1.
Bell
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A bell is a directly struck idiophone percussion instrument. Most bells have the shape of a cup that when struck vibrates in a single strong strike tone. The strike may be made by an internal clapper or uvula, Bells are usually cast from bell metal for its resonant properties, but can also be made from other hard materials, this depends on the function. Many public or institutional buildings house bells, most commonly as clock bells to sound the hours and quarters, historically, bells have been associated with religious rituals, and are still used to call communities together for religious services. Later, bells were made to important events or people and have been associated with the concepts of peace. The study of bells is called campanology and it is popularly but not certainly related to the former sense of to bell which gave rise to bellow. The earliest archaeological evidence of dates from the 3rd millennium BC. Clapper-bells made of pottery have found in several archaeological sites. The pottery bells later developed into metal bells, in West Asia, the first bells appear in 1000 BC. The earliest metal bells, with one found in the Taosi site, early bells not only have an important role in generating metal sound, but arguably played a prominent cultural role. See also Klang Bell of the British Museum collection, in the western world, the common form of bell is a church bell or town bell, which is hung within a tower or bell cote. Such bells are fixed in position or mounted on a beam so they can swing to. Bells that are hung dead are normally sounded by hitting the bow with a hammer or occasionally by pulling an internal clapper against the bell. Where a bell is swung it can either be swung over an arc by a rope. As the bell swings higher the sound is projected rather than downwards. Bells hung for full circle ringing are swung through just over a circle from mouth uppermost. A stay engages a mechanism to allow the bell to rest just past its balance point, the rope is attached to one side of a wheel so that a different amount of rope is wound on and off as it swings to and fro. Swinging bells are sounded by an internal clapper, the clapper may have a longer period of swing than the bell
2.
Musical note
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In music, the term note has three primary meanings, A sign used in musical notation to represent the relative duration and pitch of a sound, A pitched sound itself. Notes are the blocks of much written music, discretizations of musical phenomena that facilitate performance, comprehension. In the former case, one note to refer to a specific musical event, in the latter. Two notes with fundamental frequencies in an equal to any integer power of two are perceived as very similar. Because of that, all notes with these kinds of relations can be grouped under the pitch class. However, within the English-speaking and Dutch-speaking world, pitch classes are represented by the first seven letters of the Latin alphabet. A few European countries, including Germany, adopt an almost identical notation, the eighth note, or octave, is given the same name as the first, but has double its frequency. The name octave is also used to indicate the span between a note and another with double frequency, for example, the now-standard tuning pitch for most Western music,440 Hz, is named a′ or A4. There are two systems to define each note and octave, the Helmholtz pitch notation and the scientific pitch notation. Letter names are modified by the accidentals, a sharp ♯ raises a note by a semitone or half-step, and a flat ♭ lowers it by the same amount. In modern tuning a half step has a ratio of 12√2. The accidentals are written after the name, so, for example, F♯ represents F-sharp, B♭ is B-flat. Additional accidentals are the double-sharp, raising the frequency by two semitones, and double-flat, lowering it by that amount, in musical notation, accidentals are placed before the note symbols. Systematic alterations to the seven lettered pitches in the scale can be indicated by placing the symbols in the key signature, explicitly noted accidentals can be used to override this effect for the remainder of a bar. A special accidental, the natural symbol ♮, is used to indicate an unmodified pitch, effects of key signature and local accidentals do not accumulate. If the key signature indicates G♯, a flat before a G makes it G♭, though often this type of rare accidental is expressed as a natural. Likewise, a sharp sign on a key signature with a single sharp ♯ indicates only a double sharp. Assuming enharmonicity, many accidentals will create equivalences between pitches that are written differently, for instance, raising the note B to B♯ is equal to the note C
3.
Prime number
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n
4.
