1.
Octave
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In music, an octave or perfect octave is the interval between one musical pitch and another with half or double its frequency. It is defined by ANSI as the unit of level when the base of the logarithm is two. The octave relationship is a phenomenon that has been referred to as the basic miracle of music. The most important musical scales are written using eight notes. For example, the C major scale is typically written C D E F G A B C, two notes separated by an octave have the same letter name and are of the same pitch class. Three commonly cited examples of melodies featuring the perfect octave as their opening interval are Singin in the Rain, Somewhere Over the Rainbow, the interval between the first and second harmonics of the harmonic series is an octave. The octave has occasionally referred to as a diapason. To emphasize that it is one of the intervals, the octave is designated P8. The octave above or below a note is sometimes abbreviated 8a or 8va, 8va bassa. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, the ratio of frequencies of two notes an octave apart is therefore 2,1. Further octaves of a note occur at 2n times the frequency of that note, such as 2,4,8,16, etc. and the reciprocal of that series. For example,55 Hz and 440 Hz are one and two away from 110 Hz because they are 1⁄2 and 4 times the frequency, respectively. After the unison, the octave is the simplest interval in music, the human ear tends to hear both notes as being essentially the same, due to closely related harmonics. Notes separated by a ring together, adding a pleasing sound to music. For this reason, notes an octave apart are given the note name in the Western system of music notation—the name of a note an octave above A is also A. The conceptualization of pitch as having two dimensions, pitch height and pitch class, inherently include octave circularity, thus all C♯s, or all 1s, in any octave are part of the same pitch class. Octave equivalency is a part of most advanced cultures, but is far from universal in primitive. The languages in which the oldest extant written documents on tuning are written, leon Crickmore recently proposed that The octave may not have been thought of as a unit in its own right, but rather by analogy like the first day of a new seven-day week
2.
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
3.
Acoustics
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Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of society with the most obvious being the audio. Hearing is one of the most crucial means of survival in the animal world, accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound, art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsays Wheel of Acoustics is a well accepted overview of the fields in acoustics. The word acoustic is derived from the Greek word ἀκουστικός, meaning of or for hearing, ready to hear and that from ἀκουστός, heard, audible, which in turn derives from the verb ἀκούω, I hear. The Latin synonym is sonic, after which the term used to be a synonym for acoustics. Frequencies above and below the range are called ultrasonic and infrasonic. If, for example, a string of a length would sound particularly harmonious with a string of twice the length. In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of tuning, the tones in between are then given by 16,9 for D,8,5 for E,3,2 for F,4,3 for G,6,5 for A. Aristotle understood that sound consisted of compressions and rarefactions of air which falls upon, a very good expression of the nature of wave motion. The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution, mainly Galileo Galilei but also Marin Mersenne, independently, discovered the complete laws of vibrating strings. Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne, meanwhile, Newton derived the relationship for wave velocity in solids, a cornerstone of physical acoustics. The eighteenth century saw advances in acoustics as mathematicians applied the new techniques of calculus to elaborate theories of sound wave propagation. Also in the 19th century, Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics, the twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by then in place. The first such application was Sabine’s groundbreaking work in architectural acoustics, Underwater acoustics was used for detecting submarines in the first World War
4.
Harmonic
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A harmonic is any member of the harmonic series, the divergent infinite series. Every term of the series after the first is the mean of the neighboring terms. The phrase harmonic mean likewise derives from music, the term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves, a harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the frequency, the sum of harmonics is also periodic at that frequency. On strings, harmonics that are bowed have a glassy, pure tone, harmonics may also be called overtones, partials or upper partials. In some music contexts, the harmonic, overtone and partial are used fairly interchangeably. Most acoustic instruments emit complex tones containing many individual partials, rather, a musical note is perceived as one sound, the quality or timbre of that sound being a result of the relative strengths of the individual partials. Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are long and thin. Wind instruments whose air column is open at one end, such as trumpets and clarinets. However they only produce partials matching the odd harmonics, at least in theory, the reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials, antique singing bowls are known for producing multiple harmonic partials or multiphonics. An overtone is any partial higher than the lowest partial in a compound tone, the relative strengths and frequency relationships of the component partials determine the timbre of an instrument. This chart demonstrates how the three types of names are counted, In many musical instruments, it is possible to play the upper harmonics without the note being present. In a simple case this has the effect of making the note go up in pitch by an octave, in some cases it also changes the timbre of the note. This is part of the method of obtaining higher notes in wind instruments. The extended technique of playing multiphonics also produces harmonics, on string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch
5.
Atonality
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Atonality in its broadest sense is music that lacks a tonal center, or key. The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, erialism arose partly as a means of organizing more coherently the relations used in the preserial free atonal music. Thus many useful and crucial insights about even strictly serial music depend only on such basic atonal theory, the term atonality was coined in 1907 by Joseph Marx in a scholarly study of tonality, which was later expanded into his doctoral thesis. Their music arose from what was described as the crisis of tonality between the nineteenth century and early twentieth century in classical music. The connections between harmonies were uncertain even on the lowest—chord-to-chord—level, on higher levels, long-range harmonic relationships and implications became so tenuous that they hardly functioned at all. At best, the probabilities of the style system had become obscure, at worst. The first phase, known as free atonality or free chromaticism, Works of this period include the opera Wozzeck by Alban Berg and Pierrot Lunaire by Schoenberg. This period included Bergs Lulu and Lyric Suite, Schoenbergs Piano Concerto, his oratorio Die Jakobsleiter and numerous smaller pieces, however, actual analysis of Weberns twelve-tone works has so far failed to demonstrate the truth of this assertion. One analyst concluded, following an examination of the Piano Variations. 27, that while the texture of this music may superficially resemble that of serial music. None of the patterns within separate nonpitch characteristics makes audible sense in itself, the point is that these characteristics are still playing their traditional role of differentiation. Twelve-tone technique, combined with the parametrization of Olivier Messiaen, would be taken as the inspiration for serialism, Atonality emerged as a pejorative term to condemn music in which chords were organized seemingly with no apparent coherence. In Nazi Germany, atonal music was attacked as Bolshevik and labeled as degenerate along with music produced by enemies of the Nazi regime. Many composers had their works banned by the regime, not to be played until after its collapse after World War II, after Schoenbergs death, Igor Stravinsky used the twelve-tone technique. The twelve-tone technique was preceded by Schoenbergs freely atonal pieces of 1908–1923, the twelve-tone technique was also preceded by nondodecaphonic serial composition used independently in the works of Alexander Scriabin, Igor Stravinsky, Béla Bartók, Carl Ruggles, and others. Additionally George Perle explains that, the free atonality that preceded dodecaphony precludes by definition the possibility of self-consistent, in other words, reverse the rules of the common practice period so that what was not allowed is required and what was required is not allowed. This is what was done by Charles Seeger in his explanation of dissonant counterpoint, kostka and Payne list four procedures as operational in the atonal music of Schoenberg, all of which may be taken as negative rules. Equal-interval chords are often of indeterminate root, mixed-interval chords are often best characterized by their interval content, Perle also points out that structural coherence is most often achieved through operations on intervallic cells
6.
Johann Sebastian Bach
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Johann Sebastian Bach was a German composer and musician of the Baroque period. Bachs compositions include the Brandenburg Concertos, the Goldberg Variations, the Mass in B minor and his music is revered for its technical command, artistic beauty, and intellectual depth. He is now regarded as one of the greatest composers of all time. Bach was born in Eisenach, in the duchy of Saxe-Eisenach and his father Johann Ambrosius Bach was the director of the town musicians, and all of his uncles were professional musicians. His father probably taught him to play the violin and harpsichord, apparently at his own initiative, Bach attended St. Michaels School in Lüneburg for two years. He received the title of Royal Court Composer from Augustus III in 1736, Bachs health and vision declined in 1749, and he died on 28 July 1750. Johann Sebastian Bach was born in Eisenach, the capital of the duchy of Saxe-Eisenach, in present-day Germany and he was the son of Johann Ambrosius Bach, the director of the town musicians, and Maria Elisabeth Lämmerhirt. He was the eighth and youngest child of Johann Ambrosius, who taught him violin. His uncles were all musicians, whose posts included church organists, court chamber musicians. One uncle, Johann Christoph Bach, introduced him to the organ, Bachs mother died in 1694, and his father died eight months later. The 10-year-old Bach moved in with his eldest brother, Johann Christoph Bach, there he studied, performed, and copied music, including his own brothers, despite being forbidden to do so because scores were so valuable and private and blank ledger paper of that type was costly. He received valuable teaching from his brother, who instructed him on the clavichord, also during this time he was taught theology, Latin, Greek, French and Italian at the local gymnasium. By 3 April 1700 Bach and his schoolfriend Georg Erdmann–who was two years Bachs elder–were enrolled in the prestigious St. Michaels School in Lüneburg, some two weeks travel north of Ohrdruf and their journey was probably undertaken mostly on foot. His two years there were critical in exposing Bach to a range of European culture. In addition to singing in the choir, he played the Schools three-manual organ and he came into contact with sons of aristocrats from northern Germany, sent to the highly selective school to prepare for careers in other disciplines. While in Lüneburg, Bach had access to St. Johns Church and possibly used the famous organ from 1553. His role there is unclear, but it probably included menial, non-musical duties, despite strong family connections and a musically enthusiastic employer, tension built up between Bach and the authorities after several years in the post. Bach was dissatisfied with the standard of singers in the choir and he called one of them a Zippel Fagottist
7.
