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For other uses, see Harmonic (disambiguation). The term harmonic in its strictest sense describes any member of the harmonic series. The term isHarmonic oscillator (2,700 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; suchSimple harmonic motion (1,182 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) (2,221 words) [view diff] no match in snippet view article

A harmonic series is the sequence of sounds where the base frequency of each sound is an integral multiple of the lowest base frequency. Pitched musicalHarmonic analysis (1,050 words) [view diff] no match in snippet view article find links to article

process of determining the structure of a piece of music, see Harmony. Harmonic analysis is a branch of mathematics concerned with the representation ofHarmonic mean (2,947 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 PythagoreanHarmonic 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, mathematicalQuantum harmonic oscillator (2,668 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 shorteningHarmonic series (mathematics) (2,045 words) [view diff] no match in snippet view article

In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengthsHarmonic 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)Minor scale (1,961 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 scaleList 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 towardsHarmonic major scale (1,123 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 employedWeakly 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 (1,023 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 sinusoidalHarmonic (mathematics) (123 words) [view diff] no match in snippet view article

analysis Harmonic conjugate Projective harmonic conjugate Harmonic division Harmonic function Harmonic number Harmonic series Alternating harmonic seriesLeibniz 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 (724 words) [view diff] no match in snippet view article find links to article

For geometric conjugate points, see Projective harmonic conjugates. "Conjugate function" redirects here. For the convex conjugate of a function, see ConvexHarmonic number (1,444 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 numberGeometric–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 seventh (834 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 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 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 closedTap 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 atDouble harmonic scale (879 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 majorLamé 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 frequencyHarmonic drive (1,042 words) [view diff] no match in snippet view article find links to article

Harmonic Drive is a strain wave gear which can improve certain characteristics compared to traditional gearing systems. Harmonic Drive is trademarked byHarmonic map (955 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 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 seventh chord (915 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 narrowerHarmonic 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 equationsMajor third (646 words) [view diff] no match in snippet view article find links to article

The major third may be derived from the harmonic series as the interval between the fourth and fifth harmonics. The major scale is so named because ofMinor third (960 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 commonlyProjective 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 progression (mathematics) (360 words) [view diff] no match in snippet view article

the musical term, see Chord progression. In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocalsDistortion (1,501 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 (946 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 asOptical 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 generationPotential theory (1,297 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 (4,215 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 soundingThe 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 22 NovemberParallel 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 movementHarmonic 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 eruptionTriad (music) (913 words) [view diff] no match in snippet view 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)Pinch harmonic (1,009 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'sPositive 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 measureHarmonic coordinates (572 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, meaningOvertone 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 woodwindTotal harmonic distortion (1,746 words) [view diff] no match in snippet view article find links to article

The total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ratio of the sum of the powersHarmonic mixing (546 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'sHarmonic Inc. (833 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, processDiatonic function (2,344 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)Overtone singing (2,125 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 resonancesGeometric mean (2,685 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 leastHarmonic 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 pulls back real-valued harmonic functions on the codomain to harmonic functionsHigh harmonic generation (1,734 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 aHarmonic 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 recordingsAccompaniment (631 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 vanishRiemannian theory (366 words) [view diff] no match in snippet view article find links to article

by a concept of harmonic functions. Riemann's "dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists. The termNoncommutative harmonic analysis (464 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 that are not commutativeGypsy 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 butGuitar harmonics (994 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 containNeutral 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 hairHarmonic 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 ofHarmonic 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 ofMinor 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)Harmonics (electrical power) (1,341 words) [view diff] no match in snippet view 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 frequentSpherical harmonics (4,831 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 usedVan der Corput lemma (harmonic analysis) (183 words) [view diff] no match in snippet view article

In mathematics, in the field of harmonic analysis, the van der Corput lemma is an estimate for oscillatory integrals named after the Dutch mathematicianPaul 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 asHarmonic scalpel (352 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 vibrationsProjective 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 thisHungarian minor scale (805 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 isRadó's theorem (harmonic functions) (132 words) [view diff] no match in snippet view 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 (3,722 words) [view diff] no match in snippet view article find links to article

