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, alike 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).