1.
Inversion (music)
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In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, the concept of inversion also plays a role in musical set theory. An interval is inverted by raising or lowering either of the notes using displacement of the octave so that retain their names. Under inversion, perfect intervals remain perfect, major intervals become minor and vice versa, augmented intervals become diminished, traditional interval names add together to make nine, seconds become sevenths and vice versa, thirds become sixes and vice versa, and fourths become fifths and vice versa. Thus a perfect fourth becomes a fifth, an augmented fourth becomes a diminished fifth, and a simple interval and its inversion. A chords inversion describes the relationship of its bass to the tones in the chord. For instance, a C major triad contains the tones C, E and G, its inversion is determined by which of these tones is the bottom note in the chord. The term inversion is used to categorically refer to the different possibilities. In texts that make this restriction, the position may be used instead to refer to all of the possibilities as a category. A root-position chord Play is sometimes known as the parent chord of its inversions. For example, C is the root of a C major triad and is in the bass when the triad is in position, the 3rd. The following chord is also a C major triad in root position, the rearrangement of the notes above the bass into different octaves and the doubling of notes, is known as voicing. In an inverted chord, the root is not in the bass, the inversions are numbered in the order their bass tones would appear in a closed root position chord. In the second inversion Play, the bass is G—the 5th of the triad—with the root and the 3rd above it, forming a 4th and a 6th above the bass of G, respectively. This inversion can be either consonant or dissonant, and analytical notation sometimes treats it differently depending on the harmonic, for more details, look at Second inversion Third inversions exist only for chords of four or more tones, such as 7th chords. In a third-inversion chord Play, the 7th of the chord is in the bass position, each numeral expresses the interval that results from the voices above it. For example, in root-position triad C-E-G, the intervals above bass note C are a 3rd and a 5th, giving the figures 5-3. If this triad were inverted, the figures 6-3 would apply, due to the intervals of third and sixth appearing above bass note E. Figured bass is similarly applied to 7th chords, certain arbitrary conventions of abbreviation exist in the use of figured bass
2.
Unison
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In music, unison is two or more musical parts sounding the same pitch or at an octave interval, usually at the same time. Rhythmic patterns which are homorhythmic are also called unison, two pitches that are the same or two that move as one. Unison or perfect unison may refer to the interval formed by a tone and its duplication, for example C–C, as differentiated from the second, C–D, in the unison the two pitches have the ratio of 1,1 or 0 half steps and zero cents. This is because a pair of tones in unison come from different locations or can have different colors, voices with different colors have, as sound waves, different waveforms. These waveforms have the fundamental frequency but differ in the amplitudes of their higher harmonics. The unison is considered the most consonant interval while the near unison is considered the most dissonant, the unison is also the easiest interval to tune. The unison is abbreviated as P1, a point is the beginning of a line, although, it is not itself a line. But a line is not composed of points, since a point has no length, width, or depth that can be extended, or joined to another point. So a unison is only the beginning of consonance or interval, it is neither consonance nor interval, several singers singing a melody together. In orchestral music unison can mean the simultaneous playing of a note by different instruments, either at the pitch, or in a different octave, for example, cello. Typically a section string player plays unison with the rest of the section, thus, in the divisi first violins the outside players might play the top note of the chord, while the inside seated players play the middle note, and the second violins play the bottom note. At the point where the first violins no longer play divisi, when several people sing together, as in a chorus, the simplest way for them to sing is to sing in one voice, in unison. If there is an instrument accompanying them, then the instrument must play the notes being sung by the singers. Otherwise the instrument is considered a voice and there is no unison. If there is no instrument, then the singing is said to be a cappella, Music in which all the notes sung are in unison is called monophonic. From this sense can be derived another, figurative, sense, if people do something in unison it means they do it simultaneously, in tandem. Related terms are univocal and unanimous, monophony could also conceivably include more than one voice which do not sing in unison but whose pitches move in parallel, always maintaining the same interval of an octave. A pair of notes sung one or a multiple of an octave apart are almost in unison, when there are two or more voices singing different notes, this is called part singing
3.
Semitone
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A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale, for example, C is adjacent to C♯, the interval between them is a semitone. In music theory, a distinction is made between a diatonic semitone, or minor second and a semitone or augmented unison. In twelve-tone equal temperament all semitones are equal in size, in other tuning systems, semitone refers to a family of intervals that may vary both in size and name. In quarter-comma meantone, seven of them are diatonic, and 117.1 cents wide, while the five are chromatic. 12-tone scales tuned in just intonation typically define three or four kinds of semitones, for instance, Asymmetric five-limit tuning yields chromatic semitones with ratios 25,24 and 135,128, and diatonic semitones with ratios 16,15 and 27,25. The condition of having semitones is called hemitonia, that of having no semitones is anhemitonia, a musical scale or chord containing semitones is called hemitonic, one without semitones is anhemitonic. The minor second occurs in the scale, between the third and fourth degree, and between the seventh and eighth degree. It is also called the diatonic semitone because it occurs between steps in the diatonic scale, the minor second is abbreviated m2. Its inversion is the major seventh, listen to a minor second in equal temperament. Here, middle C is followed by D♭, which is a tone 100 cents sharper than C, melodically, this interval is very frequently used, and is of particular importance in cadences. In the perfect and deceptive cadences it appears as a resolution of the leading-tone to the tonic, in the plagal cadence, it appears as the falling of the subdominant to the mediant. It also occurs in many forms of the cadence, wherever the tonic falls to the leading-tone. Harmonically, the interval usually occurs as some form of dissonance or a tone that is not part of the functional harmony. It may also appear in inversions of a seventh chord. In unusual situations, the second can add a great deal of character to the music. For instance, Frédéric Chopins Étude Op.25, No.5 opens with a melody accompanied by a line that plays fleeting minor seconds and these are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned the piece its nickname, the wrong note étude and this kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgskys Ballet of the Unhatched Chicks
4.
Interval class
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For example, the interval class between pitch classes 4 and 9 is 5 because 9 −4 =5 is less than 4 −9 = −5 ≡7. See modular arithmetic for more on modulo 12, the largest interval class is 6 since any greater interval n may be reduced to 12 − n. The concept of interval class accounts for octave, enharmonic, consider, for instance, the following passage, (To hear a MIDI realization, click the following,106 KB In the example above, all four labeled pitch-pairs, or dyads, share a common intervallic color. In atonal theory, this similarity is denoted by interval class—ic 5, tonal theory, however, classifies the four intervals differently, interval 1 as perfect fifth,2, perfect twelfth,3, diminished sixth, and 4, perfect fourth. The unordered pitch class interval i may be defined as i = the smaller of i ⟨ a, b ⟩ and i ⟨ b, a ⟩, where i <a, b> is an ordered pitch-class interval. While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert Morris, prefer to use braces, pitch interval Similarity relation Morris, Robert. Class Notes for Atonal Music Theory, ISBN 0-300-04536-0 ISBN 0-300-04537-9 Solomons Set Theory Primer
5.