Fundamental frequency
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The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as f0, in other contexts, it is more common to abbreviate it as f1, the first harmonic. All sinusoidal and many non-sinusoidal waveforms are periodic, which is to say they repeat exactly over time. The period of a waveform is the T for which the equation is true. This means that this equation and a definition of the values over any interval of length T is all that is required to describe the waveform completely. Every waveform may be described using any multiple of this period, there exists a smallest period over which the function may be described completely and this period is the fundamental period. The fundamental frequency is defined as its reciprocal, f 0 =1 T Since the period is measured in units of time, when the time units are seconds, the frequency is in s −1, also known as Hertz. For a tube of length L with one end closed and the end open the wavelength of the fundamental harmonic is 4 L. If the ends of the tube are now both closed or both opened as in the last two animations, the wavelength of the fundamental harmonic becomes 2 L. By the same method as above, the frequency is found to be f 0 = v 2 L. At 20 °C the speed of sound in air is 343 m/s and this speed is temperature dependent and does increase at a rate of 0.6 m/s for each degree Celsius increase in temperature. The fundamental may be created by vibration over the length of a string or air column. The fundamental is one of the harmonics, a harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The reason a fundamental is also considered a harmonic is because it is 1 times itself, the fundamental is the frequency at which the entire wave vibrates. Overtones are other components present at frequencies above the fundamental. All of the components that make up the total waveform, including the fundamental
5.
Erfurt Cathedral
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The Catholic Erfurt Cathedral is a 1200-year-old church located on Cathedral Hill of Erfurt, in Thuringia, Germany. It is of an International Gothic style, and is known as St Marys Cathedral. It is the seat of the Roman Catholic Diocese of Erfurt. The site of the present Cathedral has been the location of many other Christian buildings, for example a Romanesque basilica, martin Luther was ordained in the cathedral in 1507. Saint Boniface erected a church in the year 724 on the mound which the Erfurt Cathedral now sits, the foundations of the original church were used for a Romanesque basilica in the mid 12th century. The mound was enlarged in the early 14th century to make room for the St. Marys cathedral. The architecture of the Erfurt Cathedral is mainly Gothic and stems from around the 14th and 15th centuries, there are many things of note as far as the architecture is concerned, not least the stained glass windows and furnishings of the interior of the cathedral. The central spire of the three towers that sit aloft the cathedral harbours the Maria Gloriosa which, at the time of its casting by Geert van Wou in 1497, was the worlds largest free-swinging bell and it is the largest existing medieval bell in the world. It is known to have purity and beauty of tone
6.
Harmonic series (music)
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A harmonic series is the sequence of sounds where the base frequency of each sound is an integer multiple of the lowest base frequency. Pitched musical instruments are based on an approximate harmonic oscillator such as a string or a column of air. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves, interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency. The musical timbre of a tone from such an instrument is determined by the relative strengths of each harmonic. A complex tone can be described as a combination of many simple periodic waves or partials, each with its own frequency of vibration, amplitude, a partial is any of the sine waves of which a complex tone is composed. A harmonic is any member of the series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The fundamental is also considered a harmonic because it is 1 times itself, a harmonic partial is any real partial component of a complex tone that matches an ideal harmonic. An inharmonic partial is any partial that does not match an ideal harmonic, Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial. Unpitched, or indefinite-pitched instruments, such as cymbals, gongs, or tam-tams make sounds that are rich in inharmonic partials, an overtone is any partial except the lowest partial. The term overtone does not imply harmonicity or inharmonicity and has no special meaning other than to exclude the fundamental. It is the relative strengths of the different overtones that gives an instrument its particular timbre, some electronic instruments, such as synthesizers, can play a pure frequency with no overtones. Synthesizers can also combine pure frequencies into more complex tones, such as to other instruments. Certain flutes and ocarinas are very nearly without overtones, in most pitched musical instruments, the fundamental is accompanied by other, higher-frequency harmonics. Thus shorter-wavelength, higher-frequency waves occur with varying prominence and give each instrument its characteristic tone quality, the fact that a string is fixed at each end means that the longest allowed wavelength on the string is twice the length of the string. Other allowed wavelengths are 1/2, 1/3, 1/4, 1/5, 1/6, theoretically, these shorter wavelengths correspond to vibrations at frequencies that are 2,3,4,5,6, etc. times the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator it vibrates against often alter these frequencies, the harmonic series is an arithmetic series. In terms of frequency, the difference between consecutive harmonics is therefore constant and equal to the fundamental, but because human ears respond to sound nonlinearly, higher harmonics are perceived as closer together than lower ones
7.
