Unreferenced date December 2009 To produce an artificialharmonic , a stringed instrument player holds down a note on the neck with the Handedness non dominant hand , thereby shortening the vibrational length of the string, uses a finger to lightly touch a point on the string that is an integer divisor of its vibrational length, and plucks or bow music bow s the side of the string that is closer to the bridge. This technique is used to produce harmonic tones that are otherwise inaccessible on the instrument. To guitar players, one variety of this technique is known as a pinch harmonic . This technique, like natural harmonics, works by canceling out the fundamental tone and one or more partial tones by deadening their modes of vibration. See node physics node . Details explanation Overtones Image Flageolette.svg thumb right 256px Playing a harmonic on a string click to enlarge . Image Table of Harmonics.svg thumb right 256px Table of harmonics of a stringed instrument with colored dots indicating which positions can be lightly fingered to generate Just intonation just intervals up to the 7th harmonic. Main Overtone When a Strings music string is plucked or bowed, the string Vibration vibrates at several frequency frequencies . The vibration along the entire length of the string is known as the fundamental , while vibrations occurring between points along the string known as node physics nodes are referred to as overtone s. The fundamental and overtones, when sounded together, are perceived by the listener as a single tone, though the relative prominence of the frequencies varies among instruments, and contribute to its timbre . Harmonics Main HarmonicHarmonic s are produced on the instrument by lightly touching a string as opposed to fretting it at any of several points ... also 3rd Bridge Harmonic Pinch harmonic DEFAULTSORT ArtificialHarmonic Category String instruments ... natural. If the string is fretted, the harmonics are termed Artificial harmonics artificial . Natural ... more details
string are harmonics. A harmonic of a wave is a component frequency of the signal that is an integer .... Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found ..., but several frequencies known as Harmonic series music partials . When the oscillator is long and thin ... a result of the relative strengths of the individual harmonic frequencies. bell instrument Bells have ... for their unique quality of producing multiple harmonic partials or multiphonics . Harmonics and overtones ... Hz n 1 fundamental tone 1st harmonic 2 f 880 Hz n 2 1st overtone 2nd harmonic 3 f 1320 Hz n 3 2nd overtone 3rd harmonic 4 f 1760 Hz n 4 3rd overtone 4th harmonic Harmonics ... and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially ... 200px Playing a harmonic on a string The following table displays the stop points on a stringed instrument, such as the guitar guitar harmonics , at which gentle touching of a string will force it into a harmonic ... & Grantham, ibid, p.71. ref class wikitable Harmonic Stop note Sounded note relative to open string ... text align right 702.0 7 septimal minor third 2P8 harmonic seventh septimal minor seventh m7 style ... fingered to generate Just intonation just intervals up to the 7th harmonic Other information Harmonics ... Violin harmonics.ogg title Violin harmonics description Violin natural harmonic stop points on the A string ... that each harmonic is presented at the same signal level as the fundamental the sample tones sound louder as they increase in frequency format2 Ogg Aristoxenus Artificialharmonic Harmonics electrical power Electronic tuner Formant Fourier series Fundamental frequency Harmonic oscillator Harmonic series music Harmony Inharmonic Just intonation Overtones Pinch harmonic Pure tone Pythagorean tuning Scale of harmonics Singing bowl Stretched octave Tap harmonic Xenharmonic References Reflist External ... etudes and notation issues Cite EB1911 wstitle Harmonic http www.dranetz bmi.com pdf harmonicsall.pdf ... more details