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
6.
Cent (music)
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The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each, alexander J. Ellis based the measure on the acoustic logarithms decimal semitone system developed by Gaspard de Prony in the 1830s, at Robert Holford Macdowell Bosanquets suggestion. It has become the method of representing and comparing musical pitches. Like a decibels relation to intensity, a cent is a ratio between two close frequencies, for the ratio to remain constant over the frequency spectrum, the frequency range encompassed by a cent must be proportional to the two frequencies. An equally tempered semitone spans 100 cents by definition, an octave—two notes that have a frequency ratio of 2, 1—spans twelve semitones and therefore 1200 cents.0005777895. For example, in just intonation the major third is represented by the frequency ratio 5,4, applying the formula at the top shows that this is about 386 cents. The equivalent interval on the piano would be 400 cents. The difference,14 cents, is about a seventh of a half step, as x increases from 0 to 1⁄12, the function 2x increases almost linearly from 1.00000 to 1.05946. The exponential cent scale can therefore be accurately approximated as a linear function that is numerically correct at semitones. That is, n cents for n from 0 to 100 may be approximated as 1 +0. 0005946n instead of 2 n⁄1200. The rounded error is zero when n is 0 or 100, and is about 0.72 cents high when n is 50 and this error is well below anything humanly audible, making this piecewise linear approximation adequate for most practical purposes. It is difficult to establish how many cents are perceptible to humans, one author stated that humans can distinguish a difference in pitch of about 5–6 cents. The threshold of what is perceptible, technically known as the just noticeable difference, also varies as a function of the frequency, the amplitude and the timbre. In one study, changes in tone quality reduced student musicians ability to recognize, as out-of-tune and it has also been established that increased tonal context enables listeners to judge pitch more accurately. Free, online web sites for self-testing are available, while intervals of less than a few cents are imperceptible to the human ear in a melodic context, in harmony very small changes can cause large changes in beats and roughness of chords. When listening to pitches with vibrato, there is evidence that humans perceive the mean frequency as the center of the pitch, normal adults are able to recognize pitch differences of as small as 25 cents very reliably. Adults with amusia, however, have trouble recognizing differences of less than 100 cents, iring noticed that the Grad/Werckmeister and the schisma are nearly the same and both may be approximated by 600 steps per octave. Yasser promoted the decitone, centitone, and millitone, for example, Equal tempered perfect fifth =700 cents =175.6 savarts =583.3 millioctaves =350 centitones
7.
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
8.
Quarter tone
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A quarter tone play, is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide as a semitone, which is half a whole tone. Many composers are known for having written music including quarter tones or the quarter-tone scale —proposed by 19th-century music theorists Heinrich Richter in 1823, george Tucker, Ivan Alexandrovich Wyschnegradsky, and Iannis Xenakis. The term quarter tone can refer to a number of different intervals, for example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments. In the quarter tone scale, also called 24 tone equal temperament, the tone is 50 cents, or a frequency ratio of 24√2 or approximately 1.0293. In this scale the quarter tone is the smallest step, a semitone is thus made of two steps, and three steps make a three-quarter tone play or neutral second, half of a minor third. The 8-TET scale is composed of three-quarter tones, in just intonation the quarter tone can be represented by the septimal quarter tone,36,35, or by the undecimal quarter tone,33,32, approximately half the semitone of 16,15 or 25,24. The ratio of 36,35 is only 1.23 cents narrower than a 24-TET quarter tone and this just ratio is also the difference between a minor third and septimal minor third. Quarter tones and intervals close to also occur in a number of other equally tempered tuning systems. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, 72-TET also has equally tempered quarter-tones, and indeed contains 3 quarter tone scales, since 72 is divisible by 24. Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33,32, because many musical instruments manufactured today are designed for the 12-tone scale, not all are usable for playing quarter tones. Sometimes special playing techniques must be used, other instruments can be used to play quarter tones when using audio signal processing effects such as pitch shifting. Pairs of conventional instruments tuned a tone apart can be used to play some quarter tone music. Indeed, quarter-tone pianos have been built, which consist essentially of two stacked one above the other in a single case, one tuned a quarter tone higher than the other. Many Persian dastgah and Arabic maqamat contain intervals of three-quarter tone size, the quarter tone scale may be primarily a theoretical construct in Arabic music. Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, the Japanese multi-instrumentalist and experimental musical instrument builder Yuichi Onoue developed a 24-TET quarter tone tuning on his guitar. Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from Missouri, the enharmonic genus of the Greek tetrachord consisted of a ditone or an approximate major third, and a semitone, which was divided into two microtones. Intervals matched particularly closely include the second, neutral third. The septimal minor third and septimal major third are approximated rather poorly, overall, 24-TET can be viewed as matching the 11th and 13th harmonics more closely than the 7th
9.
Music
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Music is an art form and cultural activity whose medium is sound organized in time. The common elements of music are pitch, rhythm, dynamics, different styles or types of music may emphasize, de-emphasize or omit some of these elements. The word derives from Greek μουσική, Ancient Greek and Indian philosophers defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as the harmony of the spheres and it is music to my ears point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, There is no noise, the creation, performance, significance, and even the definition of music vary according to culture and social context. There are many types of music, including music, traditional music, art music, music written for religious ceremonies. For example, it can be hard to draw the line between some early 1980s hard rock and heavy metal, within the arts, music may be classified as a performing art, a fine art or as an auditory art. People may make music as a hobby, like a teen playing cello in a youth orchestra, the word derives from Greek μουσική. According to the Online Etymological Dictionary, the music is derived from mid-13c. Musike, from Old French musique and directly from Latin musica the art of music and this is derived from the. Greek mousike of the Muses, from fem. of mousikos pertaining to the Muses, from Mousa Muse. In classical Greece, any art in which the Muses presided, Music is composed and performed for many purposes, ranging from aesthetic pleasure, religious or ceremonial purposes, or as an entertainment product for the marketplace. With the advent of recording, records of popular songs. Some music lovers create mix tapes of their songs, which serve as a self-portrait. An environment consisting solely of what is most ardently loved, amateur musicians can compose or perform music for their own pleasure, and derive their income elsewhere. Professional musicians sometimes work as freelancers or session musicians, seeking contracts and engagements in a variety of settings, There are often many links between amateur and professional musicians. Beginning amateur musicians take lessons with professional musicians, in community settings, advanced amateur musicians perform with professional musicians in a variety of ensembles such as community concert bands and community orchestras. However, there are many cases where a live performance in front of an audience is also recorded and distributed. Live concert recordings are popular in classical music and in popular music forms such as rock, where illegally taped live concerts are prized by music lovers
10.
