Through history, as said before, many philosophers have supported and developed what Pythagoras first exposed to the world. One of the most important philosophers to support Pythagoras’s ideas was Plato. In some of his writings he discusses the creation of the universe based on the musical proportions discovered by Pythagoras (Timaeus), and the explanation of the sound emitted by the planets, which is exposed in the “Myth of Er” in The Republic. It talks about a man who died and came back to life who narrates how he saw the space and how, in every “sphere,” there was a being singing constantly, each one in a different tone, so a perfect harmony was built. Nevertheless, not everyone agreed with this theory, being one of its most important critics Aristotle, who claimed that Plato’s arguments where false in his text On the Heavens. He acknowledges that it is a creative and innovative theory, but it is absurd to think that such music, which is imperceptible to us, exists in a harmonic way up in the heavens. I am not going to go deeper into that for it is not relevant for the text. As the years went on, many people continued developing this theory. Nevertheless, this philosophical theory, not truly explained until later on, was an inspiration for many artists and that is why not only philosophers but many other artists mention and base their works upon this theory. “Follow me, modern musicians, and attribute it to your arts, unknown to antiquity: in these last centuries, Nature, always prodigal of herself, has at last brought forth, after an incubation of twice a thousand years, you, the first true offprints of the Universal Whole. By your harmonizing of various voices, and through your ears, she has whispered of herself, as she i... ... middle of paper ... ... Again he positioned these two as “G” and positioned the rest according to the relation between the numbers (Kepler: Book V). Looking at all that has been mentioned, Kepler found that in fact Pythagoras had a certain approach to what the music scale, in relation to the planets, was. He managed to built melodies of the numbers that he discovered by observing the planets that brought together would create what he believed was the one true Harmony of the World. As it has already been mentioned before, Kepler believed that God’s creation should be able to be discovered by humans and since he also believed in the celestial music created by God himself, that scale should be the “one” scale thought by God. Nonetheless, though the theoretical explanation of this is quite obscure and complex, it can be better understood if we analyze how it applies to musical compositions.
In order to understand the changes which occurred in music and which affected the Liturgy in the Renaissance period, it is necessary to give a brief sketch of music in earlier times. The first notable aspect of Renaissance music and musical thought is the pace at which it developed. This rapidity stands in contrast to all previous music history. The history of Western art music properly begins with the music of the Christian Church at the end of the ancient world (circa 400AD). This was a world in which music alwa...
Johannes Kepler was a German astronomer and mathematician ho discovered that planetary motion is elliptical. Early in his life, Kepler wanted to prove that the universe obeyed Platonistic mathematical relationships, such as the planetary orbits were circular and at distances from the sun proportional to the Platonic solids (see paragraph below). However, when his friend the astronomer Tycho Brahe died, he gave Kepler his immense collection of astronomical observations. After years of studying these observations, Kepler realized that his previous thought about planetary motion were wrong, and he came up with his three laws of planetary motion. Unfortunately, he did not have a unifying theory for these laws. This had to until Newton formulated his laws of gravity and motion.
Plato was born in Athens, Greece around 427 B.C. He was always interested in politics, until he witnessed his mentor and teacher, Socrates, death. After learning of the callousness of politics, Plato changed his mind and eventually opened up The Academy, which is considered if not the first, one of the first Universities. Students at the Academy studied many different fields of science, including biological and astronomical. The students also studied many other fields, such as math. Plato developed many views that were mathematical in nature. He expressed these views through his writings. According to Dr. Calkins of Andrew University, "Timaeus is probably the most renowned of Plato's thirty-five dialogues. [In it] Plato expresses that he believes that the heavenly bodies are arranged in perfect geometric form. He said that because the heavens are perfect, the various heavenly bodies move in exact circles." (Calkins 1). Of course that is a much summarized view of what Plato discusses in Timaeus, but still a solid view on Plato's beliefs about cosmology. Cosmology can be loosely defined as everything being explained and in its place or beautiful. The cosmos is beautiful because everything is perfect. Plato understood that when he defined the most perfect geometric design as the circle. In a circle one line is always equidistance from one point. In Plato's universe there are two realms, eternity and time. The factor that creates "time" out of the chaos of "eternity" is the Demiurge. Plato's Demiurge can be defined as an architect creator theological entity. The importance of the Demiurge in this paper is to compare and contrast him with Boethius's God in The Consolation of Philosophy.
Around 700 BC, the poet Hesiod’s Theogony wrote the first cosmogony, or origin story, of Greek mythology. The poet tells the story of the universe’s journey from nothingness to being, and details a family tree of gods and goddesses who evolved from Chaos and descended from Earth, Sea, Sky and the Underworld.
