1.
David Klavins
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David Klavins is a German-Latvian piano maker. With his Modell 370 he introduced the worlds largest piano, in 2012, a digital version of the Modell 370 was published as a software instrument under the name The Giant. In 1945, David Klavinss parents, Paulis and Zeltite, arrived as refugees from Latvia in Germany, David is the third of eight children. His mother played the piano and his father was a violinist, after finishing middle school in 1971, David Klavins started an apprenticeship as a piano maker at the Wilhelm Schimmel Pianofortefabrik in Braunschweig. In 1976, he started his own business, the Klavierhaus Klavins in Bonn and he mainly restored and sold used home and grand pianos. In 1980, he became a craftsman, which, in Germany. While restoring and studying the architecture of grand pianos, Klavins became a critic of the way to construct these instruments. He stated that the used in common piano making are outdated. In November 1987, he presented the Klavins Klavier Modell 370 to the public in the German city of Bonn and it had its name from its height,370 centimetres. In contrast to horizontally built grand pianos, the Modell 370 is laid out vertically and it weighs two tons and stretches over two floors. The piano player sits on the bench in the top floor, while the part of the strings. Due to this construction, the board, responsible for the acoustic breadth of the instrument, is of double size of an ordinary concert grand piano. This leads to a sound and a larger spectrum of overtones. The lowest bass string is 3.03 meters long – about three times longer than in a standard piano, as of 2012, the Modell 370 is the largest piano worldwide. The instrument was first played to the public by the classical pianist Cyprien Katsaris, today it is stored in the Pfleghofsaal of the Institute Of Music Science, Eberhard Karls University, Tübingen. Klavins never intended to produce the instrument in series, many pianists asked Klavins for a grand piano with his construction technique. This led to the Modell 408, which is was scheduled to enter production in the summer of 2014, in May 2012, the Berlin music software developer Native Instruments introduced the Modell 370 as a software instrument, sampled by Uli Baronowsky, under the name The Giant. On June 7,2014, working closely with Nils Frahm and this further lead to a live showcase on June 10,2014 with Nils Frahm in Michelberger Hotel, Berlin
2.
Piano
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The piano is an acoustic, stringed musical instrument invented around the year 1700, in which the strings are struck by hammers. It is played using a keyboard, which is a row of keys that the performer presses down or strikes with the fingers and thumbs of both hands to cause the hammers to strike the strings. The word piano is a form of pianoforte, the Italian term for the early 1700s versions of the instrument. The first fortepianos in the 1700s had a sound and smaller dynamic range. An acoustic piano usually has a wooden case surrounding the soundboard and metal strings. Pressing one or more keys on the keyboard causes a padded hammer to strike the strings. The hammer rebounds from the strings, and the continue to vibrate at their resonant frequency. These vibrations are transmitted through a bridge to a soundboard that amplifies by more efficiently coupling the acoustic energy to the air, when the key is released, a damper stops the strings vibration, ending the sound. Notes can be sustained, even when the keys are released by the fingers and thumbs and this means that the piano can play 88 different pitches, going from the deepest bass range to the highest treble. The black keys are for the accidentals, which are needed to play in all twelve keys, more rarely, some pianos have additional keys. Most notes have three strings, except for the bass that graduates from one to two, the strings are sounded when keys are pressed or struck, and silenced by dampers when the hands are lifted from the keyboard. There are two types of piano, the grand piano and the upright piano. The grand piano is used for Classical solos, chamber music and art song and it is used in jazz. The upright piano, which is compact, is the most popular type, as they are a better size for use in private homes for domestic music-making. During the nineteenth century, music publishers produced many works in arrangements for piano, so that music lovers could play. The piano is widely employed in classical, jazz, traditional and popular music for solo and ensemble performances, accompaniment, with technological advances, amplified electric pianos, electronic pianos, and digital pianos have also been developed. The electric piano became an instrument in the 1960s and 1970s genres of jazz fusion, funk music. The piano was founded on earlier technological innovations in keyboard instruments, pipe organs have been used since Antiquity, and as such, the development of pipe organs enabled instrument builders to learn about creating keyboard mechanisms for sounding pitches
3.
Musical tuning
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In music, there are two common meanings for tuning, Tuning practice, the act of tuning an instrument or voice. Tuning systems, the systems of pitches used to tune an instrument. Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones, Tuning is usually based on a fixed reference, such as A =440 Hz. Out of tune refers to a pitch/tone that is too high or too low in relation to a given reference pitch. While an instrument might be in relative to its own range of notes. Some instruments become out of tune with damage or time and must be readjusted or repaired, different methods of sound production require different methods of adjustment, Tuning to a pitch with ones voice is called matching pitch and is the most basic skill learned in ear training. Turning pegs to increase or decrease the tension on strings so as to control the pitch, instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the violin can be tuned manually. Modifying the length or width of the tube of an instrument, brass instrument, pipe, bell. The sounds of instruments such as cymbals are inharmonic—they have irregular overtones not conforming to the harmonic series. Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other, a tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used. Symphony orchestras and concert bands tend to tune to an A or a B♭, respectively, interference beats are used to objectively measure the accuracy of tuning. As the two approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected, for other intervals, this is dependent on the tuning system being used. Harmonics may be used to facilitate tuning of strings that are not themselves tuned to the unison, for example, lightly touching the highest string of a cello at the middle while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the fifth between the fundamentals of the two strings. In music, the open string refers to the fundamental note of the unstopped. The strings of a guitar are tuned to fourths, as are the strings of the bass guitar. Violin, viola, and cello strings are tuned to fifths, however, non-standard tunings exist to change the sound of the instrument or create other playing options
4.
Pitch (music)
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Pitch can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major attribute of musical tones, along with duration, loudness. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property, Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration. Pitch is closely related to frequency, but the two are not equivalent, frequency is an objective, scientific attribute that can be measured. Pitch is each persons subjective perception of a wave, which cannot be directly measured. However, this not necessarily mean that most people wont agree on which notes are higher and lower. Sound waves themselves do not have pitch, but their oscillations can be measured to obtain a frequency and it takes a sentient mind to map the internal quality of pitch. However, pitches are usually associated with, and thus quantified as frequencies in cycles per second, or hertz, by comparing sounds with pure tones, Complex and aperiodic sound waves can often be assigned a pitch by this method. According to the American National Standards Institute, pitch is the attribute of sound according to which sounds can be ordered on a scale from low to high. That is, high pitch means very rapid oscillation, and low pitch corresponds to slower oscillation, despite that, the idiom relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down, the exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the frequency is increased or reduced. The pitch of tones can be ambiguous, meaning that two or more different pitches can be perceived, depending upon the observer. In a situation like this, the percept at 200 Hz is commonly referred to as the missing fundamental, Pitch depends to a lesser degree on the sound pressure level of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases, for instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder, theories of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch. In general, pitch perception theories can be divided into place coding, place theory holds that the perception of pitch is determined by the place of maximum excitation on the basilar membrane. However, a purely place-based theory cannot account for the accuracy of pitch perception in the low, temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the phase-locking and mode-locking of action potentials to frequencies in a stimulus
5.
Equal temperament
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An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio. In equal temperament tunings, the interval is often found by dividing some larger desired interval, often the octave. That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step, the standard pitch has not always been 440 but has varied and generally risen over the past few hundred years. For example, some music has been written in 19-TET and 31-TET, in Western countries, when people use the term equal temperament without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments that divide the octave and ones that divide some other interval, the equal division of the octave. According to this system, 12-TET is called 12-EDO, 31-TET is called 31-EDO. Other instruments, such as wind, keyboard, and fretted instruments, often only approximate equal temperament. Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles, the two figures frequently credited with the achievement of exact calculation of equal temperament are Zhu Zaiyu in 1584 and Simon Stevin in 1585. Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu, Zhu Zaiyu is quoted as saying that, in a text dating from 1584, I have founded a new system. I establish one foot as the number from which the others are to be extracted, altogether one has to find the exact figures for the pitch-pipers in twelve operations. Kuttner disagrees and remarks that his claim cannot be considered correct without major qualifications, kuttner proposes that neither Zhu Zaiyu or Simon Stevin achieved equal temperament, and that neither of the two should be treated as inventors. The origin of the Chinese pentatonic scale is traditionally ascribed to the mythical Ling Lun, allegedly his writings discussed the equal division of the scale in the 27th century BC. However, evidence of the origins of writing in this period in China is limited to rudimentary inscriptions on oracle bones, an approximation for equal temperament was described by He Chengtian, a mathematician of Southern and Northern Dynasties around 400 AD. He came out with the earliest recorded approximate numerical sequence in relation to equal temperament in history,900849802758715677638601570536509.5479450, historically, there was a seven-equal temperament or hepta-equal temperament practice in Chinese tradition. Zhu Zaiyu, a prince of the Ming court, spent thirty years on research based on the equal temperament idea originally postulated by his father and he described his new pitch theory in his Fusion of Music and Calendar 乐律融通 published in 1580. An extended account is given by Joseph Needham. Similarly, after 84 divisions the length was divided by a factor of 128,84 =27 =128, according to Gene Cho, Zhu Zaiyu was the first person to solve the equal temperament problem mathematically. Matteo Ricci, a Jesuit in China recorded this work in his personal journal, in 1620, Zhus work was referenced by a European mathematician
6.