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
11.
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
12.
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
13.
Scale (music)
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In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is a scale. Some scales contain different pitches when ascending than when descending, for example, the Melodic minor scale. Due to the principle of equivalence, scales are generally considered to span a single octave. A musical scale represents a division of the space into a certain number of scale steps. A measure of the width of each scale step provides a method to classify scales, based on their interval patterns, scales are put into categories including diatonic, chromatic, major, minor, and others. A specific scale is defined by its interval pattern and by a special note. The tonic of a scale is the selected as the beginning of the octave. Typically, the name of the scale specifies both its tonic and its interval pattern, for example, C major indicates a major scale with a C tonic. Scales are typically listed from low to high, most scales are octave-repeating, meaning their pattern of notes is the same in every octave. An octave-repeating scale can be represented as an arrangement of pitch classes. The distance between two notes in a scale is called a scale step. The notes of a scale are numbered by their steps from the root of the scale, for example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to other, C and E create an interval of a third. A single scale can be manifested at many different pitch levels, for example, a C major scale can be started at C4 and ascending an octave to C5, or it could be started at C6, ascending an octave to C7. As long as all the notes can be played, the octave they take on can be altered, the pitch distances or intervals among the notes of a scale tell us more about the sound of the music than does the mere number of tones. The notes of a scale form intervals with each of the notes of the chord in combination. A 5-note scale has 10 of these intervals, a 6-note scale has 15, a 7-note scale has 21
14.
Pitch class
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In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e. g. the pitch class C consists of the Cs in all octaves. The pitch class C stands for all possible Cs, in whatever octave position, important to musical set theory, a pitch class is, all pitches related to each other by octave, enharmonic equivalence, or both. Psychologists refer to the quality of a pitch as its chroma, a chroma is an attribute of pitches, just like hue is an attribute of color. A pitch class is a set of all pitches that share the same chroma, because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. Indeed, the mapping from pitch to real numbers defined in this forms the basis of the MIDI Tuning Standard. To represent pitch classes, we need to identify or glue together all pitches belonging to the same pitch class—i. e, all numbers p and p +12. The result is a quotient group that musicians call pitch class space. Points in this space can be labelled using real numbers in the range 0 ≤ x <12. These numbers provide numerical alternatives to the names of elementary music theory,0 = C,1 = C♯/D♭,2 = D,2.5 = D,3 = D♯/E♭. In this system, pitch classes represented by integers are classes of equal temperament. In music, integer notation is the translation of pitch classes and/or interval classes into whole numbers, thus if C =0, then C♯ =1. A♯ =10, B =11, with 10 and 11 substituted by t and e in some sources and this allows the most economical presentation of information regarding post-tonal materials. In the integer model of pitch, all classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone, serial. The C above this is not 12, but 0 again, thus arithmetic modulo 12 is used to represent octave equivalence. One advantage of this system is that it ignores the spelling of notes according to their diatonic functionality, there are a few disadvantages with integer notation. First, theorists have used the same integers to indicate elements of different tuning systems. Thus, the numbers 0,1,2,5, are used to notate pitch classes in 6-tone equal temperament
15.
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
16.
Pythagorean interval
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In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the fifth with ratio 3/2 and the perfect fourth with ratio 4/3 are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system, however, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation, notice that the terms ditone and semiditone are specific for Pythagorean tuning, while tone and tritone are used generically for all tuning systems. Interestingly, despite its name, a semiditone can hardly be viewed as half of a ditone, the table shows from which notes some of the above listed intervals can be played on an instrument using a repeated-octave 12-tone scale tuned with D-based symmetric Pythagorean tuning. Further details about this table can be found in Size of Pythagorean intervals, the fundamental intervals are the superparticular ratios 2/1, 3/2, and 4/3. 2/1 is the octave or diapason, 3/2 is the perfect fifth, diapente, or sesquialterum. 4/3 is the fourth, diatessaron, or sesquitertium. These three intervals and their equivalents, such as the perfect eleventh and twelfth, are the only absolute consonances of the Pythagorean system. All other intervals have varying degrees of dissonance, ranging from smooth to rough, the difference between the perfect fourth and the perfect fifth is the tone or major second. This has the ratio 9/8, also known as epogdoon and it is the only other superparticular ratio of Pythagorean tuning, two tones make a ditone, a dissonantly wide major third, ratio 81/64. The ditone differs from the just major third by the syntonic comma, likewise, the difference between the tone and the perfect fourth is the semiditone, a narrow minor third, 32/27, which differs from 6/5 by the syntonic comma. These differences are tempered out or eliminated by using compromises in meantone temperament, the difference between the minor third and the tone is the minor semitone or limma of 256/243. The difference between the tone and the limma is the major semitone or apotome of 2187/2048, there is a one-to-one correspondence between interval names and frequency ratios. Generated collection Just intonation List of meantone intervals List of intervals in 5-limit just intonation Shí-èr-lǜ Whole-tone scale Neo-Gothic usage by Margo Schulter
17.
Perfect fourth
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In classical music from Western culture, a fourth is a musical interval encompassing four staff positions, and the perfect fourth is a fourth spanning five semitones. For example, the interval from C to the next F is a perfect fourth, as the note F lies five semitones above C. Diminished and augmented fourths span the same number of staff positions, the perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor, up until the late 19th century, the perfect fourth was often called by its Greek name, diatessaron. Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions. A perfect fourth in just intonation corresponds to a ratio of 4,3, or about 498 cents, while in equal temperament a perfect fourth is equal to five semitones. A helpful way to recognize a fourth is to hum the starting of the Bridal Chorus from Wagners Lohengrin. Other examples are the first two notes of the Christmas carol Hark, the Herald Angels Sing or El Cóndor Pasa, and, for a descending perfect fourth, the second and third notes of O Come All Ye Faithful. The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, in common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. Conventionally, adjacent strings of the bass and of the bass guitar are a perfect fourth apart when unstopped, as are all pairs. Sets of tom-tom drums are also tuned in perfect fourths. The 4,3 just perfect fourth arises in the C major scale between G and C, play The use of perfect fourths and fifths to sound in parallel with and to thicken the melodic line was prevalent in music prior to the European polyphonic music of the Middle Ages. In the 13th century, the fourth and fifth together were the concordantiae mediae after the unison and octave, in the 15th century the fourth came to be regarded as dissonant on its own, and was first classed as a dissonance by Johannes Tinctoris in his Terminorum musicae diffinitorium. In practice, however, it continued to be used as a consonance when supported by the interval of a third or fifth in a lower voice. Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, the octave has the ratio of 2,1, for example the interval between a at A440 and a at 880 Hz, giving the ratio 880,440, or 2,1. The fifth has a ratio of 3,2, and its complement has the ratio of 3,4, ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the Monochord. In early western polyphony, these simpler intervals were generally preferred, however, in its development between the 12th and 16th centuries, In the earliest stages, these simple intervals occur so frequently that they appear to be the favourite sound of composers. Later, the more complex intervals move gradually from the margins to the centre of musical interest
18.
