Harmonics of a fundamental sound usually (but not always) in simple multiples of 1, 2, 3, 4, 5, etc.. of the fundamental. This term is preferred over harmonic which is generally understood to be a multiple of 2 or 2x of a tone while an overtone can be any developed secondary, tertiary or higher resultant tone. [see Law of Heat, Law of Cycles]
Ramsay
dividing itself by 2 or 3 or 5, etc., up through the whole geometrical series of numbers, not keeping fixed at one thing; but while the whole length is vibrating the fundamental partial, it keeps shifting the still nodes along its length, and sometimes longer and sometimes shorter segments are sounding the other partials which clothe the chief sound. It has been commonly said that "a musical sound is composed of three sounds," for every ear is capable of hearing these three, and with a little attention a few more than these; but many will be startled when told that there are twenty-five sounds in that sound. Eighteen of them are simply the octaves of the other seven, all of these seven except one having one or more octaves in the sound. Four of the seven also are very feeble, the one which has no octave being the feeblest of all. Two of the other three are so distinctly audible along with the chief partial that they gave rise to the saying we have quoted about a musical sound being composed of three sounds.1 If the three most pronounced partials were equally developed in one sound, it could not be called one sound - it would decidedly be a chord; and when in the system they do become developed, they form a chord; but in the one sound they, the partials, having fewer and fewer octaves to strengthen them, fade away in the perspective of sound. The sharp seventh, which in the developed system has only one place, not coming into existence until the sixth octave of the genesis, is by far the feeblest of all the partials, and Nature did well to appoint it so. These harmonics are also sometimes called "overtones," because they are higher than the fundamental one, which is the sound among the sounds, as the Bible is the book among books. [Scientific Basis and Build of Music, page 59]
which seems to show that not only has one part of a vibrating string sympathy with another part of it so as to go into harmonic partials, as we have just seen, but as if the very air itself had sympathy with harmoniously vibrating strings; for Tartini observed that two harmonious sounds being produced and sustained as they can be, for example, by a strong bow on the violin, a third sound will be heard. Tartini's name for it was simply "a third sound." This is not an overtone, as Helmholtz has called the harmonic partials of one sounding string, but an undertone, because it is a "grave harmonic," away below the sounds of the two strings which awaken it. The subject of these undertones has been carefully studied since Tartini's day, and more insight has been obtained since we are now able to count and register the vibration of any musical sound. Helmholtz has called these third sounds of Tartini's "difference sounds," because when awakened by two strings, for example, the vibration-number of the third tone is the difference of the vibrations-numbers of the two tones which awaken it. The note C with vibration-number 512, and another C whose vibration-number is 256, the octave, awakened no third sound, because there is no difference between the two numbers - the one is just the doubled or halved; but if we take C256 and G381, its fifth, the difference number is 128; this being a low octave of C256, it has the effect of strengthening the upper one. Helmholtz found this to be the law of the third sound as to its producing, and the effect of it when produced. This third sound, mysteriously arising in the air through the sympathy it has with all concordant things, is another among many more suggestions that the whole Creation is measured and numbered to be in sympathy one part with another. The Creation is a universe. [Scientific Basis and Build of Music, page 60]
Russell
Also known as "overtones of the wave", overtone position, etc.
"Inductive energy ever pulls toward the overtones of the waves, which are the points of maximum opposition." [The Universal One; Book 01 - Chapter 11 - Energy Transmission]
"It is also difficult to realize that our whole solar system is subject to the gravitational pull of the north overtone point of the wave of which it is but one atom." [The Universal One; Book 02 - Chapter 12 - Gravitation and Radiation]
"The apices of the cones are the overtones of the wave." [The Universal One; Book 02 - Chapter 12 - Gravitation and Radiation]
"South is the plane of inertia where every expression of energy begins to gather its force from the expanded area of its harmonic circles, with the intent of overcoming the inertia of substance by concentrating it into harmonic spheres at its overtone points of north." [The Universal One; Book 02 - Chapter 13 - Expressions of Gravitation and Radiation]
"North is the meeting point of all of the positive-negative, plus-minus, male-female pressure walls which have been erected toward both northerly overtone points of every wave, to help sustain the illusion of stability which this universe of motion constantly produces." [The Universal One; Book 02 - Chapter 13 - Expressions of Gravitation and Radiation]
"The bi-sexual plane of the overtone of every wave is the flywheel of the universal machine, revolving with gyroscopic perfection of balance at an angle of 90° to the inertial plane of concept of its wave of energy." [The Universal One; Book 02 - Chapter 13 - Expressions of Gravitation and Radiation]
"The overtone plane of gyroscopic perfection is the plane where north meets south and East meets west in bi-sexual unity.
"The overtones of gyroscopic perfection are where the electric poles have contracted to a point, and where the ever shortening positive cones of energy turn their outer positive contours to inner negative ones by expanding their bases to the planes of their apices." [Universal One; Book 02 - Chapter 13 - Expressions of Gravitation and Radiation]
"The electric pole measures the northern opposed distance limitations of the wave at trough and crest in points of wave altitudes which we shall call the overtones." [The Universal One; Book 02 - Chapter 15 - Expressions of Gravitation and Radiation]
"By connecting the overtones with every point of the harmonic circles, opposing cones are produced." [The Universal One; Book 02 - Chapter 15 - Expressions of Gravitation and Radiation]
"Magnetism, in seeking to suppress motion actually assists it by drawing the harmonic circles of its area dimension gradually into the plane of the electric north, thus creating a new south plane of zero latitude around the point of north at the overtone position of each wave. This plane is reflected at the equator of each mass of each wave." [The Universal One; Book 02 - Chapter 15 - Expressions of Gravitation and Radiation]
"The ecliptics of all elements between the inertial harmonic circles and the overtones vary in their expansion and contraction according to their position and the relative expansion and contraction of the opposing cones of energy.