Piano key frequencies
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This is a list of the absolute frequencies in hertz of the keys of a modern 88-key standard or 102-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A, tuned to 440 Hz. Each successive pitch is derived by multiplying or dividing the previous by the root of two. For example, to get the frequency a semitone up from A4, to go from A4 to B4, multiply 440 twice by the twelfth root of two. For other tuning schemes refer to musical tuning and this list of frequencies is for a theoretically ideal piano. To compensate for this, octaves are tuned slightly wide, stretched according to the characteristics of each instrument. This deviation from equal temperament is called the Railsback curve, keys shaded gray are rare and only appear on extended pianos. Piano tuning Scientific pitch notation Music and mathematics interactive piano frequency table – A PHP script allowing the pitch of A4 to be altered from 440 Hz. PySynth – A simple Python-based software synthesizer that prints the key frequencies table, notefreqs – A complete table of note frequencies and ratios for midi, piano, guitar, bass, and violin. Includes fret measurements for building instruments
7.
A440 (pitch standard)
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A440 or A4, which has a frequency of 440 Hz, is the musical note A above middle C and serves as a general tuning standard for musical pitch. Prior to the standardization on 440 Hz, many countries and organizations followed the French standard since the 1860s of 435 Hz, which had also been the Austrian governments 1885 recommendation. Johann Heinrich Scheibler recommended A440 as a standard in 1834 after inventing the tonometer to measure pitch, the American music industry reached an informal standard of 440 Hz in 1926, and some began using it in instrument manufacturing. In 1936 the American Standards Association recommended that the A above middle C be tuned to 440 Hz and this standard was taken up by the International Organization for Standardization in 1955 as ISO16. It is designated A4 in scientific pitch notation because it occurs in the octave that starts with the fourth C key on a standard 88-key piano keyboard, A440 is widely used as concert pitch in the United Kingdom and the United States. In continental Europe the frequency of A4 commonly varies between 440 Hz and 444 Hz, in the period instrument movement, a consensus has arisen around a modern baroque pitch of 415 Hz, baroque for some special church music at 466 Hz, and classical pitch at 430 Hz. A440 is often used as a reference in just intonation regardless of the fundamental note or key. The US time and frequency station WWV broadcasts a 440 Hz signal at two minutes past every hour, with WWVH broadcasting the same tone at the first minute past every hour and this was added in 1936 to aid orchestras in tuning their instruments. History of pitch standards in Western music Concert pitch Pitch Electronic tuner A
8.
Piano Technicians Guild
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The Piano Technicians Guild is an American organization for Registered Piano Technicians, headquartered in Kansas City, Kansas. The PTG was formed in 1957 when the American Society of Piano Technicians, the PTG is primarily an American trade association with open membership. It states that anyone with a professional or avocational interest in technology may join. The title of Registered Piano Technician must be earned by passing a series of examinations, for the tuning exam, RPTs perform a standardized piano tuning on a test piano until they agree no improvements on the tuning can be made. The results of this tuning are then stored on an electronic tuning device. The piano is then detuned so the examinee can tune it, an Associate is a member who has not taken or passed the RPT examinations. Associates may be piano retailers, refinishers or technicians working toward, Guild members improve their skills through training offered by local chapters and seminars held on the regional and national level. The Piano Technicians Guild also publishes a technical magazine, the Piano Technicians Journal. Piano Technicians Guild web site Official Facebook Page
9.
Beat (acoustics)
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In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. When tuning instruments that can produce sustained tones, beats can readily be recognized, tuning two tones to a unison will present a peculiar effect, when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively, as the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. It can be proven that the envelope of the maxima and minima form a wave frequency is half the difference between the frequencies of the two original waves. Instead, it is perceived as a variation in the amplitude of the first term in the expression above. It can be said that the lower frequency cosine term is an envelope for the higher frequency one, the frequency of the modulation is f1 + f2/2, that is, the average of the two frequencies. It can be noted that every second burst in the pattern is inverted. Each peak is replaced by a trough and vice versa, however, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. A physical interpretation is that when cos =1 the two waves are in phase and they interfere constructively, when it is zero, they are out of phase and interfere destructively. Beats occur also in more complex sounds, or in sounds of different volumes, beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the harmonic of the bass note beats with the second harmonic of the other note. Musicians commonly use interference beats to objectively check tuning at the unison, perfect fifth, piano and organ tuners even use a method involving counting beats, aiming at a particular number for a specific interval. The composer Alvin Lucier has written many pieces that feature interference beats as their main focus, composer Phill Niblocks music is entirely based on beating caused by microtonal differences. Binaural beats are heard when the right ear listens to a different tone than the left ear. Here, the tones do not interfere physically, but are summed by the brain in the olivary nucleus and this effect is related to the brains ability to locate sounds in three dimensions. Combination tone Gamelan tuning Heterodyne Consonance and dissonance Moiré pattern, a form of interference that generates new frequencies
10.
Humidity
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Humidity is the amount of water vapor present in the air. Water vapor is the state of water and is invisible. Humidity indicates the likelihood of precipitation, dew, or fog, higher humidity reduces the effectiveness of sweating in cooling the body by reducing the rate of evaporation of moisture from the skin. This effect is calculated in an index table or humidex. The amount of vapor that is needed to achieve saturation increases as the temperature increases. As the temperature of a parcel of water becomes lower it will not reach the point of saturation without adding or losing water mass. The differences in the amount of vapor in a parcel of air can be quite large. For example, a parcel of air that is near saturation may contain 28 grams of water per cubic meter of air at 30 °C, there are three main measurements of humidity, absolute, relative and specific. Absolute humidity is the content of air expressed in gram per cubic meter. Relative humidity, expressed as a percent, measures the current absolute humidity relative to the maximum for that temperature, specific humidity is the ratio of the mass of water vapor to the total mass of the moist air parcel. Absolute humidity is the mass of water vapor present in a given volume of air. It does not take temperature into consideration, absolute humidity in the atmosphere ranges from near zero to roughly 30 grams per cubic meter when the air is saturated at 30 °C. Absolute humidity is the mass of the vapor, divided by the volume of the air and water vapor mixture. The absolute humidity changes as air temperature or pressure changes and this makes it unsuitable for chemical engineering calculations, e. g. for clothes dryers, where temperature can vary considerably. Mass of water per unit volume as in the equation above is defined as volumetric humidity. Because of the confusion, British Standard BS1339 suggests avoiding the term absolute humidity. Units should always be carefully checked, many humidity charts are given in g/kg or kg/kg, but any mass units may be used. The field concerned with the study of physical and thermodynamic properties of mixtures is named psychrometrics
11.
Sound board (music)
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A sound board, or soundboard, is the surface of a string instrument that the strings vibrate against, usually via some sort of bridge. Pianos, guitars, banjos, and many other stringed instruments incorporate soundboards, the resonant properties of the sound board and the interior of the instrument greatly increase the loudness of the vibrating strings. The sound board operates by the principle of forced vibration, the string gently vibrates the board, and despite their differences in size and composition, makes the board vibrate at exactly the same frequency. This produces the sound as the string alone, differing only in timbre. The string would produce the amount of energy without the board present, but the greater surface area of the sound board moves a greater volume of air. Sound boards are made of wood, though other materials are used. Wooden sound boards typically have one or more sound holes of various shapes, round, oval, or F-holes appear on many plucked instruments, such as guitars and mandolins. F-holes are usual in violin family instruments, the upper surface of the sound board, depending on the instrument, is called a top plate, table, sound-table, or belly. It is usually made of a softwood, often spruce, the rear part, known as the back, typically does not contain sound holes and is made of a hardwood such as maple or pear. In a grand piano, the board is part of the case. In an upright piano, the board is a large vertical plate at the back of the instrument. The harp has a sound board below the strings, more generally, any hard surface can act as a sound board. An example is when someone strikes a tuning fork and holds it against a top to amplify its sound. Ernst Chladni Harpsichord Piano Piano acoustics Soundboard Wood Preparation
12.
