harmonicadj.n.

Brit.

/hɑːˈmɒnɪk/, U.S.

/hɑrˈmɑnɪk/

Etymology: < Latin harmonicus, < Greek ἁρμονικός skilled in music, musical, in neuter plural ἁρμονικά as noun, theory of music, music, < ἁρμονία harmony n.: see -ic suffix. Compare French harmonique (14th cent. in Hatzfeld & Darmesteter).

A. adj.

a. Relating to music, musical; in reference to ancient music, Relating to melody as distinguished from rhythm. Obsolete except in specific uses. harmonic hand: a figure of the left hand, having the finger-joints marked with the syllables denoting the notes of Guido d'Arezzo's scale. harmonic telegraph: see quot. a1884; also, harmonic telegraphy.

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society > leisure > the arts > music > [adjective]

musica1382

musical1447

rural1488

harmonic1570

harmonical1603

pure1605

tuneful1697

melophonic1843

society > communication > telecommunication > telegraphy or telephony > telegraphy > telegraph > [noun] > types of

field telegraph1795

enunciator1847

needle telegraph1847

indicator-telegraph1875

multiple telegraph1876

harmonic telegraph1878

Fullerphone1917

telecon1946

society > communication > telecommunication > telegraphy or telephony > telegraphy > [noun] > types or systems of

multiple telegraphy1876

quadruplex1878

cable system1887

harmonic telegraphy1902

typo-telegraphy1903

telex1932

1570 P. Levens Manipulus Vocabulorum sig. Kiii/1 Harmonicke, harmonicus.

1603 P. Holland tr. Plutarch Morals 1259 The Harmonique skill conteineth the knowledge of intervals, compositions, sounds, notes and mutations.

1694 W. Holder Treat. Harmony Introd. sig. B2^v Of the Nature of Sound in General; and then, more particularly, of Harmonick Sounds.

1782 C. Burney Gen. Hist. Music II. 90 No proof can be found in the writings of Guido that the Harmonic Hand was of his construction.

1853 C. Dickens Bleak House xi. 102 At the Sol's Arms, where the Harmonic Meetings take place.

1878 Telegraphic Jrnl. 6 cxxxiii. 348/1 Gray's harmonic telegraph can now be seen in operation at the Paris Exhibition.

1880 W. H. Husk in Grove Dict. Music I. 82 An association for..printing the best music..called the Royal Harmonic Institution.

1880 W. H. Husk in Grove Dict. Music I. 691 Harington..born in 1727..founded the Harmonic Society of Bath.

a1884 E. H. Knight Pract. Dict. Mech. Suppl. 438/2 Harmonic telegraph, a telephone, which sends messages by audible musical tones.

1902 Westm. Gaz. 8 Jan. 6/2 The extensive adoption of..harmonic telegraphy.

1925 Telegr. & Teleph. Jrnl. 11 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.Apparently an isolated use.

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1796 C. Burney Mem. Life Metastasio II. 200 Heroes of the harmonic family.

1796 C. Burney Mem. Life Metastasio II. 377 Take care of your health, for the honour of the harmonic family.

a. Sounding together with pleasing effect; harmonious, in harmony, concordant. harmonic triad: (an old name for) the common chord.

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the world > physical sensation > hearing and noise > degree, kind, or quality of sound > pleasantness of sound > [adjective] > musical or harmonious

musica1382

cordant1382

melodiousa1425

musicala1449

consonant?1521

warbling1549

harmoniousc1550

tunable1579

symphonical1589

symphoniacal1650

symphonious1652

consonous1654

harmonic1667

symphonous1814

symphonic1864

society > leisure > the arts > music > musical sound > [adjective] > melodious or harmonious

sweetc900

merryOE

softc1230

accordanta1325

well-soundingc1350

cordant1382

sootc1385

songfula1400

melodiousa1425

sugaredc1430

well-toneda1500

tunable1504

dulcea1513

equivalenta1513

consonant?1521

harmonicala1527

harmoniousc1550

consorteda1586

Orphean1593

concentful1595

melodical1596

sweet-recording1598

tuneful1598

sirenical1599

high-tuned1603

nightingale-like1611

soundful?1615

according1626

modulaminous1637

undiscording1645

canorous1646

symphonious1652

concinnous1654

consonous1654

harmonic1667

sirenica1704

symphonial1773

concentual1782

chantant1785

Memnonian1800

melodized1807

Orphic1817

undiscordant1819

concentuous1850

fluting1852

melodic1871

well-orchestrated1872

jarless1876

tuny1885

tunesome1890

society > leisure > the arts > music > musical sound > harmony or sounds in combination > [adjective]

harmonic1667

harmonical1728

vertical1889

1667 J. Milton Paradise Lost iv. 687 With Heav'nly touch of instrumental sounds In full harmonic number joind.

1728 A. Pope Dunciad ii. 232 Ass intones to Ass, Harmonic twang! of leather, horn, and brass.

a1806 H. K. White Remains (1807) I. 322 Softest flute or reeds harmonic join'd.

