COMPUTER-GENERATED MUSIC Human comp

COMPUTER-GENERATED MUSIC
Human composers may incorporate random or chance elements in their work, but wisely tend to let such processes guide them rather than dictate the final results. Getting a computer to compose music means letting go of that human input, and gives rise to many problems. A number of attempts to have a computer compose music were made as early as the 1950s, with limited success. Sometimes the resulting pieces had snatches of tuneful music, but were overall disappointing, while other attempts produced listenable, but extremely simple tunes. In 1959 the ILLIAC computer,an early supercomputer,was programmed with the rules of composition that had been written during the period of Baroque music. The Illiac Suite for String Quartet was performed successfully,but the composition was not considered to be of high quality. The problems with computer composition were that when there are few rules for generating the notes,the result- ing tunes are too random in structure, resembling white noise. The music generated has no direction or coherence. If the rules are stricter, then some coherence can be found in some tunes, because rather than white noise the use of strict algorithms often produces brown noise. Brown noise, named after Robert Brown (1773–1858), refers to a type of process that can be thought of as a random walk.The start- ing point can be set, but after that the walker may end up moving forward or back,to the sides,or some combination. Over time, the walker will have progressed somewhere and how they will get there cannot be determined. Not surpris- ingly,brown-noise computer compositions sometimes have a direction,of sorts,but can be rambling and dull. Fractal mathematics, popularized by Benoit Mandel- brot (1924–) in the 1970s, offer a different type of struc- ture for computer-generated music. Fractals are curves, surfaces, and objects that have non-integer dimensions.A point has a dimension of zero, a line a dimension of one, a square two, and a cube three. However, fractals have dimensions that lie between these; for example,a geomet- ric construction called Koch’s cube has a dimension of about 1.26.Surprisingly,a number of natural phenomena displays fractal properties,such as clouds,coastlines,land- scapes, plants, and many more. Fractional dimensions produce some interesting patterns that usually have a degree of self-similarity in them; that is, the large-scale pattern resembles smaller structures within the pattern, which in turn resemble smaller structures within them- selves. For example, a tree has a growth pattern that resembles that of a single branch, and within a branch there can be smaller branches with the same pattern.
Compositions that use fractal formulas sound more coherent that other types of computer-generated chance music. The property of self-similarity means that fractal compositions repeat themes in complex ways, which closely mimics a common property of human composi- tion. Without knowing it, composers like Prokofiev and Cage had already used fractals in their music by using landscapes and star patterns to determine notes. How- ever,most computer-generated music still sounds aimless and flat in comparison with human compositions.While many musicians have embraced the flexibility and inspi- ration that computer generation can give to a composi- tion, computers are in no danger of taking over the writing of music just yet. There is still something human choices can give to music that cannot be fully simulated. Randomness was originally seen as a negative when it entered music as unexpected or unwanted noise, yet when harnessed in the right manner it has produced many innovative and important pieces of music. Ran- domness has also entered into the way music is listened to, from CD-shuffling stereos to mp3 players with a ran- dom song selection, the old structures of albums and playlists are often sidestepped.
FREQUENCY OF CONCERT
A Sometimes mathematics and music have come into conflict, such as the long debates over the correct fre- quency of the notes in the Western scale. Orchestras and many other musicians often tune their instruments to the note known as concert A,and from that all the other notes in the scale are then set by their musical intervals from that frequency. However, the choice of this frequency is arbitrary. At first, Western music had no standard fre- quency for concert A, as there was very little communica- tion across medieval Europe. Different regions sang and performed with their own pitches, because they had their own frequencies for the same notes. However, as contact between musicians increased across Europe,a rough stan- dard was introduced and in the eighteenth century, con- cert A, as estimated by music historians, was about 420–425 Hz (Hertz, or cycles per second). Once sound frequencies became better understood, and methods of measuring frequency were available, there were attempts to introduce a more specific and uni- versal standard for concert A, although national pride and politics got in the way. The French and English set different frequencies, of 435 Hz (cycles per second) for the French and 439 Hz for the English. Then in 1939, an international standard of 440 Hz was introduced, but against the will of a mathematical lobby that wished concert A to be set at 426.7 Hz, so that
middle C would be at 256 Hz. This was called the philo- sophical pitch, as 256 is 28 (two to the power of eight, or two multiplied by itself eight times),and so seemed to the mathematicians a more formal, even Pythagorean, derivation of the note. The musicians, however, did not want such a dramatic change to the pitch of the music they played, as such a low number for concert A would have altered the sound of all existing music.
