Harmonics - "The aliquot part of a complex or compound wave form always multiples of the fundamental." ACOUSTICS § 15, 16

Mode Subdivision Particle
Dominant Etheric Etheron
Harmonic atomic Atom
Enharmonic Molecular Molecule

see Etheric Elements, Subdivision

Harmonic Scale "A harmonic scale is formed by taking a series of notes produced by vibrations whose numbers in a given time are respectively as 1, 2, 3, 4, etc. If we take as fundamental tone the open C string of the violoncello, the series of tones which with it form a harmonic scale will be as pictured.

"The scale formed by a series of natural harmonics. It should be noted that our conventional music scale is a melodic modification of a naturally occurring harmonic scale or series of naturally occurring tones.

"As the character of a sound depends upon that of the vibrations by which it is caused, it is important to know of what kind the latter must be in order that they may give the sensation of a perfectly simple tone, i.e., one which the ear cannot resolve into any others. Such a vibration is perhaps best realised by comparison with that of the pendulum of a clock when it is swinging only a little to and fro. Under these circumstances it is performing what are called harmonic vibrations, and when the air particles in the neighborhood of the ear are caused by any means to vibrate according to the same law as that which the pendulum follows, and also with sufficient rapidity, a perfect simple tone is the result. Such a tone is, however, rarely heard except when produced by means specially contrived for the purpose. If a note on the pianoforte is struck, the impact of the hammer on the string throws it into a state of vibration, which, though periodic, is not really harmonic; consequently we do not hear a perfectly simple tone, but one which is in reality a mixture of several higher simple tones with that one which corresponds to the actual length of the string. The former are, however, generally faint, and become associated by habit with the latter, appearing to form with it a single note of determinate pitch. These higher tones are harmonics of the string, and are produced by vibrations whose numbers per second are respectively twice, three times, four times, etc., as great as those of the fundamental tone of the string." A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900

"The Harmonic chord is the third current of the terrestrial stream." Keely

""Concordance of vibrations on harmonic levels as in the action of gravity." Keely and His Discoveries, pg 302

"Keely estimates that, after the introductory impulse is given on the harmonic thirds, molecular vibration is increased from 20,000 per second to 100,000,000." The Snell Manuscript

"The fundamental mode of vibration changes in the atomic subdivision to the harmonic, or true fifth of the mass chord.'' [ATOMIC THIRD SUBDIVISION]

Partial, Overtone
"If a violin string is bowed steadily, the frequencies of the partials of the resulting complex tone will be integral multiples of the lowest fundamental frequency, and the partials may properly be called harmonics. If, however, the same string is struck or plucked and then allowed to vibrate freely, the frequencies of the partials in the airborne sound and the frequencies of the corresponding modes of vibration are, in general, no longer exactly in the ratios of integers, and the partials and modes of vibration are inharmonic." A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900

"Modes of vibration whose frequencies are multiples of the frequency of the fundamental mode." The Science of Sound; Addison-Wesley Publishing Company, 1982.

"Sinusoidal quantity at a frequency which is an integer multiple of the fundamental frequency." Field of Rotating Machinery Measurment, Monitoring and Analysis; Bentley Nevada Corporation

See Also

Figure 8.5 - Summation Tones
Full Harmonic Chord
Law of Harmonic Pitch
Law of Harmonic Vibrations
Overtone Series
Power of Beat Harmonics
Resultant Tone
Table of Plate Harmonics and Intervals
1.23 - Power of Harmonics through Summation Tones
14.13 - Full Harmonic Chord
8.17 - Law of Harmonic Vibrations
8.22 - Law of Harmonic Pitch
9.23 - Circular Harmonic Orbit
9.24 - Elliptical Enharmonic Orbit
9.8 - Spontaneous Creation of Harmonic Series
9.9 - Sympathy or Harmony Between Harmonics or Overtones

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