Commonscat Harmonics Harmonic usually refers to the frequency components of a time varying signal, such as a musical note. Mathematics, science and engineering Harmonic mathematics , a number of concepts in mathematics Harmonic analysis , representing signals by superposition of basic waves Harmonic oscillator , a concept in classical mechanics Simple harmonic motion , a concept in classical mechanics Distortion Harmonic distortion Harmonic distortion , a measurement of signal distortion Harmonics electrical power Harmonic tremor , a rhythmic earthquake which may indicate volcanic activity Music Artificialharmonic , a string instrument playing technique Enharmonic , a spelling issue in music Guitar harmonics , a guitar playing technique Scale of harmonics , a musical scale based on harmonic nodes of a string Stanford Harmonics The Harmonics , a rock a cappella group from Stanford University Harmony , the musical use of simultaneous pitches, or chords Inharmonicity , the degree of overtones departure from integral multiples of the fundamental frequency Overtone , any resonant frequency higher than the fundamental frequency Other uses Harmonic color , a relationship between three colors Harmonic Convergence , a New Age astrological term Harmonics , the twelfth movement of Mike Oldfield s Tubular Bells 2003 album Disambig ... more details
wiktionarypar harmonic For Harmonic scale , see Harmonic minor scale Harmonic major scale Harmonic Scale . See also Scale of harmonics disambig ... more details
about several concepts in mathematics that are called harmonic other uses of the word harmonic disambiguation In mathematics , a number of concepts employ the word harmonic. The similarity of this terminology to that of harmonic music is not accidental the equations of motion of vibrating strings, drums and columns of air are given by formulas involving Laplacian s the solutions to which are given by eigenvalue s corresponding to their modes of vibration. Thus, the term harmonic is applied when one is considering functions with sinusoidal variations, or solutions of Laplace s equation and related concepts. See harmonic analysis harmonic division harmonic form harmonic function harmonic mean harmonic mode harmonic number harmonic series mathematics harmonic series Category Mathematical terminology nn Harmonisk i matematikk ... more details
Commonscat Harmonic series Harmonic series may refer to either of two related concepts Harmonic series mathematics Harmonic series music disambig bs Harmonijski red vor es Serie arm nica pt S rie harm nica ... more details
Harmonic motion can mean The motion of a Harmonic oscillator in physics , which can be Simple harmonic motion Complex harmonic motion Keplers laws of planetary motion in physics , known as the harmonic law Quasi harmonic motion Unit hyperbola Parametrization Musica universalis in medieval astronomy , the music of the spheres Chord progression in music , harmonic progression See also Pendulum Harmonograph Circular motion disambig ... more details
Pinch Harmonic Examples at ActionTab Category Guitar performance techniques Category Heavy metal performance techniques ca Pinch harmonic es Arm nico artificial it Pinch harmonic nl Pinch harmonic ...Listen filename Pinch harmonic1.ogg title Example of pinch harmonic description Pinch harmonic example on the 3rd fret of the G string, made on an Ibanez Prestige played through a distortion pedal and played with vibrato A pinch harmonic or pick harmonic ref http www.xtrememusician.com info guitar techniques 1.html ref is a guitar technique in which the player s thumb or index finger on the picking hand slightly catches the string after it is picked, canceling the fundamental frequency fundamental of the string, and letting one of the overtone s dominate. This results in a high Pitch music pitch ed sound . By using string bending, a whammy bar , a wah wah pedal , or other effects, electric guitar ... ensures that the otherwise subtle harmonic is greatly amplified. An early example can be heard in Roy ... the tremolo arm and high gain amps together with the pinch harmonic to produce horse like ... in death metal is notable in that pinch harmonic notes are included in riff s, rather than being reserved ... played by both rhythm guitarists if there are two , the pinch harmonic notes leap ... performed on an acoustic guitar A pinch harmonic is produced when the thumb of the picking hand lightly ... harmonic nodes for the note to sound. For example, to produce a pinch harmonic one octave higher than ... i.e. its own harmonic s will share the nodes of the lower overtone, so won t be muted. They will, however, be at a much lower volume and since they form the selected overtone s own harmonic series ... overtone, no higher overtones will sound. A single harmonic overtone is far quieter than ... over a pickup, it won t sound through that pickup. The playing of a pinch harmonic combined with use ... the whammy bar and sounding an open string pinch harmonic, usually on the G and B strings, then slowly ... more details