MATH-ROCK
Most musicians do not consider the mathematics that lie behind their music. Music can be composed and performed extremely well without any mathematical input from those involved. However, with the introduc- tion of electronic instruments, it has become easier to introduce mathematical concepts into music. There is even a genre of rock music that calls itself math-rock,and is categorized by the creative use of time signatures. A time or meter signature can be thought of as the number of beats in a measure of music,or in basic rhyth- mic terms, the number of drum beats in a set period of time. Normally, all the instruments in a piece of music will play in the same time, as this makes it easy to keep together, and usually sounds better. If one instrument plays in a different meter than the others, the result is usually unpleasant to the listeners. In math-rock, how- ever, the musicians play in different meters on purpose. For example, in the Frank Zappa (1940–1993) instru- mental Toads of the Short Forest from the 1970 album “Weasels Ripped My Flesh”there are two drummers, one playing in 7/8 time, while the other plays in 3/4. At the same time the organist plays in 5/8, creating an effect known as polyrhythm, or polymeter. The roots of polyrhythmic music go back to Indian and African music, as well as Latin music. Music performance and composition are art forms, and many have called mathematics at its highest levels more art than science.Yet, when the basics of mathemat- ics or music are learned,they both must start with simple rules and learned by rote, memorizing the building blocks of the subject until they become second nature.As learning progresses,the rules become more complex,and the effort needed to master them increases. For some people the effort is too great, or the rules too complex. Only a few people master a branch of mathematics or a genre of music, and at the highest levels the rules do not seem to be so important. They are still there, underpin- ning everything, but can be used in new ways, or stretched, or combined with unexpected results. For those people on the outside looking in, these highest workings of music and mathematics may be fascinating, spellbinding,even beautiful,but are strange and unexplain- able; they are to be enjoyed,but never fully understood.
Potential Applications
Mathematics and music have become more entwined than ever before.The ways music is made,produced,trans- mitted,and listened to all rely heavily on mathematics,and many practical applications in music have come from abstract mathematical concepts. The shift to digital for- mats for music has been accompanied by continuing work in compression, error correction, and improving quality. Work in the field of music has produced mathematical
tools and applications for other areas,and will continue to do so.In turn,mathematical ideas in other fields have suc- cessfully been transposed into musical applications. The experimental ethos that is at the heart of musical expres- sion also exists in the field of musical instrumentation and engineering,and new devices are constantly being created

Kết quả (Anh) 1:

COMPUTER-GENERATED MUSIC Human composers may incorporate random or chance elements in their work, but wisely tend to let such processes guide them rather than dictate the final results. Getting a computer to compose music means letting go of that human input, and gives rise to many problems. A number of attempts to have a computer compose music were made as early as the bearer, with limited success. Sometimes the resulting pieces had snatches of tuneful music, but were overall disappointing, while other attempts produced listenable, but extremely simple tunes. In 1959 the ILLIAC computer, an early supercomputer, was programmed with the rules of composition that had been written during the period of Baroque music. The Illiac Suite for String Quartet was performed successfully, but the composition was not considered to be of high quality. The problems with computer composition were that when there are few rules for generating the notes, the result-ing tunes are too random in structure, resembling designs white noise. The music generated has no direction or coherence. If the rules are stricter, then some coherence can be found in some tunes, because rather than white noise the use of strict algorithms often produces brown noise. Brown noise, named after Robert Brown (1773-1858), refers to a type of process that can be thought of as a random walk.The start-ing point can be set, but after that the walker may end up moving forward or back, to the sides, or some combination. Over time, the walker will have progressed somewhere and how they will get there cannot be determined. Not surpris ingly-, brown-noise computer compositions sometimes have a direction, of sorts, but can be rambling and dull. Fractal mathematics, popularized by Benoit Mandel-brot (1924-) in the 1970s, offer a different type of struc-ture for computer-generated music. Fractals are curves, surfaces, and objects that have non-integer dimensions.A point has a dimension of zero, a line of a dimension of square one, a two, and a cube three. However, fractals have dimensions that lie between these; for example, a geomet-ric construction called Koch cube has a dimension of about 