Infobox VG title Sigma Harmonics image File Sigma Harmonics.jpg 256px caption developer Square Enix br Think Garage ref name thinkgarage cite web url http www.thinkgarage.co.jp products.html title Think Garage Works History author work date accessdate ref publisher Square Enix director Hiroki Chiba producer Yoshinori Kitase artist Yusaku Nakaaki composer Masashi Hamauzu released vgrelease JP 21 August 2008 ref cite web author Square Enix title Sigma Harmonics year 2008 accessdate 2008 05 29 url http www.square enix.co.jp sigma ref ratings vgratings CERO B genre Role playing video game modes Single player platforms Nintendo DS series nihongo Sigma Harmonics Shiguma H monikusu is a role playing video game developed and produced by Square Enix for the Nintendo DS handheld game console. ref cite web url http ds.ign.com articles 862 862207p1.html title New From Square Enix Sigma Harmonics author Tanaka, John work ds.ign.com date 2008 03 26 accessdate 2008 03 27 ref Gameplay The game is played using the Nintendo DS system s book orientation. Solving one chapter s case changes the past which leads to a new murder. Plot The story revolves around Sigma Kurogami, a high school student ... Tsukiyumi Neon voiced by Aya Hirano . Development Sigma Harmonics was first revealed as one of the trademarks ... name 1up cite web author Balistrieri, Emily date April 7, 2008 title Famitsu Interviews Sigma Harmonics ... by Masashi Hamauzu , ref cite web url http squaremusic.blogspot.com 2008 03 sigma harmonics pour hamauzu.html title Sigma Harmonics pour Hamauzu author J r mie date 2008 03 27 ref who provided ... Harmonics debuted on the Japanese sales charts at number 8, selling 23,000 units. ref cite web author ... ja icon http blog.square enix.com sigma Sigma Harmonics official blog ja icon Category 2008 video ... Category Role playing video games Category Square Enix games ja no Sigma Harmonics ru Sigma Harmonics zh ... more details
Image ZhongNiShi.jpg thumb 250px The Guqin Image Moodswingerscale.svg thumb 250px Scale of harmonics on the Moodswinger The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a strings music string . Fact date January 2009 This musical scale is present on the guqin , regarded as one of the first string instrument s with a musical scale ref Yin, Wei. Zhongguo Qinshi Yanyi . Pages 1 10. ref . Most fret positions appearing on Non Western string instruments lute s ? are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding Undertone series undertone s of the overtone s from the Harmonic series music harmonic series . The distance from the nut to the fret is an integer number lower than the distance of the played area. Origin On the guqin, the left end of the dotted scale is a mirror image of the right end. The instrument is played with flageolet tone s harmonics as well as pressing the strings on the wood. The flageolets appear on the harmonic positions of the overtone series , therefore these positions are marked as the musical scale of this instrument. The flageolet positions also represent the harmonic consonant relation of the pressed string part with the open string, similar to the calculations Pythagoras did on his monochord . The guqin has one anomaly in its scale. The guqin scale represents the first six harmonics and the eighth harmonic. The seventh harmonic is left out. However this tone is still consonant related to the open string otherwise it would not be a harmonic and has a lesser consonant relation to all other harmonic positions. This is the main reason all ... , also functions with the scale of harmonics. On this instrument only the right half from the view ... is played. The scale of harmonics was, together with the book of Helmholtz an inspiration for Harry ... also wrote a thesis on the scale of harmonics, claiming this to be the oldest usable scale, frequent ... more details
