In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave in half. In classical music, the tritone is a harmonic and melodic dissonance and is important in the study of musical harmony; the tritone can be used to avoid traditional tonality: "Any tendency for a tonality to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality."
Contrarily, the tritone found in the dominant seventh chord helps establish the tonality of a composition. These contrasting uses exhibit the flexibility and distinctness of the tritone in music; the condition of having tritones is called tritonia. A musical scale or chord containing tritones is called tritonic. Since a chromatic scale is formed by 12 pitches, it contains 12 distinct tritones, each starting from a different pitch and spanning six semitones. According to a complex but used naming convention, six of them are classified as augmented fourths, the other six as diminished fifths. Under that convention, a fourth is an interval encompassing four staff positions, while a fifth encompasses five staff positions; the augmented fourth and diminished fifth are defined as the intervals produced by widening the perfect fourth and narrowing the perfect fifth by one chromatic semitone. They both span six semitones, they are the inverse of each other, meaning that their sum is equal to one perfect octave.
In twelve-tone equal temperament, the most used tuning system, the A4 is equivalent to a d5, as both have the size of half an octave. In most other tuning systems, they are not equivalent, neither is equal to half an octave. Any augmented fourth can be decomposed into three whole tones. For instance, the interval F–B is an augmented fourth and can be decomposed into the three adjacent whole tones F–G, G–A, A–B, it is not possible to decompose a diminished fifth into three adjacent whole tones. The reason is that a whole tone is a major second, according to a rule explained elsewhere, the composition of three seconds is always a fourth. To obtain a fifth, it is necessary to add another second. For instance, using the notes of the C major scale, the diminished fifth B–F can be decomposed into the four adjacent intervals B–C, C–D, D–E, E–F. Using the notes of a chromatic scale, B–F may be decomposed into the four adjacent intervals B–C♯, C♯–D♯, D♯–E♯, E♯–F♮. Notice that the latter diminished second is formed by two enharmonically equivalent notes.
On a piano keyboard, these notes are produced by the same key. However, in the above-mentioned naming convention, they are considered different notes, as they are written on different staff positions and have different diatonic functions within music theory. A tritone is traditionally defined as a musical interval composed of three whole tones; as the symbol for whole tone is T, this definition may be written as follows: TT = T+T+TOnly if the three tones are of the same size can this formula be simplified to: TT = 3TThis definition, has two different interpretations. In a chromatic scale, the interval between any note and the previous or next is a semitone. Using the notes of a chromatic scale, each tone can be divided into two semitones: T = S+SFor instance, the tone from C to D can be decomposed into the two semitones C–C♯ and C♯–D by using the note C♯, which in a chromatic scale lies between C and D; this means that, when a chromatic scale is used, a tritone can be defined as any musical interval spanning six semitones: TT = T+T+T = S+S+S+S+S+S.
According to this definition, with the twelve notes of a chromatic scale it is possible to define twelve different tritones, each starting from a different note and ending six notes above it. Although all of them span six semitones, six of them are classified as augmented fourths, the other six as diminished fifths. Within a diatonic scale, whole tones are always formed by adjacent notes and therefore they are regarded as incomposite intervals. In other words, they cannot be divided into smaller intervals. In this context the above-mentioned "decomposition" of the tritone into six semitones is not allowed. If a diatonic scale is used, with its 7 notes it is possible to form only one sequence of three adjacent whole tones; this interval is an A4. For instance, in the C major diatonic scale, the only tritone is from F to B, it is a tritone because F–G, G–A, A–B are three adjacent whole tones. It is a fourth because the notes from F to B are four (F
Music theory is the study of the practices and possibilities of music. The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is what is otherwise called'rudiments' taught as the elements of notation, of key signatures, of time signatures, of rhythmic notation, so on; the second is the study of writings about music from ancient times onwards. The third is an area of current musicological study that seeks to define processes and general principles in music — a sphere of research that can be distinguished from analysis in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built. Music theory is concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics; because of the ever-expanding conception of what constitutes music, a more inclusive definition could be that music theory is the consideration of any sonic phenomena, including silence, as they relate to music.
