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Mathematics in music introduction
Mathematics in music introduction
Mathematics in music introduction
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Music and mathematics are incredible forms of art that have been apart of every day life for centuries and continue to do so. It seems that most people would not consider mathematics to fall under the category of art because generally the stereotypical thoughts of math consist of numbers and equations. However, art is defined as the expression or application of human creative skill and imagination. Math is a skill that humans have developed overtime and it is a prominent factor that is integrated in music. Though it is not literally seen or heard, aspects of mathematics are present in not only the physical sound but also in the theory of music. The human ear has a tendency to favor consonant music. Consonance is a term used to define musical intervals, melodies, or harmonies that sound pleasing, and it is both a physical and psychological attraction. According to Ancient Greek history, these “consonant sounds” relate to simple number ratios which was discovered in an experiment conducted by Pythagoras (Fauvel, p 15). In his experiment, it is said that he listened to a blacksmith strike four hammers weighing twelve, nine, eight, and six pounds. He listened to the twelve pound hammer while cycling through the other weights simultaneously. From this observation he was able to derive the intervals: 12:6 = 2:1 12:8 = 3:2 12:9 = 4:3 Sound is produced by vibrations in the air which, in this experiment, came from the hammer. The vibrations are a set of frequencies measured in units of Hertz (Hz). The faster the vibration frequency, the higher the sound will be in pitch. Pythagoras’s 2:1 ratio simply means that both tones are the same however the second tone’s frequency rate is doubled. For example, the blacksmith strike... ... middle of paper ... ... how the melody is organized. In bars one and three there are four quarter notes. Since a quarter gets one beat, bars one and three match the time signature (1 + 1 + 1 + 1 = 4). In measures two and four there are two quarter notes and one half. Knowing that a half note equals two beats, bars two and four match the time signature as well ( 1 + 1 + 2 = 4). This displays how many concepts of math, including its most basic forms, are accommodated in music. After reviewing the history of the development of music, it seems that without mathematics music would not exist. The relationship between the two could even foster embellishing opportunities for education. Students may be more intrigued to learn about math if it is compared to music or vice versa. With this strong combination, it is important to consider that mathematics is as much of an art as music.
1. Music is a strictly local expression, rich in variety since each culture expresses affective differences through art, 2. Music is a poetic process--complex, vague, and irrational--based upon borrowed traditional musical materials (melodies, rhythms, forms, etc.), 3. Music is for a religious, elitist-class performer who can understand and appreciate its mysterious nature and power, 4. Music is played softly in intimate gatherings, 5. Music making is the activity of Everyman, exacting the talents of variously trained amateurs who, with industry and practice, decorate their recreation and leisure in moments of social intercourse.
Its pendulum swung to and fro with a dull, heavy, monotonous clang; and when the minute-hand made the circuit of the face, and the hour was to be stricken, there came from the brazen lungs of the clock a sound which was clear and loud and deep and exceedingly musical, but of so peculiar a note and emphasis that, at each lapse of an hour, the musicians of the orchestra were constrained to pause, momentarily, in their performance, to harken to the sound; and thus the waltzers perforce ceased their evolutions; and there was a brief disconcert of the whole gay company; and, while the chimes of the clock yet rang, it was observed that the giddiest grew pale, and the more aged and sedate passed their hands over their brows as if in confused revery or meditation. But when the echoes had fully ceased, a light laughter at once pervaded the assembly; the musicians looked at each other and smiled as if at their own nervousness and folly, and made whispering vows, each to the other, that the next chiming of the clock should produce in them no similar emotion; and then, after the lapse of sixty minutes, (which embrace three thousand and six hundred seconds of the Time that flies,) there came yet another chiming of the clock, and then were the same disconcert and tremulousness and meditation as
Pitched sounds are, however, not of the essence: drum motives are so effective rhythmically precisely because they lack pitch definition. By and large, rhythmic motives are used to endow pitch relationships with identifiable durational characteristics.” Because of this, rhythmic identity is used to establish the motive connections between different time intervals. A great example of this is the opening of Beethoven’s Symphony No. 5 in C Minor Opus 67. This part of this masterpiece serves as an effective element of structural cohesion in the overall scale of this large work.
Music is far more than the sum of its parts. It can be thought of in a highly mathematical sense, which leaves one in awe of the seemingly endless combinations of rhythm, tone and intervals that a good musician can produce. Admiring music in this way is a lot like admiring an intricate snowflake, or shapes in the clouds; it's beautiful, but at the same time very scientific, based on patterns. All of the aforementioned qualities of music have one thing in common: they can be defined with numeric, specific values. However, the greatest aspect of music lies elsewhere, and cannot be specifically defined with words. It is the reaction that each individual has when they are confronted with their favorite (or least favorite) kind of music.
