Harmonic Cross Ratio
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Harmonic Cross Ratio
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st harmonic''; the other harmonics are known as ''higher harmonics''. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a '' harmonic series''. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50  Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. In music, harmonics are used on string instruments and w ...
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Bow (music)
In music, a bow () is a tensioned stick which has hair (usually horse-tail hair) coated in rosin (to facilitate friction) affixed to it. It is moved across some part (generally some type of strings) of a musical instrument to cause vibration, which the instrument emits as sound. The vast majority of bows are used with string instruments, such as the violin, viola, cello, and bass, although some bows are used with musical saws and other bowed idiophones. Materials and manufacture A bow consists of a specially shaped stick with other material forming a ribbon stretched between its ends, which is used to stroke the string and create sound. Different musical cultures have adopted various designs for the bow. For instance, in some bows a single cord is stretched between the ends of the stick. In the Western tradition of bow making—bows for the instruments of the violin and viol families—a hank of horsehair is normally employed. The manufacture of bows is considered a demandi ...
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Singing Bowl
A standing bell or resting bell is an inverted bell, supported from below with the rim uppermost. Such bells are normally bowl-shaped, and exist in a wide range of sizes, from a few centimetres to a metre in diameter. They are often played by striking, but some—known as singing bowls—may also be played by rotating a suede covered mallet around the outside rim to produce a sustained musical note. Struck bowls are used in some Buddhist religious practices to accompany periods of meditation and chanting. Struck and singing bowls are widely used for music making, meditation and relaxation, as well for personal spirituality. They have become popular with music therapists, sound healers and yoga practitioners. Standing bells originated in China. An early form called took the shape of a stemmed goblet, mounted with rim uppermost, and struck on the outside with a mallet. The manufacture and use of bowls specifically for 'singing' is believed to be a modern phenomenon. Bowls that w ...
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Pizzicato
Pizzicato (, ; translated as 'pinched', and sometimes roughly as 'plucked') is a playing technique that involves plucking the strings of a string instrument. The exact technique varies somewhat depending on the type of instrument: * On bowed string instruments it is a method of playing by plucking the strings with the fingers, rather than using the bow. This produces a very different sound from bowing, short and percussive rather than sustained. * On keyboard string instruments, such as the piano, pizzicato may be employed (although rarely seen in traditional repertoire, this technique has been normalized in contemporary music, with ample examples by George Crumb, Tōru Takemitsu, Helmut Lachenmann, and others) as one of the variety of techniques involving direct manipulation of the strings known collectively as " string piano". * On the guitar, it is a muted form of plucking, which bears an audible resemblance to pizzicato on a bowed string instrument with its relatively ...
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Piano
A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a chromatic scale in equal temperament. A musician who specializes in piano is called a pianist. There are two main types of piano: the #Grand, grand piano and the #Upupright piano. The grand piano offers better sound and more precise key control, making it the preferred choice when space and budget allow. The grand piano is also considered a necessity in venues hosting skilled pianists. The upright piano is more commonly used because of its smaller size and lower cost. When a key is depressed, the strings inside are struck by felt-coated wooden hammers. The vibrations are transmitted through a Bridge (instrument), bridge to a Soundboard (music), soundboard that amplifies the sound by Coupling (physics), coupling the Sound, acoustic energy t ...
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Inharmonicity
In music, inharmonicity is the degree to which the frequency, frequencies of overtones (also known as Harmonic series (music)#Partial, partials or partial tones) depart from Integer, whole multiples of the fundamental frequency (harmonic series (music), harmonic series). Acoustically, a note perceived to have a single distinct pitch in fact contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and Tubular bells, chimes, create complex and inharmonic sounds. Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exact harmonic modes of vibration. In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from this ideal and has some small or large amount of inharmonicity. For instance, a very thick string behaves less as an ideal string and m ...