1.26. Surprisingly, a number of natural phenomena displays fractal properties, such as clouds, coastlines, land-scapes, plants, and many more. Fractional dimensions produce some interesting patterns that usually have a degree of self-similarity in them; that is, the large-scale pattern resembles smaller structures within the pattern, which in turn resemble smaller structures within them-selves. For example, a tree has a growth pattern that resembles that of a single branch, and within a branch there can be smaller branches with the same pattern.Compositions that use fractal formulas sound more coherent that other types of computer-generated chance music. The property of self-similarity means that fractal compositions repeat themes in complex ways, which closely mimics a common property of human composi-tion. Without knowing it, composers like Prokofiev and Cage had already used fractals in their music by using landscapes and star patterns to determine the notes. How-ever, most computer-generated music still sounds aimless and flat in comparison with human compositions.While many musicians have embraced the flexibility and inspi-ration that computer generation can give to a composi-tion, computers are in no danger of taking over the writing of music just yet. There is still something human choices can give to music that cannot be fully simulated. Randomness was originally seen as a negative when it entered music as unexpected or unwanted noise, yet when harnessed in the right manner it has produced many innovative and important pieces of music. Ran-domness has also entered into the way music is listened to, from CD-shuffling stereos to mp3 players with a ran-dom song selection, the old structures of albums and playlists are often sidestepped.FREQUENCY OF CONCERT A "Sometimes" mathematics and music have come into conflict, such as the long debates over the correct fre-quency of the notes in the Western scale. Orchestras and many other musicians often tune their instruments to the note known as A concert, and from that all the other notes in the scale are then set by their musical intervals from that frequency. However, the choice of this frequency is arbitrary. At first, Western music had no standard fre-quency for concert A, as there was very little communica-tion across medieval Europe. Different regions sang and performed with their own pitches, because they had their own frequencies for the same notes. However, as contact between musicians increased across Europe, a rough stan-dard was introduced and in the eighteenth century, con-cert A, as estimated by music historians, was about 420-425 Hz (Hertz, or cycles per second). Once sound frequencies became better understood, and methods of measuring frequency were available, there were attempts to introduce a more specific and uni-versal standard for concert A, although national pride and politics got in the way. The French and English set different frequencies, of 435 Hz (cycles per second) for the French and 439 Hz for the English. Then in 1939, an international standard of 440 Hz was introduced, but against the will of a mathematical lobby that wished A concert to be set at 426.7 Hz, so thatmiddle C would be at 256 Hz. This was called the philo-sophical pitch, as 256 is 28 (two to the power of eight, or two any Riemannian metric on by itself eight times), and so seemed to the mathematicians a more formal, even Pythagorean, derivation of the note. The musicians, however, did not want such a dramatic change to the pitch of the music they played, as such a low number for A concert would have altered the sound of all existing music.MATH-ROCK Most musicians do not consider the mathematics that lie behind their music. Music can be composed and performed extremely well without any mathematical input from those involved. However, with the introduc- tion of electronic instruments, it has become easier to introduce mathematical concepts into music. There is even a genre of rock music that calls itself math-rock,and is categorized by the creative use of time signatures. A time or meter signature can be thought of as the number of beats in a measure of music,or in basic rhyth- mic terms, the number of drum beats in a set period of time. Normally, all the instruments in a piece of music will play in the same time, as this makes it easy to keep together, and usually sounds better. If one instrument plays in a different meter than the others, the result is usually unpleasant to the listeners. In math-rock, how- ever, the musicians play in different meters on purpose. For example, in the Frank Zappa (1940–1993) instru- mental Toads of the Short Forest from the 1970 album “Weasels Ripped My Flesh”there are two drummers, one playing in 7/8 time, while the other plays in 3/4. At the same time the organist plays in 5/8, creating an effect known as polyrhythm, or polymeter. The roots of polyrhythmic music go back to Indian and African music, as well as Latin music. Music performance and composition are art forms, and many have called mathematics at its highest levels more art than science.Yet, when the basics of mathemat- ics or music are learned,they both must start with simple rules and learned by rote, memorizing the building blocks of the subject until they become second nature.As learning progresses,the rules become