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
19.
Musical note
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In music, the term note has three primary meanings, A sign used in musical notation to represent the relative duration and pitch of a sound, A pitched sound itself. Notes are the blocks of much written music, discretizations of musical phenomena that facilitate performance, comprehension. In the former case, one note to refer to a specific musical event, in the latter. Two notes with fundamental frequencies in an equal to any integer power of two are perceived as very similar. Because of that, all notes with these kinds of relations can be grouped under the pitch class. However, within the English-speaking and Dutch-speaking world, pitch classes are represented by the first seven letters of the Latin alphabet. A few European countries, including Germany, adopt an almost identical notation, the eighth note, or octave, is given the same name as the first, but has double its frequency. The name octave is also used to indicate the span between a note and another with double frequency, for example, the now-standard tuning pitch for most Western music,440 Hz, is named a′ or A4. There are two systems to define each note and octave, the Helmholtz pitch notation and the scientific pitch notation. Letter names are modified by the accidentals, a sharp ♯ raises a note by a semitone or half-step, and a flat ♭ lowers it by the same amount. In modern tuning a half step has a ratio of 12√2. The accidentals are written after the name, so, for example, F♯ represents F-sharp, B♭ is B-flat. Additional accidentals are the double-sharp, raising the frequency by two semitones, and double-flat, lowering it by that amount, in musical notation, accidentals are placed before the note symbols. Systematic alterations to the seven lettered pitches in the scale can be indicated by placing the symbols in the key signature, explicitly noted accidentals can be used to override this effect for the remainder of a bar. A special accidental, the natural symbol ♮, is used to indicate an unmodified pitch, effects of key signature and local accidentals do not accumulate. If the key signature indicates G♯, a flat before a G makes it G♭, though often this type of rare accidental is expressed as a natural. Likewise, a sharp sign on a key signature with a single sharp ♯ indicates only a double sharp. Assuming enharmonicity, many accidentals will create equivalences between pitches that are written differently, for instance, raising the note B to B♯ is equal to the note C
20.
Italian language
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By most measures, Italian, together with Sardinian, is the closest to Latin of the Romance languages. Italian is a language in Italy, Switzerland, San Marino, Vatican City. Italian is spoken by minorities in places such as France, Montenegro, Bosnia & Herzegovina, Crimea and Tunisia and by large expatriate communities in the Americas. Many speakers are native bilinguals of both standardized Italian and other regional languages, Italian is the fourth most studied language in the world. Italian is a major European language, being one of the languages of the Organisation for Security and Cooperation in Europe. It is the third most widely spoken first language in the European Union with 65 million native speakers, including Italian speakers in non-EU European countries and on other continents, the total number of speakers is around 85 million. Italian is the working language of the Holy See, serving as the lingua franca in the Roman Catholic hierarchy as well as the official language of the Sovereign Military Order of Malta. Italian is known as the language of music because of its use in musical terminology and its influence is also widespread in the arts and in the luxury goods market. Italian has been reported as the fourth or fifth most frequently taught foreign language in the world, Italian was adopted by the state after the Unification of Italy, having previously been a literary language based on Tuscan as spoken mostly by the upper class of Florentine society. Its development was influenced by other Italian languages and to some minor extent. Its vowels are the second-closest to Latin after Sardinian, unlike most other Romance languages, Italian retains Latins contrast between short and long consonants. As in most Romance languages, stress is distinctive, however, Italian as a language used in Italy and some surrounding regions has a longer history. What would come to be thought of as Italian was first formalized in the early 14th century through the works of Tuscan writer Dante Alighieri, written in his native Florentine. Dante is still credited with standardizing the Italian language, and thus the dialect of Florence became the basis for what would become the language of Italy. Italian was also one of the recognised languages in the Austro-Hungarian Empire. Italy has always had a dialect for each city, because the cities. Those dialects now have considerable variety, as Tuscan-derived Italian came to be used throughout Italy, features of local speech were naturally adopted, producing various versions of Regional Italian. Even in the case of Northern Italian languages, however, scholars are not to overstate the effects of outsiders on the natural indigenous developments of the languages
21.
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
22.
Twinkle, Twinkle, Little Star
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Twinkle, Twinkle, Little Star is a popular English lullaby. The lyrics are from an early 19th-century English poem by Jane Taylor, the poem, which is in couplet form, was first published in 1806 in Rhymes for the Nursery, a collection of poems by Taylor and her sister Ann. The English lyrics have five stanzas, although only the first is widely known and it has a Roud Folk Song Index number of 7666. This song is performed in the key of C Major. The song is in the domain, and has many adaptations around the world. Additional variations exist such as from 1896 in Song Stories for the Kindergarten by Mildred J. Hill, an adaptation of the song, named Twinkle, Twinkle, Little Earth, was written by Charles Randolph Grean, Fred Hertz and Leonard Nimoy. It is included on his first 1967 album Leonard Nimoy Presents Mr. Spocks Music From Outer Space, a version using synonyms from Rogets Thesaurus exists. Ah. vous dirai-je, maman Alphabet song Baa, Baa, a European Union, government-funded education project to collect lullabies from across Europe - includes samples in seven languages. SoundBeep Twinkle Twinkle Little Star with two Instrument versions, piano and kalimba, audio segment from BBC Radio 4 Womans Hour
23.