This is not an absolute guideline. However, this medieval discipline became the basis for tuning systems in centuries, it is included in modern scholarship on the history of music theory. Music theory as a practical discipline encompasses the methods and concepts composers and other musicians use in creating music; the development and transmission of music theory in this sense may be found in oral and written music-making traditions, musical instruments, other artifacts. For example, ancient instruments from Mesopotamia and prehistoric sites around the world reveal details about the music they produced and something of the musical theory that might have been used by their makers. In ancient and living cultures around the world, the deep and long roots of music theory are visible in instruments, oral traditions, current music making. Many cultures, at least as far back as ancient Mesopotamia and ancient China, have considered music theory in more formal ways such as written treatises and music notation.
Practical and scholarly traditions overlap, as many practical treatises about music place themselves within a tradition of other treatises, which are cited just as scholarly writing cites earlier research. 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, contemplation, theory a sight, a spectacle; as such, it is concerned with abstract musical aspects such as tuning and tonal systems, scales and dissonance, rhythmic relationships, but there is a body of theory concerning practical aspects, such as the creation or the performance of music, ornamentation and electronic sound production. A person who researches, teaches, or writes articles about music theory is a music theorist. University study to the M. A. or Ph. D level, is required to teach as a tenure-track music theorist in Canadian university. Methods of analysis include mathematics, graphic analysis, analysis enabled by Western music notation.
Comparative, descriptive and other methods are used. Music theory textbooks in the United States of America include elements of musical acoustics, considerations of musical notation, techniques of tonal composition, among other topics. Preserved prehistoric instruments and depictions of performance in artworks can give clues to the structure of pitch systems in prehistoric cultures. See for instance Paleolithic flutes, Gǔdí, Anasazi flute. Several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature lists of intervals and tunings; the scholar Sam Mirelman reports that the earliest of these texts dates from before 1500 BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, "All the Mesopotamian texts are united by the use of a terminology for music that, according to the approximate dating of the texts, was in use for over 1,000 years." Much of Chinese music history and theory remains unclear.
The earliest texts about Chinese music theory are inscribed on the stone and bronze bells excavated in 1978 from the tomb of Marquis Yi of the Zeng state. They include more than 2800 words describing 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 and eight. Twelve refers to the number of pitches; 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 and nodes. Blowing on one of these like a pipe, he found its sound agreeable and named it huangzhong, the "Yellow Bell." He heard phoenixes singing. The male and female phoenix each sang six tones. Ling Lun cut his bamboo pipes to match the pitches of the phoenixes, producing twelve pitch pipes in two sets: six from the male phoenix and six from the female: these were called the lülü or the shierlü.
The lülü formed the ritual scale to which
In music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice. Tuning systems, the various systems of pitches used to tune an instrument, their theoretical bases. 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 based on a fixed reference, such as A = 440 Hz; the term "out of tune" refers to a pitch/tone, either too high or too low in relation to a given reference pitch. While an instrument might be in tune relative to its own range of notes, it may not be considered'in tune' if it does not match the chosen reference pitch; some instruments become'out of tune' with temperature, damage, or just time, must be readjusted or repaired. Different methods of sound production require different methods of adjustment: Tuning to a pitch with one's voice is called matching pitch and is the most basic skill learned in ear training. Turning pegs to decrease the tension on strings so as to control the pitch.
Instruments such as the harp 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 a wind instrument, brass instrument, bell, or similar instrument to adjust the pitch; the sounds of some 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 a piano is used. Symphony orchestras and concert bands tune to an A440 or a B♭ provided by the principal oboist or clarinetist, who tune to the keyboard if part of the performance; when only strings are used the principal string has sounded the tuning pitch, but some orchestras have used an electronic tone machine for tuning. Interference beats are used to objectively measure the accuracy of tuning.
As the two pitches 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. For example 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 and judged than the quality of the perfect fifth between the fundamentals of the two strings. In music, the term open string refers to the fundamental note of the full string; the strings of a guitar are tuned to fourths, as are the strings of the bass guitar and double bass. Violin and cello strings are tuned to fifths. However, non-standard tunings exist to change the sound of the instrument or create other playing options. To tune an instrument only one reference pitch is given; this reference is used to tune one string, to which the other strings are tuned in the desired intervals.