Claude Debussy
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Achille-Claude Debussy, known since the 1890s as Claude-Achille Debussy or Claude Debussy, was a French composer. He and Maurice Ravel were the most prominent figures associated with Impressionist music and he was made Chevalier of the Legion of Honour in 1903. He was among the most influential composers of the late 19th and early 20th centuries, Debussys music is noted for its sensory content and frequent usage of nontraditional tonalities. The prominent French literary style of his period was known as Symbolism, Debussy, the oldest of five children, was born Achille-Claude Debussy on 22 August 1862 in Saint-Germain-en-Laye, France. His father, Manuel-Achille Debussy, owned a shop there, his mother. The family moved to Paris in 1867, but in 1870 Debussys pregnant mother fled with Claude to his aunts home in Cannes to escape the Franco-Prussian War. At the age of seven, he began lessons with an Italian violinist in his early 40s named Jean Cerutti. In 1871 he drew the attention of Marie Mauté de Fleurville, Debussy always believed her, although there is no independent evidence to support her claim. His talents soon became evident, and in 1872, at age ten, Debussy entered the Paris Conservatoire and he also became a lifelong friend of fellow student and distinguished pianist Isidor Philipp. After Debussys death, many pianists sought Philipps advice on playing his works, Debussy was experimental from the outset, favouring dissonances and intervals that were not taught at the Academy. Like Georges Bizet, he was a brilliant pianist and a sight reader. However, Debussy never once won a competition, and his personal opinion on competitions are that it is rather. The rules are taught in places called Conservatories, Art Schools, the contests, preceded by strict training, take place once a year and the umpires of the game are members of the institute —Monsieur Croche. The pieces he played in public at this time included sonata movements by Beethoven, Schumann and Weber,2, a movement from the Piano Concerto No. 1, and the Allegro de concert, during the summers of 1880,1881, and 1882, he accompanied Nadezhda von Meck, the wealthy patroness of Pyotr Ilyich Tchaikovsky, as she travelled with her family in Europe. Despite von Mecks closeness to Tchaikovsky, the Russian master appears to have had effect on Debussy. In September 1880 she sent his Danse bohémienne for Tchaikovskys perusal, a month later Tchaikovsky wrote back to her, It is a pretty piece. Not a single idea is expressed fully, the form is terribly shriveled, Debussy did not publish the piece, and the manuscript remained in the von Meck family, it was eventually sold to B
8.
Polyphony
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Within the context of the Western musical tradition, the term polyphony is usually used to refer to music of the late Middle Ages and Renaissance. Baroque forms such as fugue, which might be called polyphonic, are usually described instead as contrapuntal. In all cases the conception was probably what Margaret Bent calls dyadic counterpoint, with part being written generally against one other part. The term polyphony is also used more broadly, to describe any musical texture that is not monophonic. Such a perspective considers homophony as a sub-type of polyphony, traditional polyphony has a wide, if uneven, distribution among the peoples of the world. Most polyphonic regions of the world are in sub-Saharan Africa, Europe and it is believed that the origins of polyphony in traditional music vastly predate the emergence of polyphony in European professional music. Currently there are two approaches to the problem of the origins of vocal polyphony, the Cultural Model. Although the exact origins of polyphony in the Western church traditions are unknown,900, are usually considered the oldest extant written examples of polyphony. These treatises provided examples of two-voice note-against-note embellishments of chants using parallel octaves, fifths, rather than being fixed works, they indicated ways of improvising polyphony during performance. 1000, is the oldest extant example of notated polyphony for chant performance, European polyphony rose out of melismatic organum, the earliest harmonization of the chant. Twelfth-century composers, such as Léonin and Pérotin developed the organum that was introduced centuries earlier, the lyrics of love poems might be sung above sacred texts in the form of a trope, or the sacred text might be placed within a familiar secular melody. The oldest surviving piece of music is the English rota Sumer is icumen in. These musical innovations appeared in a context of societal change. After the first millennium, European monks decided to start translating the works of Greek philosophers into the vernacular, Western Europeans were aware of Plato, Socrates, and Hippocrates during the Middle Ages. However they had largely lost touch with the content of their surviving works because the use of Greek as a language was restricted to the lands of the Eastern Roman Empire. Once these ancient works started being translated thus becoming accessible, the philosophies had a impact on the mind of Western Europe. This sparked a number of innovations in medicine, science, art, European polyphony rose prior to, and during the period of the Western Schism. Avignon, the seat of the antipopes, was a center of secular music-making
9.
Noise in music
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In music, noise is variously described as unpitched, indeterminate, uncontrolled, loud, unmusical, or unwanted sound. Noise is an important component of the sound of the voice and all musical instruments, particularly in unpitched percussion instruments. Electronic instruments create various colours of noise, the influence of modernism in the early 20th century lead composers such as Edgar Varese to explore the use of noise-based sonorities in an orchestral setting. In the same period the Italian Futurist Luigi Russolo created a noise orchestra using instruments he called intonarumori, later in the 20th century the term noise music came to refer to works consisting primarily of noise-based sound. In more general usage, noise is any unwanted sound or signal, in this sense, even sounds that would be perceived as musically ordinary in another context become noise if they interfere with the reception of a message desired by the receiver. In conventional musical practices sounds that are considered unmusical tend to be treated as noise, oscillations and Waves defines noise as irregular vibrations of an object, in contrast to the periodical, patterned structure of music. More broadly, electrical engineering professor Bart Kosko in the chapter of his book Noise defines noise as a signal we dont like. Composer and music educator R. Murray Schafer divided noise into four categories, Unwanted noise, unmusical sound, any system. By all accounts there is no single and intercultural universal concept defining what music might be, Musical tones produced by the human voice and all acoustical musical instruments incorporate noises in varying degrees. Most consonants in speech are characterised by distinctive noises. When they are not excessive, listeners make themselves deaf to these noises by ignoring them, many unpitched percussion instruments, such as the snare drum or maracas, make use of the presence of random sounds or noise to produce a sound without any perceived pitch. Unpitched percussion is used to maintain a rhythm or to provide accents. Although percussion instruments were generally rather unimportant in ancient Greek music, the former required instruments providing a sharply defined rhythm, particularly krotala and kymbala. An altogether darker picture of the function of noise music is painted by Livy in Ab urbe condita xxxix. 8–10. He describes a Greek of mean condition, a low operator in sacrifices, and a soothsayer. A teacher of secret mysteries who imported to Etruria and then to Rome a Dionysian cult which attracted a large following, all manner of debaucheries were practised by this cult, including rape and secret murders. The bodies could not even be found for burial, a Tahitian traditional dance genre dating back to before the first contact with European explorers is ʻōteʻa, danced by a group of men accompanied solely by a drum ensemble. The drums consist of a drum called tō‘ere, a single-headed upright drum called fa‘atete, a single-headed hand drum called pahu tupa‘i rima
10.
Noise music
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Noise music is a category of music that is characterised by the expressive use of noise within a musical context. This type of music tends to challenge the distinction that is made in conventional musical practices between musical and non-musical sound, Noise music includes a wide range of musical styles and sound-based creative practices that feature noise as a primary aspect. Some of the music can feature acoustically or electronically generated noise, there may also be emphasis on high volume levels and lengthy, continuous pieces. More generally noise music may contain aspects such as improvisation, extended technique, cacophony, in many instances, conventional use of melody, harmony, rhythm or pulse is dispensed with. Contemporary noise music is associated with extreme volume and distortion. In the domain of experimental rock, examples include Jimi Hendrixs use of feedback, Lou Reeds Metal Machine Music, genres such as industrial, industrial techno, lo-fi music, black metal, sludge metal, and glitch music employ noise-based materials. According to Danish noise and music theorist Torben Sangild, one definition of noise in music is not possible. According to Murray Schafer there are four types of noise, unwanted noise, unmusical sound, any sound. Definitions regarding what is considered noise, relative to music, have changed over time, ben Watson, in his article Noise as Permanent Revolution, points out that Ludwig van Beethovens Grosse Fuge sounded like noise to his audience at the time. Indeed, Beethovens publishers persuaded him to remove it from its setting as the last movement of a string quartet. He did so, replacing it with a sparkling Allegro and he defines noise at different times as intrusive, unwanted, lacking skill, not being appropriate and a threatening emptiness. He traces these trends starting with 18th-century concert hall music, Hegarty contends that it is John Cages composition 433, in which an audience sits through four and a half minutes of silence, that represents the beginning of noise music proper. Writing about Japanese noise music, Hegarty suggests that it is not a genre, but it is also a genre that is multiple, Japanese noise music can come in all styles, referring to all other genres. But crucially asks the question of genre—what does it mean to be categorized, in Noise, The Political Economy of Music, Jacques Attali explores the relationship between noise music and the future of society. He indicates that noise in music is a predictor of social change, like much of modern and contemporary art, noise music takes characteristics of the perceived negative traits of noise mentioned below and uses them in aesthetic and imaginative ways. In common use, the word noise means unwanted sound or noise pollution, Noise can block, distort, or change the meaning of a message in both human and electronic communication. White noise is a signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency, White noise is considered analogous to white light which contains all frequencies
11.