high Pitch music pitch notes difficult or impossible to reach by fret ting. Guitar harmonics also ... musical variety. Technique Harmonics are mainly generated manually by different playing techniques ... vibration of certain string harmonics. A third method, magnetic string drivers like the EBow , can generate string harmonics. Harmonics are most often played by lightly placing a finger on a string ... physics nodes of natural harmonics are located at the following points along a guitar s neck. Note ..., and resulting harmonics are called artificial harmonics . Image Guitar harmonic nodes.svg 600px Harmonic ... m 1 math . Note that certain nodes of higher harmonics are coincident with nodes of lower harmonics ... align right 0.0 Image Table of Harmonics.svg thumb centre 700px Table of harmonics, indicating in colors on which positions the same overtones occur Advanced techniques Pinch harmonics See Pinch harmonic ... is plucked therefore varies depending on the desired note. Most harmonics have several accessible ..., guitar players often increase the guitar volume to play harmonics. Thicker strings, stronger pickups ... is heard. Tapped harmonics This technique was popularized by Eddie van Halen . Tap harmonic Tapped harmonics are an extension of the tapping technique. The note is fretted as usual, but instead ... can be extended to artificial harmonics. For instance, for an octave harmonic 12 fret nodal point press at the third fret, and tap the fifteenth fret, as 12 3 15. String harmonics driven by a magnetic ... and harmonics of steel strings. There are harmonic mode switches as provided by newer versions .... Harmonics control by harmonic mode switching and by the playing technique is applied by the Guitar Resonator where harmonics can be alternated by changing the string driver position at the fretboard while playing. See also 3rd Bridge Portal Guitar Guitars DEFAULTSORT Guitar Harmonics Category Guitars ... more details
Primarysources date February 2008 infobox record label name Psy Harmonics image image bg white parent founded 1993 founder Ollie Olsen , Bruce Butler, Andrew Till distributor genre Electronic music country Australia location Melbourne url http www.psy harmonics.com.au Psy Harmonics is an Australia n independent record label specialising in electronic music . When Psy Harmonics began in 1993 it was the first local label to explore the sonic possibilities of the techno trance sound. As the pace and volume of the techno trance movement has grown around the world, Psy Harmonics continues to be at the forefront of releasing electronic music that both defines and defies genre. Its success lies in its ability to release music of enormous variety whilst maintaining an identity that is recognisable without being predictable. Past and present artists on its roster include Mimesis, Shaolin Wooden Men , Hesius Dome , Rip Van Hippy , Ollie Olsen , Snog , Black Lung , Ad Astra, Joujouka, Antediluvian Rocking Horse, Masaray, Krang, Mystic Force, Lumukanda, Zen Paradox, EYE, The Visitors, Matt Thomas musician Aquila , Third Eye, Pound System, Abel & HJ, Reflecta, Soft, AOA, Makoto Kawamoto , Testeagles, Ito, Battery Cheese Girls, Kerri Simpson, In Honour, Lion Feed, Rip n Eiji, WEYE, Quark, Germinator, Insurge, Fluro Conspiracy, T.Tokuda, H.A.H, Wangina, Y, Insectoid, Psyko Disko, All Sonic Include, Special Go Man, Crazy Party, X Tron, Spies, Choufu Dark Duck, Society Droid, Christine 23 Onna, Sonic Sufi, Ree K, Grey Area and other artists from Australia and elsewhere. See also List of record labels External links Category Australian independent record labels Category Record labels established in 1993 Category Melbourne record labels Category Electronic music record labels Category Australian techno groups ... more details
Image Harmoniki.png right thumb 300px Visual representations of the first few spherical harmonics. Red ... the function is negative. In mathematics , spherical harmonics are the angular portion of a set ... coordinates , Laplace s spherical harmonics math Y ell m math are a specific set of spherical harmonics ... account of various approaches to spherical harmonics in three dimensions can be found in Chapter IV of harvnb MacRobert 1967 . The term Laplace spherical harmonics is in common use see harvnb Courant Hilbert 1962 and harvnb Meijer Bauer 2004 . ref Spherical harmonics are important in many theoretical ... computer graphics , spherical harmonics play a special role in a wide variety of topics including ... radiance transfer , etc. and recognition of 3D shapes. History Spherical harmonics were first investigated ... are the Legendre polynomials , and they are a special case of spherical harmonics. Subsequently, in his ... spherical