On a guitar the lowest string is tuned to an E. From this, each successive string can be tuned by fingering the fifth fret of an tuned string and comparing it with the next higher string played open; this works with the exception of the G string, which must be stopped at the fourth fret to sound B against the open B string above. Alternatively, each string can be tuned to its own reference tone. Note that while the guitar and other modern stringed instruments with fixed frets are tuned in equal temperament, string instruments without frets, such as those of the violin family, are not; the violin and cello are tuned to beatless just perfect fifths and ensembles such as string quartets and orchestras tend to play in fifths based Pythagorean tuning or to compensate and play in equal temperament, such as when playing with other instruments such as the piano. For example, the cello, tuned down from A220, has three more strings and the just perfect fifth is about two cents off from the equal tempered perfect fifth, making its lowest string, C-, about six cents more flat than the equal tempered C.
This table lists open strings on their standard tunings. Violin scordatura was employed in the 17th and 18th centuries by Italian and German composers, Biagio Marini, Antonio Vivaldi, Heinrich Ignaz Franz Biber, Johann Pachelbel and Johann Sebastian Bach, whose Fifth Suite For Unaccompanied Cello calls for the lowering of the A string to G. In Mozart's Sinfonia Concertante in E-flat major, all the strings of the solo viola are raised one half-step, ostensibly to give the instrument a brighter tone so the solo violin does not overshadow it. Scordatura for the violin was used in the 19th and 20th centuries in works by Niccolò Paganini, Robert Schumann, Camille Saint-Saëns and Béla Bartók. In Saint-Saëns' "Danse Macabre", the high string of the violin is lower half a tone to the E♭ so as to have the most accented note of the main theme sound on an open string. In Bartók's Contrasts, the violin is tuned G♯-D-A-E♭ to facilitate the playing of tritones on open strings. American folk violinists of the Appalachians and Ozarks employ alternate tunings for dance songs and
Mechanics is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle and Archimedes. During the early modern period, scientists such as Galileo and Newton laid the foundation for what is now known as classical mechanics, it is a branch of classical physics that deals with particles that are either at rest or are moving with velocities less than the speed of light. It can be defined as a branch of science which deals with the motion of and forces on objects; the field is yet less understood in terms of quantum theory. Classical mechanics came first and quantum mechanics is a comparatively recent development. Classical mechanics originated with Isaac Newton's laws of motion in Philosophiæ Naturalis Principia Mathematica. Both are held to constitute the most certain knowledge that exists about physical nature.
Classical mechanics has often been viewed as a model for other so-called exact sciences. Essential in this respect is the extensive use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them. Quantum mechanics is of a bigger scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the correspondence principle, there is no contradiction or conflict between the two subjects, each pertains to specific situations; the correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of large quantum numbers. Quantum mechanics has superseded classical mechanics at the foundation level and is indispensable for the explanation and prediction of processes at the molecular and sub-atomic level. However, for macroscopic processes classical mechanics is able to solve problems which are unmanageably difficult in quantum mechanics and hence remains useful and well used.
Modern descriptions of such behavior begin with a careful definition of such quantities as displacement, velocity, acceleration and force. Until about 400 years ago, motion was explained from a different point of view. For example, following the ideas of Greek philosopher and scientist Aristotle, scientists reasoned that a cannonball falls down because its natural position is in the Earth. Cited as father to modern science, Galileo brought together the ideas of other great thinkers of his time and began to calculate motion in terms of distance traveled from some starting position and the time that it took, he showed that the speed of falling objects increases during the time of their fall. This acceleration is the same for heavy objects as for light ones, provided air friction is discounted; the English mathematician and physicist Isaac Newton improved this analysis by defining force and mass and relating these to acceleration. For objects traveling at speeds close to the speed of light, Newton's laws were superseded by Albert Einstein’s theory of relativity.
For atomic and subatomic particles, Newton's laws were superseded by quantum theory. For everyday phenomena, Newton's three laws of motion remain the cornerstone of dynamics, the study of what causes motion. In analogy to the distinction between quantum and classical mechanics, Einstein's general and special theories of relativity have expanded the scope of Newton and Galileo's formulation of mechanics; the differences between relativistic and Newtonian mechanics become significant and dominant as the velocity of a massive body approaches the speed of light. For instance, in Newtonian mechanics, Newton's laws of motion specify that F = ma, whereas in relativistic mechanics and Lorentz transformations, which were first discovered by Hendrik Lorentz, F = γma. Relativistic corrections are needed for quantum mechanics, although general relativity has not been integrated; the two theories remain incompatible, a hurdle which must be overcome in developing a theory of everything. The main theory of mechanics in antiquity was Aristotelian mechanics.