Harmonic Grammar is a linguistic model proposed by Geraldine Legendre , Yoshiro Miyata , and Paul Smolensky in 1990. It is a connectionism connectionist approach to modeling linguistic well formedness. Related Optimality Theory Bibliography Keller, Frank. 2000 . Gradience in grammar Experimental and computational aspects of degrees of grammaticality . Doctoral dissertation, University of Edinburgh . Online http homepages.inf.ed.ac.uk keller papers phd.html homepages.inf.ed.ac.uk keller papers phd.html . Keller, Frank. 2006 . Linear Optimality Theory as a model of gradience in grammar. In G. Fanselow, C. Fery, R. Vogel, & M. Schlesewsky Eds. , Gradience in grammar Generative perspectives . Oxford Oxford University Press. Online http homepages.inf.ed.ac.uk keller papers oup06a.html homepages.inf.ed.ac.uk keller papers oup06a.html . Legendre, G raldine Miyata, Yoshiro & Smolensky, Paul. 1990 . Can connectionism contribute to syntax? Harmonic Grammar, with an application. In M. Ziolkowski, M ..., Paul. 1990 . Can connectionism contribute to syntax? Harmonic grammar, with an application . Report ... . Harmonic Grammar A formal multi level connectionist theory of linguistic well formedness Theoretical .... 1990 . Harmonic Grammer A formal multi level connectionist theory of linguistic well formedness Theoretical ... & Smolensky, Paul. 1990 . Harmonic Grammar A formal multi level connectionist theory of linguistic ... & Smolensky, Paul. 1990 . Harmonic Grammar A formal multi level connectionist theory of linguistic well ... & Smolensky, Paul. 2006 . The Optimality Theory Harmonic Grammar connection. In P. Smolensky & G. Legendre Eds. , The harmonic mind From neural computation to Optimality Theoretic grammar pp ... & Bhatt, Rajesh. 2007 . Harmonic Grammar with linear programming. University of Massachusetts, Amherst ... of symbolic structures in connectionist networks. Artificial Intelligence , 46 , 159 216. Smolensky, Paul & Legendre, G raldine. 2006 . The harmonic mind From neural computation to Optimality Theoretic ... more details
Infobox Album See Wikipedia WikiProject Albums Name Harmonic Generator Type EP Artist The Datsuns Cover Harmonic Generator cover Datsuns .gif Genre Rock Producer The Datsuns Last album The Datsuns br 2002 This album Harmonic Generator Next album Outta Sight, Outta Mind br 2004 Harmonic Generator is a Japanese six track Extended play EP by New Zealand rock band The Datsuns . It contains radio sessions of three songs and live studio recordings of a further three see below for track listing . It also contains the music video for Harmonic Generator as an enhanced multimedia track. It is named after the guitar distortion pedal used on the track the Prunes & Custard Harmonic Generator Intermodulator manufactured by Crowther Audio. Track listing Harmonic Generator live Sittin Pretty live Fink for the man live Little Bruise O Woe is Me Freeze Sucker Harmonic Generator Enhanced track Category The Datsuns albums ... more details
A harmonic spectrum is a spectrum of an operator spectrum containing only frequency components whose frequency frequencies are whole number multiples of the fundamental frequency such frequencies are known as harmonic s. In other words, if math omega , math is the fundamental frequency, then a harmonic spectrum has the form math dots, 2 omega, omega, 0, omega, 2 omega, dots . math A standard result of Fourier analysis is that a function has a harmonic spectrum if and only if it is periodic function periodic . See also Fourier series Periodic function Scale of harmonics Mathanalysis stub Signal processing stub Category Functional analysis ... more details