harmonics in their Treatise on Natural Philosophy , and also first introduced the name of spherical harmonics for these functions. The solid harmonics were homogeneous function homogeneous ... and Tait recovered Laplace s spherical harmonics. The term Laplace s coefficients was employed by William ... others reserved this designation for the zonal spherical harmonics that had properly been introduced ... of vibration in a vibrating string string , the spherical harmonics represent the fundamental modes ... be generalized by taking expansions in spherical harmonics rather than trigonometric functions. This was a boon ... studied by Laplace and Legendre. The prevalence of spherical harmonics already in physics set ... harmonics are eigenfunction s of the square of the orbital angular momentum operator math i hbar mathbf ... of atomic orbitals . Laplace s spherical harmonics Image Rotating spherical harmonics.gif thumb right Real Laplace spherical harmonics math Y ell m math for math ell 0 math to math 4 math top to bottom and math m 0 math to math 4 math left to right . The negative order harmonics math Y ... more details
In physics and mathematics , the solid harmonics are solutions of the Laplace equation in spherical polar coordinates . There are two kinds the regular solid harmonics math R m ell mathbf r math , which vanish at the origin and the irregular solid harmonics math I m ell mathbf r math , which are singular at the origin. Both sets of functions play an important role in potential theory , and are obtained by rescaling spherical harmonics appropriately math R m ell mathbf r r ell Y m ell theta, phi . math Derivation, relation to spherical harmonics Introducing r , , and for the spherical polar coordinates ... harmonics known that spherical harmonics Y sup m sup sub l sub are eigenfunctions of L sup 2 sup ... solutions of the total Laplace equation are regular solid harmonics math R m ell mathbf r equiv sqrt frac 4 pi 2 ell 1 r ell Y m ell theta, varphi , math and irregular solid harmonics math I m ell ... expansion for irregular solid harmonics gives an infinite series, math I m ell mathbf r mathbf a sum ... combination of solid harmonics of m these functions are transformed into real functions. The real regular solid harmonics, expressed in cartesian coordinates, are homogeneous polynomials of order ... of the real regular harmonics will now be derived. Linear combination We write in agreement ... harmonics Condon Shortley phase Condon Shortley phase . The following expression defines the real regular solid harmonics math begin pmatrix C ell m S ell m end pmatrix equiv sqrt 2 r ell Theta m ell ... and the complex solid harmonics is the same. z dependent part Upon writing u cos &theta the m ... 5z i 2 r i 2 y i . math Spherical harmonics in Cartesian form The following expresses normalized spherical harmonics in Cartesian coordinates Condon Shortley phase math r ell , begin pmatrix Y ell m ... listed Table of spherical harmonics Spherical harmonics with l .3D 3 here and Table of spherical harmonics Spherical harmonics with l .3D 4 here . DEFAULTSORT Solid Harmonics Category ... more details
The Stanford Harmonics are a coeducational a cappella group from Stanford University in the United States, known for their rock repertoire and award winning recordings. They have garnered international recognition for their performances, and have been featured on BOCA, Sing, and Voices Only a cappella compilations. The Harmonics are one of the only collegiate a cappella groups to own their own microphone assortment and live soundboard, and have developed a live performance which includes the use of electronic distortion, sound effects and audience participation. In 2006, the Harmonics won the A Cappella Community Awards for Favorite Mixed Collegiate Group and Favorite Scholastic Album. On December 4, 2008, they released their eighth studio album, Escape Velocity , which was the winner of 3 Contemporary A cappella Recording Award s, including Best Mixed Collegiate Album. Along with the Tufts Beelzebubs and UPenn Off The Beat , the Stanford Harmonics are considered one of the Holy Trinity of collegiate a cappella groups. ref http www.casa.org node 5633 ref Members 2011 2012 Erin Baumann Historian Amy DuBose Josh Eisner Financial