appears to move back and forth within the head at the rate of the difference of the pitches. This is commonly but inaccurately described as “hearing the difference frequency”. You can experiment with this effect with a light and sound machine that generates controlled sine wave binaural beats.
Copyright: Michael J. Landgraf & Mindmachines.com, Granada Hills, CA. / November, 2012 All rights reserved. No part of this book may be copied or duplicated without prior written approval by Michael Landgraf.
Published by Little Minnie’s Publishing House. ISBN 10: 0966259602. ISBN 13: 978-0966259605. All inquiries pertaining to this book should contact https://www.mindmachines.com/contact-us/.