Image Harmonic series klang.png thumb Harmonic series on C, partials 1 5 numbered audio Harmonic series klang.mid Play . Image Harmonic series klang G.png thumb Harmonic series on G, partials 1 5 numbered audio Harmonic series klang G.mid Play . The Harmonic Scale is a Super Just musical scale allowing extended just intonation , beyond 5 limit music limit to the 19th harmonic audio 19th harmonic on C.mid Play , and free modulation music modulation through the use of synthesizer s. It includes 144 note music notes per octave and two circle of fifths circles of fifths . For example, if the harmonic scale is tuned to a fundamental frequency fundamental of C then C is also the 16th and 32nd harmonic s, C music is the 17th audio Minor diatonic semitone on C.mid Play , D the 18th audio Major tone on C.mid Play , E music b the 19th audio 19th harmonic on C.mid Play , E music natural the 20th audio Just major third on C.mid Play , F the 21st a natural seventh above G, but not a great interval above C audio Twenty first harmonic on C.mid Play , F music the 22nd audio Eleventh harmonic on C.mid Play , G the 24th audio Just perfect fifth on C.mid Play , A music b the 26th audio Tridecimal neutral sixth on C.mid Play , A music natural the 27th a just fifth above D audio Pythagorean major sixth on C.mid Play , B music b the 28th audio Harmonic seventh on C.mid Play , B music natural the 30th audio Just major seventh on C.mid Play , and some harmonics are not included. ref name Milano Milano, Dominic November 1986 . http www.wendycarlos.com other PDF Files Kbd86Tunings .pdf A Many Colored Jungle of Exotic Tunings , Keyboard . ref It was used invented by Wendy Carlos and used on her album Beauty in the Beast 1986 . Transpositions and tuning table s are controlled by left hand on the appropriate note on a one octave keyboard. ref name Milano Sources reflist Musical tuning Scales Category 19 limit tuning Category Musical scales music theory stub ... more details
In music theory , harmonic rhythm , also known as harmonic tempo is the rate at which the Chord music chords change. According to Joseph Swain 2002 p.4 it is simply that perception of rhythm that depends on changes in aspects of harmony. According to Walter Piston 1944 , the rhythmic life contributed to music by means of the underlying changes of harmony. The pattern of the harmonic rhythm of a given piece of music, derived by noting the root chord root changes as they occur, reveals important and distinctive features affecting the Music genre style and Texture music texture . Harmonic rhythm is rarely notated or described exactly rather, analysts compare the overall pace of harmonic rhythm from one piece to another, or the amount of variation of harmonic rhythm within a piece. For example, a key stylistic difference between Baroque music and Classical music era Classical period music is that the latter exhibits much more variety of harmonic rhythm, even though the harmony itself is less complex. Alexander Scriabin s music features an increasingly slow harmonic rhythm beginning in his middle period. Prelude no. 1 in C major audio Bach C Major Prelude Equal.ogg Play BWV 846 from Johann Sebastian Bach J. S. Bach s Well Tempered Clavier illustrates the difference between melodic and harmonic rhythm through a constant stream of sixteenth note s, Bach changes chord music chords only once per measure. Source Piston, Walter 1944 . Cited in Swain, Joseph P. 2002 . Harmonic Rhythm Analysis and Interpretation . ISBN 0 19 515087 2. Category Rhythm Category Harmony ca Ritme harm nic ... more details
In geometry , harmonic division of a line segment AB means identifying two Point geometry point s C and D such that AB is divided internally and externally in the same ratio math frac CA CB frac DA DB . math In the example shown below, the ratio is two. Specifically, the distance AC is one inch, the distance CB is half an inch, the distance AD is three inches, and the distance BD is 1.5 inches. Image Harmonic division.png frame center Harmonic division of AB by points C and D Harmonic division of a line segment is reciprocal if points C and D divide the line segment AB harmonically, the points A and B also divide the line segment CD harmonically. In that case, the ratio is given by math frac BC BD frac AC AD math which equals one third in the example above. Note that the two ratios are not equal Harmonic division of a line segment is a special case of Apollonius of Perga Apollonius definition of the circle . It is also related to the cross ratio . See also projective harmonic conjugate References C. Stanley Ogilvy 1990 Excursions in Geometry , Dover. ISBN 0 486 26530 7. Category Euclidean plane geometry de Harmonische Teilung fr Division harmonique nl Harmonische ligging ro Diviziune armonic ... more details