Nonlinear optics remained unexplored until the discovery in 1961 of Second harmonic generation by Peter Franken et al. at University of Michigan, shortly afterZonal 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 particularThe City Harmonic (1,253 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 Convergence (992 words) [view diff] no match in snippet view article find links to article

Not to be confused with Harmonic series (mathematics)#Divergence. The Harmonic Convergence is the name given to one of the world's first globally synchronizedDirac 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 propagationHodge 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: HodgeList 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 modesDiphthong (5,043 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 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 transformationHammond organ (8,103 words) [view diff] no match in snippet view article find links to article

the big band. Jimmy Smith's use of the Hammond B-3, with its additional harmonic percussion feature, inspired a generation of organ players, and its useHarmonic 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 toNonchord tone (1,660 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 functionalComplex harmonic motion (1,081 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 balancer (375 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 crankshaftExciter (effect) (549 words) [view diff] no match in snippet view article

For other uses, see Exciter (disambiguation). An exciter (also called a harmonic exciter or aural exciter) is an audio signal processing technique usedRiemann–Lebesgue lemma (292 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 transformMaximum 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, thenLaplace's equation (2,072 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 fieldsChord 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 oftenConsonance and dissonance (6,686 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 superimposedOscillation (884 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 attachedMajor seventh (864 words) [view diff] no match in snippet view article find links to article

century, the major seventh was used increasingly both as a melodic and a harmonic interval, particularly by composers of the Second Viennese School. AntonList of pitch intervals (944 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 musicWolstenholme 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, 266681Bôcher'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 domainTritone (4,548 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 harmonyDamping (1,975 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 oscillatorC minor (394 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 inCodazzi tensor (79 words) [view diff] no match in snippet view article find links to article

arise very naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strictTime-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 (182 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 sameTotal 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)Augmented second (382 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,Spherical 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 CatherineTime 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 bothG 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 majorMajor sixth (757 words) [view diff] no match in snippet view article find links to article

perfect fifths (C-A = C-G-D-A = 702+702+702-1200=906) or by playing 27th harmonic and the next lowest octave of the fundamental frequency (16) together.De 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 smallerSpurious 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 consideredHeavy metal music (13,923 words) [view diff] no match in snippet view article find links to article

According to Robert Walser, heavy metal harmonic relationships are "...often quite complex" and the harmonic analysis done by metal players and teachersUnified 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-toneCapacity 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 condenserContrafact (456 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 chordKepler's laws of planetary motion (4,903 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 ofHarmonic balance (939 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 nonlinear differential equations , and is mostly applied to nonlinear electricalAcoustic 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 moreHarnack'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 subsetChord progression (3,056 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)Pedal 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.Modal frame (573 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 triadPhrygian dominant scale (510 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 belowPluriharmonic function (952 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 theBebop (3,085 words) [view diff] no match in snippet view article find links to article

instrumental virtuosity, and improvisation based on a combination of harmonic structure and occasional references to the melody. It was developed inDavid 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, TibetanList 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 minorPlancherel theorem (300 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'sSeptimal 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 inTuned mass damper (2,038 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 applicationPhänomene (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.: EditionPotential (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 factAnharmonicity (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 oscillatorTrombone (7,941 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♭2Minor seventh (453 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 intervalsDyad (music) (341 words) [view diff] no match in snippet view article

The reason fifths are so common is because of the harmonic series.[citation needed] The harmonic series is built over a fundamental pitch, and the restOvertone (1,552 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 multiplesWitold 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, theList 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 correlationDirichlet'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 minimizerMean (1,683 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 definedSeptimal 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 factHomophony (1,197 words) [view diff] no match in snippet view article find links to article

differentiated roles for parts emerged in tandem with tonality, which gave distinct harmonic functions to the soprano, bass and inner voices. A homophonic texture maySeptimal 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)Harmonic distribution (926 words) [view diff] no match in snippet view article find links to article