Piano wire
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Piano wire, or music wire, is a specialized type of wire made for use in piano strings. It is made from tempered high-carbon steel, also known as spring steel, the oldest record of wire being made for musical instruments is from Augsburg in 1351, this probably predates the harpsichord and may have been wire for a psaltery. Earlier wire, used in harpsichords, was of brass or iron, starting around 1800, the piano began to be built ever more ambitiously, with sturdier framing and greater string tension. This led to innovations in making tougher piano wire, the technological developments also benefited from demands of consistency from other special wire products like telegraph and barbed wire. Innovative piano makers kept pace with advances by augmenting metal framing in their instruments. General-purpose, high-carbon steel, drawn music wire is manufactured in inch and metric music wire gauges in diameters as small as 0.15 mm up to 4.8 mm. A small number of companies produce the tough, high tensile polished wire intended for limited music instrument markets, unlike many other forms of wire, piano wire has no twist and is not formed from bundles of smaller-diameter wires. Piano strings are among the most demanding of all applications of steel, placed under high tension, they are subject to repeated blows, they are stretched and slackened during tuning and are still expected to last for decades. Similar challenges arise in plucked instruments, along with the demand of being bent when plucked. The tensile strength of one brand of piano wire is listed as 2620–2930 MPa. Piano wire must also be consistent in size, variations greater than 8 μm will produce audible falseness in modern instruments. Piano wire is sold by weight and packaged in tight coils and it springs back to a gentle curve but can be straightened using a series of opposed rollers. It requires careful handling for safety and appearance, since it can be marred by perspiration and it is also commonly used in hobby applications such as model railroading, both control line and radio-controlled aircraft, and knitting. At least in urban legend, it is employed by assassins as a garrote, Piano acoustics Dolge, Alfred Pianos and Their Makers, A Comprehensive History of the Development of the Piano from the Monochord to the Concert Grand Player Piano. Louchet, Jean The Keyboard Stringing Guide — for the restoration of pianos, Jean Louchet, Stringing gauge table and equivalents Edward Swenson, Chronologically arranged wire tests. Stephen Birkett & Paul Poletti, Reproduction of Authentic Historical Soft Iron Wire for Musical Instruments Steel Music Wire. Report of the Tests of Metals and Other Materials for Industrial Purposes, made with the United States Testing Machine at Watertown Arsenal, Massachusetts, government Printing Office, Washington, D. C.1895
13.
Hertz
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The hertz is the unit of frequency in the International System of Units and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide proof of the existence of electromagnetic waves. Hertz are commonly expressed in SI multiples kilohertz, megahertz, gigahertz, kilo means thousand, mega meaning million, giga meaning billion and tera for trillion. Some of the units most common uses are in the description of waves and musical tones, particularly those used in radio-. It is also used to describe the speeds at which computers, the hertz is equivalent to cycles per second, i. e. 1/second or s −1. In English, hertz is also used as the plural form, as an SI unit, Hz can be prefixed, commonly used multiples are kHz, MHz, GHz and THz. One hertz simply means one cycle per second,100 Hz means one hundred cycles per second, and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, the rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second,1 Bq is 1 aperiodic radionuclide event per second, the conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is ω =2 π f and f = ω2 π. This SI unit is named after Heinrich Hertz, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, the hertz is named after the German physicist Heinrich Hertz, who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission in 1930, the term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc. Mc. etc. units, sound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of waves as pitch. Each musical note corresponds to a frequency which can be measured in hertz. An infants ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz, the range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond. Electromagnetic radiation is described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation is measured in kilohertz, megahertz, or gigahertz
14.
Interference (wave propagation)
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In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves or matter waves. If a crest of a wave meets a crest of wave of the same frequency at the same point. If a crest of one wave meets a trough of another wave, constructive interference occurs when the phase difference between the waves is an even multiple of π, whereas destructive interference occurs when the difference is an odd multiple of π. If the difference between the phases is intermediate between two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values. Consider, for example, what happens when two identical stones are dropped into a pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped, when the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement, in other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above, prime examples of light interference are the famous Double-slit experiment, laser speckle, optical thin layers and films and interferometers. Dark areas in the slit are not available to the photons. Thin films also behave in a quantum manner, the above can be demonstrated in one dimension by deriving the formula for the sum of two waves. Suppose a second wave of the frequency and amplitude but with a different phase is also traveling to the right W2 = A cos where ϕ is the phase difference between the waves in radians. Constructive interference, If the phase difference is a multiple of pi. Interference is essentially a redistribution process. The energy which is lost at the interference is regained at the constructive interference. One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave, assuming that the two waves are in phase at the point B, then the relative phase changes along the x-axis. Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, a fringe pattern is produced, where the separation of the maxima is d f = λ sin θ
15.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, for example, if a newborn babys heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as vibrations, audio signals, radio waves. For cyclical processes, such as rotation, oscillations, or waves, in physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν or ν. For a simple motion, the relation between the frequency and the period T is given by f =1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz, a previous name for this unit was cycles per second. The SI unit for period is the second, a traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. As a matter of convenience, longer and slower waves, such as ocean surface waves, short and fast waves, like audio and radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the axis is replaced by one or more spatial displacement axes. Y = sin = sin d θ d x = k Wavenumber, in the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has a relationship to the wavelength. Even in dispersive media, the frequency f of a wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave. In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes, f = c λ. When waves from a monochrome source travel from one medium to another, their remains the same—only their wavelength. For example, if 71 events occur within 15 seconds the frequency is, the latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an error in the calculated frequency of Δf = 1/, or a fractional error of Δf / f = 1/ where Tm is the timing interval. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small, an older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope
16.
Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
17.
Tension (physics)
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Tension is the opposite of compression. At the atomic level, when atoms or molecules are pulled apart each other and gain potential energy with a restoring force still existing. Each end of a string or rod under such tension will pull on the object it is attached to, to restore the string/rod to its relaxed length. In physics, tension, as a force, as an action-reaction pair of forces. The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected and these forces due to tension are also called passive forces. Tension in a string is a scalar quantity. A string or rope is often idealized as one dimension, having length but being massless with zero cross section. If there are no bends in the string, as occur with vibrations or pulleys, then tension is a constant along the string, by Newtons Third Law, these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it still have constant tension along its length in the idealized situation that the pulleys are massless and frictionless. A vibrating string vibrates with a set of frequencies that depend on the strings tension and these frequencies can be derived from Newtons laws of motion. Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, tension = τ where x is the position along the string. If the string has curvature, then the two pulls on a segment by its two neighbors will not add to zero, and there will be a net force on that segment of the string, causing an acceleration. With solutions that include the various harmonics on a stringed instrument, tension is also used to describe the force exerted by the ends of a three-dimensional, continuous material such as a rod or truss member. Such a rod elongates under tension, a system is in equilibrium when the sum of all forces is zero. ∑ F → =0 For example, consider a system consisting of an object that is being lowered vertically by a string with tension, T, at a constant velocity. ∑ F → = T → + m g → =0 A system has a net force when a force is exerted on it. Acceleration and net force always exist together, ∑ F → ≠0 For example, consider the same system as above but suppose the object is now being lowered with an increasing velocity downwards therefore there exists a net force somewhere in the system. In this case, negative acceleration would indicate that | m g | > | T |
18.
Harpsichord
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A harpsichord is a musical instrument played by means of a keyboard. It produces sound by plucking a string when a key is pressed, Harpsichord designates the whole family of similar plucked keyboard instruments, including the smaller virginals, muselar, and spinet. The harpsichord was used in Renaissance and Baroque music. During the late 18th century, it disappeared from the musical scene with the rise of the piano. In the 20th century, it made a resurgence, being used in historically informed performances of music, in compositions. Harpsichords vary in size and shape, but all have the basic functional arrangement. The player depresses a key that rocks over a pivot in the middle of its length, the other end of the key lifts a jack that holds a small plectrum, which plucks the string. When the player releases the key, the far end returns to its rest position, the plectrum, mounted on a tongue that can swivel backwards away from the string, passes the string without plucking it again. As the key reaches its rest position, a felt damper atop the jack stops the strings vibrations and these basic principles are explained in detail below. The keylever is a pivot, which rocks on a balance pin that passes through a hole drilled through the keylever. The jack is a thin, rectangular piece of wood that sits upright on the end of the keylever, the jacks are held in place by the registers. These are two strips of wood, which run in the gap between pinblock and bellyrail. The registers have rectangular mortises through which the pass as they can move up. The registers hold the jacks in the location needed to pluck the string. In the jack, a plectrum juts out almost horizontally and passes just under the string, historically, plectra were made of bird quill or leather, many modern harpsichords have plastic plectra. When the front of the key is pressed, the back of the key rises, the jack is lifted, the vertical motion of the jack is then stopped by the jackrail, which is covered with soft felt to muffle the impact. When the key is released, the falls back down under its own weight. This is made possible by having the plectrum held in a tongue attached with a pivot and a spring to the body of the jack
19.
