harmonicphysics
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human voice speech
A second attribute of vocal sound, harmonic structure, depends on the wave form produced by the vibrating vocal cords. Like any musical instrument, the human voice is not a pure tone (as produced by a tuning fork); rather, it is composed of a fundamental tone (or frequency of vibration) and a series of higher frequencies called upper harmonics, usually corresponding to a simple mathematical...
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sound waves sound
Here n is called the harmonic number, because the sequence of frequencies existing as standing waves in the string are integral multiples, or harmonics, of the fundamental frequency.
tones
tone...others, overtones. The frequencies of the overtones may be whole multiples (e.g., 2, 3, 4, etc., of the fundamental frequency, in which case they are called the second, third, fourth, etc., harmonics of the fundamental tone, itself known as the first harmonic). A combination of harmonic tones is pleasant to hear and is therefore called a musical tone.
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combination tones combination tone
A similar subjective phenomenon, aural harmonics, results from the ear’s distortion of a single pure tone. The distortions produce frequencies in the ear corresponding to multiples of the original frequency (2f, 3f, 4f,…), and aural harmonics thus have the same pitch as externally produced harmonics.
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overtones overtone
in acoustics, tone sounding above the fundamental tone when a string or air column vibrates as a whole, producing the fundamental, or first harmonic. If it vibrates in sections, it produces overtones, or harmonics. The listener normally hears the fundamental pitch clearly; with concentration, overtones may be...
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discussed in biography Ptolemy
Among Ptolemy’s earliest treatises, the Harmonics investigated musical theory while steering a middle course between an extreme empiricism and the mystical arithmetical speculations associated with Pythagoreanism. Ptolemy’s discussion of the roles of reason and the senses in acquiring scientific knowledge have bearing beyond music theory.
in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same, and the force responsible for the motion is always directed toward the equilibrium position and is directly proportional to the distance from it.
Many physical systems exhibit simple harmonic motion (assuming no energy loss): an oscillating pendulum, the electrons in a wire carrying alternating current, the vibrating particles of the medium in a sound wave, and other assemblages involving relatively small oscillations about a position of stable equilibrium.
A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling. At the maximum displacement −x, the spring is under its greatest tension, which forces the mass upward. At the maximum displacement +x, the spring reaches its greatest compression, which forces the mass back downward again. At either position of maximum displacement, the force is greatest and is directed toward the equilibrium position, the velocity (v) of the mass is zero, its acceleration is at a maximum, and the mass changes direction. At the equilibrium position, the velocity is at its maximum and the acceleration (a) has fallen to zero. Simple harmonic motion is characterized by this changing acceleration that always is directed toward the equilibrium position and is proportional to the displacement from the equilibrium position. Furthermore, the interval of time for each complete vibration is constant and does not depend on the size of the maximum displacement. In some form, therefore, simple harmonic motion is at the...
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development analog computer
...special-purpose machines, as for example the tide predictor developed in 1873 by William Thomson (later known as Lord Kelvin). Along the same lines, A.A. Michelson and S.W. Stratton built in 1898 a harmonic analyzer (q.v.) having 80 components. Each of these was capable of generating a sinusoidal motion, which could be multiplied by constant factors by adjustment of a fulcrum on levers....
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harmonic analysis harmonic analysis
The use of a larger number of terms will increase the accuracy of the approximation, and the large amounts of calculations needed are best done by machines called harmonic (or spectrum) analyzers; these measure the relative amplitudes of sinusoidal components of a periodically recurrent function. The first such instrument was invented by the British mathematician and physicist William Thomson...
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human hearing sound
The ear actually functions as a type of Fourier analysis device, with the mechanism of the inner ear converting mechanical waves into electrical impulses that describe the intensity of the sound as a function of frequency. Ohm’s law of hearing is a statement of the fact that the perception of the tone of a sound is a function of the amplitudes of the harmonics and not of the phase...
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music synthesis music synthesizer
The aforementioned synthesizers used subtractive synthesis—removing unwanted components from a signal containing a fundamental tone and all related overtones (sawtooth-wave signals). The harmonic-tone generator developed by James Beauchamp at the University of Illinois, in contrast, used additive synthesis—building tones from signals for pure tones, i.e., without overtones...
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