Western Music has developed in many ways since the middle ages through its form, sound, and message. Throughout these different periods in western music one thing has remained constant, the true essence of music, a way to communicate with someone on a much more divine level than be by rudimentary conversation. Though Ludwig Van Beethoven and Paul McCartney may seem completely opposite they have one in common through their music they changed the world’s perception of its self
As the child is, so will the man be… So it is in music that the songs which a child assimilates in his youth will determine the musical manhood…the musical influence upon his afterlife and also that the melodies which composers evolve in their maturity are but the flowers which bloom from the fields which were sown with the seed of the folk-song in their childhood. (Barham, 9).
The evolution of music, from the single note plainchants of the Middle Ages to the complex multiple instrumental symphonies of the Classical Era, was a long process. Each age built on the advances of the previous age, even as some parts were rejected by the following age. In the end the advancements and changes to the ways and means to combine rhythm, melody and harmony makes for a rich music heritage and a foundation for future musicians to build on.
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...
John Warrack, author of 6 Great Composers, stated, “Any study of a composer, however brief, must have as its only purpose encouragement of the reader to greater enjoyment of the music” (Warrack, p.2). The composers and musicians of the Renaissance period need to be discussed and studied so that listeners, performers, and readers can appreciate and understand the beginnings of music theory and form. The reader can also understand the driving force of the composer, whether sacred or secular, popularity or religious growth. To begin understanding music composition one must begin at the birth, or rebirth of music and the composers who created the great change.
Plato, like Pythagoras, believes that knowledge of pure Forms and of “Being” is the direct path to someone living a life of salvation and of the highest quality. Plato, like Pythagoras, also believed that all of the forms are geometric figures and mathematical in nature. Also, Plato, like Heraclitus, believed that our world is constantly changing, or in a constant flux. Plato, also agreed with Parmenides, who believed that the real world is not the same as the world of our experience.
As a result of these nuanced views on cosmic creation, the Greek philosophers proposed the ideas of multiple, pleasant, ordered heavens that were only accessible by the virtuous and the righteous. Similarly, they discussed how the the Earth was, in comparison, a chaotic and disordered place, thus implying that an Earthy existence limited and burdened
Since the first Egyptian farmers discovered the annual reappearance of Sirius just before dawn a few days before the yearly rising of the Nile, ancient civilizations around the Mediterranean have sought to explain the movements of the heavens as a sort of calendar to help guide them conduct earthly activities. Counting phases of the moon or observing the annual variations of day length could, after many years' collection of observations, serve as vital indicators for planting and harvesting times, safe or stormy season for sailing, or time to bring the flocks from winter to summer pastures. With our millennia of such observation behind us, we sometimes forget that seeing and recording anything less obvious than the rough position of sun or nightly change of moon phase requires inventing both accurate observation tools (a stone circle, a gnomon used to indicate the sun's shadow, a means to measure the position of stars in the sky) and a system of recording that could be understood by others. The ancient Greeks struggled with these problems too, using both native technology and inquiry, and drawing upon the large body of observations and theories gradually gleaned from their older neighbors across the sea, Egypt and Babylonia. Gradually moving from a system of gods and divine powers ordering the world to a system of elements, mathematics, and physical laws, the Greeks slowly adapted old ideas to fit into a less supernatural, hyper-rational universe.
Much to the dismay of the Church, two astronomers Galileo and Kepler had the audacity to challenge the authorities by suggesting that the sun-not the earth-was at the center of the universe. The church had a stronghold on the way the spiritual and physical world worked, so these discoveries only added to the Church’s resistance to their aims. Their discoveries came only after Kepler and Galileo began to question ancient theories about how the world functioned. These ancient truths were widely held but were inconsistent with the new observations that they had made. Kepler had discovered the laws of planetary motion which suggested that the planet would move in elliptical orbits, while Galileo followed with his discovery of the principle of inertia. Galileo concluded his finding b...
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.
.... Throughout the book Ptolemy compared his own observations with those of Hipparchus, regarding the motion of the sun; Ptolemy found the lengths of the seasons and introduced a simple model for the sun which was a circular motion of uniform angular velocity however the earth would be displaced from the center referred to as eccentricity. He also used his own observations and those of Hipparchus to show that the fixed stars always maintain the same position relative to each other. Concerning his planetary theory, according to his model the path of a planet consisted of a circular motion on an epicycle while the center of the epicycle moving around a circle whose was offset from the earth. It is important to mention that the planetary theory introduces by Ptolemy was considered to be a noticeable achievement, since it predicted the motion of the planets fairly well.