Unreferenced stub auto yes date December 2009 Tap harmonic is a technique used with fretted string instruments, usually guitar . It is executed by tapping on the actual fret wire most commonly at the 12th fret, but also can be executed by tapping any of the fret wires with proper technique. It can also be done by gently touching the string over the fret wire instead of tapping the fret wire if the string is already ringing. See also Guitar harmonics Harmonics Shred Guitar DEFAULTSORT Tap Harmonic Category Guitar performance techniques Guitar stub it Tap harmonic ... more details
About color relationships other uses of the word harmonic disambiguation Orphan date February 2009 Color s or hue s are said to be harmonic if their spacing on the color wheel meets certain criteria. ref cite journal last1 Cohen Or first1 Daniel year 2006 title Color Harmonization journal ACM Transactions on Graphics publisher ACM volume 25 3 pages 624 issn 0730 0301 url http portal.acm.org citation.cfm?id 1141911.1141933&coll portal&dl ACM&idx J778&part transaction&WantType Transactions&title TOG&CFID en.wikipedia.org wiki ACM Transactions on Graphics&CFTOKEN en.wikipedia.org wiki ACM Transactions on Graphics ref Harmonic colors are said to be color coordinated, and work well together in principles of design and art . Notes references DEFAULTSORT Harmonic Color Category Color Color stub ... more details
Orphan date February 2009 The Harmonic scalpel is a cutting instrument used during surgical procedures to simultaneously cut and coagulate tissue. The Harmonic brand is manufactured and distributed by Ethicon Endo Surgery a subsidiary of Johnson & Johnson . The instrument is similar to a Bovie , but superior in that it can cut through thicker tissue, creates less smoke, and may offer greater precision. However, the harmonic scalpel is not as easily maneuverable as the Bovie, and takes longer to cut and coagulate tissue. Additionally, while a Bovie can be used to coagulate bleeding tissue at any time, the Harmonic scalpel only coagulates as it cuts. The Harmonic scalpel causes less lateral thermal damage than the Bovie . Whereas a Bovie performs its action via an electrical current and production of heat , the Harmonic scalpel cuts via vibration. The scalpel surface itself cuts through tissue by vibrating in the range of 55,500 Hz. The vibration cuts through the tissue and seals it using protein denaturization, rather than heat. A good analogy is whisking an egg white denaturation of the protein by vibration rather than heat. References cite journal author Msika S, Deroide G, Kianmanesh R, et al. title Harmonic scalpel in laparoscopic colorectal surgery journal Dis. Colon Rectum volume 44 issue 3 pages 432 6 year 2001 month March pmid 11289292 doi url cite journal author Awwad JT, Isaacson K title The harmonic scalpel an intraoperative complication journal Obstet Gynecol volume 88 issue 4 Pt 2 pages 718 20 year 1996 month October pmid 8841266 doi url cite journal author Siperstein AE, Berber E, Morkoyun E title The use of the harmonic scalpel vs conventional knot tying for vessel ligation in thyroid surgery journal Arch Surg volume 137 issue 2 pages 137 42 year 2002 month February pmid 11822946 doi url Category Surgery cs Harmonick skalpel ... more details
Infobox musical artist name The City Harmonic image caption image size upright 1 background group or band genre Alternative rock , Christian rock , Worship music origin Hamilton, Ontario , Canada years active 2006&ndash present label Kingsway ref http www.myspace.com thecityharmonic The City Harmonic on Myspace Music Myspace . ref website thecityharmonic.com http www.thecityharmonic.com current members ... article the.city.harmonic 26898.htm The City Harmonic Christian Today . ref The City Harmonic is a Covenant ... up The City Harmonic. ref http www.christiantoday.com article the.city.harmonic 26898.htm The City Harmonic ... ref http www.christiantoday.com article the.city.harmonic 26898.htm The City Harmonic Christian ... Harmonic 2010 present The band released their major label debut Extended play EP , Introducing The City Harmonic , on November 23, 2010 in Canada and the United States , ref http jesusfreakhideout.com cdreviews IntroducingTheCityHarmonicEP.asp The City Harmonic, Introducing The City Harmonic Review ...?v o 6JQDsbtlM YouTube ref their debut single, Manifesto The City Harmonic single Manifesto , was quick ... Harmonic shot to 5 on the iTunes sales charts in the Christian & Gospel Albums category. As of 2011 ... When date July 2011 at 19 still charting . ref http www.billboard.com song the city harmonic manifesto ... news.php?aid 847 The City Harmonic s Manifesto Unifies Christians ref was recently played at a San ... introducing the city harmonic Introducing The City Harmonic Kingsway UK . ref The band will be releasing ... . ref http thecityharmonic.com 2011 08 the city harmonic to release i have a dream it feels like home 10 18 The City Harmonic to release I Have A Dream It Feels Like Home 10.18 ref Discography Albums ... I Have a Dream It Feels Like Home author The City Harmonic date 2011 10 18 publisher Amazon.com accessdate ... Introducing the City Harmonic US 97,000 ref http www.yourmusiczone.com news.php?area &aid 962 ref References reflist External links Official website http www.thecityharmonic.com DEFAULTSORT City Harmonic ... more details
about harmonic functions in mathematics harmonic function in music diatonic functionality Image Laplace s equation on an annulus.jpg right thumb 300px A harmonic function defined on an Annulus mathematics annulus . In mathematics , mathematical physics and the theory of stochastic process es, a harmonic ... Examples of harmonic functions of two variables are The real and imaginary part of any holomorphic ... due to a long cylindrical mass The function math , f x 1,x 2 e x 1 sin x 2 math Examples of harmonic ... math frac x r r z , math Line of x directed dipoles on negative z axis Harmonic functions are determined by their singularities. The singular points of the harmonic functions above are expressed as charges and charge densities using the terminology of electrostatics, and so the corresponding harmonic .... Each function above will yield another harmonic function when multiplied by a constant, rotated ... harmonic function which has singularities which are the images of the original singularities in a spherical mirror . Also, the sum of any two harmonic functions will yield another harmonic function. Finally, examples of harmonic functions of n variables are The constant, linear and affine functions ... on math mathbb R n backslash lbrace 0 rbrace math for math n 2 math . Remarks The set of harmonic ... and is therefore a vector space over R sums, differences and scalar multiples of harmonic functions are again harmonic. If f is a harmonic function on U , then all partial derivative s of f are also harmonic functions on U . The Laplace operator and the partial derivative operator will commute on this class of functions. In several ways, the harmonic functions are real analogues to holomorphic function s. All harmonic functions are analytic function analytic , i.e. they can be locally ... is a major example. The uniform limit of a convergent sequence of harmonic functions is still harmonic. This is true because any continuous function satisfying the mean value property is harmonic. Consider ... more details
Infobox Interval main interval name harmonic seventh inverse Septimal major second complement complement music other names Septimal minor seventh, Subminor seventh abbreviation m7 semitones 9.7 interval class 2.3 just interval 7 4 ref Haluska, Jan 2003 . The Mathematical Theory of Tone Systems , p.xxiii. ISBN 0824747143. Harmonic seventh. ref cents equal temperament 1000 cents 24T equal temperament 950 cents just intonation 968.826 Image Harmonic seventh on C.png thumb right Harmonic seventh audio Harmonic seventh on C.mid Play , septimal seventh. Image Septimal major second on B7b.png thumb right Inverse, septimal major second on B7 music b audio Septimal major second on B7b.mid Play . The harmonic seventh interval audio Harmonic seventh on C.mid play , also known as the septimal minor seventh ref Gann, Kyle 1998 . http www.kylegann.com Octave.html Anatomy of an Octave , Just Intonation ... temperament ratio of 1000 cents 2 sup 5 6 sup 1 . The harmonic seventh may be derived from the Harmonic series music harmonic series as the interval between the seventh harmonic and the fourth harmonic. Composer Ben Johnston uses a small 7 as an accidental to indicate a note is lowered septimal ..., in C major, the seventh partial, or harmonic seventh, is notated as music flat B with 7 written ... , pp. 106 137. ref The harmonic seventh is also used by Barbershop music Barbershop Quartet singers when they tune Dominant seventh chord dominant seventh chords harmonic seventh chord , and is an essential aspect of the Barbershop style. Image Origin of seconds and thirds in harmonic series.png thumb center Origin of large and small seconds and thirds in harmonic series ref Leta E. Miller, ed ... . The harmonic seventh differs from the augmented sixth by septimal kleisma 224 225 7.71 cents , or about .... 145 153. Published by Oxford University Press on behalf of the Royal Musical Association. ref The harmonic ... resolved final chord. ref name Mathieu pp. 318 319 Mathieu, W.A. 1997 . Harmonic Experience , pp ... more details