Just intonation
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In music, just intonation or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval, pure intervals are important in music because they correspond to the vibrational patterns found in physical objects which correlate to human perception. The two notes in any just interval are members of the harmonic series. Frequency ratios involving large integers such as 1024,729 are not generally said to be justly tuned, the Indian classical music system uses just intonation tuning as codified in the Natya Shastra. Various societies perceive pure intervals as pleasing or satisfying consonant and, conversely, however, various societies do not have these associations. Just intonation can be contrasted and compared with equal temperament, which dominates Western instruments of fixed pitch, however, except for doubling of frequencies, no other intervals are exact ratios of small integers. Each just interval differs a different amount from its analogous, equally tempered interval, justly tuned intervals can be written as either ratios, with a colon, or as fractions, with a solidus. For example, two tones, one at 300 hertz, and the other at 200 hertz are both multiples of 100 Hz and as members of the harmonic series built on 100 Hz. Thus 3,2, known as a fifth, may be defined as the musical interval between the second and third harmonics of any fundamental pitch. Just intonation An A-major scale, followed by three major triads, and then a progression of fifths in just intonation, equal temperament An A-major scale, followed by three major triads, and then a progression of fifths in equal temperament. By listening to the file, and then listening to this one, one might be able to hear the beating in this file. Equal temperament and just intonation compared A pair of major thirds, the first in each pair is in equal temperament, the second is in just intonation. Equal temperament and just intonation compared with square waveform A pair of major chords, the first is in equal temperament, the second is in just intonation. The pair of chords is repeated with a transition from equal temperament to just temperament between the two chords, in the equal temperament chords a roughness or beating can be heard at about 4 Hz and about 0.8 Hz. In the just intonation triad, this roughness is absent, the square waveform makes the difference between equal and just temperaments more obvious. Harmonic intervals come naturally to horns, vibrating strings, and in human singing voices. Pythagorean tuning, perhaps the first tuning system to be theorized in the West, is a system in all tones can be found using powers of the ratio 3,2. It is easier to think of this system as a cycle of fifths
20.
Pythagorean tuning
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Pythagorean tuning is a tuning of the syntonic temperament in which the generator is the ratio 3,2, which is 702 cents wide. Hence, it is a system of tuning in which the frequency ratios of all intervals are based on the ratio 3,2. This ratio, also known as the perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear. As Novalis put it, The musical proportions seem to me to be particularly correct natural proportions, the so-called Pythagorean tuning was used by musicians up to the beginning of the 16th century. The Pythagorean system would appear to be ideal because of the purity of the fifths, Pythagorean tuning is based on a stack of intervals called perfect fifths, each tuned in the ratio 3,2, the next simplest ratio after 2,1. Since notes differing in frequency by a factor of 2 are given the same name, the purpose of this adjustment is to move the 12 notes within a smaller range of frequency, namely within the interval between the base note D and the D above it. This interval is called the basic octave. For instance, the A is tuned such that its frequency equals 3,2 times the frequency of D—if D is tuned to a frequency of 288 Hz, then A is tuned to 432 Hz. Similarly, the E above A is tuned such that its frequency equals 3,2 times the frequency of A, or 9,4 times the frequency of D—with A at 432 Hz, this puts E at 648 Hz. Since this E is outside the basic octave, it is usual to halve its frequency to move it within the basic octave. Therefore, E is tuned to 324 Hz, a 9,8 above D, the B at 3,2 above that E is tuned to the ratio 27,16 and so on. This frequency is doubled to bring it into the basic octave. When extending this tuning however, a problem arises, no stack of 3,2 intervals will fit exactly into any stack of 2,1 intervals. For instance a stack such as this, obtained by adding one note to the stack shown above A♭–E♭–B♭–F–C–G–D–A–E–B–F♯–C♯–G♯ will be similar. More exactly, it will be about a quarter of a semitone larger, thus, A♭ and G♯, when brought into the basic octave, will not coincide as expected. This discrepancy, of about 23.46 cents, or nearly one quarter of a semitone, is known as a Pythagorean comma, to get around this problem, Pythagorean tuning constructs only twelve notes as above, with eleven fifths between them. For example, one may use only the 12 notes from E♭ to G♯. This, as shown above, the remaining interval is left badly out-of-tune, meaning that any music which combines those two notes is unplayable in this tuning. A very out-of-tune interval such as one is known as a wolf interval
21.
Meantone temperament
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Meantone temperament is a musical temperament, which is a system of musical tuning. Quarter-comma meantone is the best known type of meantone temperament, Meantone can receive the following equivalent definitions, The meantone is the mean between the major whole tone and the minor whole tone, i. e. the geometric mean of 9,8 and 10,9. The meantone is the mean of the just major third, i. e. the square root of 5,4, all meantone temperaments are linear temperaments, distinguished by the width of its generator in cents, as shown in the central column of Figure 1. Historically notable meantone temperaments, discussed below, occupy a portion of this tuning continuum. In Figure 1, the tuning ranges of 5-limit, 7-limit, and 11-limit tunings are shown. This last ratio was termed R by American composer, pianist and theoretician Easley Blackwood, if we multiply by 1200, we have the size of fifth in cents. In these terms, some historically notable meantone tunings are listed below, the relationship between the first two columns is exact, while that between them and the third is closely approximate. Equal temperaments useful as meantone tunings include 19-ET, 50-ET, 31-ET, 43-ET, the farther the tuning gets away from quarter-comma meantone, however, the less related the tuning is to harmonic timbres, which can be overcome by tempering the timbre to match the tuning. A whole number of just perfect fifths will never add up to a number of octaves. If a stacked-up whole number of perfect fifths is to close with the octave, then one of the fifths must have a different width than all of the others. For example, to make the 12-note chromatic scale in Pythagorean tuning close at the octave, one fifth must be out of tune by the Pythagorean comma, wolf intervals are an artifact of keyboard design. This can be shown most easily using a keyboard, such as that shown in Figure 2. On an isomorphic keyboard, any musical interval has the same shape wherever it appears. On the keyboard shown in Figure 2, from any given note, there are no wolf intervals within the note-span of this keyboard. The problem is at the edge, on the note E♯, the note thats a perfect fifth higher than E♯ is B♯, which is not included on the keyboard shown. Because there is no B♯ button, when playing an E♯ power chord, one must choose some other note, such as C, even edge conditions produce wolf intervals only if the isomorphic keyboard has fewer buttons per octave than the tuning has enharmonically-distinct notes. When the perfect fifth is exactly 700 cents wide then the tuning is identical to the familiar 12-tone equal temperament and this appears in the table above when R =2,1. Because of the forced on meantone tunings by the one-dimensional piano-style keyboard, well temperaments
22.
The Well-Tempered Clavier
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The Well-Tempered Clavier, BWV 846–893, is a collection of two series of Preludes and Fugues in all 24 major and minor keys, composed for solo keyboard by Johann Sebastian Bach. In the German of Bachs time Clavier was a name indicating a variety of keyboard instruments, most typically a harpsichord or clavichord –. The modern German spelling for the collection is Das wohltemperierte Klavier, some 20 years later Bach compiled a second book of the same kind, which became known as The Well-Tempered Clavier, Part Two. Modern editions usually refer to both parts as The Well-Tempered Clavier, Book I and The Well-Tempered Clavier, Book II, the collection is generally regarded as being among the most influential works in the history of Western classical music. Each set contains twenty-four pairs of preludes and fugues, the first pair is in C major, the second in C minor, the third in C♯ major, the fourth in C♯ minor, and so on. The rising chromatic pattern continues until every key has been represented, the first set was compiled in 1722 during Bachs appointment in Köthen, the second followed 20 years later in 1742 while he was in Leipzig. The C♯ major prelude and fugue in book one was originally in C major – Bach added a key signature of seven sharps, although the Well-Tempered Clavier was the first collection of fully worked keyboard pieces in all 24 keys, similar ideas had occurred earlier. His contemporary Johann Heinrich Kittel also composed a cycle of 12 organ preludes in successive keys, Fischer was published in 1702 and reissued 1715. It is a set of 20 prelude-fugue pairs in ten major and nine minor keys, Bach knew the collection and borrowed some of the themes from Fischer for the Well-Tempered Clavier. Finally, a lost collection by Johann Pachelbel, Fugen und Praeambuln über die gewöhnlichsten Tonos figuratos and it was later shown that this was the work of a composer who was not even born in 1689, Bernhard Christian Weber. It was in written in 1745–50, and in imitation of Bachs example. Bachs title suggests that he had written for a tuning system in which all keys sounded in tune. The opposing system in Bachs day was meantone temperament in which keys with many accidentals sound out of tune, Bach would have been familiar with different tuning systems, and in particular as an organist would have played instruments tuned to a meantone system. There is debate whether Bach meant a range of temperaments, perhaps even altered slightly in practice from piece to piece. During much of the 20th century it was assumed that Bach wanted equal temperament, internal evidence for this may be seen in the fact that in Book 1 Bach paired the E♭ minor prelude with its enharmonic key of D♯ minor for the fugue. This represents an equation of the most tonally remote enharmonic keys where the flat, any performance of this pair would have required both of these enharmonic keys to sound identically tuned, thus implying equal temperament in the one pair, as the entire work implies as a whole. However, research has continued into various unequal systems contemporary with Bachs career, accounts of Bachs own tuning practice are few and inexact. The three most cited sources are Forkel, Bachs first biographer, Friedrich Wilhelm Marpurg, who received information from Bachs sons and pupils, and Johann Kirnberger, one of those pupils
23.