Atonal
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Atonality in its broadest sense is music that lacks a tonal center, or key. The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, erialism arose partly as a means of organizing more coherently the relations used in the preserial free atonal music. Thus many useful and crucial insights about even strictly serial music depend only on such basic atonal theory, the term atonality was coined in 1907 by Joseph Marx in a scholarly study of tonality, which was later expanded into his doctoral thesis. Their music arose from what was described as the crisis of tonality between the nineteenth century and early twentieth century in classical music. The connections between harmonies were uncertain even on the lowest—chord-to-chord—level, on higher levels, long-range harmonic relationships and implications became so tenuous that they hardly functioned at all. At best, the probabilities of the style system had become obscure, at worst. The first phase, known as free atonality or free chromaticism, Works of this period include the opera Wozzeck by Alban Berg and Pierrot Lunaire by Schoenberg. This period included Bergs Lulu and Lyric Suite, Schoenbergs Piano Concerto, his oratorio Die Jakobsleiter and numerous smaller pieces, however, actual analysis of Weberns twelve-tone works has so far failed to demonstrate the truth of this assertion. One analyst concluded, following an examination of the Piano Variations. 27, that while the texture of this music may superficially resemble that of serial music. None of the patterns within separate nonpitch characteristics makes audible sense in itself, the point is that these characteristics are still playing their traditional role of differentiation. Twelve-tone technique, combined with the parametrization of Olivier Messiaen, would be taken as the inspiration for serialism, Atonality emerged as a pejorative term to condemn music in which chords were organized seemingly with no apparent coherence. In Nazi Germany, atonal music was attacked as Bolshevik and labeled as degenerate along with music produced by enemies of the Nazi regime. Many composers had their works banned by the regime, not to be played until after its collapse after World War II, after Schoenbergs death, Igor Stravinsky used the twelve-tone technique. The twelve-tone technique was preceded by Schoenbergs freely atonal pieces of 1908–1923, the twelve-tone technique was also preceded by nondodecaphonic serial composition used independently in the works of Alexander Scriabin, Igor Stravinsky, Béla Bartók, Carl Ruggles, and others. Additionally George Perle explains that, the free atonality that preceded dodecaphony precludes by definition the possibility of self-consistent, in other words, reverse the rules of the common practice period so that what was not allowed is required and what was required is not allowed. This is what was done by Charles Seeger in his explanation of dissonant counterpoint, kostka and Payne list four procedures as operational in the atonal music of Schoenberg, all of which may be taken as negative rules. Equal-interval chords are often of indeterminate root, mixed-interval chords are often best characterized by their interval content, Perle also points out that structural coherence is most often achieved through operations on intervallic cells
8.
Inharmonicity
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In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency. Acoustically, a note perceived to have a distinct pitch in fact contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex, any departure from this ideal harmonic series is known as inharmonicity. The less elastic the strings are, the more inharmonicity they exhibit, 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 exactly 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 thick string behaves less as an ideal string and more like a cylinder. For this reason, a single tone played by a string instrument, brass instrument. The inharmonicity of a string depends on its characteristics, such as tension, stiffness. For instance, a string under low tension exhibits a high degree of inharmonicity. A wound string generally exhibits less inharmonicity than the equivalent solid string, in 1943, Schuck and Young were the first scientists to measure the spectral inharmonicity in piano tones. They found that the spectral partials in piano tones are progressively stretched—that is to say, in 1962, research by Harvey Fletcher and his collaborators indicated that the spectral inharmonicity is important for tones to sound piano-like. They proposed that inharmonicity is responsible for the warmth property common to real piano tones, according to their research synthesized piano tones sounded more natural when some inharmonicity was introduced. In general, electronic instruments that duplicate acoustic instruments must duplicate both the inharmonicity and the resulting stretched tuning of the original instruments. When pianos are tuned by piano tuners, the technician sometimes listens for the sound of beating when two notes are played together, and tunes to the point that minimizes roughness between tones. Piano tuners must deal with the inharmonicity of piano strings, which is present in different amounts in all of the ranges of the instrument, the result is that octaves are tuned slightly wider than the harmonic 2,1 ratio. Because of the problem of inharmonicity, electronic piano tuning devices used by piano technicians are not designed to tune according to a harmonic series. Rather, the use various means to duplicate the stretched octaves
9.