Chord (music)
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A chord, in music, is any harmonic set of pitches consisting of two or more notes that are heard as if sounding simultaneously. In everyday use by musical ensembles such as bands and orchestras, however, the notes of a chord do not have to be played together at the same time, arpeggios and broken chords may, for many practical and theoretical purposes, also constitute chords. Other chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in classical music, jazz. Triads commonly found in the Western classical tradition are major and minor chords, the descriptions major, minor, augmented, and diminished are referred to collectively as chordal quality. Chords are also classified by their root note—for instance, a C major triad consists of the pitch classes C, E. While most chords have at least three notes, power chords, which are used in rock music, particularly in hard rock. An ordered series of chords is called a chord progression, one example of a widely used chord progression in Western traditional music and blues is the 12 bar blues progression, the simplest versions of which include tonic, subdominant and dominant chords. To describe this, Western music theory has developed the practice of numbering chords using Roman numerals which represent the number of steps up from the tonic note of the scale. Common ways of notating or representing chords in Western music include Roman numerals, figured bass, macro symbols, the chords in a song or piece are also given names which refer to their function. The chord built on the first note of a scale is called the tonic chord. The chord built on the note of a major scale is called the subdominant chord. The chord built on the degree of the major scale is called the dominant chord. There are names for the built on every note of the major scale. Chords can be played on instruments, including piano, pipe organ, guitar. Chords can also be performed when multiple musicians play together in an ensemble or when multiple singers sing in a choir. The English word chord derives from Middle English cord, a shortening of accord in the sense of agreement and later. A sequence of chords is known as a progression or harmonic progression. These are frequently used in Western music, a chord progression aims for a definite goal of establishing a tonality founded on a key, root or tonic chord
12.
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
13.
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
14.
Music theory
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Music theory is the study of the practices and possibilities of music. The term is used in three ways in music, though all three are interrelated. The first is what is otherwise called rudiments, currently taught as the elements of notation, of key signatures, of time signatures, of rhythmic notation, Theory in this sense is treated as the necessary preliminary to the study of harmony, counterpoint, and form. The second is the study of writings about music from ancient times onwards, Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. However, this medieval discipline became the basis for tuning systems in later centuries, Music theory as a practical discipline encompasses the methods and concepts composers and other musicians use in creating music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, musical instruments, and other artifacts. In ancient and living cultures around the world, the deep and long roots of music theory are clearly visible in instruments, oral traditions, and current music making. Many cultures, at least as far back as ancient Mesopotamia and ancient China, have also considered music theory in more formal ways such as written treatises, in modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Etymologically, music theory is an act of contemplation of music, from the Greek θεωρία, a looking at, viewing, contemplation, speculation, theory, also a sight, a person who researches, teaches, or writes articles about music theory is a music theorist. University study, typically to the M. A. or Ph. D level, is required to teach as a music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by Western music notation, comparative, descriptive, statistical, and other methods are also used. See for instance Paleolithic flutes, Gǔdí, and Anasazi flute, several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these dates from before 1500 BCE. Further, All the Mesopotamian texts are united by the use of a terminology for music that, much of Chinese music history and theory remains unclear. The earliest texts about Chinese music theory are inscribed on the stone and they include more than 2800 words describing theories and practices of music pitches of the time. The bells produce two intertwined pentatonic scales three tones apart with additional pitches completing the chromatic scale, Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed, the Lüshi chunqiu from about 239 BCE recalls the legend of Ling Lun. On order of the Yellow Emperor, Ling Lun collected twelve bamboo lengths with thick, blowing on one of these like a pipe, he found its sound agreeable and named it huangzhong, the Yellow Bell
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Voice leading
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Voice leading practices can be codified into rules for pedagogical purposes. In these settings, voice leading is often synonymous with part writing, David Huron has demonstrated that many of the standard pedagogical rules have a basis in perceptual principles. A more nuanced view of voice leading principles is found in the theories of Heinrich Schenker, Schenkerian analysis examines how the outer voices work together to establish form in common-practice music. See Linear progression for an example from Beethovens Sonata op,109. that popular music has no voice leading in it, the largest amount of popular music is simply conceived with chords as blocks of information, and melodies are layered on top of the chords. The score in the following example reproduces the first four measures of Johann Sebastian Bachs Preludium in C major from the 1722 keyboard work Well Tempered Keyboard, letter presents the original score while and present reductions intended to clarify the harmony and implied voice leading, respectively. The four chords result from the fact that not every voice moves at the same time. To see this, look at the highest note of each chord - E, F, F, and E - this corresponds to 1), the second highest note of each chord is C, D, D, and C - corresponding to 2) etc. Voice leading developed as an independent concept when Heinrich Schenker stressed its importance in free counterpoint and he wrote, All musical technique is derived from two basic ingredients, voice leading and the progression of scale degrees. Of the two, voice leading is the earlier and the original element. The theory of voice leading is to be presented here as a discipline unified in itself, on a chord-to-chord level, common-practice conventions dictate that lines should be smooth and independent. In other words, the practical, technical, and aesthetic considerations surrounding voice leading reinforce one another, move each voice the shortest distance possible. One of the conventions of common-practice part-writing is that, between successive harmonies, voices should avoid leaps and retain common tones as much as possible. This principle was discussed among 17th- and 18th-century musicians as a rule of thumb. For example, Rameau taught one cannot pass from one note to another, in the 19th century, as music pedagogy became a more theoretical discipline in some parts of Europe, the 18th-century rule of thumb became codified into a more strict definition. The parts which do not remain, follow the law of the shortest way and this rule was taught by Bruckner to Schoenberg and Schenker, who both had followed his classes in Vienna. This kind of line manifests what is called melodic fluency, Schenker attributed the rule to Cherubini, but this is the result of a somewhat inexact German translation. Cherubini only said that conjunct movement should be preferred, franz Stoepel, the German translator, used the expression Fließender Gesang to translate mouvement conjoint. The concept of Fließender Gesang is a concept of German counterpoint theory
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Dominant seventh chord
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In music theory, a dominant seventh chord, or major minor seventh chord, is a chord composed of a root, major third, perfect fifth, and minor seventh. It can be viewed as a major triad with an additional minor seventh. When using popular-music symbols, it is denoted by adding a superscript 7 after the letter designating the chord root, the dominant seventh is found almost as often as the dominant triad. In Roman numerals it is represented as V7, the chord can be represented by the integer notation. Of all the chords, perhaps the most important is the dominant seventh. It was the first seventh chord to appear regularly in classical music, the name comes from the fact that it occurs naturally in the seventh chord built upon the dominant of a given major diatonic scale. Take for example the C major scale, The note G is the dominant degree of C major—its fifth note, the note F is a minor seventh from G, and it is also called the dominant seventh with respect to G. The function of the dominant seventh chord is to drive to or resolve to the note or chord. The demand of the V7 for resolution is, to our ears, the dominant seventh is, in fact, the central propulsive force in our music, it is unambiguous and unequivocal. This basic dominant seventh chord is useful to composers because it both a major triad and the interval of a tritone. The major triad confers a very strong sound, the tritone is created by the co-occurrence of the third degree and seventh degree. In a diatonic context, the third of the chord is the leading-tone of the scale, the seventh of the chord acts as an upper leading-tone to the third of the scale. Because of this usage, it also quickly became an easy way to trick the listeners ear with a deceptive cadence. The dominant seventh may work as part of a progression, preceded by the supertonic. S. A. and Loggins. Chuck Berrys Rock And Roll Music uses the dominant seventh on I, IV, the dominant seventh is enharmonically equivalent to the German sixth, causing the chords to be spelled enharmonically, for example the German sixth G♭–B♭–D♭–E and the dominant seventh F♯–A♯–C♯–E. The dominant seventh is used to approximate a Harmonic seventh chord. Others include 20,25,30,36 Play, found on I, renaissance composers decided in terms of intervals rather than chords, however, certain dissonant sonorities suggest that the dominant seventh chord occurred with some frequency. Monteverdi and other early baroque composers begin to treat the V7 as a chord as part of the introduction of functional harmony, the V7 was in constant use during the classical period, with similar treatment to that of the baroque
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Cadence (music)
