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Harmonic
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components of periodic signals. For other uses, see Harmonic (disambiguation). A harmonic of a wave is a component frequency of the signal thatHarmonic oscillator (2,674 words) [view diff] no match in snippet view article find links to article

harmonic oscillator in classical mechanics. For its uses in quantum mechanics, see quantum harmonic oscillator. In classical mechanics, a harmonic oscillatorHarmonic divisor number (649 words) [view diff] no match in snippet view article find links to article

article is about harmonic divisor numbers. For meanings of harmonic number, see harmonic number (disambiguation). In mathematics, a harmonic divisor numberHarmonic spectrum (72 words) [view diff] no match in snippet view article find links to article

A harmonic spectrum is a spectrum containing only frequency components whose frequencies are whole number multiples of the fundamental frequency; suchHarmonic mean (2,464 words) [view diff] no match in snippet view article find links to article

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the PythagoreanSimple harmonic motion (1,172 words) [view diff] no match in snippet view article find links to article

In mechanics and physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement andHarmonic series (music) (1,975 words) [view diff] no match in snippet view article find links to article

A harmonic series is the sequence of all multiples of a base frequency. Pitched musical instruments are often based on an approximate harmonic oscillatorHarmonic function (2,079 words) [view diff] no match in snippet view article find links to article

This article is about harmonic functions in mathematics. For harmonic function in music, see diatonic functionality. In mathematics, mathematicalHarmonic number (1,399 words) [view diff] no match in snippet view article find links to article

The term harmonic number has multiple meanings. For other meanings, see harmonic number (disambiguation). In mathematics, the n-th harmonic numberHarmonic series (mathematics) (1,900 words) [view diff] no match in snippet view article find links to article

In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengthsQuantum harmonic oscillator (2,672 words) [view diff] no match in snippet view article find links to article

the Houston area. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potentialArtificial harmonic (289 words) [view diff] no match in snippet view article find links to article

To produce an artificial harmonic, a stringed instrument player holds down a note on the neck with one finger of the non-dominant hand (thereby shorteningMinor scale (1,963 words) [view diff] no match in snippet view article find links to article

semitones) above the first. This includes (among others) the natural minor, harmonic minor, and melodic minor scales. A minor scale differs from a major scaleHarmonic seventh (776 words) [view diff] no match in snippet view article find links to article

The harmonic seventh interval play (help·info), also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969Harmonic rhythm (439 words) [view diff] no match in snippet view article find links to article

harmonizations of "Yankee Doodle" In music theory, harmonic rhythm, also known as harmonic tempo is the rate at which the chords change (or progress)Double harmonic scale (792 words) [view diff] no match in snippet view article find links to article

In music, the double harmonic major scale is a scale whose gaps may sound "exotic" to Western listeners. This is also known as the Arabic, Gypsy majorList of harmonic analysis topics (205 words) [view diff] no match in snippet view article find links to article

This is a list of harmonic analysis topics. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towardsWeakly harmonic function (85 words) [view diff] no match in snippet view article find links to article

In mathematics, a function is weakly harmonic in a domain if for all with compact support in and continuous second derivatives, where Δ is the LaplacianFundamental frequency (687 words) [view diff] no match in snippet view article find links to article

abbreviate it as f1, the first harmonic. (The second harmonic is then f2 = 2⋅f1, etc. In this context, the zeroth harmonic would be 0 Hz.) All sinusoidalLeibniz harmonic triangle (314 words) [view diff] no match in snippet view article find links to article

The Leibniz harmonic triangle is a triangular arrangement of fractions in which the outermost diagonals consist of the reciprocals of the row numbers andHarmonic conjugate (709 words) [view diff] no match in snippet view article find links to article

For geometric conjugate points, see Projective harmonic conjugates. In mathematics, a function defined on some open domain is said to have as a conjugateGeometric–harmonic mean (338 words) [view diff] no match in snippet view article find links to article

In mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0 = x andHarmonic Scale (263 words) [view diff] no match in snippet view article find links to article

The Harmonic Scale is a "super-Just" musical scale allowing extended just intonation, beyond 5-limit to the 19th harmonic ( Play (help·info)), and freeHarmonic major scale (796 words) [view diff] no match in snippet view article find links to article

In music theory, the harmonic major scale is a musical scale which found occasional use during the common practice era and is now occasionally employedHarmonic (mathematics) (115 words) [view diff] no match in snippet view article find links to article

concepts. Harmonic analysis Harmonic division Harmonic function Harmonic number Harmonic series Harmonic form Harmonic mean Harmonic mode Harmonic tremorLamé function (279 words) [view diff] no match in snippet view article find links to article