Johann Sebastian Bach
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Johann Sebastian Bach was a German composer and musician of the Baroque period. Bachs compositions include the Brandenburg Concertos, the Goldberg Variations, the Mass in B minor and his music is revered for its technical command, artistic beauty, and intellectual depth. He is now regarded as one of the greatest composers of all time. Bach was born in Eisenach, in the duchy of Saxe-Eisenach and his father Johann Ambrosius Bach was the director of the town musicians, and all of his uncles were professional musicians. His father probably taught him to play the violin and harpsichord, apparently at his own initiative, Bach attended St. Michaels School in Lüneburg for two years. He received the title of Royal Court Composer from Augustus III in 1736, Bachs health and vision declined in 1749, and he died on 28 July 1750. Johann Sebastian Bach was born in Eisenach, the capital of the duchy of Saxe-Eisenach, in present-day Germany and he was the son of Johann Ambrosius Bach, the director of the town musicians, and Maria Elisabeth Lämmerhirt. He was the eighth and youngest child of Johann Ambrosius, who taught him violin. His uncles were all musicians, whose posts included church organists, court chamber musicians. One uncle, Johann Christoph Bach, introduced him to the organ, Bachs mother died in 1694, and his father died eight months later. The 10-year-old Bach moved in with his eldest brother, Johann Christoph Bach, there he studied, performed, and copied music, including his own brothers, despite being forbidden to do so because scores were so valuable and private and blank ledger paper of that type was costly. He received valuable teaching from his brother, who instructed him on the clavichord, also during this time he was taught theology, Latin, Greek, French and Italian at the local gymnasium. By 3 April 1700 Bach and his schoolfriend Georg Erdmann–who was two years Bachs elder–were enrolled in the prestigious St. Michaels School in Lüneburg, some two weeks travel north of Ohrdruf and their journey was probably undertaken mostly on foot. His two years there were critical in exposing Bach to a range of European culture. In addition to singing in the choir, he played the Schools three-manual organ and he came into contact with sons of aristocrats from northern Germany, sent to the highly selective school to prepare for careers in other disciplines. While in Lüneburg, Bach had access to St. Johns Church and possibly used the famous organ from 1553. His role there is unclear, but it probably included menial, non-musical duties, despite strong family connections and a musically enthusiastic employer, tension built up between Bach and the authorities after several years in the post. Bach was dissatisfied with the standard of singers in the choir and he called one of them a Zippel Fagottist
24.
Wolf interval
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In music theory, the wolf fifth is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a tuning system, widely used in the sixteenth and seventeenth centuries. More broadly, it is used to refer to similar intervals produced by other tuning systems. In mean-tone systems, this interval is usually from C♯ to A♭ or from G♯ to E♭, the eleven perfect fifths sound almost perfectly consonant. Conversely, the sixth is severely dissonant and seems to howl like a wolf. Since the diminished sixth is meant to be equivalent to a perfect fifth. Besides the above-mentioned quarter comma meantone, other tuning systems may produce severely dissonant diminished sixths. Conversely, in 12-tone equal temperament, which is currently the most commonly used tuning system, by extension, any interval which is perceived as severely dissonant and may be regarded as howling like a wolf may be called a wolf interval. In 12-tone scales, the value of the twelve fifths must equal the 700 cents of equal temperament. If eleven of them have a value of 700 − ε cents, as in quarter-comma meantone and most other meantone temperament tuning systems, the value of ε changes depending on the tuning system. In other tuning systems, eleven fifths may have a size of 700 + ε cents, if 11ε is very large, as in the quarter-comma meantone tuning system, the diminished sixth is regarded as a wolf fifth. In terms of ratios, the product of the fifths must be 128. We likewise find varied tunings for the thirds, three of these diminished fourths form major triads with perfect fifths, but one of them forms a major triad with the diminished sixth. If the diminished sixth is an interval, this triad is called the wolf major triad. Similarly, we obtain nine minor thirds of 300 ± 3ε cents, meantone tunings with slightly flatter fifths produce even closer approximations to the subminor and supermajor thirds and corresponding triads. These thirds therefore hardly deserve the appellation of wolf, and in fact historically have not been given that name, a fifth this flat can also be regarded as howling like a wolf. There are also now eight sharp and four major thirds. Five-limit tuning determines one diminished sixth of size 1024,675, whether this interval should be considered dissonant enough to be called a wolf fifth is a controversial matter
25.
Normal mode
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A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at the fixed frequencies and these fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge or molecule, has a set of modes and their natural frequencies that depend on its structure, materials. The most general motion of a system is a superposition of its normal modes, the modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other, when relating to music, normal modes of vibrating instruments are called harmonics or overtones. The concept of normal modes also finds application in optics, quantum mechanics, most dynamical system can be excited under several modes. Each mode is characterized by one or several frequencies, according the modal variable field, for example, a vibrating rope in the 2D space is defined by a single-frequency, but a vibrating rope in the 3D space is defined by two frequencies -2D axial displacement-. For a given amplitude on the variable, each mode will store a specific amount of energy. From all the modes of a system, the normal or dominant mode of a system, will be the mode storing the minimum amount of energy. Or equivalently, for a given stored amount of energy, will be the mode imposing the maximum amplitude of the modal variable, a mode of vibration is characterized by a modal frequency and a mode shape. It is numbered according to the number of waves in the vibration. For example, if a beam with both ends pinned displayed a mode shape of half of a sine wave it would be vibrating in mode 1. If it had a full sine wave it would be vibrating in mode 2, in a system with two or more dimensions, such as the pictured disk, each dimension is given a mode number. Using polar coordinates, we have a radial coordinate and an angular coordinate, if one measured from the center outward along the radial coordinate one would encounter a full wave, so the mode number in the radial direction is 2. The other direction is trickier, because half of the disk is considered due to the antisymmetric nature of a disks vibration in the angular direction. Thus, measuring 180° along the direction you would encounter a half wave. So the mode number of the system is 2-1 or 1-2, depending on which coordinate is considered the first, in linear systems each mode is entirely independent of all other modes. In general all modes have different frequencies and different mode shapes, in a one-dimensional system at a given mode the vibration will have nodes, or places where the displacement is always zero
26.
Harmonic
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A harmonic is any member of the harmonic series, the divergent infinite series. Every term of the series after the first is the mean of the neighboring terms. The phrase harmonic mean likewise derives from music, the term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves, a harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the frequency, the sum of harmonics is also periodic at that frequency. On strings, harmonics that are bowed have a glassy, pure tone, harmonics may also be called overtones, partials or upper partials. In some music contexts, the harmonic, overtone and partial are used fairly interchangeably. Most acoustic instruments emit complex tones containing many individual partials, rather, a musical note is perceived as one sound, the quality or timbre of that sound being a result of the relative strengths of the individual partials. Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are long and thin. Wind instruments whose air column is open at one end, such as trumpets and clarinets. However they only produce partials matching the odd harmonics, at least in theory, the reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials, antique singing bowls are known for producing multiple harmonic partials or multiphonics. An overtone is any partial higher than the lowest partial in a compound tone, the relative strengths and frequency relationships of the component partials determine the timbre of an instrument. This chart demonstrates how the three types of names are counted, In many musical instruments, it is possible to play the upper harmonics without the note being present. In a simple case this has the effect of making the note go up in pitch by an octave, in some cases it also changes the timbre of the note. This is part of the method of obtaining higher notes in wind instruments. The extended technique of playing multiphonics also produces harmonics, on string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch
27.
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
28.
