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Pythagorean Philosophy And Its Influence On Musical

Essay, Research Paper


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


became recordable. From the Pythagorean scale and


simple mathematical calculations, different scales or modes


were developed. "The Dorian, Lydian, Locrian, and


Ecclesiastical modes were all developed from the


foundation of Pythagoras." (Johnston, 1989). "The basic


foundations of musical education are based on the various


modes of scalar relationships." (Ferrara, 1991).


Pythagoras? discoveries created a starting point for


structured music. From this, diverse educational schemes


were created upon basic themes. Pythagoras and his


mathematics created the foundation for musical education


as it is now known. According to Rowell, Pythagoras


began his experiments demonstrating the tones of bells of


different sizes. "Bells of variant size produce different


harmonic ratios." (Ferrara, 1991). Analyzing the different


ratios, Pythagoras began defining different musical pitches


based on bell diameter, and density. "Based on


Pythagorean harmonic relationships, and Pythagorean


geometry, bell-makers began constructing bells with the


principal pitch prime tone, and hum tones consisting of a


fourth, a fifth, and the octave." (Johnston, 1989). Ironically


or coincidentally, these tones were all members of the


Pythagorean scale. In addition, Pythagoras initiated


comparable experimentation with pipes of different lengths.


Through this method of study he unearthed two astonishing


inferences. When pipes of different lengths were


hammered, they emitted different pitches, and when air was


passed through these pipes respectively, al

ike results were


attained. This sparked a revolution in the construction of


melodic percussive instruments, as well as the wind


instruments. Similarly, Pythagoras studied strings of


different thickness stretched over altered lengths, and found


another instance of numeric, musical correspondence. He


discovered the initial length generated the strings primary


tone, while dissecting the string in half yielded an octave,


thirds produced a fifth, quarters produced a fourth, and


fifths produced a third. "The circumstances around


Pythagoras? discovery in relation to strings and their


resonance is astounding, and these catalyzed the


production of stringed instruments." (Benade, 1976). In a


way, music is lucky that Pythagoras? attitude to


experimentation was as it was. His insight was indeed


correct, and the realms of instrumentation would never be


the same again. Furthermore, many composers adapted a


mathematical model for music. According to Rowell,


Schillinger, a famous composer, and musical teacher of


Gershwin, suggested an array of procedures for deriving


new scales, rhythms, and structures by applying various


mathematical transformations and permutations. His


approach was enormously popular, and widely respected.


"The influence comes from a Pythagoreanism. Wherever


this system has been successfully used, it has been by


composers who were already well trained enough to


distinguish the musical results." In 1804, Ludwig van


Beethoven began growing deaf. He had begun composing


at age seven and would compose another twenty-five years


after his impairment took full effect. Creating music in a


state of inaudibility, Beethoven had to rely on the


relationships between pitches to produce his music.


"Composers, such as Beethoven, could rely on the


structured musical relationships that instructed their


creativity." (Ferrara, 1991). Without Pythagorean musical


structure, Beethoven could not have created many of his


astounding compositions, and would have failed to establish


himself as one of the two greatest musicians of all time.


Speaking of the greatest musicians of all time, perhaps


another name comes to mind, Wolfgang Amadeus Mozart.


"Mozart is clearly the greatest musician who ever lived."


(Ferrara, 1991). Mozart composed within the arena of his


own mind. When he spoke to musicians in his orchestra, he


spoke in relationship terms of thirds, fourths and fifths, and


many others. Within deep analysis of Mozart?s music,


musical scholars have discovered distinct similarities within


his composition technique. According to Rowell, initially


within a Mozart composition, Mozart introduces a primary


melodic theme. He then reproduces that melody in a


different pitch using mathematical transposition. After this, a


second melodic theme is created. Returning to the initial


theme, Mozart spirals the melody through a number of


pitch changes, and returns the listener to the original pitch


that began their journey. "Mozart?s comprehension of


mathematics and melody is inequitable to other composers.


This is clearly evident in one of his most famous works, his


symphony number forty in G-minor" (Ferrara, 1991).


Without the structure of musical relationship these


aforementioned musicians could not have achieved their


musical aspirations. Pythagorean theories created the basis


for their musical endeavours. Mathematical music would


not have been produced without these theories. Without


audibility, consequently, music has no value, unless the


relationship between written and performed music is so


clearly defined, that it achieves a new sense of mental


audibility to the Pythagorean skilled listener.. As clearly


stated above, Pythagoras? correlation between music and


numbers influenced musical members in every aspect of


musical creation. His conceptualization and experimentation


molded modern musical practices, instruments, and music


itself into what it is today. What Pathagoras found so


wonderful was that his elegant, abstract train of thought


produced something that people everywhere already knew


to be aesthetically pleasing. Ultimately music is how our


brains intrepret the arithmetic, or the sounds, or the nerve


impulses and how our interpretation matches what the


performers, instrument makers, and composers thought


they were doing during their respective creation.


Pythagoras simply mathematized a foundation for these


occurances. "He had discovered a connection between


arithmetic and aesthetics, between the natural world and


the human soul. Perhaps the same unifying principle could


be applied elsewhere; and where better to try then with the


puzzle of the heavens themselves." (Ferrara, 1983).

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