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In Western musical theory, a cadence is a melodic or harmonic configuration that creates a sense of resolution. A harmonic cadence is a progression of two chords that concludes a phrase, section, or piece of music, a rhythmic cadence is a characteristic rhythmic pattern that indicates the end of a phrase. A cadence is labeled more or less weak or strong depending on its sense of finality, harmonic rhythm plays an important part in determining where a cadence occurs. Cadences are strong indicators of the tonic or central pitch of a passage or piece, edward Lowinsky proposed that the cadence was the cradle of tonality. In music of the common practice period, cadences are divided into four types according to their progression, authentic, plagal, half. Typically, phrases end on authentic or half cadences, and the terms plagal, each cadence can be described using the Roman numeral system of naming chords, Authentic cadence, V to I. A seventh above the root is added to create V7. The The Harvard Concise Dictionary of Music and Musicians says, This cadence is a microcosm of the tonal system and it is virtually obligatory as the final structural cadence of a tonal work. A perfect cadence is a progression from V to I in major keys and this is generally the strongest type of cadence and often found at structurally defining moments. This strong cadence achieves complete harmonic and melodic closure and it has to be noted that Beethoven in particular gets so much mileage out of this cadence as for it to become one of his most characteristic and recognizable musical thumbprints. The Diabelli Variations and the C major climax of the movement of the Opus 132 String Quartet - even though it is described as being in Lydian mode on F - are two powerful examples. Imperfect authentic cadence, best divided into three categories,1. Root position IAC, similar to a PAC, but the highest voice is not the tonic, inverted IAC, similar to a PAC, but one or both chords is inverted. Leading tone IAC, the V chord is replaced with the viio/subV chord, evaded cadence, V42 to I6. Because the seventh must fall step wise, it forces the cadence to resolve to the less stable first inversion chord, usually to achieve this a root position V changes to a V42 right before resolution, thereby evading the cadence. Half cadence, any cadence ending on V, whether preceded by II, ii, vi, IV, with the addition of motion in the upper part to the sixth degree, it becomes the Landini cadence. Lydian cadence, The Lydian half-cadence is similar to the Phrygian-half, involving iv6-V in the minor, the difference is that in the Lydian-half, the whole iv6 is raised by a half-step. In other words, the Phrygian-half begins with the first chord built on scale degree P4, Burgundian cadences, Became popular in Burgundian music
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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
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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
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Major third
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In classical music from Western culture, a third is a musical interval encompassing three staff positions, and the major third is a third spanning four semitones. Along with the third, the major third is one of two commonly occurring thirds. It is qualified as major because it is the larger of the two, the major third spans four semitones, the third three. The major third may be derived from the series as the interval between the fourth and fifth harmonics. The major scale is so named because of the presence of this interval between its tonic and mediant scale degrees, the major chord also takes its name from the presence of this interval built on the chords root. The older concept of a made a dissonantly wide major third with the ratio 81,64. The septimal major third is 9,7, the major third is 14,11. A helpful way to recognize a third is to hum the first two notes of Kumbaya or of When the Saints Go Marching In. A descending major third is heard at the starts of Goodnight, Ladies and Swing Low, in equal temperament three major thirds in a row are equal to an octave. This is sometimes called the circle of thirds, in just intonation, however, three 5,4 major thirds are less than an octave. For example, three 5,4 major thirds from C is B♯, the difference between this just-tuned B♯ and C, like that between G♯ and A♭, is called a diesis, about 41 cents. The major third is classed as an imperfect consonance and is considered one of the most consonant intervals after the unison, octave, perfect fifth, a diminished fourth is enharmonically equivalent to a major third. For example, B–D♯ is a third, but if the same pitches are spelled B and E♭. B–E♭ occurs in the C harmonic minor scale, the major third is used in guitar tunings. For the standard tuning, only the interval between the 3rd and 2nd strings is a third, each of the intervals between the other pairs of consecutive strings is a perfect fourth. In an alternative tuning, the tuning, each of the intervals are major thirds. Decade, compound just major third Ear training List of meantone intervals Doubling the cube, 21/3 = 3√2
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Minor sixth
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In classical music from Western culture, a sixth is a musical interval encompassing six staff positions, and the minor sixth is one of two commonly occurring sixths. It is qualified as minor because it is the smaller of the two, the minor sixth spans eight semitones, the major sixth nine. For example, the interval from A to F is a sixth, as the note F lies eight semitones above A. Diminished and augmented sixths span the same number of staff positions, in equal temperament, the minor sixth is enharmonically equivalent to the augmented fifth. It occurs in first inversion major and dominant seventh chords and second inversion minor chords, the ratios of both major and minor sixths are corresponding numbers of the Fibonacci sequence,5 and 8 for a minor sixth and 3 and 5 for a major. The 11,7 undecimal minor sixth is 782.49 cents, in Pythagorean tuning, the minor sixth is the ratio 128,81, or 792.18 cents. In just intonation, the sixth is classed as a consonance of the 5-limit. Any note will appear in major scales from any of its minor sixth major scale notes. Musical tuning List of meantone intervals Sixth chord Subminor sixth
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Minor third
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In the music theory of Western culture, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the third as encompassing three staff positions. The minor third is one of two commonly occurring thirds and it is called minor because it is the smaller of the two, the major third spans an additional semitone. For example, the interval from A to C is a minor third, diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones. The minor third is a skip melodically, notable examples of ascending minor thirds include the opening two notes of Greensleeves and of Light My Fire. The minor third may be derived from the series as the interval between the fifth and sixth harmonics, or from the 19th harmonic. The minor third is used to express sadness in music. It is also a quartal tertian interval, as opposed to the major thirds quintality, the minor third is also obtainable in reference to a fundamental note from the undertone series, while the major third is obtainable as such from the overtone series. The minor scale is so named because of the presence of this interval between its tonic and mediant scale degrees, minor chords too take their name from the presence of this interval built on the chords root. A minor third, in just intonation, corresponds to a ratio of 6,5 or 315.64 cents. In an equal tempered tuning, a third is equal to three semitones, a ratio of 21/4,1, or 300 cents,15.64 cents narrower than the 6,5 ratio. If a minor third is tuned in accordance with the fundamental of the series, the result is a ratio of 19,16. The 12-TET minor third more closely approximates the 19-limit minor third 16,19 Play with only 2.49 cents error. Other pitch ratios are given related names, the minor third with ratio 7,6. The minor third is classed as an imperfect consonance and is considered one of the most consonant intervals after the unison, octave, perfect fifth, instruments in A – most commonly the A clarinet, sound a minor third lower than the written pitch. In music theory, a semiditone is the interval 32,27 and it is the minor third in Pythagorean tuning. The 32,27 Pythagorean minor third arises in the C major scale between D and F, Play It can be thought of as two octaves minus three justly tuned fifths. It is narrower than a justly tuned minor third by a syntonic comma, musical tuning List of meantone intervals Pythagorean interval
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Major sixth
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In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions, and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the larger of the two, the major sixth spans nine semitones. Its smaller counterpart, the sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth and its a sixth because it encompasses six note letter names and six staff positions. Its a major sixth, not a sixth, because the note A lies nine semitones above C. Diminished and augmented sixths span the same number of letter names and staff positions. A commonly cited example of a melody featuring the major sixth as its opening is My Bonnie Lies Over the Ocean. The major sixth is one of the consonances of common practice music, along with the unison, octave, perfect fifth, major and minor thirds, minor sixth, in just intonation, the major sixth is classed as a consonance of the 5-limit. Assuming close-position voicings for the examples, the major sixth occurs in a first inversion minor triad, a second inversion major triad. It also occurs in the second and third inversions of a dominant seventh chord, the septimal major sixth is approximated in 53 tone equal temperament by an interval of 41 steps or 928 cents. Many intervals in a various tuning systems qualify to be called major sixth, the following examples are sorted by increasing width. In just intonation, the most common major sixth is the ratio of 5,3. In 12-tone equal temperament, a sixth is equal to nine semitones, exactly 900 cents. The 27,16 Pythagorean major sixth arises in the C Pythagorean major scale between F and D, as well as between C and A, G and E, and D and B. Play The septimal major sixth is approximated in 53-tone equal temperament by an interval of 41 steps, giving a frequency ratio of the root of 2 over 1. Another just major sixth is the 12,7 septimal major sixth or supermajor sixth of approximately 933 cents, the nineteenth subharmonic is a major sixth, A = 32/19 =902.49 cents. Musical tuning list of meantone intervals sixth chord Duckworth, William, in Sound and Light, La Monte Young, Marian Zazeela, edited by William Duckworth and Richard Fleming, p.167. Lewisburg, Bucknell University Press, London and Cranbury, NJ, Associated University Presses
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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
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Pythagoras
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Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and the putative founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written centuries after he lived. He was born on the island of Samos, and travelled, visiting Egypt and Greece, around 530 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild. In 520 BC, he returned to Samos, Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a mathematician and scientist and is best known for the Pythagorean theorem which bears his name. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues, some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato. Burkert states that Aristoxenus and Dicaearchus are the most important accounts, Aristotle had written a separate work On the Pythagoreans, which is no longer extant. However, the Protrepticus possibly contains parts of On the Pythagoreans and his disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus had written on the same subject. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, while adding some legendary accounts. Herodotus, Isocrates, and other writers agree that Pythagoras was the son of Mnesarchus and born on the Greek island of Samos. His father is said to have been a gem-engraver or a wealthy merchant, a late source gives his mothers name as Pythais. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates, at the age of 40, around 530 BC he arrived in the Greek colony of Croton in what was then Magna Graecia. There he founded his own school the members of which he engaged to a disciplined. He furthermore aquired some political influence, on Greeks and non-Greeks of the region, following a conflict with the neighbouring colony of Sybaris, internal discord drove most of the Pythagoreans out of Croton. Pythagoras left the city before the outbreak of civil unrest and moved to Metapontum, after his death, his house was transformed into a sanctuary of Demeter, out of veneration for the philosopher, by the local population. In ancient sources there was disagreement and inconsistency about the late life of Pythagoras. His tomb was shown at Metapontum in the time of Cicero, according to Walter Burkert, Most obvious is the contradiction between Aristoxenus and Dicaearchus, regarding the catastrophe that overwhelmed the Pythagorean society
