harmonic

Definitions

  • WordNet 3.6
    • adj harmonic involving or characterized by harmony
    • adj harmonic relating to vibrations that occur as a result of vibrations in a nearby body "sympathetic vibration"
    • adj harmonic of or relating to harmony as distinct from melody and rhythm "subtleties of harmonic change and tonality"- Ralph Hill"
    • adj harmonic of or relating to the branch of acoustics that studies the composition of musical sounds "the sound of the resonating cavity cannot be the only determinant of the harmonic response"
    • adj harmonic of or relating to harmonics
    • n harmonic any of a series of musical tones whose frequencies are integral multiples of the frequency of a fundamental
    • n harmonic a tone that is a component of a complex sound
    • ***
Webster's Revised Unabridged Dictionary
  • Interesting fact: The silhouette on the MLB logo is Harmon Killebrew.
    • n Harmonic här*mŏn"ĭk (Mus) A musical note produced by a number of vibrations which is a multiple of the number producing some other; an overtone. See Harmonics.
    • Harmonic Concordant; musical; consonant; as, harmonic sounds. "Harmonic twang! of leather, horn, and brass."
    • Harmonic (Math) Having relations or properties bearing some resemblance to those of musical consonances; -- said of certain numbers, ratios, proportions, points, lines, motions, and the like.
    • Harmonic (Mus) Relating to harmony, -- as melodic relates to melody; harmonious; esp., relating to the accessory sounds or overtones which accompany the predominant and apparent single tone of any string or sonorous body.
    • ***
Century Dictionary and Cyclopedia
    • harmonic Pertaining or relating to harmony of sounds; of or pertaining to music; in general, concordant; consonant; in music, specifically, pertaining to harmony, as distinguished from melody and rhythm.
    • harmonic In acoustics, noting the secondary tones which accompany the primary tone in a complex musical tone. See II., 1.
    • harmonic In mathematics, involving or of the nature of the harmonic mean; similar to or constructed upon the principle of the harmonic curve. The first application of the adjective harmonic (in Greek) to mathematics was in the phrase harmonic proportion, said to have been used by Archytas, a contemporary of Plato. Three numbers are said to be in harmonic proportion when the first divided by the third is equal to the quotient of the excess of the first over the second divided by the excess of the second over the third; or, otherwise stated, when the reciprocal of the second is the arithmetical mean of the reciprocals of the first and third, the second number is said to be the harmonic mean of the first and third. Pythagoras first discovered that a vibrating string stopped at half its length gave the octave of the original note, and stopped at two thirds of its length gave the fifth. Now, as 1, ⅔, and ½ are in harmonic proportion, and as this phrase arose among the Pythagoreans, the word harmonic has always been held to have reference here to this fact (although Nicomachus explains it otherwise, from the properties of the cube, as ἁρμονία, or norm). The harmonic proportion or ratio, as thus defined, plays a considerable part in modern geometry as an important case of the anharmonic ratio, and has given rise to the phrases harmonic axis, center, pencil, etc. (See below.) A harmonic curve is the figure of a vibrating string. It can assume many forms, but all may be regarded as derived, by summation of displacements, from simple harmonic curves, or curves of sines. The development of this idea has given rise to the theory of harmonics, which is one of the great engines of mathematical analysis. This gives the phrases harmonic analysis, function, motion, etc.
    • harmonic In anatomy, forming or formed by a harmonia: as, a harmonic articulation or suture.
    • harmonic Also harmonical.
    • harmonic In music, the analysis of the harmonic structure of a piece.
    • harmonic The amplification of a harmonic passage by the introduction of passing-notes, etc.
