. . Music is the basis of agreement among things in nature and of thebest government in the universe. As a rule it assumes the guiseof harmony in the universe, of lawful government in a state, andof a sensible way of life in the home. It brings together andunites. ” – The PythagoreansEvery school student will recognize his name as theoriginator of that theorem which offers many cheerful facts aboutthe square on the hypotenuse.
Many European philosophers willcall him the father of philosophy. Many scientists will call himthe father of science. To musicians, nonetheless, Pythagoras isthe father of music. According to Johnston, it was a much toldstory that one day the young Pythagoras was passing ablacksmith’s shop and his ear was caught by the regularintervals of sounds from the anvil. When he discovered that thehammers were of different weights, it occured to him that theintervals might be related to those weights.
Pythagoras wascorrect. Pythagorean philosophy maintained that all things arenumbers. Based on the belief that numbers were the buildingblocks of everything, Pythagoras began linking numbers and music. Revolutionizing music, Pythagoras’ findings generated theoremsand standards for musical scales, relationships, instruments, andcreative formation. Musical scales became defined, andtaught.
Instrument makers began a precision approach to deviceconstruction. Composers developed new attitudes of compositionthat encompassed a foundation of numeric value in addition tomelody. All three approaches were based on Pythagoreanphilosophy. Thus, Pythagoras’ relationship between numbers andmusic had a profound influence on future musical education,instrumentation, and composition. The intrinsic discovery made by Pythagoras was the potentialorder to the chaos of music. Pythagoras began subdividingdifferent intervals and pitches into distinct notes.
Mathematicallyhe divided intervals into wholes, thirds, andhalves. “Four distinct musical ratios were discovered: the tone,its fourth, its fifth, and its octave. ” (Johnston, 1989). Fromthese ratios the Pythagorean scale was introduced.
This scalerevolutionized music. Pythagorean relationships of ratios heldtrue for any initial pitch. This discovery, in turn, reformedmusical education. “With the standardization of music, musicalcreativity could be recorded, taught, and reproduced. ” (Rowell,1983).
Modern day finger exercises, such as the Hanons, areneither based on melody or creativity. They are simply based onthe Pythagorean scale, and are executed from various initialpitches. Creating a foundation for musical representation, worksbecame recordable. From the Pythagorean scale and simplemathematical calculations, different scales or modes weredeveloped. “The Dorian, Lydian, Locrian, and Ecclesiasticalmodes were all developed from the foundation of Pythagoras.
“(Johnston, 1989). “The basic foundations of musicaleducation are based on the various modes of scalarrelationships. ” (Ferrara, 1991). Pythagoras’ discoveries createda starting point for structured music.
From this, diverseeducational schemes were created upon basic themes. Pythagorasand his mathematics created the foundation for musical educationas it is now known. According to Rowell, Pythagoras began his experimentsdemonstrating the tones of bells of different sizes. “Bells ofvariant size produce different harmonic ratios. ” (Ferrara, 1991).
Analyzing the different ratios, Pythagoras began definingdifferent musical pitches based on bell diameter, and density. “Based on Pythagorean harmonic relationships, and Pythagoreangeometry, bell-makers began constructing bells with the principalpitch 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.
Inaddition, Pythagoras initiated comparable experimentation withpipes of different lengths. Through this method of study heunearthed two astonishing inferences. When pipes of differentlengths were hammered, they emitted different pitches, andwhen air was passed through these pipes respectively, alikeresults were attained. This sparked a revolution in theconstruction of melodic percussive instruments, as well as thewind instruments. Similarly, Pythagoras studied strings ofdifferent thickness stretched over altered lengths, and foundanother instance of numeric, musical correspondence. Hediscovered the initial length generated the strings primary tone,while dissecting the string in half yielded an octave, thirdsproduced a fifth, quarters produced a fourth, and fifths produceda third.
“The circumstances around Pythagoras’ discovery inrelation to strings and their resonance is astounding, and thesecatalyzed the production of stringed instruments. ” (Benade,1976). In a way, music is lucky that Pythagoras’ attitude toexperimentation 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 modelfor music.
According to Rowell, Schillinger, a famous composer,and musical teacher of Gershwin, suggested an array of proceduresfor deriving new scales, rhythms, and structures by applyingvarious mathematical transformations and permutations. Hisapproach was enormously popular, and widely respected. “Theinfluence comes from a Pythagoreanism. Wherever this system hasbeen successfully used, it has been by composers who werealready well trained enough to distinguish the musical results. “In 1804, Ludwig van Beethoven began growing deaf. He had beguncomposing at age seven and would compose another twenty-fiveyears after his impairment took full effect.
Creating music in astate of inaudibility, Beethoven had to rely on the relationshipsbetween pitches to produce his music. “Composers, such asBeethoven, could rely on the structured musical relationshipsthat instructed their creativity. ” (Ferrara, 1991). WithoutPythagorean musical structure, Beethoven could not have createdmany of his astounding compositions, and would have failed toestablish himself as one of the two greatest musicians of alltime. Speaking of the greatest musicians of all time, perhapsanother name comes to mind, Wolfgang Amadeus Mozart.
“Mozart isclearly the greatest musician who ever lived. ” (Ferrara, 1991). Mozart composed within the arena of his own mind. When he spoketo musicians in his orchestra, he spoke in relationship terms ofthirds, fourths and fifths, and many others. Within deepanalysis of Mozart’s music, musical scholars have discovereddistinct similarities within his composition technique.
According to Rowell, initially within a Mozart composition,Mozart introduces a primary melodic theme. He then reproducesthat melody in a different pitch using mathematicaltransposition. After this, a second melodic theme is created. Returning to the initial theme, Mozart spirals the melody througha number of pitch changes, and returns the listener to theoriginal pitch that began their journey. “Mozart’s comprehensionof mathematics and melody is inequitable to other composers. This is clearly evident in one of his most famous works, hissymphony number forty in G-minor” (Ferrara, 1991).
Without thestructure of musical relationship these aforementioned musicianscould not have achieved their musical aspirations. Pythagoreantheories created the basis for their musical endeavours. Mathematical music would not have been produced without thesetheories. Without audibility, consequently, music has no value,unless the relationship between written and performed music is soclearly defined, that it achieves a new sense of mentalaudibility to the Pythagorean skilled listener.
. As clearly stated above, Pythagoras’ correlation betweenmusic and numbers influenced musical members in every aspect ofmusical creation. His conceptualization and experimentationmolded modern musical practices, instruments, and music itselfinto what it is today. What Pathagoras found so wonderful wasthat his elegant, abstract train of thought produced somethingthat people everywhere already knew to be aesthetically pleasing. Ultimately music is how our brains intrepret the arithmetic, orthe sounds, or the nerve impulses and how our interpretationmatches what the performers, instrument makers, andcomposers thought they were doing during their respectivecreation.
Pythagoras simply mathematized a foundation for theseoccurances. “He had discovered a connection between arithmeticand 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 heavensthemselves. ” (Ferrara, 1983). BibliographyBenade, Arthur H. (1976).
Fundamentals of Musical Acoustics. NewYork: Dover PublicationsFerrara, Lawrence (1991). Philosophy and the Analysis of Music. New York: Greenwood Press.
Johnston, Ian (1989). Measured Tones. New York: IOPPublishing. Rowell, Lewis (1983). Thinking About Music.
Amhurst: TheUniversity of Massachusetts Press.