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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
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Musical tuning
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In music, there are two common meanings for tuning, Tuning practice, the act of tuning an instrument or voice. Tuning systems, the systems of pitches used to tune an instrument. Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones, Tuning is usually based on a fixed reference, such as A =440 Hz. Out of tune refers to a pitch/tone that is too high or too low in relation to a given reference pitch. While an instrument might be in relative to its own range of notes. Some instruments become out of tune with damage or time and must be readjusted or repaired, different methods of sound production require different methods of adjustment, Tuning to a pitch with ones voice is called matching pitch and is the most basic skill learned in ear training. Turning pegs to increase or decrease the tension on strings so as to control the pitch, instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the violin can be tuned manually. Modifying the length or width of the tube of an instrument, brass instrument, pipe, bell. The sounds of instruments such as cymbals are inharmonic—they have irregular overtones not conforming to the harmonic series. Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other, a tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used. Symphony orchestras and concert bands tend to tune to an A or a B♭, respectively, interference beats are used to objectively measure the accuracy of tuning. As the two approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected, for other intervals, this is dependent on the tuning system being used. Harmonics may be used to facilitate tuning of strings that are not themselves tuned to the unison, for example, lightly touching the highest string of a cello at the middle while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the fifth between the fundamentals of the two strings. In music, the open string refers to the fundamental note of the unstopped. The strings of a guitar are tuned to fourths, as are the strings of the bass guitar. Violin, viola, and cello strings are tuned to fifths, however, non-standard tunings exist to change the sound of the instrument or create other playing options
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Timbre
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The physical characteristics of sound that determine the perception of timbre include spectrum and envelope. Singers and instrumental musicians can change the timbre of the music they are singing/playing by using different singing or playing techniques, for example, a violinist can use different bowing styles or play on different parts of the string to obtain different timbres. On electric guitar and electric piano, performers can change the timbre using effects units, in simple terms, timbre is what makes a particular musical sound have a different sound from another, even when they have the same pitch and loudness. For instance, it is the difference in sound between a guitar and a playing the same note at the same volume. Experienced musicians are able to distinguish between different instruments of the type based on their varied timbres, even if those instruments are playing notes at the same pitch. Tone quality and tone color are synonyms for timbre, as well as the attributed to a single instrument. However, the texture can also refer to the type of music, such as multiple. The sound of an instrument may be described with words such as bright, dark, warm, harsh. There are also colors of noise, such as pink and white, in visual representations of sound, timbre corresponds to the shape of the image. The Acoustical Society of America Acoustical Terminology definition 12, Timbre has been called. the psychoacousticians multidimensional waste-basket category for everything that cannot be labeled pitch or loudness. Many commentators have attempted to decompose timbre into component attributes, the richness of a sound or note a musical instrument produces is sometimes described in terms of a sum of a number of distinct frequencies. The lowest frequency is called the frequency, and the pitch it produces is used to name the note. The dominant frequency is the frequency that is most heard, for example, the dominant frequency for the transverse flute is double the fundamental frequency. Other significant frequencies are called overtones of the frequency, which may include harmonics. Harmonics are whole number multiples of the frequency, such as ×2, ×3, ×4. There are also sometimes subharmonics at whole number divisions of the fundamental frequency, most instruments produce harmonic sounds, but many instruments produce partials and inharmonic tones, such as cymbals and other indefinite-pitched instruments. When the tuning note in an orchestra or concert band is played, each instrument in the orchestra or concert band produces a different combination of these frequencies, as well as harmonics and overtones. The sound waves of the different frequencies overlap and combine, the timbre of a sound is also greatly affected by the following aspects of its envelope, attack time and characteristics, decay, sustain, release and transients
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Critical band
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Roughly, the critical band is the band of audio frequencies within which a second tone will interfere with the perception of the first tone by auditory masking. Critical bands are closely related to auditory masking phenomena – reduced audibility of a sound signal when in the presence of a second signal of higher intensity within the same critical band. Masking phenomena have wide implications, ranging from a relationship between loudness and intensity to sound compression algorithms. Filters are used in many aspects of audiology and psychoacoustics including the peripheral auditory system, a filter is a device that boosts certain frequencies and attenuates others. In particular, a filter allows a range of frequencies within the bandwidth to pass through while stopping those outside the cut-off frequencies. The shape and organization of the membrane means that different frequencies resonate particularly strongly at different points along the membrance. This leads to an organisation of the sensitivity to frequency ranges along the membrane. They are non-linear, level-dependent and the bandwidth decreases from the base to apex of the cochlea as the tuning on the basilar membrane changes from high to low frequency, the bandwidth of the auditory filter is called the critical bandwidth, as first suggested by Fletcher. If a signal and masker are presented simultaneously then only the masker frequencies falling within the critical bandwidth contribute to masking of the signal, the larger the critical bandwidth the lower the signal-to-noise ratio and the more the signal is masked. Another concept associated with the filter is the equivalent rectangular bandwidth. The ERB shows the relationship between the filter, frequency, and the critical bandwidth. An ERB passes the same amount of energy as the auditory filter it corresponds to and shows how it changes with input frequency. At low sound levels, the ERB is approximated by the following equation according to Glasberg and Moore, ERB =24.7 * Where the ERB is in Hz and it is thought that each ERB is the equivalent of around 0. 9mm on the basilar membrane. The ERB can be converted into a scale that relates to frequency, one filter type used to model the auditory filters is the gammatone filter. The shapes of auditory filters are found by analysis of psychoacoustic tuning, psychoacoustic tuning curves can be measured using the notched-noise method. This form of measurement can take a considerable amount of time, in the notched-noise method the subject is presented with a notched noise as the masker and a sinusoid as the signal. Notched noise is used as a masker to prevent the subject hearing beats that occur if a sinusoidal masker is used, the notched noise is noise with a notch around the frequency of the signal the subject is trying to detect, and contains noise within a certain bandwidth. The bandwidth of the changes and the masked thresholds for the sinusoid are measured
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Ernst Krenek
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Ernst Krenek was an Austrian, later American, composer of Czech origin. He explored atonality and other styles and wrote a number of books, including Music Here and Now, a study of Johannes Ockeghem. Krenek wrote two pieces using the pseudonym Thornton Winsloe, Krenek was born in Vienna as Ernst Křenek as the son of a Czech soldier in the Austro-Hungarian army. He studied there and in Berlin with Franz Schreker before working in a number of German opera houses as conductor, during World War I, Krenek was drafted into the Austrian army, but he was stationed in Vienna, allowing him to go on with his musical studies. In 1922 he met Alma Mahler, widow of Gustav Mahler,2, and whom he married in March 1924. That marriage ended in divorce before its first anniversary, at the time of his marriage to Anna Mahler, Krenek was completing his Violin Concerto No. In gratitude, Krenek dedicated the concerto to Moodie, and she premiered it on 5 January 1925, krenek’s divorce from Anna Mahler became final a few days after the premiere. Krenek did not attend the premiere, but he did have an affair with Moodie and he never managed to hear her play the concerto, but he did immortalize some aspects of her personality in the character of Anita in his opera Jonny spielt auf. In 1938 Krenek moved to the United States, where he taught music at various universities and he later taught at Hamline University in Saint Paul, Minnesota from 1942 to 1947. There he met and married his wife, his student. He became an American citizen in 1945 and he later moved to Toronto, Ontario, Canada, where he taught at The Royal Conservatory of Music during the 1950s. His students included Milton Barnes, Lorne Betts, Roque Cordero, Samuel Dolin, Robert Erickson, Halim El-Dabh, Richard Maxfield, Will Ogdon and he died in Palm Springs, California, where he had lived since 1966. In 1998 Gladys Nordenstrom founded the Ernst Krenek Institute, in 2004 the private foundation moved from Vienna to Krems, after meeting Krenek in 1922, Alma Mahler asked him to complete her late husbands Symphony No.10. Krenek assisted in editing the first and third movements but went no further, in his notes to the Lev recording, dated July 1947, Krenek offered insights into the challenges of completing another composers works in general and the Schubert sonata in particular. Completing the unfinished work of a master is a very delicate task. In my opinion it can honestly be undertaken if the original fragment contains all of the main ideas of the unfinished work. Even then the artist who goes about the task will feel slightly uneasy. He is more conscious of the fact that unpredictability is one of the most jealously guarded prerogatives of genius
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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
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Resolution (music)
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Resolution in western tonal music theory is the move of a note or chord from dissonance to a consonance. Dissonance, resolution, and suspense can be used to create musical interest, where a melody or chordal pattern is expected to resolve to a certain note or chord, a different but similarly suitable note can be resolved to instead, creating an interesting and unexpected sound. A dissonance has its resolution when it moves to a consonance, when a resolution is delayed or is accomplished in surprising ways—when the composer play with our sense of expectation—a feeling of drama or suspense is created. Resolution has a basis in tonal music, since atonal music generally contains a more constant level of dissonance. The concept of resolution, and the degree to which resolution is expected, is contextual as to culture and this is an example of a suspended chord. In reference to chords and progressions for example, an ending with the following cadence IV-V. However, if this cadence were changed to V-I, an authentic cadence, circle of fifths Corelli clash Irregular resolution Doubling