more complex,and the effort needed to master them increases. For some people the effort is too great, or the rules too complex. Only a few people master a branch of mathematics or a genre of music, and at the highest levels the rules do not seem to be so important. They are still there, underpin- ning everything, but can be used in new ways, or stretched, or combined with unexpected results. For those people on the outside looking in, these highest workings of music and mathematics may be fascinating, spellbinding,even beautiful,but are strange and unexplain- able; they are to be enjoyed,but never fully understood.Potential ApplicationsMathematics and music have become more entwined than ever before.The ways music is made, produced, trans-mitted, and listened to all rely heavily on mathematics, and many practical applications in music have come from abstract mathematical concepts. The shift to digital for-mats for music has been accompanied by continuing work in compression, error correction, and improving quality. Work in the field of music has produced mathematicaltools and applications for other areas, and will continue to do so.In turn, the mathematical ideas in other fields have suc-cessfully been transposed into musical applications. The experimental ethos that is at the heart of musical expres-sion also exists in the field of musical instrumentation and engineering, and new devices are constantly being created

Kết quả (Anh) 2:

COMPUTER-GENERATED MUSIC
sewing Human composers incorporate random or chance elements trong work, but Wisely Tend to let vd guide added thay coal processes dictate the final results. Getting a computer to compose music nghĩa Letting go of rằng human input, and Gives rise to many problems'. A number of attempts have a computer to compose music made ​​là là là early 1950s, with limited success. Sometimes Do quả the pieces had snatches of music Tuneful, but overall disappointing Were, while other points attempts Produced listenable, but extremely simple tunes. In 1959 the ILLIAC computer, police early supercomputer, was Programmed with the rules of composition rằng the during the period Had Been Written speaker of Baroque music. The Illiac Suite for String Quartet was Performed successfully, but the composition was not Considered to be of high quality. The problems' with computer composition rằng khi Were there rules for generating ít are the notes, the result- ing tunes are too random in structure, resembling white noise. The music generated has no direction or coherence. If the rules are stricter, then some coherence thể found in some tunes, thay coal vì the use of strict white noise produces Algorithms often Do brown noise. Brown Noise, named after Robert Brown (1773-1858), Refers to a type of process rằng thể Thought as a start- ing point walk.The random thể set, but after sewing walker rằng end up moving forward or back , to the sides, or some Combination. Over time, the walker sẽ have progressed and how chúng somewhere sẽ thể quyết định get there. Not surpris- ingly, brown-noise compositions computers sometimes have a direction, of sorts, but thể rambling and dull. Fractal mathematics, popularized by Benoit Mandel- BROT (1924-) in the 1970s, offer khác type of struc- ture for computer-generated music. Fractals are Curves, Surfaces, and objects have non-integer rằng dimensions.A point has a dimension of zero, a line a dimension of one, a square two, three and a cube. Tuy nhiên, fractals have dimensions rằng giữa những cork; for example, a geomet- ric construction gọi Koch's cube has a dimension of about 1.26.Surprisingly, a number of natural phenomena displays fractal properties, như clouds, coastlines, Land- scapes, plants, and many more. Fractional dimensions tạo some interesting patterns Thường rằng have a degree of self-similarity in additional; That is, the large-scale pattern resembles the pattern trong smaller structures, in turn resemble mà them- selves trong smaller structures. For example, a tree has a Growth pattern resembles rằng của a single branch, and a branch there trong thể smaller branches with the same pattern.
Compositions rằng Formulas fractal sound more coherent use rằng khác Chance types of computer-generated music. The property of self-similarity fractal nghĩa rằng repeat themes in complex compositions Ways mà closely mimics a common property of human composi- tion. Knowing Without it, composers like Prokofiev and Cage had already USED fractals trong music by using Landscapes and star patterns to quyết notes. How- Ever, Still nhất computer-generated music sounds aimless and flat in Comparison with human compositions.While many musicians have embraced the flexibility and inspi- ration rằng generation computer give courage to a composi- tion, computers are in no danger of taking over the writing of music just yet. There is something human STILL give courage to music choices rằng thể fully simulated. Originally randomness was seen as a negative khi gõ music as unexpected or unwanted noise, yet harnessed in the right khi a manner it has many Innovative and Important Produced pieces of music. Into Ran- domness has cũng gõ way music is listened to, from CD-shuffling Stereos to mp3 players but with a ran- dom selection, the old structures of albums and playlists are often Do sidestepped.
