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Mathematical contributions of pythagoras
Pythagoras and his contribution to mathematics
Mathematical contributions of pythagoras
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Fundamentals of Musical Acoustics. New York: Dover
Publications Ferrara, Lawrence (1991). Philosophy and the
Analysis of Music. New York: Greenwood Press.
Johnston, Ian (1989). Measured Tones. New York: IOP
Publishing. Rowell, Lewis (1983). Thinking About Music.
Amhurst: The University of Massachusetts Press. "Music is the harmonization of opposites, the unification of disparate things, and the conciliation of warring elements...Music is the basis of agreement among things in nature and of the best government in the universe. As a rule it assumes the guise of harmony in the universe, of lawful government in a state, and of a sensible way of life in the home. It brings together and unites." - The Pythagoreans Every school student will recognize his name as the originator of that theorem which offers many cheerful facts about the square on the hypotenuse. Many European philosophers will call him the father of philosophy. Many scientists will call him the father of science. To musicians, nonetheless,
Pythagoras is the father of music. According to Johnston, it was a much told story that one day the young Pythagoras was passing a blacksmith’s shop and his ear was caught by the regular intervals of sounds from the anvil. When he discovered that the hammers were of different weights, it occured to him that the intervals might be related to those weights. Pythagoras was correct. Pythagorean philosophy maintained that all things are numbers. Based on the belief that numbers were the building blocks of everything,
Pythagoras began linking numbers and music.
Revolutionizing music, Pythagoras’ findings generated theorems and standards for musical scales, relationships, instruments, and creative formation. Musical scales became defined, and taught. Instrument makers began a precision approach to device construction. Composers developed new attitudes of composition that encompassed a foundation of numeric value in addition to melody. All three approaches were based on Pythagorean philosophy. Thus,
Pythagoras’ relationship between numbers and music had a profound influence on future musical education, instrumentation, and composition. The intrinsic discovery made by Pythagoras was the potential order to the chaos of music. Pythagoras began subdividing different intervals and pitches into distinct notes. Mathematically he divided intervals into wholes, thirds, and halves. "Four distinct musical ratios were discovered: the tone, its fourth, its fifth, and its octave." (Johnston, 1989). From these ratios the
Pythagorean scale was introduced. This scale revolutionized music. Pythagorean relationships of ratios held true for any initial pitch. This discovery, in turn, reformed musical education. "With the standardization of music, musical creativity could be recorded, taught, and reproduced." (Rowell, 1983). Modern day finger exercises, such as the Hanons, are neither based on melody or creativity. They are simply based on the Pythagorean scale, and are executed from various initial pitches.
Creating a foundation for musical representation, works
I would say that the mood in John Prine's music is basically depressing. The two songs that I could relate to were Sam Stone and Grandpa was a Carpenter. The first song on the Prime Prine album, which is called Sam Stone, would make people very depressed and think of some instance in their own life when something similar has happened. The music seems to remind me of people who live in poverty and need to turn to drugs to ease their failure. When you think of the lyrics in the song you think about how this happened in so many different cases. It wasn't just this one guy and his family. This song relates to many different families at the time.
Most people are familiar with the word "music", however they barely consider the definition of it. After carefully think, everyone has their own opinions on this term and it is hard to have an uniform criterion of music sounds. According to the text book, Michael B. Bakan states five propositions to define the music. The first one is about the tone and the second one talks about the music is organized in some way. The next two are claims that music is human organized and a product of human intention and perception. The last proposition argues music cannot separate from Western culture. Among these propositions, I think the music is a product of human intention and perception is most interesting and worth to discuss. So I assert that the most
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Music has been around since the dawn of time, ever since man first inhabited this planet we have learned to communicate in ways other then conventional speaking. Different Cultures all have there own specific way of communicating through music. Music is basically broken into two specific groups Eastern Music and Western Music. Eastern music is mainly derived from the orient and India. While, Western music first emerged from Europe. Western music has developed in many ways since the middle ages through its form, sound, and message.
People relate to music. We sing it. We cry to it. We laugh to it. The reason: we can see ourselves in music. We can let go of our feelings and just relate to the words or the instruments. One way the songwriter connects the listener to the music is through plot: the problem or reaction to a problem a character/singer is expressing. Whether it is a fight with a lover, a fight with a friend, finding a lover/friend, or any other, the plot is helps the listener relate to the song.