1845 Encycl. Metrop. V. 774 Harmonic triad..another name for the common chord.

1872 T. H. Huxley Lessons Elem. Physiol. (ed. 6) 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.

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1815 W. H. Ireland Scribbleomania 36 Harmonic and vigorous poesy.

3. Music. Relating to harmony (as distinct from melody and rhythm); belonging to the combination of musical notes in chords.

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1661 T. Blount Glossographia (ed. 2) Harmonick..that pertains to harmony, which is the accord of divers sounds or notes.

1784 W. Jones Mus. Modes Hindus in Wks. (1799) I. 413 Natural philosophy..limits the number of mixed, or harmonick, sounds to a certain series.

1869 F. A. G. Ouseley Treat. Counterpoint 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.

1879 Sat. 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.

a. Acoustics and Music. Applied to the tones produced by the vibration of a sonorous body in aliquot parts of its length (see sense 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.

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the world > matter > physics > science of sound > vibration > [adjective] > involving length

harmonical1728

longitudinal1797

harmonic1832

society > leisure > the arts > music > musical sound > pitch > system of sounds or intervals > [noun] > other scales

hendecachord1761

pentachord1786

Scotch scale1786

maqam1793

pelog1817

harmonic scale1880

whole-tone scale1900

pentatonic1909

harmonic series1910

blues scale1939

society > leisure > the arts > music > musical instrument > keyboard instrument > organ > [noun] > stop > other stops

twenty-secondc1700

vox humana1708

chorus1776

decima1825

glockenspiel1825

unison stop1830

montre1876

pyramidon1876

harmonic stop1880

orage1891

pipe stop1906

society > leisure > the arts > music > musical sound > pitch > system of sounds or intervals > [noun] > diatonic scale series > harmonic minor

harmonic minor mode1884

1832 D. Brewster Lett. Nat. Magic viii. 182 The acute sounds given out by each of the vibrating portions are called harmonic sounds.

1867 J. Tyndall 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.

1880 E. J. Payne in Grove Dict. Music I. 665 Any brass instrument, such as the hunting horn or military bugle..yields the familiar harmonic scale.

1880 E. J. Hopkins in Grove Dict. Music I. 666 Harmonic stops have in recent years come into great favour.

1880 C. A. Edwards Organs ii. xxii. 157 [The] Harmonic-flute..is an open flue stop..of extreme beauty, the tone being full and fluty.

1884 Maitland in Grove Dict. Music 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.

1889 E. Prout Harmony (ed. 10) vii. §171 This form is known as the Harmonic Minor Scale, the other two being called Melodic Minor Scales.

1910 Encycl. 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. Obsolete.

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1831 D. Brewster Treat. 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.

1858 G. 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. Mathematics.

a. Applied to the relation of quantities whose reciprocals are in arithmetical progression (e.g. 1, ¹/ ₂, ¹/ ₃, ¹/ ₄,…); or to points, lines, functions, etc., involving such a relation; = harmonical adj. 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 ¹/ ₂, 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 senses A. 4, B. 2. harmonic average: = harmonic mean harmonic 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. harmonic 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. harmonic 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. harmonic progression: the relation of a series of quantities whose reciprocals are in arithmetical progression, or such a series itself. harmonic proportion: the relation of three quantities in harmonic progression; the second is said to be a harmonic mean between the first and third. harmonic range (also harmonic row): a series of four points in a straight line, forming two pairs of harmonic conjugates. harmonic ratio: = harmonic proportion; harmonic series: = harmonic progression, esp. the series 1 + ¹/ ₂ + ¹/ ₃ + ¹/ ₄ + …

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the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets > of sequences > progression

geometrical1543

harmonical1569

progressional1570

musical1589

equidifferent1696

harmonic1706

synharmonic1850

preferred1922

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression > numerical elements in or parts of

parcel1561

figurate numbers1666

harmonic mean1706

harmonical1796

arithmetical1798

harmonic average1949

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression > numerical elements in or parts of > relation between

harmonic proportion1706

cross-ratio1881

harmonic ratio1949

the world > relative properties > number > geometry > line > [noun] > set or system of

peacock's tail1570

harmonicala1746

pencil1840

harmonic pencil1862

sheaf1863

congruency1864

linkage1874

congruence1879

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression

progressionc1450

arithmetical progression1553

geometrical progression1557

geometric progression1696

geometric ratio1736

arithmetical ratio1798

geometrical ratio1798

arithmetic progression1886

harmonic series1964

1706 W. Jones Synopsis Palmariorum Matheseos 79 Whence, if the 2 first Terms of an Harmonic Proportion be given, the 3d. is readily found.