Hearing
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Hearing, or auditory perception, is the ability to perceive sound by detecting vibrations, changes in the pressure of the surrounding medium through time, through an organ such as the ear. Sound may be heard through solid, liquid, or gaseous matter and it is one of the traditional five senses, partial or total inability to hear is called hearing loss. Like touch, audition requires sensitivity to the movement of molecules in the world outside the organism, both hearing and touch are types of mechanosensation. There are three components of the human ear, the outer ear, the middle ear. The outer ear includes the pinna, the part of the ear, as well as the ear canal which terminates at the eardrum. The pinna serves to focus sound waves through the ear canal toward the eardrum, because of the asymmetrical character of the outer ear of most mammals, sound is filtered differently on its way into the ear depending on what vertical location it is coming from. This gives these animals the ability to localize sound vertically, the eardrum is an airtight membrane, and when sound waves arrive there, they cause it to vibrate following the waveform of the sound. The middle ear consists of a small air-filled chamber that is located medial to the eardrum, within this chamber are the three smallest bones in the body, known collectively as the ossicles which include the malleus, incus and stapes. They aid in the transmission of the vibrations from the eardrum to the inner ear, the purpose of the middle ear ossicles is to overcome the impedance mismatch between air and water, by providing impedance matching. Also located in the ear are the stapedius and tensor tympani muscles which protect the hearing mechanism through a stiffening reflex. The stapes transmits sound waves to the ear through the oval window. The round window, another flexible membrane, allows for the displacement of the inner ear fluid caused by the entering sound waves. The inner ear consists of the cochlea, which is a spiral-shaped, fluid-filled tube and it is divided lengthwise by the organ of Corti, which is the main organ of mechanical to neural transduction. Inside the organ of Corti is the membrane, a structure that vibrates when waves from the middle ear propagate through the cochlear fluid – endolymph. The basilar membrane is tonotopic, so that frequency has a characteristic place of resonance along it. Characteristic frequencies are high at the entrance to the cochlea. Basilar membrane motion causes depolarization of the cells, specialized auditory receptors located within the organ of Corti. While the hair cells do not produce action potentials themselves, they release neurotransmitter at synapses with the fibers of the auditory nerve, which does produce action potentials
24.
Musical notation
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Types and methods of notation have varied between cultures and throughout history, and much information about ancient music notation is fragmentary. Although many ancient cultures used symbols to represent melodies and rhythms, none of them were particularly comprehensive, the seeds of what would eventually become modern western notation were sown in medieval Europe, starting with the Catholic churchs goal for ecclesiastical uniformity. The church began notating plainchant melodies so that the same chants could be used throughout the church, Music notation developed in the Renaissance and Baroque music eras. The introduction of figured bass notation in the Baroque era marked the beginning of the first compositions based around chord progressions, in the classical period and the Romantic music era, notation continued to develop as new musical instrument technologies were developed. Music notation has been adapted to many kinds of music, including music, popular music. The earliest form of notation can be found in a cuneiform tablet that was created at Nippur, in Sumer. The tablet represents fragmentary instructions for performing music, that the music was composed in harmonies of thirds, a tablet from about 1250 BC shows a more developed form of notation. Although the interpretation of the system is still controversial, it is clear that the notation indicates the names of strings on a lyre. Although they are fragmentary, these represent the earliest notated melodies found anywhere in the world. The notation consists of symbols placed above text syllables, an example of a complete composition is the Seikilos epitaph, which has been variously dated between the 2nd century BC to the 1st century AD. Three hymns by Mesomedes of Crete exist in manuscript, the Delphic Hymns, dated to the 2nd century BC, also use this notation, but they are not completely preserved. Ancient Greek notation appears to have out of use around the time of the Decline of the Roman Empire. Byzantine music has survived as music for court ceremonies, including vocal religious music. It is not known if it is based on the monodic modal singing, unlike Western notation Byzantine neumes always indicate modal steps in relation to a clef or modal key. These step symbols themselves, or better phonic neumes, resemble brush strokes and are colloquially called gántzoi in Modern Greek, Notes as pitch classes or modal keys are represented in written form only between these neumes. In modern notation they simply serve as a reminder and modal and tempo directions have been added. In Papadic notation medial signatures usually meant a change into another echos. With exception of vú and zō they do correspond to Western solmization syllables as re, mi, fa, sol, la, si
25.
Sumerian language
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Sumerian is the language of ancient Sumer and a language isolate which was spoken in southern Mesopotamia. During the 3rd millennium BC, an intimate cultural symbiosis developed between the Sumerians and the Akkadians, which included widespread bilingualism. The influence of Sumerian on Akkadian is evident in all areas, from lexical borrowing on a scale, to syntactic, morphological. This has prompted scholars to refer to Sumerian and Akkadian in the third millennium BC as a Sprachbund, then it was forgotten until the 19th century, when Assyriologists began deciphering the cuneiform inscriptions and excavated tablets left by these speakers. It succeeds the proto-literate period, which spans roughly the 35th to 30th centuries, some versions of the chronology may omit the Late Sumerian phase and regard all texts written after 2000 BC as Post-Sumerian. The term Post-Sumerian is meant to refer to the time when the language was already extinct, the extinction has traditionally been dated approximately to the end of the Third Dynasty of Ur, the last predominantly Sumerian state in Mesopotamia, about 2000 BC. The standard variety of Sumerian is called eme-ĝir, a notable variety or sociolect is called eme-sal. Eme-sal is used exclusively by female characters in some literary texts, in addition, it is dominant in certain genres of cult songs. The special features of eme-sal are mostly phonological, but words different from the language are also used. Sumerian is a language, meaning that words could consist of a chain of more or less clearly distinguishable and separable affixes and/or morphemes. Sumerian distinguishes the grammatical genders human/non-human, but it not have separate male/female gender pronouns. The human gender includes not only humans but also gods and in cases the word for statue. Sumerian has also claimed to have two tenses, but these are currently described as completive and incompletive or perfective and imperfective aspects instead. There are a number of cases, absolutive, ergative, genitive, dative/allative, locative, comitative, equative, directive/adverbial. The naming and number of the cases varies in the scientific literature, the different homophones are marked with different numbers by convention,2 and 3 being often replaced by acute accent and grave accent diacritics respectively. For example, du = go, du3 = dù = build, Sumerian is a split ergative language. It behaves as a language in the 1st and 2nd person of present-future tense/incompletive aspect. Similar patterns are found in a number of unrelated split ergative languages
26.