Interval (music)
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In music theory, an interval is the difference between two pitches. In Western music, intervals are most commonly differences between notes of a diatonic scale, the smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones and they can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic frequencies, for example, any two notes an octave apart have a frequency ratio of 2,1. This means that successive increments of pitch by the same result in an exponential increase of frequency. For this reason, intervals are often measured in cents, a derived from the logarithm of the frequency ratio. In Western music theory, the most common naming scheme for intervals describes two properties of the interval, the quality and number, examples include the minor third or perfect fifth. These names describe not only the difference in semitones between the upper and lower notes, but also how the interval is spelled, the importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G♯ and G–A♭. The size of an interval can be represented using two alternative and equivalently valid methods, each appropriate to a different context, frequency ratios or cents, the size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, Intervals with small-integer ratios are often called just intervals, or pure intervals. Most commonly, however, musical instruments are tuned using a different tuning system. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, for instance, an equal-tempered fifth has a frequency ratio of 2 7⁄12,1, approximately equal to 1.498,1, or 2.997,2. For a comparison between the size of intervals in different tuning systems, see section Size in different tuning systems, the standard system for comparing interval sizes is with cents. The cent is a unit of measurement. If frequency is expressed in a scale, and along that scale the distance between a given frequency and its double is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone equal temperament, a system in which all semitones have the same size. Hence, in 12-TET the cent can be defined as one hundredth of a semitone
29.
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
30.
Perfect fifth
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In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3,2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of five notes in a diatonic scale. The perfect fifth spans seven semitones, while the diminished fifth spans six, for example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C. Play The perfect fifth may be derived from the series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a fifth above the tonic note. The perfect fifth is more consonant, or stable, than any other interval except the unison and it occurs above the root of all major and minor chords and their extensions. Until the late 19th century, it was referred to by one of its Greek names. Its inversion is the perfect fourth, the octave of the fifth is the twelfth. The term perfect identifies the perfect fifth as belonging to the group of perfect intervals, so called because of their simple pitch relationships and their high degree of consonance. However, when using correct enharmonic spelling, the fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth. The perfect unison has a pitch ratio 1,1, the perfect octave 2,1, the perfect fourth 4,3, within this definition, other intervals may also be called perfect, for example a perfect third or a perfect major sixth. In terms of semitones, these are equivalent to the tritone, the justly tuned pitch ratio of a perfect fifth is 3,2, meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. The just perfect fifth can be heard when a violin is tuned, if adjacent strings are adjusted to the ratio of 3,2, the result is a smooth and consonant sound. Keyboard instruments such as the piano normally use a version of the perfect fifth. In 12-tone equal temperament, the frequencies of the perfect fifth are in the ratio 7 or approximately 1.498307. An equally tempered fifth, defined as 700 cents, is about two cents narrower than a just perfect fifth, which is approximately 701.955 cents. Kepler explored musical tuning in terms of ratios, and defined a lower imperfect fifth as a 40,27 pitch ratio. His lower perfect fifth ratio of 1.4815 is much more imperfect than the equal temperament tuning of 1.498, the perfect fifth is a basic element in the construction of major and minor triads, and their extensions
31.
Musical temperament
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In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system, tempering is the process of altering the size of an interval by making it narrower or wider than pure. The development of well temperament allowed fixed-pitch instruments to play well in all of the keys. The famous Well-Tempered Clavier by Johann Sebastian Bach takes full advantage of this breakthrough, however, while unpleasant intervals were avoided, the sizes of intervals were still not consistent between keys, and so each key still had its own character. In just intonation, every interval between two pitches corresponds to a whole number ratio between their frequencies, allowing intervals varying from the highest consonance to highly dissonant, for instance,660 Hz /440 Hz constitutes a fifth, and 880 Hz /440 Hz an octave. Such intervals have a stability, or purity to their sound, if, for example, two sound signals with frequencies that vary just by 0. When a musical instrument with harmonic overtones is played, the ear hears a composite waveform that includes a fundamental frequency, the waveform of such a tone is characterized by a shape that is complex compared to a simple waveform, but remains periodic. When two tones depart from exact integer ratios, the shape waveform becomes erratic—a phenomenon that may be described as destabilization, as the composite waveform becomes more erratic, the consonance of the interval also changes. Tempering an interval involves the use of such minor adjustments to enable musical possibilities that are impractical using just intonation. Before Meantone temperament became widely used in the Renaissance, the most commonly used tuning system was Pythagorean tuning, Pythagorean tuning was a system of just intonation that tuned every note in a scale from a progression of pure perfect fifths. This was quite suitable for much of the practice until then. The major third of Pythagorean tuning differed from a just major third by an amount known as syntonic comma, with the correct amount of tempering, the syntonic comma is removed from its major thirds, making them just. This compromise, however, leaves all fifths in this system with a slight beating. Pythagorean tuning also had a problem, which meantone temperament does not solve, which is the problem of modulation. A series of 12 just fifths as in Pythagorean tuning does not return to the pitch, but rather differs by a Pythagorean comma. In meantone temperament, this effect is more pronounced. The use of 53 equal temperament provides a solution for the Pythagorean tuning, when building an instrument, this can be very impractical. Well temperament is the given to a variety of different systems of temperament that were employed to solve this problem, in which some keys are more in tune than others
32.
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
33.
Tuning fork
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A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal. It resonates at a constant pitch when set vibrating by striking it against a surface or with an object. The pitch that a tuning fork generates depends on the length. It is frequently used as a standard of pitch to tune musical instruments, the tuning fork was invented in 1711 by British musician John Shore, Sergeant Trumpeter and Lutenist to the court. A tuning fork is an acoustic resonator used in many applications to produce a fixed tone. The reason for this is that the frequency of the first overtone is about 52/22 = 25/4 = 6 1⁄4 times the fundamental. When the tuning fork is struck, little of the energy goes into the overtone modes, they die out correspondingly faster. It is easier to other instruments with this pure tone. Another reason for using the shape is that, when it vibrates in its principal mode. There is a node at the base of each prong, the fork is usually struck, and then the handle is pressed against a wooden box resonator, or a table top. Without the resonator the sound of a fork is very faint. The reason for this is that the waves produced by each fork prong are 180° out of phase with the other, so at a distance from the fork they interfere. Commercial tuning forks are normally tuned to the pitch at the factory. They can be retuned by filing material off the prongs, filing the ends of the prongs raises the pitch, while filing the inside of the base of the prongs lowers it. Tuning forks used by orchestras between 1750 and 1820 mostly had a frequency of A =423.5 Hz, although there were many forks, standard tuning forks are available that vibrate at all the musical pitches within the central octave of the piano, and other pitches. Well-known manufacturers of tuning forks include Ragg and John Walker, both of Sheffield, England, the pitch of a tuning fork varies slightly with temperature, due mainly to a slight decrease in the modulus of elasticity of steel with increasing temperature. A change in frequency of one vibration in 21,000 per °F change is typical for a tuning fork. The frequency decreases with increasing temperature, tuning forks are manufactured to have their correct pitch at a standard temperature
34.
Sharp (music)
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In music, sharp, dièse, or diesis means higher in pitch. More specifically, in musical notation, sharp means higher in pitch by a semitone, and has a sharp symbol, ♯. Sharp is contrasted with flat, which refers to a lowering of pitch, intonation may be flat, sharp, or both, successively or simultaneously. Under twelve-tone equal temperament, B♯, for instance, sounds the same as, or is equivalent to, C natural. In other tuning systems, such enharmonic equivalences in general do not exist, to allow extended just intonation, composer Ben Johnston uses a sharp to indicate a note is raised 70.6 cents, or a flat to indicate a note is lowered 70.6 cents. In tuning, sharp can also slightly higher in pitch. If two simultaneous notes are out of tune, the higher-pitched one is said to be sharp with respect to the other. Furthermore, the verb sharpen means raise the frequency of a note, double sharps also exist, these are denoted by the symbol and raise a note by two semitones, or one whole tone. They should not be confused with a ghost note, less often one will encounter other sharps. A half sharp raises a note by a quarter tone =50 cents, a sharp and a half raises a note by three quarter tones =150 cents and may be denoted. Although very uncommon, a triple sharp can sometimes be found and it raises a note by three semitones. The sharp symbol may be confused with the number sign, both signs have two sets of parallel double-lines. However, a correctly drawn sharp sign must have two slanted parallel lines which rise from left to right, to avoid being obscured by the staff lines, the number sign, in contrast, has two compulsory horizontal strokes in this place. In addition, while the sharp also always has two vertical lines, the number sign may or may not contain perfectly vertical lines. The order of sharps in key signature notation is F♯, C♯, G♯, D♯, A♯, E♯, B♯, each extra sharp being added successively in the sequence of major keys. Similarly the order of flats is based on the natural notes in reverse order, B♭, E♭, A♭, D♭, G♭, C♭, F♭, encountered in the following series of major keys. In the above progression, key C♯ may be conveniently written as the harmonically equivalent key D♭
35.