In mathematics, a Lamé function (or ellipsoidal harmonic function) is a solution of Lamé's equation, a second-order ordinary differential equation. ItSecond-harmonic generation (2,088 words) [view diff] no match in snippet view article find links to article

Second harmonic generation (also called frequency doubling or abbreviated SHG) is a nonlinear optical process, in which photons with the same frequencyTap harmonic (74 words) [view diff] no match in snippet view article find links to article

Tap harmonic is a technique used with fretted string instruments, (usually guitar). It is executed by tapping on the actual fret wire most commonly atHarmonic Vector Excitation Coding (697 words) [view diff] no match in snippet view article find links to article

Harmonic Vector Excitation Coding, abbreviated as HVXC is a speech coding algorithm specified in MPEG-4 Part 3 (MPEG-4 Audio) standard for very low bitHarmonic drive (1,041 words) [view diff] no match in snippet view article find links to article

Harmonic Drive is a strain wave gear that can improve certain characteristics compared to traditional gearing systems. Harmonic Drive is trademarked byHarmonic map (951 words) [view diff] no match in snippet view article find links to article

This article is about harmonic maps between Riemannian manifolds. For harmonic functions, see harmonic function. A (smooth) map φ:M→N between RiemannianHarmonic differential (394 words) [view diff] no match in snippet view article find links to article

In mathematics, a real differential one-form ω on a surface is called a harmonic differential if ω and its conjugate one-form, written as ω*, are both closedHarmonic coordinate condition (508 words) [view diff] no match in snippet view article find links to article

The harmonic coordinate condition is one of several coordinate conditions in general relativity, which make it possible to solve the Einstein field equationsHarmonic coordinates (479 words) [view diff] no match in snippet view article find links to article

mathematics, harmonic coordinates are a coordinate system (x1,...,xn) on a Riemannian manifold each of whose coordinate functions xi is harmonic, meaningGuitar harmonics (978 words) [view diff] no match in snippet view article find links to article

guitar harmonic is a musical note played by preventing or amplifying vibration of certain overtones of a guitar string. Music using harmonics can containProjective harmonic conjugate (1,122 words) [view diff] no match in snippet view article find links to article

In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction:Harmonic seventh chord (891 words) [view diff] no match in snippet view article find links to article

The harmonic seventh chord is a major triad plus the harmonic seventh interval (ratio of 7:4, about 968.826 cents). This interval is somewhat narrowerThe Soul Harmonic (68 words) [view diff] no match in snippet view article find links to article

The Soul Harmonic EP is the second EP by the Welsh alternative band Clockwork Radio (band). Produced by the band, the album was released on November 22Parallel harmony (264 words) [view diff] no match in snippet view article find links to article

Diaphonia (genus). In music, parallel harmony, also known as harmonic parallelism, harmonic planing or parallel voice leading, is the parallel movementDistortion (1,482 words) [view diff] no match in snippet view article find links to article

the root mean square of all harmonic components: Total harmonic distortion (THD), as a percentage. The level at which harmonic distortion becomes audibleSecond-harmonic imaging microscopy (950 words) [view diff] no match in snippet view article find links to article

Second-harmonic imaging microscopy (SHIM) is based on a nonlinear optical effect known as second-harmonic generation (SHG). SHIM has been established asPotential theory (1,295 words) [view diff] no match in snippet view article find links to article

mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physicsHarmony (4,234 words) [view diff] no match in snippet view article find links to article

or from the point of view of musical texture (distinguishing between "harmonic" (simultaneously sounding pitches) and "contrapuntal" (successively soundingHarmonic progression (mathematics) (360 words) [view diff] no match in snippet view article find links to article

the musical term, see Chord progression. In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocalsHarmonic morphism (419 words) [view diff] no match in snippet view article find links to article

mathematics, a harmonic morphism is a (smooth) map between Riemannian manifolds that pull back real-valued harmonic functions on the codomain to harmonic functionsPinch harmonic (1,011 words) [view diff] no match in snippet view article find links to article

A pinch harmonic (also known as squelch picking, pick harmonic or squealy) is a guitar technique to achieve artificial harmonics in which the player'sTriad (music) (913 words) [view diff] no match in snippet view article find links to article

triad is a set of three notes that can be stacked in thirds. The term "harmonic triad" was coined by Johannes Lippius in his "Synopsis musicae novae" (1612)Optical frequency multiplier (297 words) [view diff] no match in snippet view article find links to article

harmonic generation (SHG, also called frequency doubling), or sum frequency generation which sums two non-similar frequencies. Direct third harmonic generationHarmonic tremor (247 words) [view diff] no match in snippet view article find links to article