Officer Arturo Ferrari Chris Goetz David Larson Musical Manager Marcia Levitan Boost Master Leo Martel Ale Mesa Performance Manager Katherine Robertson Sarah ... Skritch lead Bryan Tan Discography The Stanford Harmonics have released 7 full length albums and one greatest hits CD. A new full length Harmonics album is scheduled to be released sometime in 2012. On June 22, 2011, the Harmonics released a brand new single available for purchase on iTunes, the A side ... Harmonics have received various awards for their CDs The Greatest Hits of Pitchpipe BOCA Humor ... Best Mixed Collegiate Album Nominee & Best Mixed Collegiate Arrangement Runner Up Evolut10n Harmonics ... Stanford Harmonics Official Website http www.rarb.org reviews 568.html Recorded ... Collegiate a cappella groups Category Stanford University musical groups Harmonics ... more details
In mathematics , the cylindrical harmonics are a set of linear dependence linearly independent solutions to Laplace s equation Laplace s differential equation , math nabla 2 V 0 math , expressed in cylindrical coordinate system cylindrical coordinates , radial coordinate , polar angle , and z height . Each function V sub n sub k is the product of three terms, each depending on one coordinate alone. The term cylindrical harmonics is also used to refer to the Bessel function s that are cylindrical harmonics in the sense described above . Definition Each function math V n k math of this basis consists of the product of three functions math V n k rho, varphi,z P n k, rho Phi n varphi Z k,z , math where math rho, varphi,z math are the cylindrical coordinates, and n and k are constants which distinguish the members of the set from each other. As a result of the superposition principle applied to Laplace s equation, very general solutions to Laplace s equation can be obtained by linear combinations of these functions. Since all of the surfaces of constant , and z are conicoid, Laplace s equation is separable in cylindrical coordinates. Using the technique of the separation of variables , a separated solution to Laplace s equation may be written math V P rho , Phi varphi ,Z z math and Laplace s equation, divided by V , is written math frac ddot P P frac 1 rho , frac dot P P frac 1 rho 2 , frac ddot Phi Phi frac ddot Z Z 0 math The Z part of the equation is a function of z alone, and must therefore be equal to a constant math frac ddot Z Z k 2 math where k is, in general, a complex number . For a particular k , the Z z function has two linearly independent solutions. If k is real they are math Z k,z cosh kz , , , , , , mathrm or , , , , , , sinh kz , math ... harmonics for k,n are now the product of these solutions and the general solution to Laplace ... 2 z 2 int 0 infty J 0 k rho e k z ,dk. math See also Spherical harmonics References reflist Category ... more details
ffd log 2012 January 2 Summary Increasing the number of sides are like increasing how much harmonics skip. Licensing PD self date June 2007 Orphan image ... more details
Merge to Harmonics electrical power discuss Talk Harmonics electrical power Merger proposal date September 2011 Power system harmonics are integer multiples of the fundamental power system frequency. Power system harmonics are created by non linear devices connected to the power system. High levels of power system harmonics electrical power harmonics can create voltage distortion and power quality problems. Harmonics in power systems result in increased heating in the equipment and conductors, misfiring in variable speed drives, and torque pulsations in motors. Sources A pure sinusoidal voltage is a conceptual quantity produced by an ideal AC generator built with finely distributed stator and field windings that operate in a uniform magnetic field. Since neither the winding distribution nor the magnetic field are uniform in a working AC machine, voltage waveform distortions are created, and the voltage time relationship deviates from the pure sine function. The distortion at the point of generation is very small about 1 to 2 , but nonetheless it exists. Because this is a deviation from a pure sine wave, the deviation is in the form of a periodic function, and by definition, the voltage distortion contains harmonics. When a sinusoidal voltage is applied to a certain type