| 释义 |
harmonic, a. and n.|hɑːˈmɒnɪk|
[ad. L. harmonic-us, a. Gr. ἁρµονικός skilled in music, musical, in neut. pl. ἁρµονικά as n., theory of music, music, f. ἁρµονία harmony: see -ic. Cf. F. harmonique (14th c. in Hatz.-Darm.).]
A. adj.
1. a. Relating to music, musical; in reference to ancient music, Relating to melody as distinguished from rhythm. Obs. exc. in specific uses.
harmonic hand: a figure of the left hand, having the finger-joints marked with the syllables denoting the notes of Guido Aretino's scale. harmonic telegraph: see quot. 1884; also, harmonic telegraphy.
1570Levins Manip. 121/33 Harmonicke, harmonicus. 1603Holland Plutarch's Mor. 1259 The Harmonique skill conteineth the knowledge of intervals, compositions, sounds, notes and mutations. 1694W. Holder Harmony (1731) Introd., Of the Nature of Sound in General; and then, more particularly, of Harmonick Sounds. 1782Burney Hist. Mus. II. 90 No proof can be found in the writings of Guido that the Harmonic Hand was of his construction. 1852Dickens Bleak Ho. xi, At the Sol's Arms, where the Harmonic Meetings take place. 1878Telegraphic Jrnl. VI. cxxxiii. 348/1 Gray's harmonic telegraph can now be seen in operation at the Paris Exhibition. 1880W. H. Husk in Grove Dict. Mus. I. 82 An association for..printing the best music..called the Royal Harmonic Institution. Ibid. 691 Harington..born in 1727..founded the Harmonic Society of Bath. 1884Knight Dict. Mech. Supp., Harmonic telegraph, a telephone, which sends messages by audible musical tones. 1902Westm. Gaz. 8 Jan. 6/2 The extensive adoption of..harmonic telegraphy. 1925Telegr. & Teleph. Jrnl. XI. cxxii. 152/2 Mr. Cromwell Varley, who seems to have been the first to get hold of the fundamental idea of harmonic telegraphy, of sending into the telegraph line a number of different frequencies of signalling current at the same time and sorting them out at other stations.
b. Addicted to music; musical. nonce-use.
1796Burney Mem. Metastasio II. 200 Heroes of the harmonic family. Ibid. II. 377 Take care of your health, for the honour of the harmonic family.
2. a. Sounding together with pleasing effect; harmonious, in harmony, concordant.
harmonic triad, an old name for the common chord.
1667Milton P.L. iv. 687 With Heav'nly touch of instrumental sounds In full harmonic number joind. 1728Pope Dunc. ii. 254 Ass intones to Ass, Harmonic twang! of leather, horn and brass. c1800K. White Music vi, Softest flutes or reeds harmonic join'd. 1845Encycl. Metrop. V. 774 Harmonic triad..another name for the common chord. 1872Huxley Phys. viii. 212 A tuning-fork may be set vibrating, if its own particular note or one harmonic with it, be sounded in its neighbourhood.
b. Melodious, tuneful, sweet-sounding. rare.
1815W. H. Ireland Scribbleomania 36 Harmonic and vigorous poesy.
3. Mus. Relating to harmony (as distinct from melody and rhythm); belonging to the combination of musical notes in chords.
1661Blount Glossogr. (ed. 2), Harmonick..that pertains to harmony, which is the accord of divers sounds or notes. 1784Sir W. Jones Mus. Modes Hindus Wks. 1799 I. 413 Natural philosophy..limits the number of mixed, or harmonick, sounds to a certain series. 1869Ouseley Counterp. i. 1 When we look at a piece of harmonized music from the harmonic point of view, we confine our attention to the chords of which it is composed. 1879Sat. Rev. 6 Dec. 699 Chromatic notes are used..for two..purposes—a harmonic purpose in modulation to new keys, and a melodic purpose in ornamentation.
4. a. Acoustics and Mus. Applied to the tones produced by the vibration of a sonorous body in aliquot parts of its length (see B. 2); relating to such tones.
harmonic scale: the scale formed by the series of harmonics of a fundamental note. harmonic minor mode or harmonic scale: see quot. 1884. harmonic series = harmonic scale. harmonic stop: an organ-stop in which each of the pipes is pierced with a small hole in the middle of its length, so as to give the note corresponding to half the length; e.g. the harmonic flute.