1862 Mulcahy 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.

1866 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) II. 96/1 Harmonic Progression or Series, a series of numbers such that any three consecutive terms are in harmonic proportion.

1881 J. Casey 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.

1885 C. Leudesdorf tr. L. Cremona Elements Projective Geom. 41 If..the harmonic range..be projected upon any other straight line, its projection..will also be a harmonic range.

1895 N. Story-Maskelyne Crystallogr. §63. 75 Harmonic division of a zone.

1895 N. Story-Maskelyne Crystallogr. §63. 75 The harmonic division of an angle.

1949 G. James & R. C. James Math. Dict. (rev. ed.) 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.

1949 G. James & R. C. James Math. Dict. (rev. ed.) 23/2 The harmonic average is the reciprocal of the arithmetic average of reciprocals of the observations.

1964 H. K. Crowder & S. W. McCuskey Topics in Higher Anal. iv. 193 Since √(n + 1)/n>1/n for all n>0, and ∑∞n = 1 1/n is the harmonic series that diverges, ∑∞n = 1 √(n + 1)/n also diverges.

b. harmonic motion n. 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 abscissae; 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.

ΘΚΠ

the world > movement > motion in specific manner > alternating or reciprocating motion > oscillation > [noun] > harmonic motion

harmonic motion1867

the world > matter > physics > mechanics > types of motion > [noun] > vibration or oscillation > harmonic motion

harmonic motion1867

the world > relative properties > number > algebra > [noun] > expression > function > harmonic function

harmonic1867

harmonic motion1867

tesseral harmonic1873

1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. §53 Simple harmonic motion... Such motions [are] approximately those of the simplest vibrations of sounding bodies..whence their name.

1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. §56 The velocity of a point executing a simple harmonic motion is a simple harmonic function of the time.

1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. §75 A complex harmonic function, with a constant term added, is the proper expression..for any..periodic function.

1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. 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.

1882 G. M. Minchin Uniplanar Kinematics 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.

1908 Royal Soc. Catal. Sci. Papers 1800–1900 I. Pure Math. 402/1 (title) Harmonic analyser.

1910 Hawkins' Electr. Dict. 193/1 Harmonic current.

c. Of or relating to harmonics (sense A. 2b), 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.).

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society > communication > telecommunication > radio communications > [noun] > signal > interference

cross-talk1887

static1905

X1906

statics1912

click1914

jam1914

grinder1922

hash1923

mush1924

echo1928

image1928

radio echo1928

harmonic interference1929

second channel1932

the world > matter > physics > electromagnetic radiation > electronics > electronic devices or components > [noun] > device generating signal > device generating or combining harmonics

harmonic generator1929

the world > matter > physics > electromagnetic radiation > electronics > electronic phenomena > signal > [noun] > unwanted part of signal > distortion > types of

overmodulation1927

harmonic distortion1929

amplitude distortion1931

intermodulation1931

cross-modulation1933

1929 K. Henney Princ. Radio xvii. 450 We determined the percentage of harmonic distortion that occurred in an amplifier when it worked over a curved characteristic.

1930 Terms & 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.

1930 Proc. IRE 18 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.

1930 Proc. IRE 18 31 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.

1931 Trans. Amer. Inst. Electr. Engineers 50 811/1 The vacuum-tube harmonic generators of present practise are fundamentally amplifiers operated under conditions of input voltage and grid bias.

1962 A. Nisbett Technique Sound Studio 249 Harmonic distortion is most easily caused by flattening of peaks in the waveform.