"At the overtones, the ecliptic is a plane born of the melding of both contours and bases in the plane of the melded apices of the opposing cones.
"From the overtones toward inertia, the ecliptics of all waves, systems and masses expand as the bases of the generative cones expand." [The Universal One; Book 02 - Chapter 15 - Expressions of Gravitation and Radiation]
"The popular concept that light travels along undulating waves is not in conformity with the laws of motion. Waves are constructed in sequential stages until they meet at their overtone positions in trough and crest." [The Universal One; Book 02 - Chapter 16 - Expressions of Gravitation and Radiation]
"A true sphere is only possible at the exact point of north at the overtone of the wave." [The Universal One; Book 02 - Chapter 16 - Expressions of Gravitation and Radiation]
"Let us call the corners of the cube the north points, or overtones of the wave." [The Universal One; Book 02 - Chapter 16 - Expressions of Gravitation and Radiation]
"In sodium, therefore, at the beginning of the super-exhalation, the intense accumulated pressures of inhalation cause so great a storm of contraction that sodium registers her overtone in preponderance to her true tone." [The Universal One; Book 02 - Chapter 19 - Expressions of Gravitation and Radiation]
"A perfect analogy is that of the old-fashioned church organ in which the controls are not sufficiently adjusted to prevent a pipe from sounding its overtone instead of its true tone when the boy who pumps the bellows suddenly becomes over vigorous." [The Universal One; Book 02 - Chapter 19 - Expressions of Gravitation and Radiation]
"The spectrum of any element can only be obtained when that element is in a state of incandescence, which necessitates an increase of radiative, expansive pressure. This fact has much also to do with the recording of the overtone of sodium instead of the true tone." [The Universal One; Book 02 - Chapter 19 - Expressions of Gravitation and Radiation]
"This is the birth of energy in man's "spiritual" universe. The transition to man's "physical" universe of solids of matter can now be easily visualized by imagining the gradual contraction of each electric pole to the points of north at the overtones of each wave." [The Universal One; Book 02 - Chapter 20 - Expressions of Gravitation and Radiation]
"Through contraction of the electric poles, centrifugal force is born in the inertial plane and is increased in force until that plane has gyrated unsteadily to its overtone position of maximum contraction at the point of north of the cubes of motion on its outward journey to mass and is decreased in force as it returns to plane.
"Although centripetal force is preponderant on the outward journey to mass from 0= to 4++ in the positive half of the wave, centrifugal force increases in excess of centripetal force until the former overtakes and counterbalances the latter at the overtone of the wave." [The Universal One; Book 02 - Chapter 20 - Expressions of Gravitation and Radiation]
"Thus is the concept of energy in the one point of north in inertia divided into its opposites of expression in sex in the appearance of two points of north at the overtones of every wave in order that the dimensionless universe of simultaneity in inertia may become a universe of dimension with sequential intervals of reproduction of its productions." [The Universal One; Book 02 - Chapter 20 - Expressions of Gravitation and Radiation]
"The position of the charging poles represents the increase of electric force. This increase is in the direction of north at the overtone of the wave, and toward the reflections of north at the gravitative centers of all masses of the wave." [The Universal One; Book 02 - Chapter 20 - Expressions of Gravitation and Radiation]
"At the overtone of the wave, where all planets are true spheres, the ability to generate and to radiate is equally distributed over the entire area of each planet." [The Universal One; Book 02 - Chapter 21 - Expressions of Gravitation and Radiation]
"When our sun, for example, has reached its overtone position at the north point of the wave, its radio-activity will have overtaken its genero-activity." [The Universal One; Book 02 - Chapter 21 - Expressions of Gravitation and Radiation]
"The revolution of mass begins in the maximum tenuity of the inertial plane and ends in the maximum rigidity of the point of north at the overtone of the wave." [The Universal One; Book 02 - Chapter 22 - Expressions of Gravitation and Radiation]
"When the exact position of this solar system is calculated in reference to its ultimate destination at the overtone of its wave, the orbit of Neptune will be one of its important measuring units." [The Universal One; Book 02 - Chapter 22 - Expressions of Gravitation and Radiation]
"True cubic crystallization can only take place at the overtone position of the wave in the cubes of motion." [The Universal One; Book 02 - Chapter 23 - Expressions of Gravitation and Radiation]
"When the maximum of any expression of energy is reached at the overtone position of the wave, the one simple unstable plane of motion begins its complexing into many planes." [The Universal One; Book 02 - Chapter 24 - Expressions of Gravitation and Radiation]
See Also
1.23 - Power of Harmonics through Summation Tones
9.8 - Spontaneous Creation of Harmonic Series
9.9 - Sympathy or Harmony Between Harmonics or Overtones
Differentiation
Figure 8.5 - Summation Tones
Harmonic
Interval
Law of Cycles
Law of Harmonic Pitch
Law of Harmonic Vibrations
Law of Heat
major
major key
major scale
Overtone Series
Overtones Developed Musically
Power of Beat Harmonics
Principle of Regeneration
Resultant Tone
Scale
Sympathetic Vibration
Sympathy
Undertone
Vibrating Rod Harmonics
Wolf Tone