1831Brewster Nat. Magic viii. (1833) 182 The acute sounds given out by each of the vibrating portions are called harmonic sounds. 1867Tyndall Sound iii. 123 The sounds of the Eolian harp are produced by the division of suitably stretched strings into a greater or less number of harmonic parts by a current of air passing over them. 1880E. J. Payne in Grove Dict. Mus. I. 665 Any brass instrument, such as the hunting horn or military bugle..yields the familiar harmonic scale. 1880E. J. Hopkins Ibid. 666 Harmonic stops have in recent years come into great favour. 1881C. A. Edwards Organs 157 [The] Harmonic-flute..is an open flue stop..of extreme beauty, the tone being full and fluty. 1884Maitland in Grove Dict. Mus. IV. 666/2 Harmonic minor is the name applied to that version of the minor scale which contains the minor sixth together with the major seventh, and in which no alteration is made in ascending and descending. 1889E. Prout Harmony (ed. 10) vii. §171 This form is known as the Harmonic Minor Scale, the other two being called Melodic Minor Scales. 1910Encycl. Brit. XIII. 1/1 The unisonous quality of octaves is easily explained when we examine the ‘harmonic series’ of upper partials.
†b. Optics. Applied to ‘accidental’ or subjective complementary colours, formerly supposed to be analogous to harmonic sounds. Obs.
1831Brewster Optics xxxvi. 309 As in acoustics, where every fundamental sound is..accompanied with its harmonic sound, so..the sensation of one [colour] is accompanied by a weaker sensation of its accidental or harmonic colour. 1858G. Barnard Landscape Paint. 29 The term harmonic has been applied to accidental colours because the primitive and its accidental colour harmonise with each other in painting.
5. Math.
a. Applied to the relation of quantities whose reciprocals are in arithmetical progression (e.g. 1, ½, 1/3, 1/4,{ddd}); or to points, lines, functions, etc., involving such a relation; = harmonical 7.
(This application, which originated with the ancient Pythagoreans, is generally held to have arisen from the fact that a string or other sonorous body, divided into segments whose lengths are ½, 1/3, 1/4, etc. of the total length, gives a definite series of musical notes whose relations are of fundamental importance in harmony; see A. 4, B. 2.)
harmonic average = harmonic mean. h. conjugates, each of the two pairs of points AB, CD, in relation to the other pair, in a straight line ACBD divided harmonically at C and B. h. division, division of a line at four points A, C, B, D, such that the lengths AC, AB, AD, are in harmonic proportion; also analogous division of an angle or other magnitude. h. pencil, a system of four straight lines in a plane meeting at one point, such as to divide harmonically every straight line that cuts them. h. progression, the relation of a series of quantities whose reciprocals are in arithmetical progression, or such a series itself. h. proportion, the relation of three quantities in harmonic progression; the second is said to be a harmonic mean between the first and third. h. range or harmonic row, a series of four points in a straight line, forming two pairs of harmonic conjugates. h. ratio = harmonic proportion. h. series = harmonic progression; esp. the series 1 + ½ + 1/3 + 1/4 + {ddd}
1706W. Jones Syn. Palmar. Matheseos 79 Whence, if the 2 first Terms of an Harmonic Proportion be given, the 3d. is readily found. 1862Mulcahy Mod. Geom. 7 Four right lines drawn from the same point and cutting a right line harmonically (called a harmonic pencil) will also cut harmonically any other right line meeting them. 1866Brande & Cox Dict. Sci., Lit., & Art II. 96/1 Harmonic Progression or Series, a series of numbers such that any three consecutive terms are in harmonic proportion. 1881Casey Sequel to Euclid 88 If C and D be harmonic conjugates to A and B, AB is called a harmonic mean between AC and AD. 1885C. Leudesdorf Cremona's Proj. Geom. 41 If..the harmonic range..be projected upon any other straight line, its projection..will also be a harmonic range. 1895Story-Maskelyne Crystallogr. §63. 75 Harmonic division of a zone. Ibid., The harmonic division of an angle. 1942G. James Math. Dict. 199/1 Harmonic ratio. If the cross ratio of four points (or four lines) is equal to -1, it is called a harmonic ratio and the last two points are said to divide the first two harmonically. 1949G. & R. C. James Math. Dict. 23/2 The harmonic average is the reciprocal of the arithmetic average of reciprocals of the observations. 1964Crowder & McCuskey Topics in Higher Analysis iv. 193 Since √(n + 1)/n>1/n for all n>0, and {Summ}∞n = 1 1/n is the harmonic series that diverges, {Summ}∞n = 1 √(n + 1)/n also diverges.