1962 A. Nisbett Technique Sound Studio 249 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.

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the world > relative properties > order > agreement, harmony, or congruity > [adjective]

samtalec1175

samentalea1300

accordingc1300

accordantc1350

covenablec1384

concordable1393

accorda1413

suant1418

consonant1489

convenablea1500

concordant1512

semblable1513

convenient1526

modulatec1530

harmonical1531

harmoniacal1536

agreeable1540

concurrent1542

suitable1568

concinne1569

harmonial1569

sympathical1570

tunable1573

coherenta1575

conspiring1576

well-consenting1579

well-consorted1583

congruous1599

high-tuned1603

symbolizing1611

unjarring1620

concording1627

congruenta1637

harmonious1638

friendlya1641

unclashing1642

complying1646

symphoniacal1650

consistent1651

consentaneous1652

consentivea1657

symbolical1667

concordiousa1670

sympathetic1673

congenerous1677

symbolizant1685

congenial1693

symphonious1743

harmonic1756

concentual1782

undiscordant1819

concordial1822

attuned1833

connate1836

sympathetical1848

concentuous1850

consenting1858

consilient1867

tuned in1958

1756 T. Amory Life John Buncle I. 31 I came to a little harmonick building, that had every charm and proportion architecture could give it.

1784 J. Potter Virtuous Villagers I. 110 Souls..united by harmonic union.

1796 H. Hunter tr. J.-H. B. de Saint-Pierre Stud. Nature (1799) II. 3 The most harmonic of all contrasts.

1893 J. Pulsford Loyalty to Christ II. 435 He is Harmonic Man, He is God manifested.

7. Anatomy. Belonging to or of the nature of a harmonia n.

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1826 W. Kirby & W. Spence Introd. 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. In plural. A theory or system of musical sounds or intervals; that part of acoustics which relates to music. (rarely in singular.) Obsolete except in reference to ancient systems.

ΘΚΠ

society > leisure > the arts > music > musical sound > pitch > system of sounds or intervals > [noun]

systemc1580

scale1597

diagram1656

gamut1702

harmonics1702

the world > matter > physics > science of sound > [noun] > relating to music

harmonics1837

society > leisure > the arts > music > study or science of music > [noun] > of acoustical aspects

harmonics1837

tonometry1876

1702 V. Mandey tr. J. J. Hainlin Synopsis Mathematica: Theoret. Arithm. iii. 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.

1761 F. H. E. Stiles in Philos. Trans. 1760 (Royal Soc.) 51 698 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.

1837 W. Whewell Hist. Inductive Sci. I. 67 The truths of harmonics..were cultivated with much care.

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 n. at differential adj. and n. Compounds.

ΘΚΠ

society > leisure > the arts > music > musical sound > [noun] > note or tone > undertones, overtones, etc.

harmonic1772

undertone1832

subtone1838

by-tone1852

overtone1867

upper partial1873

overnote1917

1772 W. Jones Ess. Imit. Arts in Poems 206 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.

1831 H. Melvill in Preacher II. 2811 The harmonics of some Italian musician.

1880 E. J. Payne in Grove Dict. Music I. 664 The harmonics..determine..as has been lately proved by Helmholtz, the quality of musical tones.

1880 E. J. Payne in Grove Dict. Music I. 665 Natural harmonics..are an important resource in harp music..Brass instruments are richest in the practical employment of harmonics.

1884 H. R. Haweis My Musical Life i. 26–7 Playing all sort of melodies in flute-like harmonics.

b. In an alternating circuit: a component current whose frequency is a multiple of the fundamental; (also) a corresponding electro-magnetic oscillation.

ΘΚΠ

the world > matter > physics > electromagnetic radiation > electricity > circuit > [noun] > alternating circuit > component current

harmonic1894

1894 Amer. Jrnl. Sci. 148 379 The presence of upper harmonics in an alternating current wave.

1894 Amer. Jrnl. Sci. 148 383 For every harmonic of the inducing current we shall have a harmonic electromotive force of the same frequency in the resonant circuit.

1919 R. 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.

1955 Sci. Amer. June 43/3 They act like radio transmitters, emitting radio waves at the critical frequency and at harmonics of this frequency.

3. Mathematics. = harmonic function at sense A. 5b, 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, harmonic sectorial, harmonic tesseral, and zonal harmonics, etc.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > harmonic function

harmonic1867

harmonic motion1867

tesseral harmonic1873

1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. i. App. B General expressions for complete spherical harmonics of all orders.

1873 J. C. Maxwell Treat. Electr. & Magnetism 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.

1885 H. W. Watson & S. H. Burbury Math. Theory Electr. & Magn. I. 67 To express the potential at any point P of any distribution of matter in a series of spherical solid harmonics.

1885 H. W. Watson & S. H. Burbury Math. Theory Electr. & Magn. I. 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.

This entry has not yet been fully updated (first published 1898; most recently modified version published online June 2022).