The relationship between the two gets even more intriguing when applied to actual notes being played. The best sounding music is that which uses flawless mathematics. It is common knowledge that each note has a letter name—A through G—but also has a number value, measured in hertz. An A4 for instance is 440 hertz. In Beethoven’s “Moonlight Sonata,” there exist triads in triplet form. These triads are made up of D, F#, and A. Since sound is a vibrational energy, notes can be graphed as sine functions. When the triad notes are graphed, they intersect at their starting point and at the point 0.042. At this point the D has gone through two full cycles, the F# two and a half, and the A three. This results in consonance, something that sounds naturally pleasant to the ear. Thinking about this opened my eyes to all the aspects of my life with which I utilize math to
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
Suggested by the very remarkable interest taken in the music in the works of the ancient Greek philosophers, our attempt¡Xa semiotic attempt¡Xwould succeed in getting us closer to the meaning of what is called "the ethos of music" in the civilization of ancient Greeks.
In 600 BC the famed mathematician Pythagoras dissected music and developed the keystone of modern music: the octave scale. The importance of this event to humanities is obvious. Music was a passion for the Greeks. With their surplus of leisure time they were able to cultivate great artistic skills that would help composers
Astronomer Galileo Galilei observed that the entire universe “is written in the language of mathematics.” As an avid musician, I chose to study the topic of how math applies to music, more specifically how sound waves are transmitted. My passion for music urged me to research the sounds that are made and how they are produced.
Through out the history of music, acoustics have played a major role. After all if it were not for acoustics the quality of sound that we know today would not exist. The word acoustics comes from the Greek word akouein, which means, “to hear”(Encarta Encyclopedia). Since music has to be heard in most cases for enjoyment, acoustics obviously take on a very important role in the pleasure that music brings to the ear. Acoustical architecture and design are two key elements in the way music sounds. For example, an electric guitar played in a concert hall would sound very different compared to the sound produced in a small room. These differences can be explained by the acoustical design of the room and the reverb created by both the instrument and the room in which it is played. These differences signify the importance of acoustics in music.
However, one must remember that art is by no means the same as mathematics. “It employs virtually none of the resources implicit in the term pure mathematics.” Many people object that art has nothing to do with mathematics; that mathematics is unemotional and injurious to art, which is purely a matter of feeling. In The Introduction to the Visual Mind: Art and Mathematics, Max Bill refutes this argument by stati...
Starting with the staff. The staff is a groundwork where music is placed on. These include notes, rests, dynamic markings and tempo markings. It is represented by 5 lines and four spaces, upon where the notes are placed. Clefs are placed at the start of a staff and act as a point of reference where the notes are located within the staff. There are two main types of Clefs, the Treble and Bass. In music there are twelve notes. The relationship from one note to another is expressed using semi-tones and full-tones. A semi-tone is the difference of one pitch up or down from a starting pitch for example: G and G sharp, the difference between the two notes is one semi-tone as well as G and G flat where G flat is one semitone below G. The twelve notes are specified by the following: A, A#, B, C, C#, D, D#, E, F, F#, G, G# these can be also expressed as: A, Ab, G, Gb, F, E, Eb, D, Db, C, B, Bb. The “#” symbol represents sharp and the “b” represents flat. Both can be interchanged, by looking at the scale, for example, Ab would be the same musical value as G#. Another important anomaly of the musical scale would be to point out there are no real musical values for “B# / Cb” and “E# / Fb”. The relationship from B to C for example is counted as a semitone. Including the pitches of E to F. On the staff below, an annotated diagram reveals the position of the notes C and C# in the treble clef. The lines placed in between the staff are known as bar lines and indicate the end and start of a new bar. A bar acts as a limit to how many notes can be played at a
Devlin believes that mathematics has four faces 1) Mathematics is a way to improve thinking as problem solving. 2) Mathematics is a way of knowing. 3) Mathematics is a way to improve creative medium. 4) Mathematics is applications. (Mann, 2005). Because mathematics has very important role in our life, teaching math in basic education is as important as any other subjects. Students should study math to help them how to solve problems and meet the practical needs such as collect, count, and process the data. Mathematics, moreover, is required students to be capable of following and understanding the future. It also helps students to be able to think creativity, logically, and critically (Happy & Listyani, 2011,
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
...re encompassing way, it becomes very clear that everything that we do or encounter in life can be in some way associated with math. Whether it be writing a paper, debating a controversial topic, playing Temple Run, buying Christmas presents, checking final grades on PeopleSoft, packing to go home, or cutting paper snowflakes to decorate the house, many of our daily activities encompass math. What has surprised me the most is that I do not feel that I have been seeking out these relationships between math and other areas of my life, rather the connections just seem more visible to me now that I have a greater appreciation and understanding for the subject. Math is necessary. Math is powerful. Math is important. Math is influential. Math is surprising. Math is found in unexpected places. Math is found in my worldview. Math is everywhere. Math is Beautiful.