b. harmonic motion, a periodic motion, which in its simplest form (simple harmonic motion) is like that of a point in a vibrating string, and is identical with the resolved part, parallel to a diameter, of uniform motion in a circle.
harmonic function, a function consisting of a series of terms, each of which expresses a harmonic motion; in a wider sense, any function that satisfies a differential equation of a class of which that expressing a simple harmonic motion is the first example. harmonic analysis, the calculus of harmonic functions, an important part of modern mathematical analysis. harmonic curve, a curve in which the ordinates are a simple harmonic function of the abscissæ; a curve of sines. harmonic analyser, an integrating machine invented by Lord Kelvin for producing mechanically the harmonic constituents of meteorological, tidal, and other curves. harmonic current, an alternating current the variations of which, graphically represented, follow a harmonic curve.
1867Thomson & Tait Nat. Phil. I. i. §53 Simple harmonic motion..Such motions [are] approximately those of the simplest vibrations of sounding bodies..whence their name. Ibid. §56 The velocity of a point executing a simple harmonic motion is a simple harmonic function of the time. Ibid. §75 A complex harmonic function, with a constant term added, is the proper expression..for any..periodic function. Ibid. i. i. App. B, The..method..commonly referred to by English writers as that of ‘Laplace's Co-efficients’..is here called spherical harmonic analysis..A spherical harmonic function is defined as a homogeneous function, V, of x, y, z, which satisfies the equation d2V / dx2 + d2V / dy2 + d2V / dz2 = 0. 1882Minchin Unipl. Kinemat. 7 If a point..moves..round in a circle with constant velocity, the foot..of the perpendicular from the point on any diameter of the circle moves backwards and forwards..with a motion which is called a simple harmonic motion. 1908R. Soc. Catal. Sci. Papers 1800–1900 I. Pure Math. 402/1 (title) Harmonic analyser. 1910Hawkins's Electr. Dict. 193/1 Harmonic current.
c. Electr. Of or relating to harmonics (harmonic n. 2 b), as harmonic distortion, non-linear distortion of a wave-form in which harmonics of the original frequencies are introduced into it; harmonic generator, a device that generates and combines harmonics of one or more sinusoidal oscillations to produce a complex wave-form; harmonic interference, interference caused by the reception of harmonics of a transmitted signal of some other frequency; harmonic selective signalling (see quot.).
1929K. Henney Princ. Radio xvii. 450 We determined the percentage of harmonic distortion that occurred in an amplifier when it worked over a curved characteristic. 1930Terms & Def. Telegr. & Teleph. (B.S.I.) 21 Harmonic selective signalling, signalling a number of stations on one circuit by means of alternating or pulsating currents of different frequencies, each individual station being tuned to one frequency only. A calling station can call any selected station independently of the others by employing the frequency particular to the selected station. 1930Proc. Inst. Radio Engin. XVIII. 31 If a receiver with poorly designed selective circuits is subjected to relatively high local field intensities one of the radio-frequency tubes may be overloaded and may then function as a modulator or harmonic generator. Ibid., Complaints of harmonic interference are, at times, received by the operators of broadcast stations which can be traced directly to deficiencies in the design of the receivers employed. 1931Trans. Amer. Inst. Electr. Engin. L. 811/1 The vacuum-tube harmonic generators of present practise are fundamentally amplifiers operated under conditions of input voltage and grid bias. 1962A. Nisbett Technique Sound Studio 249 Harmonic distortion is most easily caused by flattening of peaks in the waveform. Ibid., 1% harmonic distortion is not usually noticeable.
6. Relating to or marked by harmony, agreement, or concord (in general sense); harmonizing in aspect or artistic effect; harmonious in feeling, etc.
1756T. Amory J. Buncle (1770) I. i. 33, I came to a little harmonic building, that had every charm and proportion architecture could give it. 1784J. Potter Virtuous Villagers I. 110 Souls..united by harmonic union. 1796H. Hunter tr. St. Pierre's Stud. Nat. (1799) II. 3 The most harmonic of all contrasts. 1893J. Pulsford Loyalty to Christ II. 435 He is Harmonic Man, He is God manifested.