    • n harmonic In acoustics: A secondary or collateral tone involved in a primary or fundamental tone, and produced by the partial vibration of the body of which the complete vibration gives the primary tone. Nearly every tone contains several distinct harmonics, which are always taken from a typical series of tones the vibration-numbers of which, beginning with that of the fundamental tone, are proportional to the series 1, 2, 3, 4, 5, 6, 7, etc. The interval from the fundamental tone to the first harmonic is, therefore, an octave; to the second, an octave and a fifth; to the third, two octaves; to the fourth, two octaves and a major third; to the fifth, two octaves and a fifth; to the Sixth, two octaves and somewhat less than a minor seventh; to the seventh, three octaves; etc. (See illustration.) Harmonics result from the elasticity of the tone-producing body, which leads it to vibrate, not only entire, but in its aliquot parts; thus, a violin-string tends to vibrate throughout its whole length, and also at the same time in each of its halves, thirds, quarters, etc. The vibration of the whole, being much the greater, gives the primary or fundamental tone; while the several partial vibrations, which diminish rapidly in force as they rise in pitch, give the harmonics. In a given tone the harmonics may usually be roughly detected by the unaided ear; but for precise and minute analysis specially constructed resonators are necessary. Tuning-forks and large stopped organ-pipes give only insignificant harmonics; certain reed-instruments, like the clarinet, give only selected sets of harmonics, as the second, fourth, sixth, etc.; while the human voice is capable of the greatest richness of harmonics. What is technically known as quality or timbre in a tone is due to the number and the relative strength of the harmonics contained in it. Different instruments and voices are thus distinguished from each other, and different uses of the same instrument or voice. In the voice, in particular, the essential difference between different vowel-sounds is a matter of harmonics. In any tone the lower harmonics are strictly consonant both with the primary tone and with each other: hence the use in the organ of mutation- and mixture-stops, whereby the consonant harmonics of a given tone are much emphasized. Many of the higher harmonics, on the other hand, are strongly dissonant both with the primary tone and with each other: hence the discordant quality of such instruments as cymbals, and the peculiar construction of the pianoforte, whereby dissonant harmonics are suppressed. In instruments of the viol and harp classes very beautiful effects are produced by suppressing the primary tone, leaving one set of its harmonics to sound alone. Such tones are called harmonic tones, or simply harmonics (though they are themselves compounded of a primary tone and its harmonics). In instruments of the trumpet class, like the horn, all the tones ordinarily used are really harmonics of the natural tone of the tube, and are produced by varying the pressure of the breath and the method of blowing. The same is true to a less degree of instruments of the wood-wind group. Harmonics are also called overtones. All the tones, primary and secondary, entering into the constitution of an actual tone are often called partial tones, or partials, the fundamental tone being the first partial, and the harmonics the upper partials.
    • n harmonic A harmonic tone. In mathematics, a function expressing the Newtonian potential of a point in terms of its coördinates.
    • harmonic In function theory, two pairs of points, one pair the intersections of a circle about with a circle through the other pair.
    • ***
Chambers's Twentieth Century Dictionary
    • adj Harmonic har-mon′ik pertaining to harmony: musical: concordant: recurring periodically
    • n Harmonic a secondary tone, overtone; a note on a stringed instrument produced by lightly stopping a string:
    • v.t Harmonic to make in harmony: to cause to agree:
    • n Harmonic (math.) one of a class of functions that enter into the development of the potential of a nearly spherical mass due to its attraction
    • v.t Harmonic (mus.) to provide parts to
    • ***