about harmonic maps between Riemannian manifolds harmonic functions harmonic function A smooth map M N between Riemannian manifolds M and N is called harmonic if it is a Calculus of variations critical ..., is a harmonic map if the rubber, when released but still constrained to stay everywhere in contact ... into a different shape. Harmonic maps are the least expanding maps in orthogonal directions. Existence of harmonic maps from a complete Riemannian manifold to a complete Riemannian manifold of non positive ... partial varphi beta partial x j . math If M is compact, then is called a harmonic map if it is a critical ... by requiring the restriction of to every compact domain to be harmonic, or, more typically, requiring ... . Equivalently, the map is harmonic if it satisfies the Calculus of variations Euler Lagrange equations ... in N in seeking the energy minimizing configuration. Examples Identity and constant maps are harmonic ... is a curve or a closed curve on N . Then is a harmonic map if and only if it is a geodesic . In this case ... . Then is a harmonic map if and only if it is a harmonic function in the usual sense i.e. a solution ... onto an open set in R sup n sup , then it gives a harmonic coordinates harmonic coordinate system . Every minimal surface in Euclidean space is a harmonic immersion. More generally, a minimal submanifold M of N is a harmonic Immersion mathematics immersion of N in M . Every totally geodesic map is harmonic ... K hler manifold s is harmonic. Problems and applications If, after applying the rubber M onto the marble ... M to N , does it contain a representative that is a harmonic map? Existence results on harmonic maps ... is known, how can a harmonic map be constructed explicitly? One fruitful method uses twistor theory . In theoretical physics , harmonic maps are also known as sigma model s. One of the original ideas ... conformal or harmonic mapping to generate regular grids. Harmonic maps between metric spaces The energy ... citation first1 J. last1 Eells first2 J.H. last2 Sampson jstor 2373037 title Harmonic mappings of Riemannian ... more details
In mathematics , the harmonic mean sometimes called the subcontrary mean is one of several kinds of average .... The harmonic mean H of the positive real number s x sub 1 sub , x sub 2 sub , ..., ... the third formula in the above equation it is more apparent that the harmonic mean is related to the arithmetic mean and geometric mean . Equivalently, the harmonic mean is the Multiplicative inverse reciprocal of the arithmetic mean of the reciprocals. As a simple example, the harmonic mean of 1 ... of the three Pythagorean means of two numbers, a and b . Harmonic mean is denoted by H in purple color. The harmonic mean is one of the three Pythagorean means . For all positive data sets containing at least one pair of nonequal values , the harmonic mean is always the least of the three ... another e.g. the harmonic, geometric, and arithmetic means of 2, 2, 2 are all 2. It is the special case M sub &minus 1 sub of the power mean . Since the harmonic mean of a list of numbers ... is often mistakenly used in places calling for the harmonic mean. ref Statistical Analysis , Ya lun ... the arithmetic mean 50 is incorrect, and too big. The harmonic mean is related to the other Pythagorean ... mean, is the geometric mean to the power n . Thus the n th harmonic mean is related ... while leaving the arithmetic mean unchanged then the harmonic mean always decreases. ref Mitchell, Douglas .... ref Weighted harmonic mean If a set of weight function weights math w 1 math , ..., math w n math is associated to the dataset math x 1 math , ..., math x n math , the weighted harmonic mean is defined by math frac sum i 1 n w i sum i 1 n frac w i x i . math The harmonic mean as defined is the special case where all of the weights are equal to 1, and is equivalent to any weighted harmonic mean ... rate mathematics rate s and ratio s, the harmonic mean provides the truest average . For instance ... distance again at a speed y e.g. 40 kilometres per hour , then its average speed is the harmonic ... more details