of load, the current drawn by the load is determined by the voltage and impedance and follows the voltage waveform. These loads are referred to as linear loads examples of linear loads are resistive heaters, incandescent lamps, and constant speed induction and synchronous motors. In contrast, some loads cause the current to vary disproportionately with the voltage during each cyclic period. These are classified as nonlinear loads, and the current taken by them has a nonsinusoidal waveform. When there is significant ... are harmonics integer multiples of the fundamental frequency, and can sometimes propagate ..., and switching mode power supplies. http ecmweb.com mag electric effects harmonics power 2 Electrical ... more details
Merge from Power system harmonics discuss Talk Harmonics electrical power Merger proposal date September 2011 Harmonics are electric voltages and currents that appear on the Electrical power industry electric power system as a result of certain kinds of electric loads. Harmonic frequencies in the power grid are a frequent cause of power quality problems. Causes In a normal alternating current power system, the voltage varies Sine wave sinusoidally at a specific frequency, usually 50 or 60 hertz . When a linear electrical load is connected to the system, it draws a sinusoidal current at the same frequency as the voltage though usually not in phase waves phase with the voltage . When a non linear load, such as a rectifier , is connected to the system, it draws a current that is not necessarily sinusoidal. The current waveform can become quite complex, depending on the type of load and its interaction with other components of the system. Regardless of how complex the current waveform becomes, as described through Fourier series analysis, it is possible to decompose it into a series of simple sinusoids, which start at the power system fundamental frequency and occur at integer multiples of the fundamental frequency. Further examples of non linear loads include common office equipment such as computers and printers, and also adjustable speed drive adjustable speed drives . Effects One of the major effects of power system harmonics is to increase the current in the system. This is particularly ... current, different pieces of electrical equipment can suffer effects from harmonics on the power ... core of the motor. These are proportional to the frequency of the current. Since the harmonics are at higher ... of 180 Hz, its higher order harmonics are high enough to interfere with telephone service if they became induced in the line. Further reading cite web url http ecmweb.com mag electric effects harmonics power 2 title Effects of harmonics on power systems accessdate 2008 09 05 last Sankaran first ... more details
distinguish spin spherical harmonics Spin weighted spherical harmonics are generalizations of the standard spherical harmonics and like the usual spherical harmonics are functions on the sphere. Unlike ordinary spherical harmonics, the spin weighted harmonics are U 1 gauge field s rather than scalar fields mathematically, they take values in a complex line bundle . The spin weighted harmonics are organized by degree , just like ordinary spherical harmonics, but have an additional spin weight s that reflects the additional U 1 symmetry. A special basis of harmonics can be derived from the Laplace spherical harmonics math Y ell m math , and are typically denoted by math sY ell m math , where and m are the usual parameters familiar from the standard Laplace spherical harmonics. In this special basis, the spin weighted spherical harmonics appear as actual functions, because the choice of a polar axis fixes the U 1 gauge ambiguity. The spin weighted spherical harmonics can be obtained from the standard spherical harmonics by application of Ladder operators spin raising and lowering operators . In particular, the spin weighted spherical harmonics of spin weight s 0 are simply the standard spherical harmonics math 0Y ell m Y ell m . math Spaces of spin weighted spherical harmonics ... as so called monopole harmonics in the study of Dirac monopole s. Spin weighted functions Regard the sphere ... of spin weight s 1. Spin weighted harmonics Just as conventional spherical harmonics are the eigenfunction s of the Laplace Beltrami operator on the sphere, the spin weight s harmonics ... of spin weight s functions. Representation as functions The spin weighted harmonics can be represented ... left sin theta s eta right . math The spin weighted spherical harmonics are then defined in terms of the usual spherical harmonics as math sY ell m sqrt frac ell s ell s eth s Y ell m , 0 leq s leq ell ... and completeness The harmonics are orthogonal over the entire sphere math int S 2 sY ell m ... more details