Stretched octave
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When used as a basis for an equal temperament, the pseudo-octave may also be called the interval of equivalence, the repeat ratio, and the nonoctave. The stretched octave, for example 2.01,1, sounds out of tune when played with true harmonic overtones, in piano tuning, stretched octaves are commonly encountered, where the inharmonicity caused by string thickness and tension makes it necessary to widen every interval very slightly. Another example is the play on clarinets of the Bohlen–Pierce scale. Stretched octaves are caused by the physics of standing waves in a stretched wire, the pitch of each overtone produced by a piano string is determined by the ratio of the strings restoring force, divided by its mass per unit length. In an ideal string, the only restoring force would be due to the tension in the string. In practice, piano strings are made from steel, which is stiff. Youngs modulus of the steel is what defines the stiffness. The stiffness adds an extra restoring force to each string, the amount of this extra force depends on the amount of bend being induced in the string, higher normal modes bend the string more, inducing more stiffness-related force and sharpening the pitch of the resulting overtone. Electronic tuner Mel scale Octave Types, BillBremmer. com
36.
Piano acoustics
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Piano acoustics are the physical properties of the piano that affect its sound. The strings of a piano vary in thickness, and therefore in mass per length, with bass strings thicker than treble, a typical range is from 1/30 inch for the highest treble strings to 1/3 inch for the lowest bass. These differences in string thickness follow from well-understood acoustic properties of strings, given two strings, equally taut and heavy, one twice as long as the other, the longer would vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, in such a hypothetical, gigantic piano, the lowest strings would travel so far in vibrating that they would strike one another, any vibrating thing produces vibrations at a number of frequencies above the fundamental pitch. When the overtones are integer multiples of the frequency, then - neglecting damping - the oscillation is periodic—i. e. It vibrates exactly the way over and over. Humans seem to enjoy the sound of periodic oscillations and that is why so many instruments are constructed of skinny strings or thin columns of air. Only when the force is much smaller than the tension of the string, are its wave-speed unchanged. The frequency-raised overtones, called partials can produce an unpleasant effect called inharmonicity, winding a string allows an effective decrease in the thickness of the string. In a wound string, only the inner core resists bending while the function only to increase the linear density of the string. The thickness of the core is limited by its strength and by its tension, stronger materials allow for thinner cores at higher tensions. Hence, piano designers choose high quality steel for their strings, as its strength, if string diameter, tension, mass, uniformity, and length compromises were the only factors—all pianos could be small, spinet-sized instruments. Piano builders, however, have found that longer wires increase instrument power, harmonicity, and reverberation, for longer wires, larger pianos achieve the longer wavelengths and tonal characteristics desired. Inharmonicity largely affects the lowest and highest notes in the piano and is one of the limits on the range of a piano. The lowest strings, which must be longest, are most limited by the size of the piano, the designer of a short piano is forced to use thick strings to increase mass density and is thus driven into inharmonicity. The highest strings must be under the greatest tension, yet must also be thin to allow for a low mass density, the limited strength of steel forces the piano designer to use very short strings whose short wavelengths thus generate inharmonicity. The natural inharmonicity of a piano is used by the tuner to make adjustments in the tuning of a piano
37.
Psychoacoustics
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Psychoacoustics is the scientific study of sound perception. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound and it can be further categorized as a branch of psychophysics. Psychoacoustics received its name from a field within psychology—i. e, recognition science—which deals with all kinds of human perceptions. It is a field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology. These nerve pulses then travel to the brain where they are perceived, the inner ear, for example, does significant signal processing in converting sound waveforms into neural stimuli, so certain differences between waveforms may be imperceptible. Data compression techniques, such as MP3, make use of this fact, in addition, the ear has a nonlinear response to sounds of different intensity levels, this nonlinear response is called loudness. Telephone networks and audio noise reduction systems make use of this fact by nonlinearly compressing data samples before transmission, another effect of the ears nonlinear response is that sounds that are close in frequency produce phantom beat notes, or intermodulation distortion products. The expression that one hears what one wants to hear may pertain in such discussions, the human ear can nominally hear sounds in the range 20 Hz to 20,000 Hz. The upper limit tends to decrease with age, most adults are unable to hear above 16 kHz, the lowest frequency that has been identified as a musical tone is 12 Hz under ideal laboratory conditions. Tones between 4 and 16 Hz can be perceived via the sense of touch. Frequency resolution of the ear is 3.6 Hz within the octave of 1000 –2000 Hz and that is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means, for example, the interference of two pitches can often be heard as a repetitive variation in volume of the tone. This amplitude modulation occurs with a equal to the difference in frequencies of the two tones and is known as beating. The semitone scale used in Western musical notation is not a frequency scale. The intensity range of sounds is enormous. Human ear drums are sensitive to variations in the sound pressure, for this reason, sound pressure level is also measured logarithmically, with all pressures referenced to 20 µPa. The lower limit of audibility is defined as 0 dB. The upper limit is more a question of the limit where the ear will be harmed or with the potential to cause noise-induced hearing loss
38.
Tuning wrench
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A tuning wrench is a specialized socket wrench used to tune string instruments such as the piano, harp, and hammer dulcimer, that have strings wrapped around tuning pins. Other string instruments do not require a wrench because their tuning pins or pegs come with handles. Tuning wrench sockets may be shaped or 8-pointed star shaped. Impact piano tuning levers differ from traditional levers in that they are fitted with a weight at the end of the handle, the tuner flicks the lever with his or her wrist, causing the weight to do the actual work of moving the tuning pin. Unlike most socket wrenches, tuning wrenches usually have a wood or nylon handle. They are found in two shapes, L-shaped and T-shaped. A short, stiff socket enables a better feel and control of the movements of the tuning pin, within the pin-block. T-shaped handles are used for many instruments such as the harpsichord, harp. T-shaped handles help keep torque parallel to the shaft of the tuning pin, picture of a piano wrench from the Grosse Pointe Public Library Tuning a Bowed Psaltery from A Psimple Psaltery
39.
Mute (music)
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A mute is a device fitted to a musical instrument to alter the sound produced, by affecting the timbre, reducing the volume, or most commonly both. The use of a mute is usually indicated in musical notation by the Italian direction con sordino and removed with the senza sordino direction, which means without mute. On string instruments of the family, the mute takes the form of a device attached to the bridge of the instrument, dampening vibrations and resulting in a softer, darker. On the cello and double bass, a mute is often attached to the G-string. On the guitar, a player may palm mute their guitar, some instruments, such as the Fender Jaguar and the Rickenbacker 4001 and 4003 electric bass guitars have built-in string mutes. A variety of mutes have been used on instruments, most of which either squeeze inside the bell of the instrument. The most common type is the mute, a hollow. The second most common brass mute is the cup mute, there are a range of other mutes for brass, such as the solotone mute, the buzz-wah mute, the Wah-wah mute, bucket mutes, and hats or plungers. Muting woodwind instruments is very uncommon, saxophone mutes which are usually made of a soft material, which is placed in the bell to soften the tone. Percussion instruments often require no specialist mutes, the triangle is muted by simply gripping the instrument with the hand, stopping it from vibrating so much. Drums may require muting if they ring too much with cloth, the soft pedal of the piano can be seen as having the effect of a mute. It used to be common for pianos to be fitted with another kind of mute — a piece of felt or similar material which would sit between the hammers and the strings and this results in a very muffled and much quieter sound. It was not used in any context, but was useful for reducing the volume of the instrument when practicing and was often termed a Practice Pedal. Few pianos, apart from some uprights, have this device today, the use of a mute is usually indicated in musical notation by the Italian direction con sordino, which means with mute. The mute should be removed with the senza sordino direction, which means without mute, when written in English the directions, mute and open or unmute are used. The equivalent German terms for with mute are mit Dämpfer, the word Dämpfer is cognate to English damper. In French music, the word for the mute is sourdine, in the case of strings, mute-on and mute-off indications are often written into their parts by players in the form of signs. One example of a sign is an E to indicate when the mute is put on
40.
Electronic tuner
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Guitar tuner redirects here, but can also refer to the string tension adjusters also called machine heads. For the radio receiver component, see Tuner In music, a tuner is a device that detects. Pitch is the highness or lowness of a note, which is typically measured in Hertz. Simple tuners indicate—typically with an analog needle-dial, LEDs, or an LCD screen—whether a pitch is lower, higher, in the 2010s, software applications can turn a smartphone, tablet, or personal computer into a tuner. More complex and expensive tuners indicate pitch more precisely, Tuners vary in size from units that fit in a pocket to 19 rack-mount units. Instrument technicians, piano tuners, and violin-family luthiers typically use more expensive, the simplest tuners detect and display tuning only for a single pitch—often A or E—or for a small number of pitches, such as the six used in the standard tuning of a guitar. More complex tuners offer chromatic tuning for all 12 pitches of the equally tempered octave, among the most accurate tuning devices, strobe tuners work differently than regular electronic tuners. They are stroboscopes that flicker a light at the frequency as the note. The light shines on a wheel that spins at a precise speed, the interaction of the light and regularly-spaced marks on the wheel creates a stroboscopic effect that makes the marks for a particular pitch appear to stand still when the pitch is in tune. These can tune instruments and audio devices more accurately than most non-strobe tuners, regular electronic tuners contain either an input jack for electric instruments, a microphone, or a clip-on sensor or some combination of these inputs. Pitch detection circuitry drives some type of display, some tuners have an output, or through-put, so the tuner can connect in-line from an electric instrument to an instrument amplifier or mixing console. Small tuners are usually battery powered, many battery powered tuners also have a jack for an optional AC power supply. Most musical instruments generate a complex waveform. It contains a number of partials, including the fundamental frequency. Each instrument produces different ratios of harmonics, which is what makes notes of the pitch played on different instruments sound different. As well, this waveform constantly changes and this means that for non-strobe tuners to be accurate, the tuner must process a number of cycles and use the pitch average to drive its display. Background noise from other musicians or harmonic overtones from the instrument can impede the electronic tuner from locking onto the input frequency. This is why the needle or display on regular electronic tuners tends to waver when a pitch is played, small movements of the needle, or LED, usually represent a tuning error of 1 cent
41.