单词	harmonic
释义	harmonicadj.n. Brit. /hɑːˈmɒnɪk/, U.S. /hɑrˈmɑnɪk/ Etymology: < Latin harmonicus, < Greek ἁρμονικός skilled in music, musical, in neuter plural ἁρμονικά as noun, theory of music, music, < ἁρμονία harmony n.: see -ic suffix. Compare French harmonique (14th cent. in Hatzfeld & Darmesteter). A. adj. 1. a. Relating to music, musical; in reference to ancient music, Relating to melody as distinguished from rhythm. Obsolete except in specific uses. harmonic hand: a figure of the left hand, having the finger-joints marked with the syllables denoting the notes of Guido d'Arezzo's scale. harmonic telegraph: see quot. a1884; also, harmonic telegraphy. ΘΚΠ society > leisure > the arts > music > [adjective] musica1382 musical1447 rural1488 harmonic1570 harmonical1603 pure1605 tuneful1697 melophonic1843 society > communication > telecommunication > telegraphy or telephony > telegraphy > telegraph > [noun] > types of field telegraph1795 enunciator1847 needle telegraph1847 indicator-telegraph1875 multiple telegraph1876 harmonic telegraph1878 Fullerphone1917 telecon1946 society > communication > telecommunication > telegraphy or telephony > telegraphy > [noun] > types or systems of multiple telegraphy1876 quadruplex1878 cable system1887 harmonic telegraphy1902 typo-telegraphy1903 telex1932 1570 P. Levens Manipulus Vocabulorum sig. Kiii/1 Harmonicke, harmonicus. 1603 P. Holland tr. Plutarch Morals 1259 The Harmonique skill conteineth the knowledge of intervals, compositions, sounds, notes and mutations. 1694 W. Holder Treat. Harmony Introd. sig. B2^v Of the Nature of Sound in General; and then, more particularly, of Harmonick Sounds. 1782 C. Burney Gen. Hist. Music II. 90 No proof can be found in the writings of Guido that the Harmonic Hand was of his construction. 1853 C. Dickens Bleak House xi. 102 At the Sol's Arms, where the Harmonic Meetings take place. 1878 Telegraphic Jrnl. 6 cxxxiii. 348/1 Gray's harmonic telegraph can now be seen in operation at the Paris Exhibition. 1880 W. H. Husk in Grove Dict. Music I. 82 An association for..printing the best music..called the Royal Harmonic Institution. 1880 W. H. Husk in Grove Dict. Music I. 691 Harington..born in 1727..founded the Harmonic Society of Bath. a1884 E. H. Knight Pract. Dict. Mech. Suppl. 438/2 Harmonic telegraph, a telephone, which sends messages by audible musical tones. 1902 Westm. Gaz. 8 Jan. 6/2 The extensive adoption of..harmonic telegraphy. 1925 Telegr. & Teleph. Jrnl. 11 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.Apparently an isolated use. ΚΠ 1796 C. Burney Mem. Life Metastasio II. 200 Heroes of the harmonic family. 1796 C. Burney Mem. Life Metastasio 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. ΘΚΠ the world > physical sensation > hearing and noise > degree, kind, or quality of sound > pleasantness of sound > [adjective] > musical or harmonious musica1382 cordant1382 melodiousa1425 musicala1449 consonant?1521 warbling1549 harmoniousc1550 tunable1579 symphonical1589 symphoniacal1650 symphonious1652 consonous1654 harmonic1667 symphonous1814 symphonic1864 society > leisure > the arts > music > musical sound > [adjective] > melodious or harmonious sweetc900 merryOE softc1230 accordanta1325 well-soundingc1350 cordant1382 sootc1385 songfula1400 melodiousa1425 sugaredc1430 well-toneda1500 tunable1504 dulcea1513 equivalenta1513 consonant?1521 harmonicala1527 harmoniousc1550 consorteda1586 Orphean1593 concentful1595 melodical1596 sweet-recording1598 tuneful1598 sirenical1599 high-tuned1603 nightingale-like1611 soundful?1615 according1626 modulaminous1637 undiscording1645 canorous1646 symphonious1652 concinnous1654 consonous1654 harmonic1667 sirenica1704 symphonial1773 concentual1782 chantant1785 Memnonian1800 melodized1807 Orphic1817 undiscordant1819 concentuous1850 fluting1852 melodic1871 well-orchestrated1872 jarless1876 tuny1885 tunesome1890 society > leisure > the arts > music > musical sound > harmony or sounds in combination > [adjective] harmonic1667 harmonical1728 vertical1889 1667 J. Milton Paradise Lost iv. 687 With Heav'nly touch of instrumental sounds In full harmonic number joind. View more context for this quotation 1728 A. Pope Dunciad ii. 232 Ass intones to Ass, Harmonic twang! of leather, horn, and brass. a1806 H. K. White Remains (1807) I. 322 Softest flute or reeds harmonic join'd. 1845 Encycl. Metrop. V. 774 Harmonic triad..another name for the common chord. 1872 T. H. Huxley Lessons Elem. Physiol. (ed. 6) 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. ΚΠ 1815 W. H. Ireland Scribbleomania 36 Harmonic and vigorous poesy. 