Octave
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In music, an octave or perfect octave is the interval between one musical pitch and another with half or double its frequency. It is defined by ANSI as the unit of level when the base of the logarithm is two. The octave relationship is a phenomenon that has been referred to as the basic miracle of music. The most important musical scales are written using eight notes. For example, the C major scale is typically written C D E F G A B C, two notes separated by an octave have the same letter name and are of the same pitch class. Three commonly cited examples of melodies featuring the perfect octave as their opening interval are Singin in the Rain, Somewhere Over the Rainbow, the interval between the first and second harmonics of the harmonic series is an octave. The octave has occasionally referred to as a diapason. To emphasize that it is one of the intervals, the octave is designated P8. The octave above or below a note is sometimes abbreviated 8a or 8va, 8va bassa. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, the ratio of frequencies of two notes an octave apart is therefore 2,1. Further octaves of a note occur at 2n times the frequency of that note, such as 2,4,8,16, etc. and the reciprocal of that series. For example,55 Hz and 440 Hz are one and two away from 110 Hz because they are 1⁄2 and 4 times the frequency, respectively. After the unison, the octave is the simplest interval in music, the human ear tends to hear both notes as being essentially the same, due to closely related harmonics. Notes separated by a ring together, adding a pleasing sound to music. For this reason, notes an octave apart are given the note name in the Western system of music notation—the name of a note an octave above A is also A. The conceptualization of pitch as having two dimensions, pitch height and pitch class, inherently include octave circularity, thus all C♯s, or all 1s, in any octave are part of the same pitch class. Octave equivalency is a part of most advanced cultures, but is far from universal in primitive. The languages in which the oldest extant written documents on tuning are written, leon Crickmore recently proposed that The octave may not have been thought of as a unit in its own right, but rather by analogy like the first day of a new seven-day week
10.
Undertone series
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In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the production of music on instruments. The overtone series being a series, the undertone series is based on arithmetic division. The hybrid term subharmonic is used in music and dynamics in a few different ways, in its pure sense, the term subharmonic refers strictly to any member of the subharmonic series. When the subharmonic series is used to refer to frequency relationships, the complex tones of acoustic instruments do not produce partials that resemble the subharmonic series. However, such tones can be produced artificially with audio software, subharmonics can be contrasted with harmonics. While harmonics can. occur in any system, there are. only fairly restricted conditions that will lead to the nonlinear phenomenon known as subharmonic generation. One way to define subharmonics is that they are. integral submultiples of the fundamental frequency, the human voice can also be forced into a similar driven resonance, also called “undertone singing”, to extend the range of the voice below what is normally available. The overtone series can be produced physically in two ways—either by overblowing a wind instrument, or by dividing a monochord string. If a monochord string is lightly damped at the point, then at 1/3, then 1/4, 1/5, etc. then the string will produce the overtone series. If instead, the length of the string is doubled in the opposite ratios, similarly, on a wind instrument, if the holes are equally spaced, each successive hole covered will produce the next note in the undertone series. In addition, José Sotorrio showed that undertones could be made through the use of an oscillator such as a tuning fork. If that oscillator is gently forced to vibrate against a sheet of paper it will make contact at various audible modes of vibration. The tritare, a guitar with Y shaped strings, cause subharmonics too and this can also be achieved by the extended technique of crossing two strings as some experimental jazz guitarists have developed. Also third bridge preparations on guitars cause timbres consisting of sets of high pitched overtones combined with a resonant tone of the unplugged part of the string. Subharmonics can be produced by signal amplification through loudspeakers, Subharmonic frequencies are frequencies below the fundamental frequency of an oscillator in a ratio of 1/n, with n a positive integer number. For example, if the frequency of an oscillator is 440 Hz, sub-harmonics include 220 Hz. Thus, they are an image of the harmonic series