Pseudo-octave
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When used as a basis for an equal temperament, the pseudo-octave may also be called the interval of equivalence, the repeat ratio, and the nonoctave. The stretched octave, for example 2.01,1, sounds out of tune when played with true harmonic overtones, in piano tuning, stretched octaves are commonly encountered, where the inharmonicity caused by string thickness and tension makes it necessary to widen every interval very slightly. Another example is the play on clarinets of the Bohlen–Pierce scale. Stretched octaves are caused by the physics of standing waves in a stretched wire, the pitch of each overtone produced by a piano string is determined by the ratio of the strings restoring force, divided by its mass per unit length. In an ideal string, the only restoring force would be due to the tension in the string. In practice, piano strings are made from steel, which is stiff. Youngs modulus of the steel is what defines the stiffness. The stiffness adds an extra restoring force to each string, the amount of this extra force depends on the amount of bend being induced in the string, higher normal modes bend the string more, inducing more stiffness-related force and sharpening the pitch of the resulting overtone. Electronic tuner Mel scale Octave Types, BillBremmer. com
42.
Stretched tuning
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In stretched tuning, two notes an octave apart, whose fundamental frequencies theoretically have an exact 2,1 ratio, are tuned slightly farther apart. For a stretched tuning the octave is greater than a factor of 2, for example, the piano features both stretched harmonics and, to accommodate those, stretched fundamentals. The fundamental note and its harmonics sound together, and the relationships among them strongly affect the perceived tone or timbre of the instrument. Each note on the keyboard has its own separate vibrating element whose tension and/or length, in electric pianos, the motion of the vibrating element is sensed by an electromagnetic pickup and amplified electronically. In tuning, the relationship between two notes is determined by evaluating their common harmonics, for example, we say two notes are an octave apart when the fundamental frequency of the upper note exactly matches the second harmonic of the lower note. On instruments strung with wire, however, neither of these assumptions is valid. Inharmonicity refers to the difference between the theoretical and actual frequencies of the harmonics or overtones of a vibrating tine or string, the theoretical frequency of the second harmonic is twice the fundamental frequency, and of the third harmonic is three times the fundamental frequency, and so on. But on metal strings, tines, and reeds, the frequencies of those harmonics are slightly higher. A digital emulation of these instruments must recreate this inharmonicity if it is to sound convincing, when a stretched wire string is excited into motion by plucking or striking, a complex wave travels outward to the ends of the string. As it travels outward, this initial impulse forces the wire out of its resting position all along its length, after the impulse has passed, each part of the wire immediately begins to return toward its resting position, which means vibration has been induced. Meanwhile, the impulse is reflected at both ends of the string and travels back toward the center. On the way, it interacts with the vibrations it induced on the initial pass. When the reflected impulses encounter each other, their interaction again cancels some components, as a rule, the amplitude of its vibration is less for higher harmonics than for lower, meaning that higher harmonics are softer—though the details of this differ from instrument to instrument. The exact combination of different harmonics and their amplitudes is a factor affecting the timbre or tone quality of a particular musical tone. In the theoretical string, however, the force acting to return a part of the string to its rest position is the tension between its ends. If you try bending a short piece of wire or guitar string slightly with your fingers. In a vibrating string, that adds to the effect of string tension in returning a given part of the string toward its rest position. The result is a frequency of vibration higher than the theoretical frequency, and because the wires resistance to bending increases as its length decreases, its effect is greater in higher harmonics than in lower
43.
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
44.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
45.
Musical keyboard
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A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument. Depressing a key on the causes the instrument to produce sounds, either by mechanically striking a string or tine, plucking a string, causing air to flow through a pipe. On electric and electronic keyboards, depressing a key connects a circuit, since the most commonly encountered keyboard instrument is the piano, the keyboard layout is often referred to as the piano keyboard. The twelve notes of the Western musical scale are laid out with the lowest note on the left, because these keys were traditionally covered in ivory they are often called the white notes or white keys. The keys for the remaining five notes—which are not part of the C major scale— are raised, because these keys receive less wear, they are often made of black colored wood and called the black notes or black keys. The pattern repeats at the interval of an octave, the arrangement of longer keys for C major with intervening, shorter keys for the intermediate semitones dates to the 15th century. The break was between middle C and C-sharp, or outside of Iberia between B and C, broken keyboards reappeared in 1842 with the harmonium, the split occurring at E4/F4. The reverse-colored keys on Hammond organs such as the B3, C3, the chromatic compass of keyboard instruments has tended to increase. Harpsichords often extended over five octaves in the 18th century, while most pianos manufactured since about 1870 have 88 keys, some modern pianos have even more notes. While modern synthesizer keyboards commonly have either 61,76 or 88 keys, organs normally have 61 keys per manual, though some spinet models have 44 or 49. An organ pedalboard is a keyboard with long pedals that are played by the organists feet, pedalboards vary in size from 12 to 32 notes. In a typical layout, black note keys have uniform width. In the larger gaps between the keys, the width of the natural notes C, D and E differ slightly from the width of keys F, G, A and B. This allows close to uniform spacing of 12 keys per octave while maintaining uniformity of seven natural keys per octave, over the last three hundred years, the octave span distance found on historical keyboard instruments has ranged from as little as 125 mm to as much as 170 mm. Several reduced-size standards have been proposed and marketed, a 15/16 size and the 7/8 DS Standard keyboard developed by Christopher Donison in the 1970s and developed and marketed by Steinbuhler & Company. There have been variations in the design of the keyboard to address technical and musical issues, thus, an octave would have eight white keys and only four black keys. During the sixteenth century, when instruments were tuned in meantone temperament, some harpsichords were constructed with the G♯. The broken octave, a variation of the short octave
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Keyboard instrument
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A keyboard instrument is a musical instrument played using a keyboard. The most common of these are the piano, organ, and various keyboards, including synthesizers. Other keyboard instruments include celestas, which are struck idiophones operated by a keyboard, and carillons, today, the term keyboard often refers to keyboard-style synthesizers. Another important use of the keyboard is in historical musicology. Particularly in the 18th century, the harpsichord, the clavichord, and the piano were in competition. Hence in a phrase like Mozart excelled as a player the word keyboard is usefully noncommittal. The earliest known keyboard instrument was the Ancient Greek hydraulis, a type of pipe organ, the keys were likely balanced and could be played with a light touch, as is clear from the reference in a Latin poem by Claudian, who says magna levi detrudens murmura tactu. Intent, that is “let him thunder forth as he presses out mighty roarings with a light touch”, from its invention until the fourteenth century, the organ remained the only keyboard instrument. Often, the organ did not feature a keyboard at all, almost every keyboard until the fifteenth century had seven naturals to each octave. The clavichord and the harpsichord appeared during the 14th century—the clavichord probably being earlier, the harpsichord and clavichord were both common until widespread adoption of the piano in the 18th century, after which their popularity decreased. The piano was revolutionary, because a pianist could vary the volume of the sound by varying the vigor with which each key was struck. The pianos full name is gravicèmbalo con piano e forte meaning harpsichord with soft and loud but can be shortened to piano-forte, which means soft-loud in Italian. In its current form, the piano is a product of the late 19th century, in fact, the modern piano is significantly different from even the 19th-century pianos used by Liszt, Chopin, and Brahms. See Piano history and musical performance, keyboard instruments were further developed in the early twentieth century. Early electromechanical instruments, such as the Ondes Martenot, appeared early in the century and this was a very important contribution to the keyboards history. Much effort has gone into creating an instrument that sounds like the piano but lacks its size, the electric piano and electronic piano were early efforts that, while useful instruments in their own right, did not convincingly reproduce the timbre of the piano. Electric and electronic organs were developed during the same period, more recent electronic keyboard designs strive to emulate the sound of specific make and model pianos using digital samples and computer models. Concerns celebrated keyboard players and the various instruments used over the centuries