3. Music. Relating to harmony (as distinct from melody and rhythm); belonging to the combination of musical notes in chords. ΚΠ 1661 T. Blount Glossographia (ed. 2) Harmonick..that pertains to harmony, which is the accord of divers sounds or notes. 1784 W. Jones Mus. Modes Hindus in Wks. (1799) I. 413 Natural philosophy..limits the number of mixed, or harmonick, sounds to a certain series. 1869 F. A. G. Ouseley Treat. Counterpoint 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. 1879 Sat. 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 Music. Applied to the tones produced by the vibration of a sonorous body in aliquot parts of its length (see sense 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. ΘΚΠ the world > matter > physics > science of sound > vibration > [adjective] > involving length harmonical1728 longitudinal1797 harmonic1832 society > leisure > the arts > music > musical sound > pitch > system of sounds or intervals > [noun] > other scales hendecachord1761 pentachord1786 Scotch scale1786 maqam1793 pelog1817 harmonic scale1880 whole-tone scale1900 pentatonic1909 harmonic series1910 blues scale1939 society > leisure > the arts > music > musical instrument > keyboard instrument > organ > [noun] > stop > other stops twenty-secondc1700 vox humana1708 chorus1776 decima1825 glockenspiel1825 unison stop1830 montre1876 pyramidon1876 harmonic stop1880 orage1891 pipe stop1906 society > leisure > the arts > music > musical sound > pitch > system of sounds or intervals > [noun] > diatonic scale series > harmonic minor harmonic minor mode1884 1832 D. Brewster Lett. Nat. Magic viii. 182 The acute sounds given out by each of the vibrating portions are called harmonic sounds. 1867 J. Tyndall 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. 1880 E. J. Payne in Grove Dict. Music I. 665 Any brass instrument, such as the hunting horn or military bugle..yields the familiar harmonic scale. 1880 E. J. Hopkins in Grove Dict. Music I. 666 Harmonic stops have in recent years come into great favour. 1880 C. A. Edwards Organs ii. xxii. 157 [The] Harmonic-flute..is an open flue stop..of extreme beauty, the tone being full and fluty. 1884 Maitland in Grove Dict. Music 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. 1889 E. Prout Harmony (ed. 10) vii. §171 This form is known as the Harmonic Minor Scale, the other two being called Melodic Minor Scales. 1910 Encycl. 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. Obsolete. ΚΠ 1831 D. Brewster Treat. 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. 1858 G. 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. Mathematics. a. Applied to the relation of quantities whose reciprocals are in arithmetical progression (e.g. 1, ¹/ ₂, ¹/ ₃, ¹/ ₄,…); or to points, lines, functions, etc., involving such a relation; = harmonical adj. 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 ¹/ ₂, 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 senses A. 4, B. 2. harmonic average: = harmonic mean harmonic 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. harmonic 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. harmonic 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. harmonic progression: the relation of a series of quantities whose reciprocals are in arithmetical progression, or such a series itself. harmonic proportion: the relation of three quantities in harmonic progression; the second is said to be a harmonic mean between the first and third. harmonic range (also harmonic row): a series of four points in a straight line, forming two pairs of harmonic conjugates. harmonic ratio: = harmonic proportion; harmonic series: = harmonic progression, esp. the series 1 + ¹/ ₂ + ¹/ ₃ + ¹/ ₄ + … ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets > of sequences > progression geometrical1543 harmonical1569 progressional1570 musical1589 equidifferent1696 harmonic1706 synharmonic1850 preferred1922 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression > numerical elements in or parts of parcel1561 figurate numbers1666 harmonic mean1706 harmonical1796 arithmetical1798 harmonic average1949 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression > numerical elements in or parts of > relation between harmonic proportion1706 cross-ratio1881 harmonic ratio1949 the world > relative properties > number > geometry > line > [noun] > set or system of peacock's tail1570 harmonicala1746 pencil1840 harmonic pencil1862 sheaf1863 congruency1864 linkage1874 congruence1879 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression progressionc1450 arithmetical progression1553 geometrical progression1557 geometric progression1696 geometric ratio1736 arithmetical ratio1798 geometrical ratio1798 arithmetic progression1886 harmonic series1964 1706 W. Jones Synopsis Palmariorum Matheseos 79 Whence, if the 2 first Terms of an Harmonic Proportion be given, the 3d. is readily found. 