7. Anat. Belonging to or of the nature of a harmonia, q.v.
1826Kirby & Sp. Entomol. (1828) III. xxxiv. 402 note, A harmonic suture is when the margins of two flat bones simply touch each other without any intermediate substance.
B. n.
1. pl. A theory or system of musical sounds or intervals; that part of acoustics which relates to music. (Rarely in sing.) Obs. exc. in reference to ancient systems.
1709–29V. Mandey Syst. Math., Arith. 48 That the Lovers of Musick may have the Proportions in view..we thought it convenient in this place to expose the Harmonicks of the Ingenious John Kepler. 1760Stiles in Phil. Trans. LI. 698 Harmonic was divided into these seven parts; 1. of sounds, 2. of intervals, 3. of genera, 4. of systems, 5. of tones, 6. of mutations, 7. of melopœïa. 1837Whewell Hist. Induct. Sc. (1857) I. 50 The truths of Harmonics..were cultivated with much care.
2. a. (Short for harmonic tone.) One of the secondary or subordinate tones produced by vibration of the aliquot parts of a sonorous body (as a string, reed, column of air in a pipe, etc.); usually accompanying the primary or fundamental tone produced by the vibration of the body as a whole. Also called overtones or upper partials (as being of higher pitch than the fundamental tone).
Harmonics are sometimes produced independently, as in the violin and other stringed instruments by varying the point of contact of the bow, or by lightly pressing the string with the finger at special points, and in certain wind instruments by varying the force or direction of the breath. natural harmonics: the series of harmonics naturally produced by the vibration of a string, etc., in halves, thirds, quarters, and so on; also, on instruments of the violin class, harmonics obtained from an open string, those from a stopped string being called artificial harmonics. grave harmonic: a name sometimes given to a low tone resulting from the combination of two tones = differential tone.
1777Sir W. Jones Ess. Arts Poems, etc. 196 These accessory sounds, which are caused by the aliquots of a sonorous body vibrating at once, are called harmonicks, and the whole system of modern Harmony depends upon them. 1831H. Melvill in Preacher II. 2811 The harmonics of some Italian musician. 1880E. J. Payne in Grove Dict. Mus. I. 664 The harmonics..determine..as has been lately proved by Helmholtz, the quality of musical tones. Ibid. 665 Natural harmonics..are an important resource in harp music..Brass instruments are richest in the practical employment of harmonics. 1884Haweis My Musical Life i. 26–7 Playing all sort of melodies in flute-like harmonics.
b. Electr. In an alternating circuit, a component current whose frequency is a multiple of the fundamental; also, a corresponding electro-magnetic oscillation.
1894Amer. Jrnl. Sci. CXLVIII. 379 The presence of upper harmonics in an alternating current wave. Ibid. 383 For every harmonic of the inducing current we shall have a harmonic electromotive force of the same frequency in the resonant circuit. 1919R. Stanley Text-bk. Wireless Telegr. (ed. 2) II. 164 When the fundamental oscillations in a circuit are accompanied by other subsidiary oscillations the latter are called harmonics. 1955Sci. Amer. June 43/3 They act like radio transmitters, emitting radio waves at the critical frequency and at harmonics of this frequency.
3. Math. = harmonic function (A. 5 b), in the wider sense. spherical harmonic, a harmonic function having a relation to Spherical Geometry akin to that which functions expressing harmonic motion have to Plane Geometry. Such are spherical solid harmonics, spherical surface harmonics, sectorial harmonic, tesseral harmonic, and zonal harmonics, etc.
1867Thomson & Tait Nat. Philos. i. i. App. B, General expressions for complete spherical harmonics of all orders. 1873Maxwell Electr. & Magn. I. 163 When the poles are given, the value of the harmonic for a given point on the sphere is a perfectly definite numerical quantity. 1885Watson & Burbury Math. Th. Electr. & Magn. I. 67 To express the potential at any point P of any distribution of matter in a series of spherical solid harmonics. Ibid. 68 It is evident that the density of this distribution on the sphere must by symmetrical about OC, and must therefore be expressible in a series of zonal harmonics with OC as axis. |