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Harmony
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In music, harmony considers the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, this means simultaneously occurring frequencies, pitches, or chords, the study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the aspect of music, as distinguished from melodic line. In popular and jazz harmony, chords are named by their root plus various terms, in many types of music, notably baroque, romantic, modern, and jazz, chords are often augmented with tensions. A tension is an additional member that creates a relatively dissonant interval in relation to the bass. Typically, in the common practice period a dissonant chord resolves to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds, in simple words, that occurs when there is a balance between tense and relaxed moments. The term harmony derives from the Greek ἁρμονία, meaning joint, agreement, concord, from the verb ἁρμόζω, to fit together, the term was often used for the whole field of music, while music referred to the arts in general. In Ancient Greece, the term defined the combination of contrasted elements, in the Middle Ages the term was used to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to denote three pitches sounding together. Aristoxenus wrote a work entitled Harmonika Stoicheia, which is thought the first work in European history written on the subject of harmony, the underlying principle behind these texts is that harmony sanctions harmoniousness by conforming to certain pre-established compositional principles. Current dictionary definitions, while attempting to give concise descriptions, often highlight the ambiguity of the term in modern use, ambiguities tend to arise from either aesthetic considerations or from the point of view of musical texture (distinguishing between harmonic and contrapuntal. The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory and this is usually accounted for by the replacement of horizontal writing, common in the music of the Renaissance, with a new emphasis on the vertical element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation, as Carl Dahlhaus puts it, It was not that counterpoint was supplanted by harmony but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the structure of chords but also their movement, like music as a whole, harmony is a process. Descriptions and definitions of harmony and harmonic practice may show bias towards European musical traditions, pitch simultaneity in particular is rarely a major consideration. Nevertheless, emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias, the conception of musics that live in oral traditions as something composed with the use of improvisatory techniques separates them from the higher-standing works that use notation. Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition, some traditions of Western music performance, composition, and theory have specific rules of harmony. This model provides that the seventh and ninth are not dissonant
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Melody
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A melody, also tune, voice, or line, is a linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combination of pitch and rhythm, while more figuratively and it may be considered the foreground to the background accompaniment. A line or part need not be a foreground melody, melodies often consist of one or more musical phrases or motifs, and are usually repeated throughout a composition in various forms. Melodies may also be described by their melodic motion or the pitches or the intervals between pitches, pitch range, tension and release, continuity and coherence, cadence, the true goal of music—its proper enterprise—is melody. All the parts of harmony have as their purpose only beautiful melody. Therefore, the question of which is the significant, melody or harmony, is futile. Beyond doubt, the means is subordinate to the end, given the many and varied elements and styles of melody many extant explanations confine us to specific stylistic models, and they are too exclusive. Paul Narveson claimed in 1984 that more than three-quarters of melodic topics had not been explored thoroughly, melodies in the 20th century utilized a greater variety of pitch resources than ha been the custom in any other historical period of Western music. While the diatonic scale was used, the chromatic scale became widely employed. Composers also allotted a structural role to the dimensions that previously had been almost exclusively reserved for pitch. Kliewer states, The essential elements of any melody are duration, pitch, and quality, texture, for example, Jazz musicians use the term lead or head to refer to the main melody, which is used as a starting point for improvisation. Rock music, melodic music, and other forms of popular music, indian classical music relies heavily on melody and rhythm, and not so much on harmony, as the music contains no chord changes. Balinese gamelan music often uses complicated variations and alterations of a melody played simultaneously. In western classical music, composers often introduce an initial melody, or theme, classical music often has several melodic layers, called polyphony, such as those in a fugue, a type of counterpoint. Often, melodies are constructed from motifs or short melodic fragments, richard Wagner popularized the concept of a leitmotif, a motif or melody associated with a certain idea, person or place. Appropriation Hocket Parsons code, a notation used to identify a piece of music through melodic motion—the motion of the pitch up. Harvard Dictionary of Music, 2nd ed. p. 517–19, the Art of Melody, p. xix–xxx. A Textbook of Melody, A course in functional melodic analysis, a History Of Melody, Barrie and Rockliff, London
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Tonality
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Tonality is a musical system that arranges pitches or chords to induce a hierarchy of perceived relations, stabilities, and attractions. In this hierarchy, the pitch or triadic chord with the greatest stability is called the tonic. The root of the chord is considered to be the key of a piece or song. Thus a piece in which the chord is C major is said to be in the key of C. Simple folk music songs often start and end with the tonic note, the most common use of the term. is to designate the arrangement of musical phenomena around a referential tonic in European music from about 1600 to about 1910. Contemporary classical music from 1910 to the 2000s may practice or avoid any sort of harmony in almost all Western popular music remains tonal. Harmony in jazz music includes many, if not all, tonal characteristics, All harmonic idioms in popular music are tonal, and none is without function. Tonality is a system of tones in which one tone becomes the central point for the remaining tones. The other tones in a piece are all defined in terms of their relationship to the tonic. In tonality, the tonic is the tone of complete relaxation and stability, the cadence in which the dominant chord or dominant seventh chord resolves to the tonic chord plays an important role in establishing the tonality of a piece. Tonal music is music that is unified and dimensional, the term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840. According to Carl Dahlhaus, however, the term tonalité was only coined by Castil-Blaze in 1821, major-minor tonality is also called harmonic tonality, diatonic tonality, common practice tonality, functional tonality, or just tonality. This sense also applies to the tonic/dominant/subdominant harmonic harmonic constellations in the theories of Jean-Philippe Rameau as well as the 144 basic transformations of twelve-tone technique, any rational and self-contained theoretical arrangement of musical pitches, existing prior to any concrete embodiment in music. For example, Sainsbury, who had Choron translated into English in 1825, while tonality qua system constitutes a theoretical abstraction from actual music, it is often hypostatized in musicological discourse, converted from a theoretical structure into a musical reality. As a term to contrast with modal and atonal, implying that tonal music is discontinuous as a form of expression from modal music on the one hand. Musical phenomena arranged or understood in relation to a referential tonic, Musical phenomena perceived or preinterpreted in terms of the categories of tonal theories. In major and minor harmonies, the fifth is often implied. To function as a tonic, a chord must be either a major or a minor triad, dominant function requires a major-quality triad with a root a perfect fifth above the affiliated tonic and containing the leading tone of the key
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Rhythm
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Rhythm generally means a movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions. In the performance arts, rhythm is the timing of events on a scale, of musical sounds and silences that occur over time, of the steps of a dance, or the meter of spoken language. In some performing arts, such as hip hop music, the delivery of the lyrics is one of the most important elements of the style. Rhythm may also refer to visual presentation, as timed movement through space, in recent years, rhythm and meter have become an important area of research among music scholars. Recent work in these areas includes books by Maury Yeston, Fred Lerdahl and Ray Jackendoff, Jonathan Kramer, Christopher Hasty, Godfried Toussaint, William Rothstein, and Joel Lester. In Thinking and Destiny, Harold W. Percival defined rhythm as the character and meaning of thought expressed through the measure or movement in sound or form, or by written signs or words. In his television series How Music Works, Howard Goodall presents theories that human rhythm recalls the regularity with which we walk, other research suggests that it does not relate to the heartbeat directly, but rather the speed of emotional affect, which also influences heartbeat. Yet other researchers suggest that certain features of human music are widespread. The perception and abstraction of rhythmic measure is the foundation of human instinctive musical participation, Joseph Jordania recently suggested that the sense of rhythm was developed in the early stages of hominid evolution by the forces of natural selection. Plenty of animals walk rhythmically and hear the sounds of the heartbeat in the womb, some types of parrots can know rhythm. There is not a report of an animal being trained to tap, peck. For this reason, the fast-transient sounds of percussion instruments lend themselves to the definition of rhythm, Musical cultures that rely upon such instruments may develop multi-layered polyrhythm and simultaneous rhythms in more than one time signature, called polymeter. Such are the cross-rhythms of Sub-Saharan Africa and the interlocking kotekan rhythms of the gamelan, for information on rhythm in Indian music see Tala. For other Asian approaches to rhythm see Rhythm in Persian music, Rhythm in Arabian music and Usul—Rhythm in Turkish music and this consists of a series of identical yet distinct periodic short-duration stimuli perceived as points in time. It is currently most often designated as a crotchet or quarter note in western notation, faster levels are division levels, and slower levels are multiple levels. Rhythms of recurrence arise from the interaction of two levels of motion, the faster providing the pulse and the slower organizing the beats into repetitive groups. Once a metric hierarchy has been established, we, as listeners, a durational pattern that synchronises with a pulse or pulses on the underlying metric level may be called a rhythmic unit. A rhythmic gesture is any pattern that, in contrast to the rhythmic unit