In the mathematics mathematical study of rotational symmetry , the zonal spherical harmonics are special spherical harmonics that are invariant under the rotation through a particular fixed axis. The zonal spherical function s are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group . On the two dimensional sphere, the unique zonal spherical harmonic of degree invariant under rotations fixing the north pole is represented in spherical coordinates by math Z ell theta, phi P ell cos theta math where P sub sub is a Legendre polynomial of degree . The general zonal spherical harmonic of degree is denoted by math Z ell mathbf x mathbf y math , where x is a point on the sphere representing the fixed axis, and y is the variable of the function. This can be obtained by rotation of the basic zonal harmonic math Z ell theta, phi . math In n dimensional Euclidean space, zonal spherical harmonics are defined as follows. Let x be a point on the n &minus 1 sphere. Define math Z ell mathbf x math to be the Riesz representation theorem dual representation of the linear functional math P mapsto P mathbf x math in the finite dimensional Hilbert space H sub sub of spherical harmonics of degree . In other words, the following reproducing kernel reproducing property holds math Y mathbf x int S n 1 Z ell mathbf x mathbf y Y mathbf y ,d Omega y math for all Y &isin H sub sub . The integral is taken with respect to the invariant probability measure. Relationship with harmonic potentials The zonal harmonics appear naturally as coefficients of the Poisson kernel for the unit ball in R sup n sup to wit, for x and y unit vectors, math frac 1 omega n 1 frac 1 r 2 mathbf x r mathbf y n sum k 0 infty r k Z k mathbf x mathbf y , math ... the ultraspherical polynomials . Thus, the zonal spherical harmonics can be expressed as follows. If &alpha ... polynomial of degree . Properties The zonal spherical harmonics are rotationally ... more details
Distinguish Spin weighted spherical harmonics In quantum mechanics , spin spherical harmonics are spinor s that are eigenstates of the square of the angular momentum operator , and so are the natural spinorial analog of vector spherical harmonics . They are given in matrix form by ref Citation last1 Biedenharn first1 L. C. last2 Louck first2 J. D. title Angular momentum in Quantum Physics Theory and Application publisher Addison Wesley place Reading volume 8 series Encyclopedia of Mathematics isbn 0 201 13507 8 year 1981 page 283 ref math Y j frac 1 2 , frac 1 2 jm left begin array c sqrt frac j m 2j Y j frac 1 2 ,m frac 1 2 sqrt frac j m 2j Y j frac 1 2 ,m frac 1 2 end array right math math Y j frac 1 2 , frac 1 2 jm left begin array c sqrt frac j m 1 2j 2 Y j frac 1 2 ,m frac 1 2 sqrt frac j m 1 2j 2 Y j frac 1 2 ,m frac 1 2 end array right math Notes Reflist References Citation last1 Edmonds first1 A. R. title Angular Momentum in Quantum Mechanics publisher Princeton University Press isbn 978 0 691 07912 7 year 1957 Category Spinors Category Rotational symmetry Category Special functions Physics stub ... more details
In mathematics, vector spherical harmonics VSH are an extension of the scalar spherical harmonics for the use with vector field s. Definition Several conventions have been used to define the VSH ref R.G. Barrera, G.A. Est vez and J. Giraldo, Vector spherical harmonics and their application to magnetostatic , Eur. J. Phys. 6 287 294 1985 ref ref B. Carrascal, G.A. Estevez, P. Lee and V. Lorenzo Vector spherical harmonics and their application to classical electrodynamics , Eur. J. Phys., 12 , 184 191 1991 ref ref E. L. Hill, The theory of Vector Spherical Harmonics , Am. J. Phys. 22 , 211 214 1954 ref ref E. J. Weinberg, Monopole vector spherical harmonics , Phys. Rev. D. 49 , 1086 1092 1994 ref ref