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String (music)
In music, strings are long flexible structures on string instruments that produce sound through vibration. Strings are held under tension so that they can vibrate freely. The pitch (frequency) at which a string will vibrate is primarily related to its vibrating length (also called speaking length), its tension, and its mass per unit of length. A vibrating string produces very little sound by itself. Therefore, most string instruments have a soundboard to amplify the sound. There are two main kinds of strings; plain and wound. "Plain" strings are simply one piece of long cylindrical material, commonly consisted of nylon or gut. "Wound" strings have a central core, with other material being tightly wound around the string . Prior to World War II, strings of many instruments (including violins and guitars) were composed of a material known as catgut, a type of cord made from refined natural fibers of animal intestines. During the mid-twentieth century however, steel and nylo ...
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Catgut
Catgut (also known as gut) is a type of cord that is prepared from the natural fiber found in the walls of animal intestines. Catgut makers usually use sheep or goat intestines, but occasionally use the intestines of cattle, hogs, horses, mules, or donkeys. Despite the name, catgut is not made from cat intestines. Etymology The word ''catgut'' may have been an abbreviation of the word ''cattlegut''. Alternatively, it may derive by folk etymology from ''kitgut'' or ''kitstring'' — the dialectal word ''kit'', meaning fiddle, having at some point been confused with the word ''kit'' for a young cat, the word "kit" being possibly derived from Welsh. In the 16th century a ''kit'' was a "small fiddle used by dancing teachers," a name probably derived from a shortening of Old English ''cythere'', from Latin , from Greek (see guitar). Common uses Musical instruments Historically, catgut was the most common material for the strings of harps, lutes, violins, violas, cellos, ...
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Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the Crystal structure, atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubber elasticity, rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be Prop ...
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Nonlinear Acoustics
Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using full systems of governing equations of fluid dynamics (for sound waves in liquids and gases) and elasticity (physics), elasticity (for sound waves in solids). These equations are generally nonlinear equation, nonlinear, and their traditional linearization is no longer possible. The solutions of these equations show that, due to the effects of nonlinearity, sound waves are being distortion, distorted as they travel. Introduction A sound wave propagates through a material as a localized pressure change. Increasing the pressure of a gas or fluid increases its local temperature. The local speed of sound in a compressible material increases with temperature; as a result, the wave travels faster during the high pressure phase of the oscillation than during the lower pressure phase. This affects the wave's frequency structure; for examp ...
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Clarinet
The clarinet is a Single-reed instrument, single-reed musical instrument in the woodwind family, with a nearly cylindrical bore (wind instruments), bore and a flared bell. Clarinets comprise a Family (musical instruments), family of instruments of differing sizes and pitches. The clarinet family is the largest woodwind family, ranging from the contrabass clarinet, BB♭ contrabass to the A-flat clarinet, A♭ piccolo. The B soprano clarinet is the most common type, and is the instrument usually indicated by the word "clarinet". German instrument maker Johann Christoph Denner is generally credited with inventing the clarinet sometime around 1700 by adding a register key to the chalumeau, an earlier single-reed instrument. Over time, additional keywork and airtight pads were added to improve the tone and playability. Today the clarinet is a standard fixture of the orchestra and concert band and is used in classical music, military bands, klezmer, jazz, and other styles. Etymol ...
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Trumpet
The trumpet is a brass instrument commonly used in classical and jazz musical ensemble, ensembles. The trumpet group ranges from the piccolo trumpet—with the highest Register (music), register in the brass family—to the bass trumpet, pitched one octave below the standard B or C trumpet. Trumpet-like instruments have historically been used as signaling devices in battle or hunting, with examples dating back to the 2nd Millenium BC. They began to be used as musical instruments only in the late 14th or early 15th century. Trumpets are used in art music styles, appearing in orchestras, concert bands, chamber music groups, and jazz ensembles. They are also common in popular music and are generally included in school bands. Sound is produced by vibrating the lips in a mouthpiece, which starts a standing wave in the air column of the instrument. Since the late 15th century, trumpets have primarily been constructed of brass tubing, usually bent twice into a rounded rectangular ...
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