In probability theory and statistics, the harmonic distribution is a continuous probability distribution. It was discovered by Étienne Halphen, who hadCadence (music) (3,118 words) [view diff] no match in snippet view 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 (atHarish-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 (1966We Are (The City Harmonic album) (484 words) [view diff] no match in snippet view article

We Are is the third studio album by The City Harmonic. Integrity Music released the album on September 4, 2015. Matt Conner, giving the album four starsA-sharp minor (220 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 sharpsRhythm guitar (2,355 words) [view diff] no match in snippet view article find links to article

element in a polyrhythm). Likewise, rhythm guitar can supply all of the harmonic input to a singer-guitarist or small band, but in ensembles that have otherLipps–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 mayQuasi-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 thermalNottingham 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 mixer (800 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 mixerBebop 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, namedA minor (455 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 sharpsRoot (chord) (1,938 words) [view diff] no match in snippet view 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 aScale 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 keyboardE-flat minor (455 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 flatsArithmetic combinatorics (769 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 associatedHungarian gypsy scale (369 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 additionalAdditive synthesis (4,041 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 differentUncertainty principle (7,792 words) [view diff] no match in snippet view article find links to article

(Refs ) Main articles: Quantum harmonic oscillator and Stationary state Consider a one-dimensional quantum harmonic oscillator (QHO). It is possibleB minor (495 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 writtenSinging bowl (739 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 areCreation and annihilation operators (1,810 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 lowersTexture (music) (567 words) [view diff] no match in snippet view article

In music, texture is how the melodic, rhythmic, and harmonic materials are combined in a composition, thus determining the overall quality of the soundPythagorean means (234 words) [view diff] no match in snippet view article find links to article

Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). They are defined by: Each mean has the following properties:Wiretap Scars (214 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 BonusHarmonic 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 recordingDe Rham cohomology (1,615 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 formsSynthetic chord (358 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 analyzedElias M. Stein (863 words) [view diff] no match in snippet view article find links to article

Stein (born January 13, 1931) is a mathematician active in the field of harmonic analysis. He is a professor emeritus of Mathematics at Princeton UniversityPersian 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 sequenceHVDC converter station (1,190 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 converterInterval (music) (7,850 words) [view diff] no match in snippet view 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. InLadder operator (1,057 words) [view diff] no match in snippet view article find links to article

ladder operators in quantum mechanics are in the formalisms of the quantum harmonic oscillator and angular momentum. Many sources credit Dirac with the inventionNormal mode (2,072 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 superpositionNorbert 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 CollegeAverage (2,225 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 positiveRiesz transform (651 words) [view diff] no match in snippet view article find links to article

In the mathematical theory of harmonic analysis, the Riesz transforms are a family of generalizations of the Hilbert transform to Euclidean spaces of dimensionSimultaneity (music) (296 words) [view diff] no match in snippet view 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, butHarmonic and Individual Lines and Noise (329 words) [view diff] no match in snippet view article find links to article

Harmonic and Individual Lines and Noise (HILN) is a parametric codec for audio. The basic premise of the encoder is that most audio, and particularly speechDominant (music) (1,287 words) [view diff] no match in snippet view article

requires the tonic for resolution. In very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary (often triadic)Seventh chord (1,565 words) [view diff] no match in snippet view article find links to article

Harmonic seventh chord The harmonic seventh chord is a dominant seventh chord formed by a major triad plus an harmonic seventh interval. The harmonicNonlinear junction detector (188 words) [view diff] no match in snippet view article find links to article

multiples of the illumination frequency (see harmonic). The detector has a sensitive receiver tuned to these harmonics, as well as appropriate processing andMediant (533 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 degreeF minor (423 words) [view diff] no match in snippet view article find links to article

based on F, consisting of the pitches F, G, A♭, B♭, C, D♭, and E♭. The harmonic minor raises the E♭ to E♮. Its key signature has four flats. Its relativeVibrational partition function (343 words) [view diff] no match in snippet view article find links to article

normal modes of the system are considered to be a set of uncoupled quantum harmonic oscillators. It is a first order approximation to the partition function