Akkadian
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Akkadian is an extinct East Semitic language that was spoken in ancient Mesopotamia. The earliest attested Semitic language, it used the writing system, which was originally used to write the unrelated Ancient Sumerian. The language was named after the city of Akkad, a centre of Mesopotamian civilization during the Akkadian Empire. The mutual influence between Sumerian and Akkadian had led scholars to describe the languages as a sprachbund, Akkadian proper names were first attested in Sumerian texts from around the mid 3rd-millennium BC. From the second half of the third millennium BC, texts written in Akkadian begin to appear. By the second millennium BC, two variant forms of the language were in use in Assyria and Babylonia, known as Assyrian and Babylonian respectively, for centuries, Akkadian was the native language in Mesopotamian nations such as Assyria and Babylonia. However, it began to decline during the Neo-Assyrian Empire around the 8th century BC, by the Hellenistic period, the language was largely confined to scholars and priests working in temples in Assyria and Babylonia. The last known Akkadian cuneiform document dates from the 1st century AD, Akkadian belongs with the other Semitic languages in the Near Eastern branch of the Afroasiatic languages, a family native to East Africa, which then spread to West, Northwest and Northeast Africa. Within the Near Eastern Semitic languages, Akkadian forms an East Semitic subgroup and this novel word order is due to the influence of the Sumerian substratum, which has an SOV order. Additionally Akkadian is the only Semitic language to use the prepositions ina and ana, other Semitic languages like Arabic and Aramaic have the prepositions bi/bə and li/lə. The origin of the Akkadian spatial prepositions is unknown, in contrast to most other Semitic languages, Akkadian has only one non-sibilant fricative, ḫ. Akkadian lost both the glottal and pharyngeal fricatives, which are characteristic of the other Semitic languages, until the Old Babylonian period, the Akkadian sibilants were exclusively affricated. Old Akkadian is preserved on clay tablets dating back to c.2500 BC and it was written using cuneiform, a script adopted from the Sumerians using wedge-shaped symbols pressed in wet clay. As employed by Akkadian scribes, the cuneiform script could represent either Sumerian logograms, Sumerian syllables, Akkadian syllables. For this reason, the sign AN can on the one hand be a logogram for the word ilum, additionally, this sign was used as a determinative for divine names. Another peculiarity of Akkadian cuneiform is that many signs do not have a phonetic value. Certain signs, such as AḪ, do not distinguish between the different vowel qualities, nor is there any coordination in the other direction, the syllable -ša-, for example, is rendered by the sign ŠA, but also by the sign NĪĜ. Both of these are used for the same syllable in the same text
27.
Cuneiform script
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Cuneiform script, one of the earliest systems of writing, was invented by the Sumerians. It is distinguished by its wedge-shaped marks on clay tablets, made by means of a blunt reed for a stylus, the name cuneiform itself simply means wedge shaped. Emerging in Sumer in the fourth millennium BC, cuneiform writing began as a system of pictograms. In the third millennium, the pictorial representations became simplified and more abstract as the number of characters in use grew smaller, the system consists of a combination of logophonetic, consonantal alphabetic and syllabic signs. Cuneiform writing was replaced by the Phoenician alphabet during the Neo-Assyrian Empire. By the second century CE, the script had become extinct, between half a million and two million cuneiform tablets are estimated to have been excavated in modern times, of which only approximately 30,000 –100,000 have been read or published. Most of these have lain in these collections for a century without being translated, studied or published, the cuneiform writing system was in use for more than three millennia, through several stages of development, from the 34th century BC down to the second century CE. Ultimately, it was replaced by alphabetic writing in the course of the Roman era. It had to be deciphered as an unknown writing system in 19th-century Assyriology. Successful completion of its deciphering is dated to 1857, the cuneiform script was developed from pictographic proto-writing in the late 4th millennium BC. Mesopotamias proto-literate period spans roughly the 35th to 32nd centuries, the first documents unequivocally written in Sumerian date to the 31st century at Jemdet Nasr. Originally, pictographs were either drawn on clay tablets in vertical columns with a reed stylus or incised in stone. This early style lacked the characteristic shape of the strokes. Proper names continued to be written in purely logographic fashion. The earliest known Sumerian king whose name appears on contemporary cuneiform tablets is Enmebaragesi of Kish, from about 2900 BC, many pictographs began to lose their original function, and a given sign could have various meanings depending on context. The sign inventory was reduced from some 1,500 signs to some 600 signs, determinative signs were re-introduced to avoid ambiguity. Cuneiform writing proper thus arises from the more primitive system of pictographs at about that time, by adjusting the relative position of the tablet to the stylus, the writer could use a single tool to make a variety of impressions. Cuneiform tablets could be fired in kilns to provide a permanent record, many of the clay tablets found by archaeologists were preserved because they were fired when attacking armies burned the building in which they were kept
28.
Lyre
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The lyre is a string instrument known for its use in Greek classical antiquity and later periods. The lyre is similar in appearance to a small harp but with distinct differences, the word comes via Latin from the Greek, the earliest reference to the word is the Mycenaean Greek ru-ra-ta-e, meaning lyrists and written in the Linear B script. The lyres of Ur, excavated in ancient Mesopotamia, date to 2500 BC, the earliest picture of a lyre with seven strings appears in the famous sarcophagus of Hagia Triada. The sarcophagus was used during the Mycenaean occupation of Crete, the recitations of the Ancient Greeks were accompanied by lyre playing. The lyre of classical antiquity was ordinarily played by being strummed with a plectrum, the fingers of the free hand silenced the unwanted strings in the chord. However, later lyres were played with a bow in Europe, one example from Wales that has been resurrected recently is the crwth. In organology, lyres are defined as yoke lutes, being lutes in which the strings are attached to a yoke which lies in the plane as the sound-table. A classical lyre has a body or sound-chest, which. Extending from this sound-chest are two raised arms, which are hollow, and are curved both outward and forward. They are connected near the top by a crossbar or yoke, an additional crossbar, fixed to the sound-chest, makes the bridge which transmits the vibrations of the strings. They were stretched between the yoke and bridge, or to a tailpiece below the bridge, according to ancient Greek mythology, the young god Hermes stole a herd of sacred cows from Apollo. In order not to be followed, he made shoes for the cows which forced them to walk backwards, Apollo, following the trails, could not follow where the cows were going. Along the way, Hermes slaughtered one of the cows and offered all, from the entrails and a tortoise/turtle shell, he created the Lyre. Apollo, figuring out it was Hermes who had his cows, Apollo was furious, but after hearing the sound of the lyre, his anger faded. Apollo offered to trade the herd of cattle for the lyre, hence, the creation of the lyre is attributed to Hermes. Other sources credit it to Apollo himself, locales in southern Europe, western Asia, or north Africa have been proposed as the historic birthplace of the genus. The instrument is played in north-eastern parts of Africa. Some of the cultures using and developing the lyre were the Aeolian and Ionian Greek colonies on the coasts of Asia bordering the Lydian empire, some mythic masters like Musaeus, and Thamyris were believed to have been born in Thrace, another place of extensive Greek colonization
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Brain