When studying Physics of Music, I was interested to research the topic of sound reflection in a theatre as I work at the Royal Manitoba Theatre Centre and wanted to research the acoustics in a theatre. In this paper, I will be using published articles to research the relationship of how people in the theatre receive sound and how the actors are able to portray sound in their space.
The book is divided into four chapters: 1) Humanly Organized Sound, 2) Music in Society and Culture, 3) Culture and Society in Music, and 4) Soundly Organized Humanity. In chapter one, Blacking discusses the analysis of sound. He begins by describing music as humanly organized sound. His overarching theme is that “the function of tones in relation to each other cannot be explained adequately as part of a closed system” (30). In other words, music can’t be analyzed simply by one set of rules. This is because every single culture has a different system that they use to structure and compose their music. In order to adequately analyze a society’s music we have to study their “system.” We must learn what music means to them. Then, and only then, can we accurately and completely analyze what a particular type or piece of music means to a particular society and culture.
ABSTRACT: Humanity requires for its satisfaction Beauty and Good, that is, love, wisdom, and courage. Put differently, the necessity of order, equilibrium, and harmony. These values ground one of the most elevated planes of the spiritual life: music. Its moral force in the education of the mind, soul, and behavior of the human person has been emphasized by the ancient Greek philosophers. This important message exists as a pattern crossing the centuries. I will try to reveal the unity ¡¥ethics¡¦/ethike - ¡¥music¡¦/melos by using the semiotic organon.
The concept of the Renaissance man is somewhat of a lost ideal, replaced by the specialized philosophy of the industrial era. From the 14th to 17th centuries; however, it would be common to find a man with a profound knowledge of both the Arts, music, poetry, literature, art, and the Sciences, mathematics, physics, chemistry, biology. The Renaissance man embraced all forms of knowledge, and through a deep passion for both the Arts and Sciences, used each discipline to expand the other. Unfortunately, in the 21st century, this same philosophy is far gone. Where these two fields once were used together to create an ultimate beauty, they are now pitted against each other by many scholars. It is not uncommon now for a mathematician or physicist to dismiss the Arts as a waste of time; or for an artist or musician to proclaim the Sciences as useless to them. As both an avid blues guitarist and an IB math student, I aim to contrast this modern opinion. I will do so by exploring the relationship between the Arts and Sciences; specifically mathematics and music. On a personal level, I find this to be extremely important, as I hold a deep value for all means of human expression and learning. I believe also that the Arts and Sciences hold one great unifying thing together, which is the search for Truth and Beauty. In a modernized world where ideas and creations can be shared so quickly; the potential for a profound knowledge and passion of both these fields has never been greater. Concepts I plan to explore are: how musical scales can be made using Fibonacci ratios, the Golden Ratio’s relationship with music, equal temperament, where else the Fibonacci numbers occur in music, the exponential nature of octaves, and how exposure to music help...
There has yet to be a culture discovered which lacks music. Making music is seen historically to be as fundamental as the characteristically human activities as drawing and painting. Many even go so far as to compare music to language and claim that music functions as a "universal language." But it is rarely the same music, however, that all peoples respond to. What is it that we are responding to when we listen to music? Strictly speaking, music is not a language, (1) because it has neither outside referents nor easily detectable meaning. Ludwig Wittgenstein explains that although we understand music in a similar way as we understand language, music is not a language because we still cannot communicate through music as we can through language. (2) More recently, Susanne Langer argues that although we understand music as symbol, because we are so caught up in seeing symbolic form function like language we tend to want to make music into a language. But, Langer argues, music is not a kind of language (3) because the significance of music lies not in w...
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.
Throughout this semester we have discussed an array of musical periods ranging from the Middle Ages and Renaissance to more recent modern times. As music progressed through time certain concepts such as melody, harmony, and texture changed along with the introduction of different instruments. In the early phases of music it was more directed toward religious ceremonies, but as time went on it became integrated into everyday life. Even though musical dynamics seem to change as the years go on, it has never failed to create some form of emotional response such as laughter or sadness.
For most people, mathematics is an unsolvable puzzle characterized by the impression of numbers and calculations taught in school. It is often associated with feelings of rejection and disinterest. To the general population mathematics appears to be to be strictly rational, abstract, cold and soulless. Music, however, is involved with emotion, with feelings, and with life. It exists in all daily routines. Everyone has sung a song, pressed a key on a piano, or blown into a flute, and therefore, in some sense, made music. People can easily interact with it. Music is a way of expression and a part of everyone’s existence.
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 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.