Harmonic tremor describes a long-duration release of seismic energy, with distinct spectral lines, that often precedes or accompanies a volcanic eruptionHigh harmonic generation (1,340 words) [view diff] no match in snippet view article find links to article

emit the high harmonics of the generation beam (above the fifth harmonics). Due to the coherent nature of the process, high harmonics generation is aMinor third (833 words) [view diff] no match in snippet view article find links to article

third may be derived from the harmonic series as the interval between the fifth and sixth harmonics, or from the 19th harmonic. The minor third is commonlyDiatonic function (2,257 words) [view diff] no match in snippet view article find links to article

—Benward & Saker Three general and inseparable essential features of harmonic function in tonal music are: Position within a gamut (the available collection)The City Harmonic (1,009 words) [view diff] no match in snippet view article find links to article

The City Harmonic is a Juno Award winning Canadian Christian rock band formed in 2009 after having served together as the house worship band for an inter-denominationalHarmonic Generator (94 words) [view diff] no match in snippet view article find links to article

Harmonic Generator is a Japanese six track EP by New Zealand rock band The Datsuns. It contains radio sessions of three songs and live studio recordingsOvertone singing (2,123 words) [view diff] no match in snippet view article find links to article

Overtone singing—also known as overtone chanting, harmonic singing or throat singing—is a type of singing in which the singer manipulates the resonancesHarmonic mixing (544 words) [view diff] no match in snippet view article find links to article

about music. For the electronic frequency-changing device, see harmonic mixer. Harmonic mixing or key mixing (Also referred to as mixing in key) is a DJ'sOvertone flute (263 words) [view diff] no match in snippet view article find links to article

a flute that is designed to play in the upper harmonics, typically well above the two or three harmonics that are the practical limit for most woodwindRiemannian theory (238 words) [view diff] no match in snippet view article find links to article

"dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists. The term "dualism" refers to the emphasis on the inversionalNeutral sixth (369 words) [view diff] no match in snippet view article find links to article

sixth, and occurs infrequently in music, as little music utilizes the 13th harmonic. play (help·info) An equal-tempered neutral sixth is 850 cents, a hairAccompaniment (634 words) [view diff] no match in snippet view article find links to article

accompaniment part usually provides the harmonic background and the rhythmic structure for the piece of music or song. The harmonic background is usually providedSolid harmonics (494 words) [view diff] no match in snippet view article find links to article

the solid harmonics are solutions of the Laplace equation in spherical polar coordinates. There are two kinds: the regular solid harmonics , which vanishPositive harmonic function (416 words) [view diff] no match in snippet view article find links to article

In mathematics, a positive harmonic function on the unit disc in the complex numbers is characterized as the Poisson integral of a finite positive measureGypsy scale (133 words) [view diff] no match in snippet view article find links to article

minor scale with raised fourth and seventh degrees, also known as Double Harmonic minor scale. Hungarian Gypsy scale, minor scale with raised fourth butHarmonic Inc. (829 words) [view diff] no match in snippet view article find links to article

Harmonic Inc. is an American technology company that develops and markets video routing, server, and storage products for companies that produce, processHarmonic polynomial (148 words) [view diff] no match in snippet view article find links to article

polynomial over a field whose Laplacian is zero is termed a harmonic polynomial. The harmonic polynomials form a vector subspace of the vector space ofNoncommutative harmonic analysis (463 words) [view diff] no match in snippet view article find links to article

In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups thatare not commutativeGeometric mean (2,567 words) [view diff] no match in snippet view article find links to article

arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the leastSpherical harmonics (4,812 words) [view diff] no match in snippet view article find links to article

other uses, see YLM (disambiguation). In mathematics, spherical harmonics are a series of special functions defined on the surface of a sphere usedPaul Erlich (303 words) [view diff] no match in snippet view article find links to article

Bachelor of Science degree in physics from Yale University. His invention of harmonic entropy has received significant attention from music theorists such asProjective range (389 words) [view diff] no match in snippet view article find links to article

quadruple results in four points likewise in the harmonic relation. Such a quadruple of points is termed a harmonic range. In 1940 Julian Coolidge described thisMinor diatonic semitone (59 words) [view diff] no match in snippet view article find links to article

minor diatonic semitone is a ratio of 17:16, making it the seventeenth harmonic or partial. Major diatonic semitone Haluška, Ján (2003)Harmonic measure (1,052 words) [view diff] no match in snippet view article find links to article

mathematics, especially potential theory, harmonic measure is a concept related to the theory of harmonic functions that arises from the solution ofRadó's theorem (harmonic functions) (132 words) [view diff] no match in snippet view article find links to article

theorem (Ramsey theory) In mathematics, Radó's theorem is a result about harmonic functions, named after Tibor Radó. Informally, it says that any "nice looking"Nonlinear optics (3,234 words) [view diff] no match in snippet view article find links to article

holds. Nonlinear optics remained unexplored until the discovery of Second harmonic generation shortly after demonstration of the first laser. (Peter FrankenZonal spherical harmonics (389 words) [view diff] no match in snippet view article find links to article

mathematical study of rotational symmetry, the zonal spherical harmonics are special spherical harmonics that are invariant under the rotation through a particularVan der Corput lemma (harmonic analysis) (183 words) [view diff] no match in snippet view article find links to article