Quotations

  • Walter Gropius
    Walter Gropius
    “A modern, harmonic and lively architecture is the visible sign of an authentic democracy.”
  • King Jr. Martin Luther
    King%20Jr.%20Martin%20Luther
    “Hatred paralyzes life; love releases it. Hatred confuses life; love harmonizes it. Hatred darkens life; love illuminates it.”
  • Henry Miller
    Henry%20Miller
    “The world is not to be put in order; the world is order, incarnate. It is for us to harmonize with this order.”
  • Benjamin Disraeli
    Benjamin%20Disraeli
    “When we would prepare the mind by a forcible appeal, and opening quotation is a symphony precluding on the chords those tones we are about to harmonize.”
  • Bertrand Russell
    Bertrand%20Russell
    “Reason is a harmonizing, controlling force rather than a creative one.”

Etymology

Webster's Revised Unabridged Dictionary
L. harmonicus, Gr. "armoniko`s; cf. F. harmonique,. See Harmony

Usage

In literature:

The idea he admits as necessitated by "the very nature of reason" but it serves a purely harmonizing office.
"Preaching and Paganism" by Albert Parker Fitch
All tended to harmonize with the natural grandeur of the scene.
"At Home And Abroad" by Margaret Fuller Ossoli
This harmonic combination is death.
"The Book of the Bush" by George Dunderdale
This addition of the third would thus fall in with the law of harmonics again.
"Critical & Historical Essays" by Edward MacDowell
The chances were that, if he were to return east now, Mr. Harmon would be home by the time he reached there, if he were not already home.
"Golden Days for Boys and Girls, Vol. XIII, Nov. 28, 1891" by Various
Its walls should harmonize in color with those of the dining room.
"The Complete Home" by Various
These vanities harmonized with character and circumstance.
"Americans and Others" by Agnes Repplier
This harmonizes with Goodhue's idea of a short residence.
"Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson" by Thomas Jefferson
Silks and moquette harmonize as well as calico and ingrain once did.
"The Secret of a Happy Home (1896)" by Marion Harland
An appropriate dress is that which so harmonizes with the figure as to make the apparel unnoticeable.
"Our Deportment" by John H. Young
But can the doctrine of man's antiquity be made to harmonize with the essentials of Christianity and the inspiration of the Scriptures?
"Continental Monthly, Volume 5, Issue 4" by Various
The county officers and county court form the harmonizing centre of this larger organization.
"The Continental Monthly, Vol. III, No. V, May, 1863" by Various
Neither do they wish to know anything save what may harmonize with their own depraved views.
"History of Rationalism Embracing a Survey of the Present State of Protestant Theology" by John F. Hurst
Modulation, harmonic and melodic: Dominant Seventh.
"Music Notation and Terminology" by Karl W. Gehrkens
The harmonic scheme rarely transgresses the limits which Chopin set himself.
"Musical Portraits" by Paul Rosenfeld
That it does not harmonize with the co-existence of closely similar structures of diverse origin.
"On the Genesis of Species" by St. George Mivart
All these harmonics are also called upper partials.
"The Recent Revolution in Organ Building" by George Laing Miller
No one can be happy who tries to harmonize his life with his animal instincts.
"Pushing to the Front" by Orison Swett Marden
His voice and his arms didn't harmonize worth a cent.
"At Good Old Siwash" by George Fitch
His musical talent was strong upon the harmonic side, but upon the melodic side his imagination was not so free.
"The Masters and their Music" by W. S. B. Mathews
***

In poetry:

They harmonize like marry'd pairs,
Yet are at odds, and keep not squares:
As mercy stands from merit far,
The letter and the spirit jar.
"The Believer's Principles : Chap. II." by Ralph Erskine
Why, with wise instinct, Nature seems
To harmonize her wide extremes,
Linking the stronger with the weak,
The haughty with the soft and meek!
"The Bridal of Pennacook" by John Greenleaf Whittier
She is most fair, and thereunto
Her life loth rightly harmonize;
Feeling or thought that was not true
Ne'er made less beautiful the blue
Unclouded heaven of her eyes.
"My Love" by James Russell Lowell
"Is it a blessing in disguise?"
Of course, things always are;
But Arctic blasts with ardent skies
Somehow do not quite harmonize,
That try to cheat by weather-lies
The calendar.
"Is It April?" by Hattie Howard
Whilst mellow sounds from distant copse arise,
Of softest flute or reeds harmonic join'd,
With rapture thrill'd each worldly passion dies,
And pleased attention claims the passive mind.
"Music" by Henry Kirke White
And taught thee from the motley mass
Each harmonizing part to class,
(Like Nature's self employ'd And then, as work'd thy wayward will,
From these with rare combining skill,
With new-created worlds to fill
Of space the mighty void.
"The Sylphs Of The Seasons" by Washington Allston

In news:

Harmon, 75, of Lafe , died Friday, Nov 30, 2001, at St Bernards Medical Center.
Technological advancements and human improbable ambition are not at par with the greatest but affordable harmonizer known as Love.
This is the way the world ends: not with a bang but a higher harmonic generation.
Nathaniel Mark Harmon, Warren and Jesse Lea Barlog, Warren.
Doug Harmon Times Record News.
Musicians who worked closely with Bill Evans tend to be profoundly influenced by his harmonic thinking.
Eater Cathy Sander is heading to a family reunion in North Carolina this summer where she and her husband plan to serve mint julep s -- the better to keep the relatives cool, relaxed and harmonizing.
Rich Wetzel's big band orchestra plays free at the Harmon this weekend, plus a new jazz meet-up site.
Minnesota Twins slugger Harmon Killebrew died of cancer Tuesday, May 17, at age 74.
A pace car leads traffic during the rolling speed harmonization testing on Interstate 70 between Silverthorne and the Eisenhower/ Johnson Memorial Tunnel Aug 13.
0 Williamsburg Bridge, New York City ( Shelley Harmon ).
Substantive Harmonization Is More Likely than a Single Universal Structure.
Junior college to continue his baseball career, which has so far thrived on speed, according to PT coach Gus Harmon.
Have you recently had your 4x4 lifted and are suffering from a harmonic oscillation that can both be felt and heard.
Considering Big Pharma's trade objectives, the success of regional regulatory harmonization is not insignificant.
***

In science:

One reason the set-up is interesting from the viewpoint of probability theory is the fact that every harmonic function can be written as a Poisson integral over the set of extreme harmonic functions (which is often the Martin boundary).
Random matrix theory over finite fields: a survey
An application of Corollary 1.4 to harmonic analysis generalizes results on the problem of harmonic density [B-Tz].
Coordinate restrictions of linear operators in $l_2^n$
For this, recall , that we say that a foliation produces harmonic morphisms if it can be locally defined by submersive harmonic morphisms.
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
Then, because ϕ is a harmonic morphism, ξ ◦ ϕ : (ϕ−1 (V ), g |ϕ−1(V ) ) → Rn is a submersive harmonic map.
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
Except for second harmonic, the photocount noise reduction in higher harmonics becomes less effective with increasing N .
Quantum, classical and semiclassical analyses of photon statistics in harmonic generation
Let Hn R (M ) be the space of real harmonic forms on M with respect to hM and Hp,q (M ) the space of harmonic forms of type (p, q ).
Higher arithmetic K-theory
The accordingly modified system will include seven components (four pertaining to the fundamental harmonic, and three to the second harmonic) and five vertices.
Polychromatic solitons in a quadratic medium
It is now well-known that Riemannian metrics have optimal regularity properties in harmonic coordinates, cf. ; this is due to the special form of the Ricci curvature in harmonic coordinates, known to relativists long ago.
Cheeger-Gromov Theory and Applications to General Relativity
Given the choice of harmonic gauge, it is natural to associate a harmonic radius rh : M → R+ , which measures the size of balls on which one has harmonic coordinates in which the metric is well controlled.
Cheeger-Gromov Theory and Applications to General Relativity
Both estimates in (2.1)-(2.2) are scale invariant, (when the harmonic coordinates are rescaled as in (1.1)), and hence the harmonic radius scales as a distance.
Cheeger-Gromov Theory and Applications to General Relativity
Key words: harmonic morphism, harmonic map, degenerate semi-Riemannian manifold, stationary manifold.
Harmonic morphisms between degenerate semi-Riemannian manifolds
Harmonic morphisms between (non-degenerate semi-)Riemannian manifolds are maps which preserve germs of harmonic functions.
Harmonic morphisms between degenerate semi-Riemannian manifolds
Then, on identifying TyN with TyN (y := πN (y )), τ (φ)x ∈ Tφ(x)N can be identified with τ (φ)x ∈ Tφ(x)N ; in particular, φ is harmonic if and only if φ is (generalized) harmonic.
Harmonic morphisms between degenerate semi-Riemannian manifolds
Any (generalized) harmonic function f : U ⊆ N → R is, by definition, radicalpreserving, and so factors to a smooth function f : πN (U ) ⊆ N → R, with f = f ◦ πN ; this function f is harmonic, by Proposition 3.4.
Harmonic morphisms between degenerate semi-Riemannian manifolds
Conversely, if f : V ⊆ N → R is harmonic, then f := f ◦ πN is (generalized) harmonic.
Harmonic morphisms between degenerate semi-Riemannian manifolds
***