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The brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. The brain is located in the head, usually close to the organs for senses such as vision. The brain is the most complex organ in a vertebrates body, in a human, the cerebral cortex contains approximately 15–33 billion neurons, each connected by synapses to several thousand other neurons. Physiologically, the function of the brain is to exert centralized control over the other organs of the body, the brain acts on the rest of the body both by generating patterns of muscle activity and by driving the secretion of chemicals called hormones. This centralized control allows rapid and coordinated responses to changes in the environment, the operations of individual brain cells are now understood in considerable detail but the way they cooperate in ensembles of millions is yet to be solved. This article compares the properties of brains across the range of animal species. It deals with the human brain insofar as it shares the properties of other brains, the ways in which the human brain differs from other brains are covered in the human brain article. Several topics that might be covered here are instead covered there because more can be said about them in a human context. The most important is brain disease and the effects of brain damage, the shape and size of the brain varies greatly between species, and identifying common features is often difficult. Nevertheless, there are a number of principles of architecture that apply across a wide range of species. Some aspects of structure are common to almost the entire range of animal species, others distinguish advanced brains from more primitive ones. The simplest way to gain information about brain anatomy is by visual inspection, Brain tissue in its natural state is too soft to work with, but it can be hardened by immersion in alcohol or other fixatives, and then sliced apart for examination of the interior. Visually, the interior of the consists of areas of so-called grey matter, with a dark color, separated by areas of white matter. Further information can be gained by staining slices of tissue with a variety of chemicals that bring out areas where specific types of molecules are present in high concentrations. It is also possible to examine the microstructure of brain tissue using a microscope, the brains of all species are composed primarily of two broad classes of cells, neurons and glial cells. Glial cells come in types, and perform a number of critical functions, including structural support, metabolic support, insulation. Neurons, however, are considered the most important cells in the brain. The property that makes neurons unique is their ability to send signals to target cells over long distances
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Enharmonic
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Thus, the enharmonic spelling of a written note, interval, or chord is an alternative way to write that note, interval, or chord. For example, in equal temperament, the notes C♯. Namely, they are the key on a keyboard, and thus they are identical in pitch, although they have different names and different roles in harmony. In other words, if two notes have the pitch but are represented by different letter names and accidentals, they are enharmonic. Enharmonic intervals are intervals with the sound that are spelled differently…, of course. Enharmonic equivalence is peculiar to post-tonal theory, much music since at least the 18th century, however, exploits enharmonic equivalence for purposes of modulation and this requires that enharmonic equivalents in fact be equivalent. Some key signatures have an enharmonic equivalent that represents a scale identical in sound, the number of sharps and flats of two enharmonically equivalent keys sum to twelve. For example, the key of B major, with 5 sharps, is equivalent to the key of C♭ major with 7 flats. Keys past 7 sharps or flats exist only theoretically and not in practice, the enharmonic keys are six pairs, three major and three minor, B major/C♭ major, G♯ minor/A♭ minor, F♯ major/G♭ major, D♯ minor/E♭ minor, C♯ major/D♭ major and A♯ minor/B♭ minor. There are practically no works composed in keys that require double sharps or double flats in the key signature, in practice, musicians learn and practice 15 major and 15 minor keys, three more than 12 due to the enharmonic spellings. Enharmonic equivalents can also used to improve the readability of a line of music, for example, a sequence of notes is more easily read as ascending or descending if the noteheads are on different positions on the staff. Doing so may reduce the number of accidentals that must be used. Thus, in the key of B♭ major, the sequence B♭-B♮-B♭ is more easily using the enharmonic spelling C♭ instead of B♮. For example the intervals of a sixth on C, on B♯. The most common enharmonic intervals are the fourth and diminished fifth, or tritone. Enharmonic equivalence is not to be confused with octave equivalence, nor are enharmonic intervals to be confused with inverted or compound intervals. In principle, the musical use of the word enharmonic to mean identical tones is correct only in equal temperament. In other tuning systems, however, enharmonic associations can be perceived by listeners, in Pythagorean tuning, all pitches are generated from a series of justly tuned perfect fifths, each with a frequency ratio of 3 to 2
31.
Major seventh
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In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions, and the major seventh is one of two commonly occurring sevenths. It is qualified as major because it is the larger of the two, the major seventh spans eleven semitones, its smaller counterpart being the minor seventh, spanning ten semitones. For example, the interval from C to B is a seventh, as the note B lies eleven semitones above C. Diminished and augmented sevenths span the same number of staff positions, the easiest way to locate and identify the major seventh is from the octave rather than the unison, and it is suggested that one sings the octave first. For example, the most commonly cited example of a melody featuring a major seventh is the seventh of the opening to Over the Rainbow. Not many songwriters begin a melody with a major seventh interval, however, two songs provide exceptions to this generalisation, Cole Porters I love you opens with a descending major seventh and Jesse Harriss Dont Know Why, starts with an ascending one. The major seventh occurs most commonly built on the root of major triads, resulting in the type also known as major seventh chord or major-major seventh chord, including I7. Major seven chords add jazziness to a musical passage, alone, a major seventh interval can sound ugly. In 24-tone equal temperament a supermajor seventh, semiaugmented seventh or, the small major seventh is a ratio of 9,5, now identified as a just minor seventh. 35,18, or 1151.23 cents, is the ratio of the septimal semi-diminished octave, the 15,8 just major seventh occurs arises in the extended C major scale between C & B and F & E. Play F & E The major seventh interval is considered one of the most dissonant intervals after its inversion the minor second, for this reason, its melodic use is infrequent in classical music. However, in the genial Gavotte from J. S, another is the closing duet from Verdis Aida, O terra addio. During the early 20th century, the seventh was used increasingly both as a melodic and a harmonic interval, particularly by composers of the Second Viennese School. Anton Weberns Variations for Piano, Op.27, opens with a major seventh, under equal temperament this interval is enharmonically equivalent to a diminished octave. The major seventh chord is very common in jazz, especially cool jazz. The major seventh chord consists of the first, third, fifth and seventh degrees of the major scale, in the key of C, it comprises the notes C E G and B. List of meantone intervals Major seventh chord Minor seventh Musical tuning
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Scientific pitch notation
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Scientific pitch notation is a method of specifying musical pitch by combining a musical note name and a number identifying the pitchs octave. Although scientific pitch notation was designed as a companion to scientific pitch. Scientific pitch is a pitch standard—a system which defines the specific frequencies of particular pitches, SPN concerns only how pitch names are notated, that is, how they are designated in printed and written text, and does not inherently specify actual frequencies. Thus the use of SPN to distinguish octaves does not depend on the standard used. The octave number increases by 1 upon an ascension from B to C, thus A4 refers to the first A above C4. In describing musical pitches, enharmonic spellings can give rise to anomalies where C♭4 is a lower frequency than B♯3, scientific pitch notation is often used to specify the range of an instrument. It is also translated into staff notation, as needed. For example, a d′ played on a B♭ trumpet is actually a C4 in scientific pitch notation, scientific pitch notation avoids possible confusion between various derivatives of Helmholtz notation which use similar symbols to refer to different notes. For example, c in Helmholtz notation refers to the C below middle C, with scientific pitch notation, middle C is always C4, and C4 is never any note but middle C. C7 is much easier to distinguish visually from C8, than is, for example, c′′′′ from c′′′′′. Although pitch notation is intended to describe audible sounds, it can also be used to specify the frequency of non-audible phenomena, for example, some MIDI software uses C5 to represent middle C. This differentiation is unnecessary and can result in confusion and this creates a linear pitch space in which an octave spans 12 semitones, where each semitone is the distance between adjacent keys of the piano keyboard. Distance in this space corresponds to musical pitch distance in a scale,2 semitones being a whole step,1 semitone being a half step. An equal-tempered semitone can also be subdivided further into 100 cents, each cent is 1⁄100 semitone or 1⁄1200 octave. This measure of pitch allows the expression of microtones not found on standard piano keyboards, the table below gives notation for pitches based on standard piano key frequencies, in other words, standard concert pitch and twelve-tone equal temperament). When a piano is tuned to just intonation, C4 refers to the key on the keyboard. Mathematically, given the number n of semitones above middle C, given the MIDI number m, the frequency is 440 ⋅2 /12 Hz. Scientific pitch is a pitch standard, first proposed in 1713 by French physicist Joseph Sauveur
33.