In mathematics, in the field of harmonic analysis, the van der Corput lemma is an estimate for oscillatory integrals named after the Dutch mathematicianHodge theory (853 words) [view diff] no match in snippet view article find links to article

canonically isomorphic to the space of harmonic sections, , in the sense that each cohomology class has a unique harmonic representative. Main article: HodgeC minor (323 words) [view diff] no match in snippet view article find links to article

pitches C, D, E♭, F, G, A♭, and B♭. The harmonic minor raises the B♭ to B♮. Changes needed for the melodic and harmonic versions of the scale are written inHungarian minor scale (688 words) [view diff] no match in snippet view article find links to article

scale, Double Harmonic minor scale, or Gypsy minor scale, is a type of combined musical scale. It is the fourth mode of the double harmonic scale. It isDirac operator (567 words) [view diff] no match in snippet view article find links to article

algebra. Solutions to the Dirac equation for spinor fields are often called harmonic spinors[1]. Example 3: The most famous Dirac operator describes the propagationHarmonic wavelet transform (436 words) [view diff] no match in snippet view article find links to article

In the mathematics of signal processing, the harmonic wavelet transform, introduced by David Edward Newland in 1993, is a wavelet-based linear transformationNonchord tone (1,659 words) [view diff] no match in snippet view article find links to article

note in a piece of music that is not part of the implied chord within the harmonic framework. Similarly, a chord tone is a note that is a part of the functionalDiphthong (4,958 words) [view diff] no match in snippet view article find links to article

rare type of diphthong that is neither opening nor closing is height-harmonic diphthongs, with both elements at the same vowel height. These occurredHarmonic Tremors (95 words) [view diff] no match in snippet view article find links to article

Harmonic Tremors is the first full-length album by American post-metal band Zozobra. The Blessing – 5:36 Kill and Crush – 3:26 Levitate – 3:00 Soon toComplex harmonic motion (1,083 words) [view diff] no match in snippet view article find links to article

harmonic motion is a complicated realm based on the simple harmonic motion. The word "complex" refers to different situations. Unlike simple harmonicHarmonic scale (16 words) [view diff] no match in snippet view article find links to article

Harmonic scale may refer to: Harmonic Scale Harmonic minor scale Harmonic major scale Scale of harmonicsHarmonics (electrical power) (1,079 words) [view diff] no match in snippet view article find links to article

Harmonic voltages and currents in an electric power system are a result of non-linear electric loads. Harmonic frequencies in the power grid are a frequentList of chord progressions (28 words) [view diff] no match in snippet view article find links to article

The following is a list of commonly used chord progressions in music. List of musical intervals List of pitch intervals List of musical scales and modesMaximum principle (525 words) [view diff] no match in snippet view article find links to article

the boundary. Harmonic functions are the classical example to which the strong maximum principle applies. Formally, if f is a harmonic function, thenHarmonic Convergence (1,004 words) [view diff] no match in snippet view article find links to article

The Harmonic Convergence is the name given to one of the world's first globally synchronized meditation events, which occurred on August 16–17, 1987, whichRiemann–Lebesgue lemma (344 words) [view diff] no match in snippet view article find links to article

named after Bernhard Riemann and Henri Lebesgue, is of importance in harmonic analysis and asymptotic analysis. The lemma says that the Fourier transformChord substitution (1,426 words) [view diff] no match in snippet view article find links to article

variety and add interest to a piece. The substitute chord must have some harmonic quality and degree of function in common with the original chord, and oftenExciter (effect) (549 words) [view diff] no match in snippet view article find links to article

For other uses, see Exciter (disambiguation). An exciter (also called a harmonic exciter or aural exciter) is an audio signal processing technique usedExciter (effect) (549 words) [view diff] no match in snippet view article find links to article

For other uses, see Exciter (disambiguation). An exciter (also called a harmonic exciter or aural exciter) is an audio signal processing technique usedLaplace's equation (2,057 words) [view diff] no match in snippet view article find links to article

known as potential theory. The solutions of Laplace's equation are the harmonic functions, which are important in many fields of science, notably the fieldsOscillation (881 words) [view diff] no match in snippet view article find links to article

swelling of Cepheid variable stars in astronomy. Main article: Simple harmonic motion The simplest mechanical oscillating system is a weight attachedConsonance and dissonance (6,323 words) [view diff] no match in snippet view article find links to article

perception of harmonic partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds (i.e.Distortionmeter (193 words) [view diff] no match in snippet view article find links to article

circuit. Harmonic distortion is equivalent to adding harmonics to a signal. When a purely sinusoidal signal is distorted, a series of harmonics is superimposedWolstenholme number (65 words) [view diff] no match in snippet view article find links to article