1862 Mulcahy 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. 1866 W. T. Brande & G. W. Cox Dict. Sci., Lit. & Art (new ed.) II. 96/1 Harmonic Progression or Series, a series of numbers such that any three consecutive terms are in harmonic proportion. 1881 J. Casey 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. 1885 C. Leudesdorf tr. L. Cremona Elements Projective Geom. 41 If..the harmonic range..be projected upon any other straight line, its projection..will also be a harmonic range. 1895 N. Story-Maskelyne Crystallogr. §63. 75 Harmonic division of a zone. 1895 N. Story-Maskelyne Crystallogr. §63. 75 The harmonic division of an angle. 1949 G. James & R. C. James Math. Dict. (rev. ed.) 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. 1949 G. James & R. C. James Math. Dict. (rev. ed.) 23/2 The harmonic average is the reciprocal of the arithmetic average of reciprocals of the observations. 1964 H. K. Crowder & S. W. McCuskey Topics in Higher Anal. iv. 193 Since √(n + 1)/n>1/n for all n>0, and ∑∞n = 1 1/n is the harmonic series that diverges, ∑∞n = 1 √(n + 1)/n also diverges. b. harmonic motion n. 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 abscissae; 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. ΘΚΠ the world > movement > motion in specific manner > alternating or reciprocating motion > oscillation > [noun] > harmonic motion harmonic motion1867 the world > matter > physics > mechanics > types of motion > [noun] > vibration or oscillation > harmonic motion harmonic motion1867 the world > relative properties > number > algebra > [noun] > expression > function > harmonic function harmonic1867 harmonic motion1867 tesseral harmonic1873 1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. §53 Simple harmonic motion... Such motions [are] approximately those of the simplest vibrations of sounding bodies..whence their name. 1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. §56 The velocity of a point executing a simple harmonic motion is a simple harmonic function of the time. 1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. §75 A complex harmonic function, with a constant term added, is the proper expression..for any..periodic function. 1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. 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. 1882 G. M. Minchin Uniplanar Kinematics 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. 1908 Royal Soc. Catal. Sci. Papers 1800–1900 I. Pure Math. 402/1 (title) Harmonic analyser. 1910 Hawkins' Electr. Dict. 193/1 Harmonic current. c. Of or relating to harmonics (sense A. 2b), 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.). ΘΚΠ society > communication > telecommunication > radio communications > [noun] > signal > interference cross-talk1887 static1905 X1906 statics1912 click1914 jam1914 grinder1922 hash1923 mush1924 echo1928 image1928 radio echo1928 harmonic interference1929 second channel1932 the world > matter > physics > electromagnetic radiation > electronics > electronic devices or components > [noun] > device generating signal > device generating or combining harmonics harmonic generator1929 the world > matter > physics > electromagnetic radiation > electronics > electronic phenomena > signal > [noun] > unwanted part of signal > distortion > types of overmodulation1927 harmonic distortion1929 amplitude distortion1931 intermodulation1931 cross-modulation1933 1929 K. Henney Princ. Radio xvii. 450 We determined the percentage of harmonic distortion that occurred in an amplifier when it worked over a curved characteristic. 1930 Terms & 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. 1930 Proc. IRE 18 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. 1930 Proc. IRE 18 31 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. 1931 Trans. Amer. Inst. Electr. Engineers 50 811/1 The vacuum-tube harmonic generators of present practise are fundamentally amplifiers operated under conditions of input voltage and grid bias. 1962 A. Nisbett Technique Sound Studio 249 Harmonic distortion is most easily caused by flattening of peaks in the waveform. 