A developer in this tradition is Hipparchus. In the Middle Ages, Aristotle's theories were criticized and modified by a number of figures, beginning with John Philoponus in the 6th century. A central problem was that of projectile motion, discussed by Hipparchus and Philoponus. Persian Islamic polymath Ibn Sīnā published his theory of motion in The Book of Healing, he said that an impetus is imparted to a projectile by the thrower, viewed it as persistent, requiring external forces such as air resistance to dissipate it. Ibn Sina made distinction between'force' and'inclination', argued that an object gained mayl when the object is in opposition to its natural motion. So he concluded that continuation of motion is attributed to the inclination, transferred to the object, that object will be in motion until the mayl is spent, he claimed that projectile in a vacuum would not stop unless it is acted upon. This conception of motion is consistent with Newton's first law of inertia. Which states that an object in motion will stay in mo
Music is an art form and cultural activity whose medium is sound organized in time. General definitions of music include common elements such as pitch, rhythm and the sonic qualities of timbre and texture. Different styles or types of music may de-emphasize or omit some of these elements. Music is performed with a vast range of instruments and vocal techniques ranging from singing to rapping; the word derives from Greek μουσική. See glossary of musical terminology. In its most general form, the activities describing music as an art form or cultural activity include the creation of works of music, the criticism of music, the study of the history of music, the aesthetic examination of music. 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 ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, for example, "There is no noise, only sound."The creation, performance and the definition of music vary according to culture and social context.
Indeed, throughout history, some new forms or styles of music have been criticized as "not being music", including Beethoven's Grosse Fuge string quartet in 1825, early jazz in the beginning of the 1900s and hardcore punk in the 1980s. There are many types of music, including popular music, traditional music, art music, music written for religious ceremonies and work songs such as chanteys. Music ranges from organized compositions–such as Classical music symphonies from the 1700s and 1800s, through to spontaneously played improvisational music such as jazz, avant-garde styles of chance-based contemporary music from the 20th and 21st centuries. Music can be divided into genres and genres can be further divided into subgenres, although the dividing lines and relationships between music genres are subtle, sometimes open to personal interpretation, controversial. For example, it can be hard to draw the line between heavy metal. Within the arts, music may be classified as a fine art or as an auditory art.
Music may be played or sung and heard live at a rock concert or orchestra performance, heard live as part of a dramatic work, or it may be recorded and listened to on a radio, MP3 player, CD player, smartphone or as film score or TV show. In many cultures, music is an important part of people's way of life, as it plays a key role in religious rituals, rite of passage ceremonies, social activities and cultural activities ranging from amateur karaoke singing to playing in an amateur funk band or singing in a community choir. People may make music as a hobby, like a teen playing cello in a youth orchestra, or work as a professional musician or singer; the music industry includes the individuals who create new songs and musical pieces, individuals who perform music, individuals who record music, individuals who organize concert tours, individuals who sell recordings, sheet music, scores to customers. The word derives from Greek μουσική. In Greek mythology, the nine Muses were the goddesses who inspired literature and the arts and who were the source of the knowledge embodied in the poetry, song-lyrics, myths in the Greek culture.
According to the Online Etymological Dictionary, the term "music" is derived from "mid-13c. Musike, from Old French musique and directly from Latin musica "the art of music," including poetry." This is derived from the "... Greek mousike " of the Muses," from fem. of mousikos "pertaining to the Muses," from Mousa "Muse". Modern spelling from 1630s. In classical Greece, any art in which the Muses presided, but music and lyric poetry." Music is composed and performed for many purposes, ranging from aesthetic pleasure, religious or ceremonial purposes, or as an entertainment product for the marketplace. When music was only available through sheet music scores, such as during the Classical and Romantic eras, music lovers would buy the sheet music of their favourite pieces and songs so that they could perform them at home on the piano. With the advent of sound recording, records of popular songs, rather than sheet music became the dominant way that music lovers would enjoy their favourite songs. With the advent of home tape recorders in the 1980s and digital music in the 1990s, music lovers could make tapes or playlists of their favourite songs and take them with them on a portable cassette player or MP3 player.
Some music lovers create mix tapes of their favorite songs, which serve as a "self-portrait, a gesture of friendship, prescription for an ideal party... an environment consisting of what is most ardently loved."Amateur musicians can compose or perf