Helmholtz pitch notation
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Helmholtz pitch notation is a system for naming musical notes of the Western chromatic scale. Developed by the German scientist Hermann von Helmholtz, it uses a combination of upper and lower case letters, and it is one of two formal systems for naming notes in a particular octave, the other being scientific pitch notation. J. Ellis as On the Sensations of Tone, helmholzs system is widely used by musicians across Europe and is the one used in the New Grove Dictionary. The Helmholtz scale always starts on the note C and ends at B, middle C is designated c′, therefore the octave upwards from middle C is c′–b′. Each octave may also be given a name based on the German method, for example, the octave from c′–b′ is called the one-line octave. The English multiple C notation uses repeated Cs in place of the sub-prime symbol, therefore C͵ is rendered as CC. The German method replaces the prime with a bar above the letter. Primes in subscript may be replaced with digits in subscript indicating the number of primes, for example ͵͵C or C2 or 2C, scientific pitch notation is a similar system that replaces primes and sub-primes with integers. Hence C4 in scientific notation is c′ and this diagram gives examples of the lowest and highest note in each octave, giving their name in the Helmholtz system, and the German method of octave nomenclature. Scientific pitch notation Dolmetsch Music theory online, staffs, clefs & pitch notation Octaves and the Major-Minor Tonal System
34.
Monochord
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A monochord, also known as sonometer, is an ancient musical and scientific laboratory instrument, involving one string. The term monochord is sometimes used as the class-name for any musical stringed instrument having only one string, according to the Hornbostel–Sachs system, string bows are bar zithers while monochords are traditionally board zithers. A string is fixed at both ends and stretched over a sound box, one or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. With its single string, movable bridge and graduated rule, the monochord straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason, however, music, mathematics, and astronomy were inexorably linked in the monochord. For example, when a string is open it vibrates at a particular frequency. When the length of the string is halved, and plucked, it produces a pitch an octave higher, half of this length will produce a pitch two octaves higher than the original—four times the initial frequency —and so on. Standard diatonic Pythagorean tuning is easily derived starting from superparticular ratios, /n, constructed from the first four counting numbers, the mathematics involved include the multiplication table, least common multiples, and prime and composite numbers. A bichord instrument is one, having two strings in unison for each note, such as the mandolin, with two strings one can easily demonstrate how various musical intervals sound. Parts of a monochord include a tuning peg, nut, string, moveable bridge, fixed bridge, calibration marks, belly or resonating box, instruments derived from the monochord include the guqin, dan bau, koto, vina, hurdy-gurdy, and clavichord. A monopipe is the wind instrument version of a monochord, an open pipe which can produce variable pitches. End correction must be used with this method, to achieve accuracy, the monochord is mentioned in Sumerian writings, while some attribute its invention to Pythagorus. Dolge attributes the invention of the bridge to Guido of Arezzo around 1000 CE. In 1618, Robert Fludd devised a mundane monochord that linked the Ptolemaic universe to musical intervals, was it physical intuition or a Pythagorean confidence in the importance of small whole numbers. 1,5 &10, which is music that uses pitch ratios extended to higher partials beyond the standard Pythagorean tuning system. A modern playing technique used in rock as well as contemporary classical music is 3rd bridge. This technique shares the same mechanism as used on the monochord, a sonometer is a diagnostic instrument used to measure the tension, frequency or density of vibrations. They are used in medical settings to test both hearing and bone density, a sonometer, or audiometer, is used to determine hearing sensitivity, while a clinical bone sonometer measures bone density to help determine such conditions as the risk of osteoporosis. In audiology, the device is used to test for hearing loss, the audiometer measures the ability to hear sounds at frequencies normally detectable by the human ear
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Sheet music
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Sheet music is a handwritten or printed form of music notation that uses modern musical symbols to indicate the pitches, rhythms and/or chords of a song or instrumental musical piece. The first printed sheet music made with a press was made in 1473. Sheet music is the form in which Western classical music is notated so that it can be learned and performed by solo singers or instrumentalists or musical ensembles. Many forms of traditional and popular Western music are commonly learned by singers and musicians by ear, Score is a common alternative term for sheet music, and there are several types of scores, as discussed below. Sheet music from the 20th and 21st century typically indicates the title of the song or composition on a page or cover, or on the top of the first page. If the song or piece is from a movie, Broadway musical, or opera, if the songwriter or composer is known, her or his name is typically indicated along with the title. Black market sheet music, such as illegal jazz fake books may or may not indicate the songwriter or composer, the type of musical notation varies a great deal by genre or style of music. In most classical music, the melody and accompaniment parts are notated on the lines of a staff using round note heads, the lyrics, if present, are written near the melody notes. However, music from the Baroque music era or earlier eras may have neither a tempo marking nor a dynamic indication. The singers and musicians of that era were expected to know what tempo and loudness to play or sing a song or piece due to their musical experience. In the contemporary music era, and in some cases before, composers often used their native language for tempo indications. These conventions of music notation, and in particular the use of English tempo instructions, are also used for sheet music versions of 20th. Popular music songs often indicate both the tempo and genre, slow blues or uptempo rock, pop songs often contain chord names above the staff using letter names, so that an acoustic guitarist or piano player can improvise a chordal accompaniment. In other styles of music, different musical notation methods may be used, in jazz, while most professional performers can read classical-style notation, many jazz tunes are notated using chord charts, which indicate the chord progression of a song and its form. Like popular music songs, jazz tunes often indicate both the tempo and genre, slow blues or fast bop, professional country music session musicians typically use music notated in the Nashville Number System, which indicates the chord progression using numbers. Chord charts using letter names, numbers, or Roman numerals are widely used for notating music by blues, R&B, rock music. Many guitar players and electric bass players learn songs and note tunes using tablature, tab is widely used rock music and heavy metal guitarists. Singers in many music styles learn a song using only a lyrics sheet
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