In Riemannian geometry , a branch of mathematics , harmonic coordinates are a coordinate system nowrap x sup 1 sup ,..., x sup n sup on a Riemannian manifold each of whose coordinate functions x sup i sup is harmonic function harmonic , meaning that it satisfies Laplace s equation math Delta x i 0. , math Here &Delta is the Laplace Beltrami operator . Equivalently, regarding a coordinate system as a local diffeomorphism nowrap &phi M &rarr R sup n sup , the coordinate system is harmonic if and only if &phi is a harmonic map of Riemannian manifolds, roughly meaning that it minimizes the elastic energy of stretching M into R sup n sup . The elastic energy is expressed via the Dirichlet energy functional math E varphi int M d varphi 2 ,dV. math In two dimensions, harmonic coordinates have been ... being a special case of the former. Harmonic coordinates in higher dimensions were developed initially in the context of general relativity by harvtxt Einstein 1916 see harmonic coordinate condition ... studied by harvtxt DeTurck Kazdan 1981 . The essential motivation for introducing harmonic coordinate ... systems. Harmonic coordinates are characterized in terms of the Christoffel symbols by means ... x k g ij Gamma ij k. math Harmonic coordinates always exist locally , a result which follows easily .... The basic regularity theorem concerning the metric in harmonic coordinates is that if the components ..., then they are in that same H lder space when expressed in harmonic coordinates. In general relativity , harmonic coordinates are solutions of the wave equation instead of the Laplace . This is known as the harmonic coordinate condition in physics. References Citation last1 DeTurck first1 Dennis ... Smith first2 S. S. last2 Sritharan year 1988 title Theory of Harmonic Grid Generation journal Complex ... first S. S. last Sritharan year 1992 title Theory of Harmonic Grid Generation II journal Applicable ... issn 0037 4474 volume 17 issue 4 pages 916 925 . Category Harmonic functions Category Riemannian ... more details
Image Harmonic tremor.jpg thumb right 250px Seismometer Seismograph recording of harmonic tremor. Image Four types seismograms.gif thumb right300px Four major types of seismograms, or seismic signatures. Harmonic tremor describes a long duration release of seismic energy, with distinct spectral harmonic lines, that often precedes or accompanies a volcanic eruption. More generally, a volcanic tremor is a sustained signal that may or may not possess these harmonic spectral features. A harmonic tremor is a sustained release of seismic and or infrasonic energy typically associated with the underground movement of magma and or venting of volcanic gases from magma. Being a long duration continuous signal from a temporally extended source, a volcanic tremor contrasts distinctly with transient sources of seismic radiation, such as tremors that are typically associated with earthquake and explosion. For more info, see the work of Bernard Chouet , a USGS volcanologist who was working at the United States Geological Survey and who first observed a relation between long period events and an imminent eruption. ref cite journal first Bernard last Chouet year 1996 title Long period volcano seismicity its sources and use in eruption forecasting journal Nature journal Nature volume 380 issue 6572 pages 309 316 doi 10.1038 380309a0 ref ref Interview with Bernard Chouet regarding his research into long period events and volcanic eruptions http www.esi topics.com volcanoes interviews BernardChouet.html . ref ref U.S. TV program on use of long period events to predict volcanic eruptions Nova Volcano s Deadly Warning http www.pbs.org wgbh nova volcano . See also Volcano Hell episode of BBC TV series Horizon on same subject http www.bbc.co.uk science horizon 2001 volcanohell.shtml . ref Notes reflist External links http adsabs.harvard.edu abs 2006AGUFM.V41A1694V Seismicity, low frequency events and tremor at the Katla subglacial volcano, Iceland http www.jonfr.com volcano ?p 84 The harmonic ... more details
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