1962 A. Nisbett Technique Sound Studio 249 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. ΘΚΠ the world > relative properties > order > agreement, harmony, or congruity > [adjective] samtalec1175 samentalea1300 accordingc1300 accordantc1350 covenablec1384 concordable1393 accorda1413 suant1418 consonant1489 convenablea1500 concordant1512 semblable1513 convenient1526 modulatec1530 harmonical1531 harmoniacal1536 agreeable1540 concurrent1542 suitable1568 concinne1569 harmonial1569 sympathical1570 tunable1573 coherenta1575 conspiring1576 well-consenting1579 well-consorted1583 congruous1599 high-tuned1603 symbolizing1611 unjarring1620 concording1627 congruenta1637 harmonious1638 friendlya1641 unclashing1642 complying1646 symphoniacal1650 consistent1651 consentaneous1652 consentivea1657 symbolical1667 concordiousa1670 sympathetic1673 congenerous1677 symbolizant1685 congenial1693 symphonious1743 harmonic1756 concentual1782 undiscordant1819 concordial1822 attuned1833 connate1836 sympathetical1848 concentuous1850 consenting1858 consilient1867 tuned in1958 1756 T. Amory Life John Buncle I. 31 I came to a little harmonick building, that had every charm and proportion architecture could give it. 1784 J. Potter Virtuous Villagers I. 110 Souls..united by harmonic union. 1796 H. Hunter tr. J.-H. B. de Saint-Pierre Stud. Nature (1799) II. 3 The most harmonic of all contrasts. 1893 J. Pulsford Loyalty to Christ II. 435 He is Harmonic Man, He is God manifested. 7. Anatomy. Belonging to or of the nature of a harmonia n. ΚΠ 1826 W. Kirby & W. Spence Introd. 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. In plural. A theory or system of musical sounds or intervals; that part of acoustics which relates to music. (rarely in singular.) Obsolete except in reference to ancient systems. ΘΚΠ society > leisure > the arts > music > musical sound > pitch > system of sounds or intervals > [noun] systemc1580 scale1597 diagram1656 gamut1702 harmonics1702 the world > matter > physics > science of sound > [noun] > relating to music harmonics1837 society > leisure > the arts > music > study or science of music > [noun] > of acoustical aspects harmonics1837 tonometry1876 1702 V. Mandey tr. J. J. Hainlin Synopsis Mathematica: Theoret. Arithm. iii. 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. 1761 F. H. E. Stiles in Philos. Trans. 1760 (Royal Soc.) 51 698 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. 1837 W. Whewell Hist. Inductive Sci. I. 67 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 n. at differential adj. and n. Compounds. ΘΚΠ society > leisure > the arts > music > musical sound > [noun] > note or tone > undertones, overtones, etc. harmonic1772 undertone1832 subtone1838 by-tone1852 overtone1867 upper partial1873 overnote1917 1772 W. Jones Ess. Imit. Arts in Poems 206 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. 1831 H. Melvill in Preacher II. 2811 The harmonics of some Italian musician. 1880 E. J. Payne in Grove Dict. Music I. 664 The harmonics..determine..as has been lately proved by Helmholtz, the quality of musical tones. 1880 E. J. Payne in Grove Dict. Music I. 665 Natural harmonics..are an important resource in harp music..Brass instruments are richest in the practical employment of harmonics. 1884 H. R. Haweis My Musical Life i. 26–7 Playing all sort of melodies in flute-like harmonics. b. In an alternating circuit: a component current whose frequency is a multiple of the fundamental; (also) a corresponding electro-magnetic oscillation. ΘΚΠ the world > matter > physics > electromagnetic radiation > electricity > circuit > [noun] > alternating circuit > component current harmonic1894 1894 Amer. Jrnl. Sci. 148 379 The presence of upper harmonics in an alternating current wave. 1894 Amer. Jrnl. Sci. 148 383 For every harmonic of the inducing current we shall have a harmonic electromotive force of the same frequency in the resonant circuit. 1919 R. 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. 1955 Sci. Amer. June 43/3 They act like radio transmitters, emitting radio waves at the critical frequency and at harmonics of this frequency. 3. Mathematics. = harmonic function at sense A. 5b, 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, harmonic sectorial, harmonic tesseral, and zonal harmonics, etc. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > harmonic function harmonic1867 harmonic motion1867 tesseral harmonic1873 1867 W. Thomson & P. G. Tait Treat. Nat. Philos. I. i. i. App. B General expressions for complete spherical harmonics of all orders. 1873 J. C. Maxwell Treat. Electr. & Magnetism 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. 1885 H. W. Watson & S. H. Burbury Math. Theory Electr. & Magn. I. 67 To express the potential at any point P of any distribution of matter in a series of spherical solid harmonics. 1885 H. W. Watson & S. H. Burbury Math. Theory Electr. & Magn. I. 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. This entry has not yet been fully updated (first published 1898; most recently modified version published online June 2022). < adj.n.1570
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