Wolstenholme number is a number that is the numerator of the generalized harmonic number Hn,2. The first such numbers are 1, 5, 49, 205, 5269, 5369, 266681Damping (1,950 words) [view diff] no match in snippet view article find links to article

about damped harmonic oscillators. For detailed mathematical description of the harmonic oscillator including forcing and damping, see Harmonic oscillatorAugmented second (387 words) [view diff] no match in snippet view article find links to article

seconds). In harmonic minor scales, the augmented second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor,Time-domain harmonic scaling (221 words) [view diff] no match in snippet view article find links to article

Time-domain harmonic scaling (TDHS) is a method for time-scale modification of speech (or other audio signals), allowing the apparent rate of speech articulationHarmonic division (163 words) [view diff] no match in snippet view article find links to article

In geometry, harmonic division of a line segment AB means identifying two points C and D such that AB is divided internally and externally in the sameMajor sixth (653 words) [view diff] no match in snippet view article find links to article

or supermajor sixth of 933 cents. The Pythagorean major sixth, or 27th harmonic, is 27:16 or 906 cents, constructed from three just perfect fifths (C-ABôcher's theorem (187 words) [view diff] no match in snippet view article find links to article

contain all the critical points of . In harmonic analysis, Bôcher's theorem states that a positive harmonic function in punctured domain (an open domainList of pitch intervals (850 words) [view diff] no match in snippet view article find links to article

subdivisions of the octave or of other intervals. For commonly encountered harmonic or melodic intervals between pairs of notes in contemporary Western musicTime Remembered (129 words) [view diff] no match in snippet view article find links to article

For Bill Evans album, see Time Remembered (album). Time Remembered is a musical piece by jazz pianist Bill Evans. Jack Reilly says that the work is bothTexture (music) (534 words) [view diff] no match in snippet view article find links to article

In music, texture is how the melodic, rhythmic, and harmonic materials are combined in a composition, thus determining the overall quality of the soundHarnack's principle (129 words) [view diff] no match in snippet view article find links to article

convergence of sequences of harmonic functions, that follow from Harnack's inequality. If the functions , , ... are harmonic in an open connected subsetG minor (549 words) [view diff] no match in snippet view article find links to article

based on G, consisting of the pitches G, A, B♭, C, D, E♭, and F. For the harmonic minor scale, the F is raised to F♯. Its relative major is B-flat majorDe Bruijn's theorem (866 words) [view diff] no match in snippet view article find links to article

results is now known as de Bruijn's theorem. According to this theorem, a "harmonic brick" (one in which each side length is a multiple of the next smallerMajor seventh (735 words) [view diff] no match in snippet view article find links to article

quarter tone (½) chromatic semitone (⅔) diatonic semitone (1⅙) whole tone (2⅓) subminor third (2⅔) supermajor third (4⅓) harmonic (subminor) seventh (9⅔)Total harmonic distortion analyzer (427 words) [view diff] no match in snippet view article find links to article

A total harmonic distortion analyzer calculates the total harmonic content of a sinewave with some distortion, expressed as total harmonic distortion (THD)Acoustic telegraphy (443 words) [view diff] no match in snippet view article find links to article

Acoustic telegraphy was also known as harmonic telegraphy. During the late 19th century, inventors developed methods of multiplexing (transmitting moreContrafact (449 words) [view diff] no match in snippet view article find links to article

musical composition consisting of a new melody overlaid on a familiar harmonic structure. Contrafact can also be explained as the use of borrowed chordHarmonic mixer (552 words) [view diff] no match in snippet view article find links to article

The harmonic mixer and subharmonic mixer are a type of frequency mixer, which is a circuit that changes one signal frequency to another. The ordinary mixerKepler's laws of planetary motion (4,851 words) [view diff] no match in snippet view article find links to article

geometric mean between rmin and rmax: The semi-latus rectum p is the harmonic mean between rmin and rmax: The eccentricity ε is the coefficient ofPhrygian dominant scale (511 words) [view diff] no match in snippet view article find links to article

is the fifth mode of the harmonic minor scale, the fifth being the dominant. Also called the altered Phrygian scale, harmonic minor perfect fifth belowModal frame (566 words) [view diff] no match in snippet view article find links to article

to other more important tones in a non-harmonic way melodic triad: arpeggiated triads in a melody. A non-harmonic arpeggio is most commonly a melodic triadPhänomene (80 words) [view diff] no match in snippet view article find links to article

reflect the composer's fascination for avant-garde orchestrations and harmonic styles of Hector Berlioz and Richard Wagner. "STRAUSS II, J.: EditionPlancherel theorem (275 words) [view diff] no match in snippet view article find links to article