P.M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II , New York McGraw Hill, 1898 1901 1953 ref . We follow that of Barrera et al. . Given a scalar spherical harmonic math Y lm theta, varphi math we define three VSH math mathbf Y lm Y lm hat mathbf r math math mathbf Psi lm r nabla Y lm math math mathbf Phi lm vec mathbf r times nabla Y lm math being math hat mathbf r math the unitary vector along the radial direction and math vec mathbf r math the position vector of the point with spherical coordinates math r math , math theta math and math phi math . The radial factors are included to guarantee that the dimensions of the VSH are the same as the ordinary spherical harmonics and that the VSH do not depend on the radial spherical coordinate. The interest of these new vector ... harmonics, the VSH satisfy math mathbf Y l, m 1 m mathbf Y lm qquad mathbf Psi l, m 1 m mathbf Psi ... 1 lm right mathbf Phi lm right math Examples First vector spherical harmonics math l 0 , math math mathbf ... expression suggest an expansion on spherical harmonics for the liquid velocity and the pressure math ... Spherical harmonics Spin spherical harmonics Multipole expansion Electromagnetic radiation Spherical ... Harmonics at Eric Weisstein s Mathworld div class references References references Category Vector ... more details
Unreferenced date December 2009 This is a table of orthonormalized spherical harmonics that employ the Condon Shortley phase up to degree l 10. Some of these formulas give the Cartesian version. This assumes ... sin varphi z & r cos theta end align math Spherical harmonics with l 0 math Y 0 0 theta, varphi 1 over 2 sqrt 1 over pi math Real spherical harmonics with l 0 math s Y 0 0 frac 1 2 sqrt frac 1 pi math Spherical harmonics with l 1 math begin align Y 1 1 theta, varphi & 1 over 2 sqrt 3 over 2 pi cdot ... x iy over r end align math Real spherical harmonics with l 1 math begin align p x & sqrt frac 1 2 left ... frac 3 4 pi cdot frac y r p z & Y 1 0 sqrt frac 3 4 pi cdot frac z r end align math Spherical harmonics ... 4 sqrt 15 over 2 pi cdot x iy 2 over r 2 math Real spherical harmonics with l 2 math d z 2 Y 2 0 frac ... 1 4 sqrt frac 15 pi cdot frac x 2 y 2 r 2 math Spherical harmonics with l 3 math Y 3 3 theta, varphi ... 3 theta quad 1 over 8 sqrt 35 over pi cdot x iy 3 over r 3 math Real spherical harmonics with l 3 ... r 3 math Spherical harmonics with l 4 math Y 4 4 theta, varphi 3 over 16 sqrt 35 over 2 pi cdot e 4i ... spherical harmonics with l 4 math g z 4 Y 4 0 frac 3 16 sqrt frac 1 pi cdot frac 35 z 4 30 z 2 r ... harmonics with l 5 math Y 5 5 theta, varphi 3 over 32 sqrt 77 over pi cdot e 5i varphi cdot sin ... 77 over pi cdot e 5i varphi cdot sin 5 theta math Spherical harmonics with l 6 math Y 6 6 theta, varphi ... harmonics with l 7 math Y 7 7 theta, varphi 3 over 64 sqrt 715 over 2 pi cdot e 7i varphi cdot ... sqrt 715 over 2 pi cdot e 7i varphi cdot sin 7 theta math Spherical harmonics with l 8 math Y 8 8 theta ... 256 sqrt 12155 over 2 pi cdot e 8i varphi cdot sin 8 theta math Spherical harmonics with l 9 math ... cdot sin 9 theta math Spherical harmonics with l 10 math Y 10 10 theta, varphi 1 over 1024 sqrt 969969 ... See also Spherical harmonics References cite journal first1 R. J. last1 Mathar journal Serbian Astronomical ... Harmonics Category Special hypergeometric functions cs Tabulka sf rick ch harmonick ch funkc es ... more details
Spherical function can refer to Spherical harmonics Zonal spherical function mathdab Long comment to avoid being listed on short pages ... more details
wiktionarypar harmonic For Harmonic scale , see Harmonic minor scale Harmonic major scale Harmonic Scale . See also Scale of harmonics disambig ... 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 Artificial harmonic , 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
Summary A lame approximation of a sine wave using subtractive synthesis of odd harmonics of square waves. Licensing PD self date October 2006 Copy to Wikimedia Commons bot Fbot ... more details
Summary Photo taken on the camera of a member of the Stanford Harmonics a cappella group at UC Berkeley for the East Coast A Cappella Showcase. Member not shown Ryan Hopkins. Licensing GFDL migration relicense ... more details
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