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Metre (music)
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The metre of music is its rhythmic structure, the patterns of accents heard in regularly recurring measures of stressed and unstressed beats at the frequency of the musics pulse. A variety of systems exist throughout the world for organising and playing music, such as the Indian system of tala. Later music for such as the pavane and galliard consisted of musical phrases to accompany a fixed sequence of basic steps with a defined tempo. The term is not very precisely defined, macPherson preferred to speak of time and rhythmic shape, Imogen Holst of measured rhythm. This perception and abstraction of rhythmic measure is the foundation of human instinctive musical participation, rhythms of recurrence arise from the interaction of two levels of motion, the faster providing the pulse and the slower organizing the beats into repetitive groups. Once a metric hierarchy has been established, we, as listeners, a definition of musical metre requires the possibility of identifying a repeating pattern of accented pulses — a pulse-group — which corresponds to the foot in poetry. Frequently a pulse-group can be identified by taking the accented beat as the first pulse in the group, frequently metres can be broken down into a pattern of duples and triples. The level of musical organisation implied by musical metre includes the most elementary levels of musical form, metrical rhythm, measured rhythm, and free rhythm are general classes of rhythm and may be distinguished in all aspects of temporality. Measured rhythm is where each time value is a multiple or fraction of a time unit. Free rhythm is where there is neither, some music, including chant, has freer rhythm, like the rhythm of prose compared to that of verse. Some music, such as some graphically scored works since the 1950s and non-European music such as Honkyoku repertoire for shakuhachi, may be considered ametric. Senza misura is an Italian musical term for without metre, meaning to play without a beat, Metric levels may be distinguished, the beat level is the metric level at which pulses are heard as the basic time unit of the piece. Faster levels are division levels, and slower levels are multiple levels, a rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or pulses on an underlying metric level. In duple metre, each measure is divided into two beats, or a multiple thereof, for example, in the time signature 24, each measure contains two quarter-note beats, and with the time signature 68, each measure contains two dotted-quarter-note beats. Corresponding quadruple metres are 44, with 2 ×2 =4 quarter-note beats per measure, triple metre is a metre in which each measure is divided into three beats, or a multiple thereof. For example, in the time signature 34, each contains three quarter-note beats, and with a time signature of 98, each measure contains three dotted-quarter beats. Simple metre and compound metre are distinguished by the way the beats are subdivided, Simple metre or simple time is a metre in which each beat of the measure divides naturally into two equal parts. The top number in the signature will be 2,3,4,5
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Bulgaria
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Bulgaria, officially the Republic of Bulgaria, is a country in southeastern Europe. It is bordered by Romania to the north, Serbia and Macedonia to the west, Greece and Turkey to the south, with a territory of 110,994 square kilometres, Bulgaria is Europes 16th-largest country. Organised prehistoric cultures began developing on current Bulgarian lands during the Neolithic period and its ancient history saw the presence of the Thracians, Greeks, Persians, Celts, Romans, Goths, Alans and Huns. With the downfall of the Second Bulgarian Empire in 1396, its territories came under Ottoman rule for five centuries. The Russo-Turkish War of 1877–78 led to the formation of the Third Bulgarian State, the following years saw several conflicts with its neighbours, which prompted Bulgaria to align with Germany in both world wars. In 1946 it became a one-party socialist state as part of the Soviet-led Eastern Bloc, in December 1989 the ruling Communist Party allowed multi-party elections, which subsequently led to Bulgarias transition into a democracy and a market-based economy. Bulgarias population of 7.2 million people is predominantly urbanised, most commercial and cultural activities are centred on the capital and largest city, Sofia. The strongest sectors of the economy are industry, power engineering. The countrys current political structure dates to the adoption of a constitution in 1991. Bulgaria is a parliamentary republic with a high degree of political, administrative. Human activity in the lands of modern Bulgaria can be traced back to the Paleolithic, animal bones incised with man-made markings from Kozarnika cave are assumed to be the earliest examples of symbolic behaviour in humans. Organised prehistoric societies in Bulgarian lands include the Neolithic Hamangia culture, Vinča culture, the latter is credited with inventing gold working and exploitation. Some of these first gold smelters produced the coins, weapons and jewellery of the Varna Necropolis treasure and this site also offers insights for understanding the social hierarchy of the earliest European societies. Thracians, one of the three primary groups of modern Bulgarians, began appearing in the region during the Iron Age. In the late 6th century BC, the Persians conquered most of present-day Bulgaria, and kept it until 479 BC. After the division of the Roman Empire in the 5th century the area fell under Byzantine control, by this time, Christianity had already spread in the region. A small Gothic community in Nicopolis ad Istrum produced the first Germanic language book in the 4th century, the first Christian monastery in Europe was established around the same time by Saint Athanasius in central Bulgaria. From the 6th century the easternmost South Slavs gradually settled in the region, in 680 Bulgar tribes under the leadership of Asparukh moved south across the Danube and settled in the area between the lower Danube and the Balkan, establishing their capital at Pliska
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Serbia
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Serbia, officially the Republic of Serbia, is a sovereign state situated at the crossroads of Central and Southeast Europe, covering the southern part of the Pannonian Plain and the central Balkans. Relative to its territory, it is a diverse country distinguished by a transitional character, situated along cultural, geographic, climatic. Serbia numbers around 7 million residents, and its capital, Belgrade, following the Slavic migrations to the Balkans from the 6th century onwards, Serbs established several states in the early Middle Ages. The Serbian Kingdom obtained recognition by Rome and the Byzantine Empire in 1217, in the early 19th century, the Serbian Revolution established the nation-state as the regions first constitutional monarchy, which subsequently expanded its territory. During the breakup of Yugoslavia, Serbia formed a union with Montenegro which dissolved peacefully in 2006, in 2008 the parliament of the province of Kosovo unilaterally declared independence, with mixed responses from the international community. Serbia is a member of organizations such as the UN, CoE, OSCE, PfP, BSEC. An EU membership candidate since 2012, Serbia has been negotiating its EU accession since January 2014, the country is acceding to the WTO and is a militarily neutral state. Serbia is an income economy with dominant service sector, followed by the industrial sector. The country ranks high on the Social Progress Index as well as the Global Peace Index, relatively high on the Human Development Index, located at the crossroads between Central and Southern Europe, Serbia is found in the Balkan peninsula and the Pannonian Plain. Serbia lies between latitudes 41° and 47° N, and longitudes 18° and 23° E. The country covers a total of 88,361 km2, which places it at 113th place in the world, with Kosovo excluded, the area is 77,474 km2. Its total border length amounts to 2,027 km, all of Kosovos border with Albania, Macedonia and Montenegro are under control of the Kosovo border police. The Pannonian Plain covers the third of the country while the easternmost tip of Serbia extends into the Wallachian Plain. The terrain of the part of the country, with the region of Šumadija at its heart. Mountains dominate the third of Serbia. Dinaric Alps stretch in the west and the southwest, following the flow of the rivers Drina, the Carpathian Mountains and Balkan Mountains stretch in a north–south direction in eastern Serbia. Ancient mountains in the southeast corner of the country belong to the Rilo-Rhodope Mountain system, elevation ranges from the Midžor peak of the Balkan Mountains at 2,169 metres to the lowest point of just 17 metres near the Danube river at Prahovo. The largest lake is Đerdap Lake and the longest river passing through Serbia is the Danube, the climate of Serbia is under the influences of the landmass of Eurasia and the Atlantic Ocean and Mediterranean Sea
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Bosnia and Herzegovina
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Bosnia and Herzegovina, sometimes called Bosnia-Herzegovina, and, in short, often known informally as Bosnia, is a country in Southeastern Europe located on the Balkan Peninsula. Sarajevo is the capital and largest city, in the central and eastern interior of the country the geography is mountainous, in the northwest it is moderately hilly, and the northeast is predominantly flatland. The inland is a larger region and has a moderate continental climate, with hot summers and cold. The southern tip of the country has a Mediterranean climate and plain topography, Bosnia and Herzegovina is a region that traces permanent human settlement back to the Neolithic age, during and after which it was populated by several Illyrian and Celtic civilizations. Culturally, politically, and socially, the country has a rich history, the Ottomans brought Islam to the region, and altered much of the cultural and social outlook of the country. This was followed by annexation into the Austro-Hungarian Monarchy, which lasted up until World War I. In the interwar period, Bosnia was part of the Kingdom of Yugoslavia and after World War II, following the dissolution of Yugoslavia, the country proclaimed independence in 1992, which was followed by the Bosnian War, lasting until late 1995. The country is home to three ethnic groups or, officially, constituent peoples, as specified in the constitution. Bosniaks are the largest group of the three, with Serbs second and Croats third, a native of Bosnia and Herzegovina, regardless of ethnicity, is identified in English as a Bosnian. The terms Herzegovinian and Bosnian are maintained as a rather than ethnic distinction. Moreover, the country was simply called Bosnia until the Austro-Hungarian occupation at the end of the 19th century, Bosnia and Herzegovina has a bicameral legislature and a three-member Presidency composed of a member of each major ethnic group. The Federation of Bosnia and Herzegovina is itself complex and consists of 10 cantons, additionally, the country has been a member of the Council of Europe since April 2002 and a founding member of the Mediterranean Union upon its establishment in July 2008. The name is believed to have derived from the hydronym of the river Bosna coursing through the Bosnian heartland. According to philologist Anton Mayer the name Bosna could be derived from Illyrian Bass-an-as which would be a diversion of the Proto-Indo-European root bos or bogh, meaning the running water. According to English medievalist William Miller the Slavic settlers in Bosnia adapted the Latin designation Basante, to their own idiom by calling the stream Bosna, the name Herzegovina originates from Bosnian magnate Stephen Vukčić Kosačas title, Herceg of Hum and the Coast. Hum, formerly Zahumlje, was a medieval principality that was conquered by the Bosnian Banate in the first half of the 14th century. Bosnia is located in the western Balkans, bordering Croatia to the north and west, Serbia to the east and it has a coastline about 20 kilometres long surrounding the city of Neum. It lies between latitudes 42° and 46° N, and longitudes 15° and 20° E, the countrys name comes from the two regions Bosnia and Herzegovina, which have a very vaguely defined border between them