In mathematics, the Plancherel theorem is a result in harmonic analysis, proven by Michel Plancherel in 1910. It states that the integral of a function'sCapacity of a set (965 words) [view diff] no match in snippet view article find links to article

energy is computed with respect to an idealized ground at infinity for the harmonic or Newtonian capacity, and with respect to a surface for the condenserPluriharmonic function (947 words) [view diff] no match in snippet view article find links to article

several complex variables. Sometimes a such function is referred as n-harmonic function, where n ≥ 2 is the dimension of the complex domain where theSeptimal minor third (756 words) [view diff] no match in snippet view article find links to article

( Play (help·info)). The septimal minor third may be derived in the harmonic series from the seventh harmonic, and as such is in inharmonic ratios with all notes inHarmonic scalpel (360 words) [view diff] no match in snippet view article find links to article

The Harmonic scalpel is a surgical instrument used to simultaneously cut and cauterize tissue. Unlike a Bovie, the harmonic uses ultrasonic vibrationsSpherical Harmonic (812 words) [view diff] no match in snippet view article find links to article

For the mathematical functions, see Spherical harmonics. Spherical Harmonic is a science fiction novel from the Saga of the Skolian Empire by CatherineBebop (3,024 words) [view diff] no match in snippet view article find links to article

instrumental virtuosity and improvisation based on the combination of harmonic structure and sometimes references to the melody. It was developed in thePotential (219 words) [view diff] no match in snippet view article find links to article

mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds. This mathematical formulation arises from the factHarmonic balance (600 words) [view diff] no match in snippet view article find links to article

Harmonic balance is a method used to calculate the steady-state response of non-linear differential equations, and is mostly applied to electrical circuitsAnharmonicity (970 words) [view diff] no match in snippet view article find links to article

deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in simple harmonic motion is known as an anharmonic oscillatorMinor seventh (459 words) [view diff] no match in snippet view article find links to article

minor seventh" ( Play (help·info)). An interval close in frequency is the harmonic seventh. Minor seventh chord Musical tuning List of meantone intervalsHarmonic balancer (386 words) [view diff] no match in snippet view article find links to article

A harmonic balancer (also called crank pulley damper, crankshaft damper, torsional damper, or vibration damper) is a device connected to the crankshaftTuned mass damper (1,993 words) [view diff] no match in snippet view article find links to article

A tuned mass damper, also known as a harmonic absorber, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their applicationChord progression (2,987 words) [view diff] no match in snippet view article find links to article

A chord progression (or harmonic progression) is a series of musical chords, or chord changes that "aims for a definite goal" of establishing (or contradicting)List of musical scales and modes (66 words) [view diff] no match in snippet view article find links to article

tone Harmonic major scale Harmonic major scale on C. Play (help·info) 1 2 3 4 5 ♭6 7 7 major harmonic Harmonic minor scale Harmonic minorTrombone (7,505 words) [view diff] no match in snippet view article find links to article

different partial in the harmonic series. In the first position (also called closed position) on a B♭ trombone, the notes in the harmonic series begin with B♭2Pedal tone (315 words) [view diff] no match in snippet view article find links to article

are special notes in the harmonic series of cylindrical-bore brass instruments. A pedal tone has the pitch of its harmonic series' fundamental tone.Overtone (1,532 words) [view diff] no match in snippet view article find links to article

fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are integer multiplesList of Fourier analysis topics (219 words) [view diff] no match in snippet view article find links to article

topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics. Multiplier (Fourier analysis) Fourier shell correlationDavid Hykes (492 words) [view diff] no match in snippet view article find links to article

a comprehensive approach to contemplative music which he calls Harmonic Chant (harmonic singing). After early research and trips studying Mongolian, TibetanSeptimal whole tone (321 words) [view diff] no match in snippet view article find links to article

septimal whole tone may be derived from the harmonic series as the interval between the seventh and eighth harmonics and the term septimal refers to the factHarnack's inequality (675 words) [view diff] no match in snippet view article find links to article

Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by A. Harnack (1887). J. Serrin (1955)Witold Lutosławski (5,555 words) [view diff] no match in snippet view article find links to article

Five songs of 1956–57, saw the significant development of Lutosławski's harmonic and contrapuntal thinking as he introduced his twelve-note system, theDirichlet's principle (198 words) [view diff] no match in snippet view article find links to article