FREQUENCY OF CONCERT
A Sometimes mathematics and music have Come Into Conflict, như the dragon Debates over the correct fre- quency of the notes in the Western scale. Many other points orchestras and musicians often Do ask for their instruments to the tune of known as concert A notes, and from all the other points rằng notes in the scale are key musical intervals set by họ from rằng frequency. Tuy nhiên, the frequency of this choice is arbitrary. At first, Western music had no standard fre- quency for a concert, as there was very little communica- tion Across medieval Europe. Performed with Different Regions and to ask for their own pitches, vì chúng had họ own frequencies for the same notes. Tuy nhiên, contact the between musicians as Increased Across Europe, a rough Stan- dard and was introduced in the eighteenth century, a con- cert, as Estimated by music historians, was about 420-425 Hz (hertz, or cycles per second). Once the sound frequencies became better understood, and available methods of measuring frequency Were, Were there attempts to Introduce a more specific and Uni- Versal standard for a concert, although national pride and Politics got in the way. The French and English set khác frequencies, of 435 Hz (cycles per second) for the French and 439 Hz for the English. Athens in 1939, international safety standard of 440 Hz was introduced, but sẽ Against the lobby of a mathematical rằng A concert wished to be set at 426.7 Hz, compared rằng
middle C at 256 Hz would be. This was the philo- sophical gọi pitch, as 256 is 28 (two to the power of eight, or two multiplied by eight times chính nó), and compared to the mathematicians Seemed a more formal, chẵn Pythagorean, the derivation of the notes. The musicians, Tuy nhiên, did not muốn vd a dramatic change to the pitch of the music is played chúng, as such a low number for a concert would have altered the sound of all existing music.
MATH-ROCK
Most musicians do not như the mathematics rằng CORK spend the weekend behind the music. Music composed and Performed thể extremely well without any input from những mathematical INVOLVED. Tuy nhiên, with the introduc- tion of electronic instruments, it has been easier to Introduce mathematical concepts trở Into music. There is a genre of rock music chẵn rằng calls chính nó math-rock, and is categorized by the creative use of time signatures. A time signature or meter thể Thought of as the number of beats in a measure of music, or in basic terms rhyth- mic, số drum beats in a set period of time. Thường, all the instruments in a piece of music sẽ play in the same time, as this Together Makes it easy to keep, and Thường sounds better. If one instrument plays khác meter coal in the others, the result is unpleasant to the listeners Thường. In math-rock, how- Ever, the musicians play in khác meters on purpose. For example, in the Frank Zappa (1940-1993) instru- mental Toads of the Short Forest from the 1970 album "Weasels Ripped My Flesh" there are two Drummers, one playing in 7/8 time, while the other points in 3 plays / 4. At the same time the organist plays in 5/8, creating the effect of known security as polyrhythm, or polymeter. The roots of polyrhythmic music go back to Indian and African music, as well as Latin music. Music performance and composition are art forms, and many have gọi mathematics more art at its Highest Level science.Yet coal, khi basics of mathemat- ics or music are Learned, chúng cả phải start with simple rules and Learned by rote, memorizing the building blocks of the second subject, an until chúng trở nature.As learning progresses, the rules trở more complex, and the effort needed to master additional increases. For some people 'the effort is too great, or the rules too complex. Only vài people 'a branch of mathematics master or a genre of music, and at the Highest Level the rules do not Seem To Be Important in comparison. They are STILL there, underpin- ning everything, but in new Ways dùng intervention, or stretched, or combined with unexpected results. Những for people 'on the outside looking in, những Highest workings of music and mathematics lẽ fascinating, spellbinding, beautiful chẵn, but are strange and unexplain- thể; They are to be enjoyed, but never fully understood.
Potential Applications
Mathematics and music have more entwined trở coal Ways Ever before.The music is made, Produced, trans- mitted, and listened to all rely heavily on mathematics, and many Practical applications in Music from the abstract mathematical concepts have come. The shift to digital for- mats for music đã accompanied by Continuing work in compression, error correction, and Improving quality. Work in the field of music has Produced mathematical
tools for other applications and which areas nên by so.In continue to turn, mathematical ideas in fields other points have suc- cessfully được Into transposed musical applications. The experimental ethos is at the heart of rằng musical expres- sion am also exists in the field of musical instrumentation and engineering, and new devices are constantly being tạo