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Albania
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Albania, officially the Republic of Albania, is a country in Southeastern Europe. It has a population of 3.03 million as of 2016, Tirana is the nations capital and largest city, followed by Durrës and Vlorë. The country has a coastline on the shore of the Mediterranean Sea, the Adriatic Sea to the west. Albania is less than 72 km from Italy, across the Strait of Otranto which connects the Adriatic Sea to the Ionian Sea. In antiquity, the area of Albania was home to several Illyrian, Thracian. After the Illyrian Wars, it part of the Roman provinces of Dalmatia, Macedonia and Moesia Superior. In 1190, the first Albanian state, the Principality of Arbanon was established by archon Progon in the region of Krujë, the territory of Albania was conquered by the Ottoman Empire in the 15th century, of which it remained part of for the next five centuries. After the collapse of the Ottoman Empire in Europe, following the Balkan Wars, the Kingdom of Albania was invaded by Italy in 1939, which formed Greater Albania, before becoming a Nazi German protectorate in 1943. The following year, a socialist Peoples Republic was established under the leadership of Enver Hoxha, Albania experienced widespread social and political transformations in the communist era, as well as isolation from much of the international community. In 1991, the Socialist Republic was dissolved and the Republic of Albania was established, Albania is a democratic and developing country with an upper-middle income economy. The service sector dominates the economy, followed by the industrial. After the fall of communism in Albania, Free-market reforms have opened the country to foreign investment, especially in the development of energy, Albania has a high HDI and provides universal health care system and free primary and secondary education to its citizens. Albania is a member of the United Nations, NATO, WTO, World Bank, the Council of Europe, the OSCE and it is also an official candidate for membership in the European Union. Albania is one of the members of the Energy Community, Organization of the Black Sea Economic Cooperation. It is home to the largest lake in Southern Europe and one of the oldest lakes in Europe, Albania is the Medieval Latin name of the country. The name may have a continuation in the name of a settlement called Albanon and Arbanon. During the Middle Ages, the Albanians called their country Arbëri or Arbëni, Albanians today call their country Shqipëri. As early as the 17th century the placename Shqipëria and the ethnic demonym Shqiptarë gradually replaced Arbëria, the two terms are popularly interpreted as Land of the Eagles and Children of the Eagles
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Latvia
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Latvia, officially the Republic of Latvia, is a country in the Baltic region of Northern Europe, one of the three Baltic states. It is bordered by Estonia to the north, Lithuania to the south, Russia to the east, Latvia has 1,957,200 inhabitants and a territory of 64,589 km2. The country has a seasonal climate. Latvia is a parliamentary republic established in 1918. The capital city is Riga, the European Capital of Culture 2014, Latvia is a unitary state, divided into 119 administrative divisions, of which 110 are municipalities and 9 are cities. Latvians and Livs are the people of Latvia. Latvian and Lithuanian are the two surviving Baltic languages. Despite foreign rule from the 13th to 20th centuries, the Latvian nation maintained its identity throughout the generations via the language, Latvia and Estonia share a long common history. Until World War II, Latvia also had significant minorities of ethnic Germans, Latvia is historically predominantly Protestant Lutheran, except for the Latgale region in the southeast, which has historically been predominantly Roman Catholic. The Russian population has brought a significant portion of Eastern Orthodox Christians. The Republic of Latvia was founded on 18 November 1918, however, its de facto independence was interrupted at the outset of World War II. The peaceful Singing Revolution, starting in 1987, called for Baltic emancipation of Soviet rule and it ended with the Declaration on the Restoration of Independence of the Republic of Latvia on 4 May 1990, and restoring de facto independence on 21 August 1991. Latvia is a democratic and developed country and member of the European Union, NATO, the Council of Europe, the United Nations, CBSS, the IMF, NB8, NIB, OECD, OSCE, and WTO. For 2014, Latvia was listed 46th on the Human Development Index and it used the Latvian lats as its currency until it was replaced by the euro on 1 January 2014. The name Latvija is derived from the name of the ancient Latgalians, one of four Indo-European Baltic tribes, henry of Latvia coined the Latinisations of the countrys name, Lettigallia and Lethia, both derived from the Latgalians. The terms inspired the variations on the name in Romance languages from Letonia. Around 3000 BC, the ancestors of the Latvian people settled on the eastern coast of the Baltic Sea. The Balts established trade routes to Rome and Byzantium, trading local amber for precious metals, by 900 AD, four distinct Baltic tribes inhabited Latvia, Curonians, Latgalians, Selonians, Semigallians, as well as the Livonians speaking a Finnic language
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Georgia (country)
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Georgia is a country in the Caucasus region of Eurasia. The capital and largest city is Tbilisi, Georgia covers a territory of 69,700 square kilometres, and its 2016 population is about 3.72 million. Georgia is a unitary, semi-presidential republic, with the government elected through a representative democracy, during the classical era, several independent kingdoms became established in what is now Georgia. The kingdoms of Colchis and Iberia adopted Christianity in the early 4th century, a unified Kingdom of Georgia reached the peak of its political and economic strength during the reign of King David IV and Queen Tamar in the 12th and early 13th centuries. Thereafter the kingdom declined and eventually disintegrated under hegemony of various powers, including the Mongols, the Ottoman Empire. Russian rule over Georgia was eventually acknowledged in various treaties with Iran. Since the establishment of the modern Georgian republic in April 1991, post-communist Georgia suffered from civil, the countrys Western orientation soon led to the worsening of relations with Russia, culminating in the brief Russo-Georgian War in August 2008. Georgia is a member of the United Nations, the Council of Europe, and it contains two de facto independent regions, Abkhazia and South Ossetia, which gained limited international recognition after the 2008 Russo-Georgian War. Georgia and a part of the international community consider the regions to be part of Georgias sovereign territory under Russian military occupation. Georgia probably stems from the Persian designation of the Georgians – gurğān, in the 11th and 12th centuries adapted via Syriac gurz-ān/gurz-iyān, starting with the Persian word gurğ/gurğān, the word was later adopted in numerous other languages, including Slavic and West European languages. This term itself might have established through the ancient Iranian appellation of the near-Caspian region. The self-designation used by ethnic Georgians is Kartvelebi, the medieval Georgian Chronicles present an eponymous ancestor of the Kartvelians, Kartlos, a great-grandson of Japheth. However, scholars agree that the word is derived from the Karts, the name Sakartvelo consists of two parts. Its root, kartvel-i, specifies an inhabitant of the core central-eastern Georgian region of Kartli, ancient Greeks and Romans referred to early western Georgians as Colchians and eastern Georgians as Iberians. Today the full, official name of the country is Georgia, before the 1995 constitution came into force the countrys name was the Republic of Georgia. The territory of modern-day Georgia was inhabited by Homo erectus since the Paleolithic Era, the proto-Georgian tribes first appear in written history in the 12th century BC. The earliest evidence of wine to date has found in Georgia. In fact, early metallurgy started in Georgia during the 6th millennium BC, the classical period saw the rise of a number of early Georgian states, the principal of which was Colchis in the west and Iberia in the east
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Nuristan Province
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Nuristan, also spelled Nurestan or Nooristan, is one of the 34 provinces of Afghanistan, located in the eastern part of the country. It is divided into seven districts and has a population of about 140,900, Parun serves as the provincial capital. It was formerly known as Kafiristan until the inhabitants were converted from a form of ancient Hinduism, to Islam in 1895, the primary occupations are agriculture, animal husbandry, and day labor. Located on the slopes of the Hindu Kush mountains in the northeastern part of the country, Nuristan spans the basins of the Alingar, Pech, Landai Sin. Nuristan is bordered on the south by Laghman and Kunar provinces, on the north by Badakhshan province, on the west by Panjshir province, the surrounding area fell to Alexander the Great in 330 B. C. It later fell to Chandragupta Maurya, the Mauryas introduced Buddhism to the region, and were attempting to expand their empire to Central Asia until they faced local Greco-Bactrian forces. Seleucus is said to have reached a treaty with Chandragupta by giving control of the territory south of the Hindu Kush to the Mauryas upon intermarriage and 500 elephants. As soon as the forces, therefore, of all the confederates were united, a battle was fought, in which Antigonus was slain, having consolidated power in the northwest, Chandragupta pushed east towards the Nanda Empire. Afghanistans significant ancient tangible and intangible Buddhist heritage is recorded through wide-ranging archeological finds, including religious, Buddhist doctrines are reported to have reached as far as Balkh even during the life of the Buddha, as recorded by Xuanzang. In this context a legend recorded by Xuanzang refers to the first two lay disciples of Buddha, Trapusa and Bhallika responsible for introducing Buddhism in that country. Originally these two were merchants of the kingdom of Balhika, as the name Bhalluka or Bhallika probably suggests the association of one with that country and they had gone to India for trade and had happened to be at Bodhgaya when the Buddha had just attained enlightenment. The region was known as Kafiristan because of its inhabitants, the Nuristani. It was conquered by Emir Abdur Rahman Khan in the late 19th century, the Kafirs are thought to be the original inhabitants of the plains country of Afghanistan in what is now Nuristan. They were driven back into the areas by the arrival of Islam in the country about 700AD. The region was renamed Nuristan, meaning Land of the enlightened, Nuristan was once thought to have been a region through which Alexander the Great passed with a detachment of his army, thus the folk legend that the Nuristani people are descendants of Alexander. Abdul Wakil Khan Nuristani is one of the most prominent figures in Nuristans history and he fought against the British-led Punjabi army and drove them out of the eastern provinces of Afghanistan. He is buried on the plateau where King Amanullah Khan is buried. Since the creation of Pakistan in 1947, Afghan politicians have been focusing on re-annexing Khyber Pakhtunkhwa and this has led to militancy on both sides of the Durand Line
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