Not to be confused with Pigeonhole principle. In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizerC-sharp minor (600 words) [view diff] no match in snippet view article find links to article

based on C♯, with the pitches C♯, D♯, E, F♯, G♯, A, and B. For the C-sharp harmonic minor, the B is raised to B♯ (which is equivalent to C). Its key signatureMean (1,537 words) [view diff] no match in snippet view article find links to article

example, the geometric mean of five values: 4, 36, 45, 50, 75 is: The harmonic mean is an average which is useful for sets of numbers which are definedJust intonation (4,882 words) [view diff] no match in snippet view article find links to article

just interval. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:927 areCadence (music) (2,916 words) [view diff] no match in snippet view article find links to article

"a falling") is, "a melodic or harmonic configuration that creates a sense of resolution [finality or pause]." A harmonic cadence is a progression of (atPoisson kernel (926 words) [view diff] no match in snippet view article find links to article

f a function on T that lies in L1(T), then the function u given by is harmonic in D and has a radial limit that agrees with f almost everywhere on theA-sharp minor (240 words) [view diff] no match in snippet view article find links to article

The A♯ minor scale has pitches A♯, B♯, C♯, D♯, E♯, F♯, and G♯. For the harmonic minor scale, G is used instead of G♯. Its key signature has seven sharpsTritone (4,523 words) [view diff] no match in snippet view article find links to article

semidiapente, or semitritonus). In classical music, the tritone is a harmonic and melodic dissonance and is important in the study of musical harmonyLipps–Meyer law (341 words) [view diff] no match in snippet view article find links to article

approximation to a lower, stronger, or higher, weaker, position in the harmonic series. The reason for the effect of finality of such interval ratios mayNottingham Harmonic Society (159 words) [view diff] no match in snippet view article find links to article

Nottingham Harmonic Society is Nottingham's civic choir, and has established itself as one of the leading provincial choruses in Britain.[citation needed]Harmonic Disorder (405 words) [view diff] no match in snippet view article find links to article

Harmonic Disorder is an album by American jazz pianist Matthew Shipp recorded in 2008 and released on Thirsty Ear's Blue Series. It was the second recordingBebop scale (778 words) [view diff] no match in snippet view article find links to article

derived from the modes of the major scale, the melodic minor scale, and the harmonic minor scale. David Baker, one of the world's finest jazz educators, namedScale of harmonics (654 words) [view diff] no match in snippet view article find links to article

The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string.[citation needed] This musical scaleHarmonic table note layout (591 words) [view diff] no match in snippet view article find links to article

The Harmonic Table note-layout, or tonal array, is a key layout for musical instruments that offers interesting advantages over the traditional keyboardRoot (chord) (1,938 words) [view diff] no match in snippet view article find links to article

chord could be represented and named by one of its notes. It is linked to harmonic thinking, that is, to the idea that vertical aggregates of notes form a100000 (number) (970 words) [view diff] no match in snippet view article find links to article

totient number 166320 – highly composite number 167400 – harmonic divisor number 173600 – harmonic divisor number 174680 – Keith number 174763 – WagstaffA minor (366 words) [view diff] no match in snippet view article find links to article

scale based on A, consisting of the pitches A, B, C, D, E, F, and G. The harmonic minor scale raises the G to G♯. Its key signature has no flats or sharpsSupertonic (554 words) [view diff] no match in snippet view article find links to article

fifth above chord V. Descending fifths are a strong basis for harmonic motion and harmonic motion through intervals of fifths is a natural way for chordsHungarian gypsy scale (419 words) [view diff] no match in snippet view article find links to article

called Hungarian minor scale or double harmonic minor scale, can be found by sharpening the 4th degree of the harmonic minor scale to introduce an additionalArithmetic combinatorics (746 words) [view diff] no match in snippet view article find links to article

in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Arithmetic combinatorics is about combinatorial estimates associatedUncertainty principle (7,683 words) [view diff] no match in snippet view article find links to article

parameter . Main articles: Quantum harmonic oscillator and Stationary state Consider a one-dimensional quantum harmonic oscillator (QHO). It is possibleE-flat minor (491 words) [view diff] no match in snippet view article find links to article

scale consisting of the pitches E♭, F, G♭, A♭, B♭, C♭, and D♭. In the harmonic minor, the D♭ is raised to D♮. Its key signature consists of six flatsSpurious emission (97 words) [view diff] no match in snippet view article find links to article

especially in a device which normally does create other frequencies. A harmonic or other signal outside a transmitter's assigned channel would be consideredAdditive synthesis (4,021 words) [view diff] no match in snippet view article find links to article

can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic partials or overtones. Each partial is a sine wave of differentHeavy metal music (13,028 words) [view diff] no match in snippet view article find links to article

fretboard. Heavy metal is usually based on riffs created with three main harmonic traits: modal scale progressions, tritone and chromatic progressions, andUnified field (305 words) [view diff] no match in snippet view article find links to article

'unity of musical space' created by the free use of melodic material as harmonic material and vice versa. The technique is most associated with the twelve-toneDe Rham cohomology (1,606 words) [view diff] no match in snippet view article find links to article

of harmonic forms and the de Rham cohomology consisting of closed forms modulo exact forms. This relies on an appropriate definition of harmonic formsSinging bowl (738 words) [view diff] no match in snippet view article find links to article

by a fundamental frequency (first harmonic) and usually two audible harmonic overtones (second and third harmonic).[citation needed] Singing bowls areWiretap Scars (216 words) [view diff] no match in snippet view article find links to article

Tarot" – 5:13 "Echodyne Harmonic" – 3:57 "Assemble the Empire" – 3:02 "Vacant Skies" – (UK/Japan Bonus Track) - 3:55 "Echodyne Harmonic (de-mix)" (Japan BonusDivergence of the sum of the reciprocals of the primes (955 words) [view diff] no match in snippet view article find links to article

describe how Euler originally discovered the result. He was considering the harmonic series He had already used the following "product formula" to show theCreation and annihilation operators (1,553 words) [view diff] no match in snippet view article find links to article

widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator lowersPythagorean means (234 words) [view diff] no match in snippet view article find links to article

Pythagorean means are the arithmetic mean (A), the geometric mean (G), and the harmonic mean (H). They are defined by: Each mean has the following properties:B minor (463 words) [view diff] no match in snippet view article find links to article

signature consists of two sharps. The harmonic minor raises the note A to A♯. Changes needed for the melodic and harmonic versions of the scale are writtenDiminished fourth (283 words) [view diff] no match in snippet view article find links to article

third; but if the same pitches are spelled B and E♭, as occurs in the C harmonic minor scale, the interval is instead a diminished fourth. In other tuningsInterval (music) (7,966 words) [view diff] no match in snippet view article find links to article

sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. InElias M. Stein (867 words) [view diff] no match in snippet view article find links to article

January 13, 1931) is a mathematician and a leading figure in the field of harmonic analysis. He is a professor emeritus of Mathematics at Princeton UniversityModal jazz (1,361 words) [view diff] no match in snippet view article find links to article

jazz is jazz that uses musical modes rather than chord progressions as a harmonic framework. Originating in the late 1950s and 1960s, modal jazz is epitomizedPersian scale (191 words) [view diff] no match in snippet view article find links to article

frequent use of chromaticism. Compare this to the one augmented second of the harmonic minor or the use of only two half-steps in all diatonic scales. The sequenceNorbert Wiener Center for Harmonic Analysis and Applications (316 words) [view diff] no match in snippet view article find links to article

The Norbert Wiener Center for Harmonic Analysis and Applications (NWC) is a division of the Mathematics Department in the University of Maryland CollegeHarish-Chandra's Ξ function (138 words) [view diff] no match in snippet view article find links to article

In mathematical harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group, studied by Harish-Chandra (1966Synthetic chord (356 words) [view diff] no match in snippet view article find links to article

In music theory and harmonic analysis, a synthetic chord is a made-up or non-traditional (synthetic) chord (collection of pitches) which cannot be analyzedNormal mode (2,041 words) [view diff] no match in snippet view article find links to article

of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones". The most general motion of a system is a superpositionSimultaneity (music) (296 words) [view diff] no match in snippet view article find links to article

a more general term than chord progression or harmonic progression: most chord progressions or harmonic progressions are then simultaneity successionsMusical acoustics (1,539 words) [view diff] no match in snippet view article find links to article

the harmonic series. Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, butAverage (1,768 words) [view diff] no match in snippet view article find links to article

was 40 km/h, then the harmonic mean speed is given by A well known inequality concerning arithmetic, geometric, and harmonic means for any set of positiveQuarter tone (2,165 words) [view diff] no match in snippet view article find links to article

tuba) (though, as with woodwinds, embouchure manipulation, as well as harmonic tones that fall closer to quarter-tones than half-tones, make quarter-toneHVDC converter station (1,191 words) [view diff] no match in snippet view article find links to article

transformers capacitors or synchronous condensers for reactive power filters for harmonic suppression, and direct current switch gear. Main article: HVDC converterDominant (music) (1,279 words) [view diff] no match in snippet view article find links to article

requires the tonic for resolution. In very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary (often triadic)Mediant (525 words) [view diff] no match in snippet view article find links to article

mediant occurs as a major chord, noted with the Roman numeral III. In harmonic minor scales and ascending melodic minor scales, the seventh scale degreeQuasi-harmonic approximation (490 words) [view diff] no match in snippet view article find links to article

The quasi-harmonic approximation is a phonon-based model of solid-state physics used to describe volume-dependent thermal effects, such as the thermal